problem solving is highly pragmatic

The Meaning and Traits of Being a Pragmatic Person: Learning the Art of Practicality

Are you someone who values practicality and efficiency do you strive to make decisions based on logic and facts rather than emotions or ideals if so, then you might be a pragmatic person. in this blog post, we will explore the meaning and traits of being a pragmatic individual , and discover how you can cultivate the art of practicality in your own life..

What does it mean to be pragmatic?

Being pragmatic means having a practical and realistic approach to situations. It is about focusing on what works and what produces tangible results, rather than getting caught up in theories or ideals. Pragmatic individuals are known for their ability to analyze problems objectively and find efficient solutions.

What are the traits of a pragmatic person?

Pragmatic individuals possess several distinct traits that set them apart. These traits include:

• Logic-driven thinking: Pragmatic people rely on logic and reasoning to make decisions. They analyze situations objectively, considering the pros and cons before taking action.
• Open-mindedness: Pragmatic individuals are willing to consider new ideas and perspectives. They are not bound by preconceived notions and are open to changing their beliefs if presented with compelling evidence.
• Efficiency: Pragmatic people prioritize efficiency and effectiveness. They seek practical solutions that yield the best results with the least amount of effort.
• Problem-solving: Pragmatic individuals excel at problem-solving. They have a knack for breaking down complex issues into manageable parts and finding practical solutions.
• Realism: Pragmatic individuals embrace realism in their thinking. They accept the limitations of a situation and adapt accordingly, rather than holding onto unrealistic expectations.

How can you develop pragmatic traits?

If you want to become more pragmatic, here are some tips to help you develop these traits:

• Cultivate critical thinking: Practice objectively analyzing situations and making decisions based on evidence and logic.
• Stay open to different perspectives: Be willing to listen to and consider alternative viewpoints, even if they contradict your own beliefs.
• Focus on practical solutions: Prioritize finding practical and efficient solutions to problems, rather than getting caught up in idealistic or theoretical approaches.
• Develop problem-solving skills: Work on honing your problem-solving abilities by breaking down complex issues and finding viable solutions.
• Embrace realism: Accept the realities and limitations of a situation, and adapt your actions accordingly.

The benefits of being pragmatic

Embracing pragmatism can bring several benefits to your personal and professional life. Some of these benefits include:

• Increased efficiency and productivity
• Improved decision-making abilities
• Enhanced problem-solving skills
• Adaptability in changing circumstances
• Better conflict resolution

By embracing pragmatism, you can become a more effective and adaptable individual, capable of navigating the complexities of life with ease.

Becoming a pragmatic person is a journey that requires dedication and practice. By developing the traits of pragmatism, you can enhance your problem-solving abilities, improve decision-making, and increase your efficiency in various aspects of life. Embrace the art of practicality, and you’ll discover a new level of effectiveness and success.

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AgileUprising

The Global Agile Practitioner Network

What is pragmatism? Why do I care? How do I practice it?

Pragmatism is possibly one of those words you’ve heard 1000 times and feel confident you know what it means. I did.

On the surface, it seems like a straightforward concept. The definition is simple:

Pragmatism /’praɡmətɪz(ə)m/ (noun) : an approach that evaluates theories or beliefs in terms of the success of their practical application.

The philosophy lies at the heart of many aspects of agile. Think about it, empiricism is deeply tied to pragmatism. The act of making something visible so that it can be examined and evaluated and adapted to be more effective is a deeply pragmatic approach.

One of the reasons, high-performing scrum teams may end up with something that is not scrum, but still agile, is a pragmatic approach brought out by the very act of following scrum. It is one beautiful paradox.

A pragmatic mindset allows us to self-reflect as people and teams to find things that truly work. One of the things that drew me to Agile Uprising was the core value of pragmatism. The organisation openly espoused that the idea was central to being a better practitioner of agile and humans.

So, beyond the definition…

What is Pragmatism?

I confess, whilst I’ve espoused the idea for some time, I had some mixed up understandings in my head about the word. It is easily done. We have a habit of overloading terms. Think about how much weight we put on “agile”…

Let’s look at some clear things that pragmatism is not.

Pragmatism is not Purism

This seems like a no-brainer. Purism seems almost antithetical to the ideal. Purism is about following the letter of the law to the nth degree. We have all seen the rigid adherence to a framework. It is about dotting the i’s and crossing the t’s.

purism /ˈpjʊərɪz(ə)m/ noun:  scrupulous or exaggerated observance of or insistence on traditional rules or structures, especially in language or style.

The problem is purism can hide in the form of pragmatism.

This sounds inane, but it stands. Many practitioners have scrum have seen this. “We practice scrum because it is a proven methodology that works in delivering high quality software on time”.  There is little wrong with the statement. Scrum is a framework that has proven itself over time.

The disconnect is that this is true at a high level, but not always reflected on the ground. Choosing to use scrum is on the surface is pragmatic, but if we practice the ceremonies with rigidity and never really get to the heart and soul of the framework we slip into purism and tyranny. It is in the intricacies of the practice that reality and theory meet. To have the courage to introspect all parts of our practice and continually improve, we will sometimes need to question the ceremonies themselves.

And I’m not having ago at Scrum, the same could be said of many practices from other frameworks such as XP with pairing or TDD. I have personally experience both in positive lights, but I’ve heard tales of dogmatic practices that have left scars. We need to question.

Purism is essentially blind faith, unthinking and uncaring. Pragmatism is true faith, being prepared to question in order to find the best way forward and moving forward.

Pragmatism is not lazy thinking

One of the misconceptions I had, was that I thought pragmatism meant accepting that we live in an imperfect world with imperfect solutions. “We are pragmatic. We do what works!”

Unfortunately that isn’t pragmatism, it is resignation.

Pragmatism is not about accepting the status quo, but acknowledging it.

To my shame, I have fallen into the trap of shortcut thinking many times in my life. I thought I was being pragmatic, because I was just “finding the solution that worked.” Unfortunately, with hindsight I can acknowledge that many of those times the trap closed, it was simply a matter of making excuses. This is otherwise known as lazy thinking.

To be truly pragmatic, we need to be prepared to measure the effects and count the cost.

Another form of lazy thinking can be in what has been dubbed  Cargo cult agile.

This typically shows up as people doing practices because “we’ve always done it this way”, “the cart isn’t broken, don’t fix it”, “I read this was good somewhere” or “I was told this works”. Two questions immediately shift from lazy thinking to pragmatic, “Why is this the best way do things?” and “How could you prove it is the best?” If someone is willing to move on those questions the lights are coming on.

Pragmatism is measuring

Let’s look at the definition again:  an approach that evaluates theories or beliefs in terms of the success of their practical application.

Pragmatism is about evaluation against success metrics. The dictionary defines evaluation as: forming an idea of the amount, number, or value of; assessment.  The quickest way to form a reasonable idea of something is to define an adequate measure.

It raises the question what is the right measure? This is a very difficult question.

I have come to accept that the answer will be radically different for many people. There are entire series of articles on metrics  and defining success. In fact the there are a few podcasts at Agile uprising such as  Actionable Agile Metrics with Daniel Vacanti  that explore the idea. I heartily recommend them.

At the end of the day it is always subjective. You will need to deal define your own definitions of success.  Have courage and be ready to be honest with yourself and your teams. This can be scary, especially if you are examining your  sacred cows .

Pragmatism is contextual

We don’t practice in a vacuum. A theory of how something should work without having tried it out, is just a nice idea.

Pragmatism looks at the  is.   Part of the reason I thought it was about accepting the now was because it examines reality vs thought. I understood that an idea had to be applied or tested to be evaluated. What I missed was that evaluating is different from accepting.

I missed that pragmatism isn’t accepting reality is flawed, it is about understanding that the  IDEA may be flawed and therefore needs to be assessed against the reality of the current circumstances.

Purism looks to blame, pragmatism to understand. It doesn’t fix the problems, but it might help you see where the holes are.

Why Pragmatism?

Pragmatism is about holding something up to the light and looking at if it REALLY works and does what it says on the label. That isn’t always comfortable. It is worthwhile.

Whilst we rarely hold the work of art that we think, we often hold the materials to make something beautiful. The only way to make beautiful things is by knowing where we stand  right now , the tools we are using  right now,  and what we have in our hands right now .  

Sometimes we need to acknowledge that what we have is less than perfect and the conditions are less than ideal, but this does not mean that we need to accept that it will always be so. Pragmatism affords us the opportunity to look for better, to look for best.

It is worth noting that the context of the situation might show that any one of the “good” practices you would normally use won’t work, right now.

You might have a genuinely great framework for dealing with work requests, but if all you meet is resistance the pragmatic response is to honestly evaluate what might be accepted right now. Move there first.

Pragmatism let’s you change the status quo by finding the optimal path through.

The challenge is to approach each day with a mind that measures and a heart that strives for bigger things; to evaluate with honesty and courage in order to meet your success.

Pragmatism is seeing clearly where the rubber meets the road and practice meet reality.

What practices do you have, that need a second look? How will you know whether the theory lives up to life?

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Pragmatism is a philosophical tradition that – very broadly – understands knowing the world as inseparable from agency within it. This general idea has attracted a remarkably rich and at times contrary range of interpretations, including: that all philosophical concepts should be tested via scientific experimentation, that a claim is true if and only if it is useful (relatedly: if a philosophical theory does not contribute directly to social progress then it is not worth much), that experience consists in transacting with rather than representing nature, that articulate language rests on a deep bed of shared human practices that can never be fully ‘made explicit’.

Pragmatism originated in the United States around 1870, and now presents a growing third alternative to both analytic and ‘Continental’ philosophical traditions worldwide. Its first generation was initiated by the so-called ‘classical pragmatists’ Charles Sanders Peirce (1839–1914), who first defined and defended the view, and his close friend and colleague William James (1842–1910), who further developed and ably popularized it. James’ Harvard colleague Josiah Royce (1855–1916), although officially allied with absolute idealism, proved a valuable interlocutor for many of these ideas. A significant influence in those early years was the scientific revolution then taking place around evolutionary theory, of which first generation pragmatists were keen observers and sometime participants (Pearce 2020). These pragmatists focused significantly on theorising inquiry, meaning and the nature of truth, although James put these themes to work exploring truth in religion. A second (still termed ‘classical’) generation turned pragmatist philosophy more explicitly towards politics, education and other dimensions of social improvement, under the immense influence of John Dewey (1859–1952) and his friend Jane Addams (1860–1935) – who invented the profession of social work as an expression of pragmatist ideas (and was awarded the Nobel Peace Prize in 1931). Also of considerable importance at this time was George Herbert Mead (1863–1931), who contributed significantly to the social sciences, developing pragmatist perspectives upon the relations between the self and the community (Mead 1934), whilst philosophy of race was germinated by pioneering African-American philosophers W.E.B Du Bois (1868–1963) and Alain Locke (1885–1954), who also engaged in productive dialogue with one another. As the progressive Deweyan ‘New Deal’ era passed away and the US moved into the Cold War, pragmatism’s influence was challenged, as analytic philosophy blossomed and became the dominant methodological orientation in most Anglo-American philosophy departments. Transitional or ‘third generation’ figures included C.I. Lewis (1883–1964) and W.V.O. Quine (1908–2000); although these philosophers developed a number of pragmatist themes, their analytic allegiance may be seen in their significant focus on theory of knowledge as first philosophy (which Dewey deprecated as ‘the epistemological industry’).

Following this dip in popularity, since the 1970s the pragmatist tradition has undergone a significant revival. Richard Rorty (1931–2007) turned consciously to pragmatism to rectify what he saw as mainstream epistemology’s crucial mistake: naively conceiving of language and thought as ‘mirroring’ the world. Rorty’s bold and iconoclastic attacks on this ‘representationalism’ birthed a so-called neopragmatism to which a number of influential recent philosophers have contributed (e.g. Hilary Putnam, Robert Brandom and Huw Price). Other pragmatists have objected to Rorty’s blithe dismissal of truth as a topic better left undiscussed (Rorty 1982), and have sought to rehabilitate classical pragmatist ideals of objectivity (e.g. Susan Haack, Christopher Hookway and Cheryl Misak). These philosophers are now sometimes referred to as New Pragmatists . Yet others have worked to place pragmatist ideas in a broader Western philosophical context, for instance tracing Peirce’s significant debt to Kant (Apel 1974, Gava 2014), and connections between pragmatism and 19th century idealism (Margolis 2010, Stern 2009). Meanwhile, classical pragmatism’s progressive social ideals lived on in some quarters, with notable contributions to philosophy of race made by Cornel West, who advanced a prophetic pragmatism drawing on both Christian and Marxian thought, and showcasing the earlier contributions of Du Bois and Locke (e.g. West 1989). A number of other liberatory philosophical projects in areas such as feminism (Seigfried 1996), ecology (Alexander 2013), Native American philosophy (Pratt 2002) and Latin American philosophy (Pappas 1998) also currently look to the pragmatist tradition as their philosophical home.

Meanwhile, increasingly pragmatism’s intellectual centre of gravity is moving out of North America, with vibrant research networks appearing in South America, Scandinavia and more recently central Europe and China.

The core of pragmatism as Peirce originally conceived it was the Pragmatic Maxim, a rule for clarifying the meaning of hypotheses by tracing their ‘practical consequences’ – their implications for experience in specific situations. For Peirce and James, a key application of the Maxim was clarifying the concept of truth . This produced a distinctive epistemological outlook: a fallibilist, anti-Cartesian explication of the norms that govern inquiry. Within that broad outlook, though, early pragmatists split significantly over questions of realism broadly conceived – essentially, whether pragmatism should conceive itself as a scientific philosophy holding monism about truth (following Peirce), or a more broad-based alethic pluralism (following James and Dewey). This dispute was poignantly emblematized in arguments between Peirce and James which led Peirce to rename his view pragmaticism , presenting this clarified viewpoint to the world as his new ‘baby’ which was, he hoped, ‘ugly enough to be safe from kidnappers’ (EP2: 355).

The first part of this entry is devoted to the classical pragmatists’ distinctive methods, and how they give rise to an original a posteriori epistemology. After that we will briefly explore some of the many other areas of philosophy in which rich pragmatist contributions have been made.

1. The Meaning of Pragmatism: James

2. the pragmatic maxim: peirce, 3.1 peirce on truth and reality, 3.2 james on truth, 4.1 skepticism versus fallibilism, 4.2 inquiry, 4.3 pragmatist conceptions of experience, 4.4 representations, 5.1 the early years, 5.2 neopragmatism, 6.1 philosophy of religion, 6.3 aesthetics, 6.4 philosophy of education, primary texts of the classical pragmatists, collections of papers by classic and contemporary pragmatists., other references and supplementary reading, other internet resources, related entries.

Pragmatism’s key ideas originated in discussions at a so-called ‘Metaphysical Club’ that met in Harvard around 1870. (For a popular history of this group, see Menand 1998.) Peirce and James participated in these discussions along with some other philosophers, psychologists and philosophically inclined lawyers. Peirce then developed these ideas in publications from the 1870s, and they achieved prominence through a series of public lectures given by James in 1898. Both James and Peirce used ‘pragmatism’ as the name of a method, principle, or ‘maxim’ for clarifying concepts and hypotheses and for identifying empty disputes, though we shall see significant differences in how they understood it.

When William James published a series of lectures on ‘Pragmatism: A New Name for Some Old Ways of Thinking’ in 1907, he began by identifying ‘The Present Dilemma in Philosophy’ (1907: 9ff), a fundamental and apparently irresoluble clash between two ways of thinking, which he promised pragmatism would overcome. James begins by observing that the history of philosophy is ‘to a great extent that of a certain clash of human temperaments’: the ‘tough-minded’ and the ‘tender-minded’. The tough-minded have an empiricist commitment to experience and going by ‘the facts’, while the tender-minded prefer a priori principles which appeal to ratiocination. The tender-minded tend to be idealistic, optimistic and religious, believing in free will, while the tough-minded are materialist, pessimistic, irreligious, dogmatic and fatalistic.

By the early twentieth century, James notes, ‘our children … are almost born scientific’ (1907: 14f). But this has not weakened religious belief. People need a philosophy that is both empiricist in its adherence to facts yet finds room for faith. But all that is on offer is ‘an empirical philosophy that is not religious enough and a religious philosophy that is not empirical enough…’ (1907: 15f). The challenge is to show how to reconcile ‘the scientific loyalty to facts’ with ‘the old confidence in human values and the resultant spontaneity, whether of the religious or of the romantic type.’ Pragmatism is presented as the ‘mediating philosophy’: we need to show how adherence to tough-minded epistemic standards does not prevent our adopting the kind of worldview to which the tender-minded aspire. Once we use what he introduced as the ‘pragmatic method’ to clarify our understanding of truth, of free will, or of religious belief the disputes—which we despaired of settling intellectually—begin to dissolve. William James thus presented pragmatism as a ‘method for settling metaphysical disputes that might otherwise be interminable.’ (1907: 28) Unless some ‘practical difference’ would follow from one or the other side’s being correct, the dispute is idle.

[T]he tangible fact at the root of all our thought-distinctions, however subtle, is that there is no one of them so fine as to consist in anything but a possible difference of practice. To attain perfect clearness in our thoughts of an object, then, we need only consider what conceivable effects of a practical kind the object may involve—what sensations we are to expect from it, and what reactions we must prepare. (1907: 29)

The lectures explained this with a memorable illustration. On a visit to the mountains, James’ friends engage in a ‘ferocious metaphysical dispute’ about a squirrel that was hanging on one side of a tree trunk while a human observer was standing on the other side:

This human witness tries to get sight of the squirrel by moving rapidly round the tree, but no matter how fast he goes, the squirrel moves as fast in the opposite direction, and always keeps the tree between himself and the man, so that never a glimpse of him is caught. The resultant metaphysical problem now is this: Does the man go round the squirrel or not? (1907: 27f)

James proposed that which answer is correct depends on what you ‘practically mean’ by ‘going round’. If you mean passing from north of the squirrel, east, south, then west, then the answer to the question is ‘yes’. If, on the other hand, you mean in front of him, to his right, behind him, to his left, and then in front of him again, then the answer is ‘no’. After pragmatic clarification disambiguates the question, all dispute comes to an end. So James offers his pragmatism as a technique for clarifying concepts and hypotheses so that metaphysical disputes that appear irresoluble will be dissolved. A good example is the dispute between free will and determinism: once we compare the practical consequences of both positions we find no conflict. As James admitted, he explained the pragmatic method through examples rather than a detailed analysis of what it involves. He did little to explain exactly what ‘practical consequences’ are. He also made no claim to originality: ‘Pragmatism represents a perfectly familiar attitude in philosophy, the empiricist attitude’, although he acknowledged that it did so ‘in a more radical and in a less objectionable form than it has ever yet assumed’ (1907: 31). It shared with other forms of empiricism an ‘anti-intellectualist tendency’ (ibid), and it recognized that theories (and presumably concepts) should be viewed as ‘instruments, not answers to enigmas’.

Peirce made this canonical statement of his Pragmatic Maxim in ‘How to Make our Ideas Clear’:

Consider what effects, which might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of those effects is the whole of our conception of the object. (EP1: 132)

This offers a distinctive method for becoming clear about the meaning of concepts and the hypotheses which contain them. We clarify a hypothesis by identifying the practical consequences we should expect if it is true. This raises some questions. First: what, exactly is the content of this maxim? What sort of thing does it recognize as a practical consequence? Second, what use does such a maxim have? Peirce’s first simple illustrative example urges that what we mean by calling something hard is that ‘it will not be scratched by many other substances.’ In this way, then, I can use the concept hard in certain contexts when I am wondering what to do, and absent such contexts, the concept is empty. The principle has something of a verificationist character: ‘our idea of anything is our idea of its sensible effects’ (EP1: 132). However the use of the phrase ‘practical consequences’ suggests that these are to be understood as having implications for what we will or should do . This is clear from Peirce’s later formulations, for example:

The entire intellectual purport of any symbol consists in the total of all general modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. (EP2: 346).

So, for instance, if I want to break a window by throwing something through it, then I need an object which is hard, not soft. It is important that, as Peirce hints here, the consequences we are concerned with are general and intelligible : we are to look for laws that govern the behaviour of hard things and show how such modes of behaviour can make a difference to what is rational for us to do.

James never worked out his understanding of ‘practical consequences’ as fully as Peirce did, and he does not share Peirce’s restriction of these consequences to general patterns of behaviour. Sometimes he writes as if the practical consequences of a proposition can simply be effects upon the individual believer: if religious belief makes me feel better, then that contributes to the pragmatic clarification of ‘God exists’. James also hopes that the attempt to clarify metaphysical hypotheses will reveal that some propositions are empty or, more important, that, as in the squirrel example, some apparent disagreements are unreal. Peirce sees uses for his maxim beyond those James had in mind. He insisted that it was a logical principle, in a broad sense of logic which includes scientific methodology. So for instance he used it to clarify concepts central to scientific reasoning such as probability , truth , and reality . (We shall discuss his views on truth and reality further below.) Pragmatism, described by Peirce as a ‘laboratory philosophy’, shows us how we test theories by carrying out experiments in the expectation that if the hypothesis is not true, then the experiment will fail to have some predetermined sensible effect.

Peirce’s description of his maxim as a logical principle is reflected in passages where he presents it as a development of a distinction that had been a staple of traditional logic texts, and familiar to readers of Descartes, between ideas that are clear and distinct (EP1: 126f). Peirce understood the first grade of clarity about the meaning of a concept as being able to identify instances of it, without necessarily being able to say how. He then took his philosophical contemporaries to hold that the highest grade of clarity, distinctness, is obtained when we can analyze a concept into its elements by providing a verbal definition (or, in more recent terminology, necessary and sufficient conditions for its application). Peirce complained that ‘nothing new is ever learned by analyzing definitions’, unless we already have a clear understanding of the defining terms. He therefore announced that the Pragmatic Maxim enabled a higher (‘third’) grade of clarity, that supplemented the verbal definition with a description of how the concept is employed in practice.

As well as treating the Pragmatic Maxim as part of a constructive account of the norms that govern inquiry, Peirce, like James, gave it a negative role as a tool for demonstrating the emptiness of a priori metaphysics. In section 3.1 we shall see how pragmatic clarification of reality may be used to undermine a flawed ‘nominalistic’ conception of reality that led to the ‘copy theory of truth’, problematic Cartesian certainty-seeking strategies in epistemology, and Kant’s concept of a ‘thing in itself’. A more vivid non-logical example of using the maxim to undermine spurious metaphysical ideas was Peirce’s early argument that the Catholic understanding of transubstantiation was empty and incoherent. Since all we mean by wine is something that has certain distinctive effects upon the senses, ‘to talk of something as having all the sensible characters of wine, yet being in reality blood, is senseless jargon’ (EP1: 131f). It is important to note, however, that the maxim is in the end only a tool for clarifying meaning; not Peirce’s theory of meaning proper. This is to be found in his theory of signs or semiotic , which is discussed below (4.4).

3. Pragmatist Theories of Truth

Peirce and James differed in how they applied their respective pragmatisms to clarifying the concept of truth . Peirce’s account of truth is presented as a means to understanding a concept that he claimed was vital for the method of science: reality (3.1). James used his account to defend pluralism about truth (3.2).

The final section of ‘How to Make our Ideas Clear’ promises to consider a fundamental logical conception, reality . This concept seems clear: ‘every child uses it with perfect confidence, never dreaming that he does not understand it.’ Thus it reaches Peirce’s first level of meaning-clarity. A (second-level) verbal definition of the concept is also readily forthcoming: ‘we may define the real as that whose characters are independent of what anybody may think them to be.’ But, Peirce announces, we shall need to apply the Pragmatic Maxim if our idea of reality is to be ‘perfectly clear’. At this stage the concept of truth enters the discussion: Peirce claims that the object represented in a true proposition is our best understanding of the real. So we have to turn to his remarks about truth to see how the mind-independence alleged in the abstract definition of reality is to be operationalized and thus properly understood from a pragmatist perspective.

His pragmatic clarification of truth is expressed as follows:

The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. That is the way I would explain reality. (EP1: 139)

Seven years earlier, in a review of a new edition of the writings of Berkeley, Peirce had described this way of thinking as the ‘realist conception of reality’ (EP1:88–9), in contrast with a ‘nominalist conception of reality’ which many early modern philosophers took for granted. Nominalists assume that the real can only be the antecedent cause of singular sensations which provide our evidence for beliefs about the external world. This naturally leads to a certain (age-old) solipsistic skepticism concerning whether a person can gain knowledge that transcends their own perceptions and epistemic perspective. Peirce’s pragmatist clarification of truth offers an alternative conceptualization of ‘being constrained by reality’, in terms of consequent convergence of opinion, through the process of inquiry, rather than as an antecedent cause of sensations.

All this has led Peirce’s account of truth to be expressed in the slogan: truth is the end of inquiry , where ‘end’ is to be understood not as a ‘finish’ (some point in time when all human questions will be settled) but as a goal, telos or final cause. This original understanding of truth has faced challenges that it is ‘too realist’ insofar as it takes for granted that inquiry will converge on just one answer to any given question. Here Bertrand Russell asked, ‘Is this an empirical generalization from the history of research? Or is it an optimistic belief in the perfectibility of man?’, concluding, ‘Whatever interpretation we adopt, we seem committed to some very rash assertion.’ (1939: 146). Similarly, Quine wrote, ‘…we have no reason to suppose that man’s surface irritations even unto eternity admit of any one systematization that is scientifically better or simpler than all possible others’ (1960: 23). However, later in life Peirce urged that the hypothesis of monistic convergence is best viewed as a regulative hope . In 1908, Peirce wrote to a friend, ‘I do not say that it is infallibly true that there is any belief to which a person would come if he were to carry his inquiries far enough. I only say that that alone is what I call Truth’ (cited Haack 1976: 246).

At the same time, others have criticised Peirce’s account of truth for not being realist enough, due to its ‘internal realist’ definition of truth in terms of belief and inquiry. Can there not be claims which no-one ever inquires into or believes, which are nonetheless true? What about ‘lost facts’, such as the number of cakes on a tray during a long-ago party (Johnston 2003: 91)? Here Peirce arguably doubles down on his fallibilism (Legg 2014: 211). How can we be sure that no amount of inquiry will settle such matters?

… it is unphilosophical to suppose that, with regard to any given question (which has any clear meaning), investigation would not bring forth a solution of it, if it were carried far enough… Who can be sure of what we shall not know in a few hundred years? (EP1: 140)

The objectivism of Peirce’s account of truth derives not from a world entirely external to our minds (a famously difficult thing to know), but from the potential infinity of the community of inquiry, which exposes all of our beliefs to future correction: ‘reality is independent, not necessarily of thought in general, but only of what you or I or any finite number of [persons] may think about it…’ (EP1: 139). By means of this mathematical analysis, Peirce deftly synthesises insights from traditional realisms and idealisms (Legg 2014: 212; Lane 2018).

James departed from Peirce in claiming that pragmatism was itself a theory of truth. And his writings on this topic rapidly became notorious. They are characteristically lively, offering contrasting formulations, engaging slogans, and intriguing claims which often seem to fly in the face of common sense. We can best summarize his view through his own words:

The true is the name of whatever proves itself to be good in the way of belief, and good, too, for definite assignable reasons. (1907: 42) ‘ The true’, to put it very briefly, is only the expedient in the way of our thinking, just as ‘the right’ is only the expedient in the way of our behaving. Expedient in almost any fashion; and expedient in the long run and on the whole, of course. (1907: 106)

Other formulations fill this out by giving a central role to experience:

Ideas … become true just in so far as they help us to get into satisfactory relation with other parts of our experience. (1907: 34) Any idea upon which we can ride …; any idea that will carry us prosperously from any one part of our experience to any other part, linking things satisfactorily, working securely, saving labor; is true for just so much, true in so far forth, true instrumentally . (1907: 34)

This might be taken to suggest that beliefs are made true by the fact that they enable us to make accurate predictions of the future run of experience, but other passages suggest that the ‘goodness of belief’ can take other forms. James assures us that it can contribute to the truth of a theological proposition that it has ‘a value for concrete life’ (1907: 40); and this can occur because the idea of God possesses a majesty which can ‘yield religious comfort to a most respectable class of minds’ (1907:40). This suggests that a belief can be made true by the fact that holding it contributes to our happiness and fulfilment.

The kind of passages just noted may seem to support Bertrand Russell’s famous objection that James is committed to the truth of “Santa Claus exists” (Russell 1946, p, 772). This is unfair; at best, James is committed to the claim that the happiness that belief in Santa Claus provides is truth-relevant . James could say that the belief was ‘good for so much’ but it would only be ‘wholly true’ if it did not ‘clash with other vital benefits’. It is easy to see that, unless it is somehow insulated from the broader effects of acting upon it, belief in Santa Claus could lead to a host of experiential surprises and disappointments.

4. Pragmatist Epistemology

The pragmatists saw their epistemology as providing a return to common sense and experience and thus as rejecting a flawed philosophical heritage which had distorted the work of earlier thinkers. The errors to be overcome include Cartesianism, Nominalism, and the ‘copy theory of truth’: these are all related.

The roots of pragmatism’s anti-skepticism can be found in Peirce’s early (1868) paper ‘Some Consequences of Four Incapacities’ (EP1: 28–30). Here he identifies ‘Cartesianism’ as a philosophical pathology that lost sight of certain insights that were fundamental to scholastic thought (for all its faults), and – he argued – more suited to the philosophical needs of his own time. The paper begins by identifying four problematic teachings of modern philosophy:

• One can and should try to doubt all of one’s beliefs at once.
• The ultimate test of certainty lies in individual consciousness.
• The ‘multiform argumentation’ characteristic of the Middle Ages is replaced by a single chain of inference.
• Where scholasticism consciously limited its explanatory capacity (purporting to explain only ‘all created things’), Cartesianism’s stated ambition to explain everything ironically renders its own presuppositions hidden, mysterious and philosophically dangerous.

The first, and in many ways most important of these Cartesian teachings was the method of universal doubt. We should retain beliefs only if they are absolutely certain and we are unable to doubt them. The test of this certainty, as Peirce next points out, lies in whether the individual consciousness is satisfied. Importantly, this self-examination includes reflection on hypothetical possibilities: we cannot trust our perceptual beliefs, for example, because we cannot rule out that they might be produced by a dream, or an evil demon. (See Hookway 2012, chapters 2,3.) The initial pragmatist response to this is that it is a strategy that in practice we cannot carry out effectively, and there is no reason to adopt it anyway. Peirce claims that any attempt to adopt the method of doubt will be an exercise in self-deception because we possess a variety of certainties which it does not occur to us can be questioned. So what is produced will not be ‘real doubt’; these beliefs will lurk in the background, influencing our reflection. Peirce urges us not to ‘pretend to doubt in philosophy what we do not doubt in our hearts’ (EP1: 29).

It is necessary to separate some different threads in his argument here. First, there is something unnatural about the Cartesian strategy. Inquiries normally occur within a context: we address particular questions or problems, relying on background certainties that it does not occur to us to doubt. The Cartesian suggestion that we should begin by trying to doubt everything appears to be an attempt to step outside of this. Second, the Cartesian strategy requires us to reflect upon each of our beliefs and ask what reason we have for holding it; skeptical challenges are then used to question the adequacy of these reasons. This is again at odds with normal practice. Many of our familiar certainties are such that we cannot offer any concrete or convincing reason for believing them. We tend to treat our established beliefs as innocent until ‘proven guilty’. The mere lack of a conclusive reason for belief does not itself provide us with a reason for doubt.

Descartes, of course, might have conceded this, but responded that the revision is required because once we allow error to enter our belief-corpus we may be unable to escape from its damaging effects. His was a time of methodological ferment, and he appreciated how many false beliefs he himself had acquired from his teachers. The pragmatist response here is to question some of Descartes’ assumptions about how we reason and form beliefs. First, his strategy is individualist and ‘to make single individuals absolute judges of truth is most pernicious’. Peirce noted that the natural sciences which were so conspicuously successful in Descartes’ day took a very different approach:

In sciences in which men come to agreement, when a theory has been broached, it is considered to be on probation until this agreement has been reached. After it is reached, the question of certainty becomes an idle one, because there is no one left who doubts it. We individually cannot reasonably hope to attain the ultimate philosophy which we pursue; we can only seek it, therefore, for the community of philosophers. (EP1: 29)

Peirce also questions Descartes’ understanding of reasoning in holding that we may rely on ‘a single thread of inference’ that is no stronger than its weakest link:

Philosophy ought to imitate the successful sciences in its methods, so far as to…trust rather to the multitude and variety of its arguments than to the conclusiveness of any one. Its reasoning should not form a chain which is no stronger than its weakest link, but a cable whose fibres may be ever so slender, provided they are sufficiently numerous and intimately connected. (EP1: 29)

Where the Cartesian holds that unless we begin from premises of which we can be absolutely certain we may never reach the truth, the pragmatist emphasises that, when we do go wrong, further discussion and investigation can identify and eliminate errors, which is our best hope for escaping their damaging effects. The possibility of error provides us with reason to be ‘contrite fallibilists’, rather than skeptics. The focus of epistemological inquiry should not be on showing how we can possess absolute certainty , but on how we can develop self-correcting methods of inquiry that make fallible progress .

William James makes similar observations. In ‘The Will to Believe’, he reminds us that we have two cognitive desiderata: to obtain truth, and to avoid error (James 1897: 30). The harder we try to avoid error, the more likely it is that we will miss out on truth; and the more strenuously we search for truth, the more likely we are to let in error. The method of doubt may make sense in special cases where enormous weight is given to avoiding error, even if that means loss of truth, but only there. Once we recognize that we are making a practical and forced decision about the relative importance of two goods, the Cartesian strategy no longer appears the only rational one. Later, Dewey in The Quest for Certainty similarly urged that a focus on eliminating all error from our beliefs is both doomed and destructive, with the added twist of a social diagnosis of the quest itself: the uncertainty, pain and fear of much early human life led to the erection of ‘priestly’ forms of knowledge which in promising to intercede with a Heavenly stability, sundered a priori theory from a posteriori practice, thereby enabling the knowing classes to insulate themselves from a more humble (and realistic) empiricism. The ‘quest’ continues, however, in many debates in contemporary mainstream epistemology.

Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge , considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry , considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper “The Fixation of Belief”. Here Peirce states that inquiry is a struggle to replace doubt with ‘settled belief’, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science , which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity ), ii) accepting an institution’s dictates (the Method of Authority ), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method ). Notable recent reinterpretations and defenses of Peircean pragmatist epistemology include (Haack 1993 and Cooke 2007). (See also Skagestad 1981.)

Dewey’s conception of inquiry, found in his Logic: the Theory of Inquiry is also rich, and arguably more radical than Peirce’s in its underlying ontology (ED2: 169–79). Dewey sees inquiry as beginning with a problem; it aims for ‘the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole’ (ED2: 171). As John E. Smith notes, where ‘Peirce aimed at “fixing” belief, Dewey aimed at “fixing” the situation’ (1978: 98). It is important to note that here the situation is objectively indeterminate, and is itself transformed by inquiry. The ‘pattern of inquiry’ that Dewey describes is common to the information-gathering of animals, practical problem solving, common sense investigations of our surroundings and scientific inquiry. He recognizes that when we face a problem, our first task is to understand it through describing its elements and identifying their relations. Identifying a concrete question that we need to answer is a sign that we are making progress. And the ‘logical forms’ we use in the course of inquiry are understood as ideal instruments, tools that help us to transform things and resolve our problem. The continuities Dewey finds between different kinds of inquiry are evidence of his naturalism and his recognition that forms of scientific investigation can guide us in all areas of our lives. All the pragmatists, but most of all Dewey, challenge the sharp dichotomy that other philosophers draw between theoretical beliefs and practical deliberations. In some sense, all inquiry is practical, concerned with transforming and evaluating the features of situations in which we find ourselves. Shared inquiry directed at resolving social and political problems or indeterminacies was also central to Dewey’s conception of the good life and, relatedly, the democratic ideal. (Recently other pragmatists, closer to Peirce than Dewey, have developed this idea: see for instance Talisse 2008; Misak 1999; Westbrook 1991.)

The Pragmatic Maxim suggests that pragmatism is a form of empiricism (an idea recently explored further in Wilson 2016). Our ability to think about so-called external things, and steadily improve our understanding of them, rests upon our experience. Yet most pragmatists adopted accounts of experience and perception radically different from the views of modern empiricists from John Locke and David Hume to Rudolf Carnap, as well as the ‘intuition’ posited by Kant. The established view interpreted experience as what is sometimes (following C.I. Lewis and Wilfrid Sellars) called ‘the given’: we are passive recipients of determinate and singular ‘sense-data’. Experience provides raw material for knowledge, but does not itself have content informed by concepts, practical needs, or anything else non-sensory. Our only contact with the external world is through receiving such experiences. So this way of thinking about experience can easily lead to skepticism about the so-called ‘external world’.

In different ways, Peirce, James, and Dewey all argued that experience is far richer than this, and that earlier philosophers were mistaken to claim that we could identify ‘experiences’ or ‘sense-data’ as antecedents to, or separable constituents of, cognition. We can begin with James’ radical empiricism , of which he said that ‘the establishment of the pragmatist theory of truth [was] a step of first-rate importance in making [it] prevail’ (1909: 6f). The connection with pragmatism is evident from the fundamental ‘postulate’ of radical empiricism: ‘the only things that shall be debatable among philosophers shall be things definable in terms drawn from experience’. But this requires that experience be newly understood. First, he announced that ‘the relations between things, conjunctive as well as disjunctive, are just as much matters of direct particular experience, neither more so nor less so, than the things themselves.’ And, second, he concludes that ‘the parts of experience hold together from next to next by relations that are themselves parts of experience. The directly apprehended universe needs, in short, no extraneous trans-empirical connective support, but possesses in its own right a concatenated or continuous structure.’

Peirce too emphasizes the continuous character of perceptual experience, and adds that we directly perceive external things as external, as ‘other’, that we can perceive necessary connections between events, and that experience contains elements of generality (citing a picture of a connected series of circles which can be seen as a stone wall, in the manner of Wittgenstein’s famous duck-rabbit dual diagram). Around 1902–3, Peirce developed a complex and original theory of perception which combines a percept , which is entirely non-cognitive, with a perceptual judgement , which is structured propositionally and lies in the space of reasons. In this way he seeks to capture how perception is both immediately felt and truth-evaluable. In contrast to standard British Empiricist analyses of the relation between impressions and ideas, Peirce does not claim that a perceptual judgment copies its percept. Rather, it indexes it, just as a weather-cock indicates the direction of the wind. Although percept and perceptual judgment are intrinsically dissimilar, over time certain habits of association between the two are reinforced, leading them to (literally) grow in our minds and link with other habits. This enables percepts and perceptual judgments to mutually inform one another, to the point where every perception is fallible and subject to reinterpretation in the light of future perceptions (Legg 2017). The end result is that, as Peirce puts it, in stark contrast to the accepted understanding of experience as ‘given’: ‘[n]othing at all…is absolutely confrontitional’, although, ‘the confrontitional is continually flowing in upon us’ (CP 7.653).

Dewey’s account of experience, which is central to his entire philosophy, contributes an additional twist. Like Peirce, he thought that experience was ‘full of inference’, but he arguably took the notion further from the mere contents of individual consciousness than any previous pragmatist. For Dewey, experience is a process through which we transact with our surroundings and meet our needs. He wrote:

Like its congeners life and history, [experience] includes what men do and suffer, what they strive for, love, believe and endure, and also how men act and are acted upon, the ways in which they do and suffer, desire and enjoy, see, believe, imagine, in short, processes of experiencing (LW1:18).

What we experience is shaped by our habits of expectation and there is no basis for extracting from this complex process the kind of ‘thin given’ beloved of sense datum theorists. We experience all sorts of objects, events and processes, and just as experience is inextricable from the ‘external’ world of things, Nature (its co-ordinate concept: what is experienced) is inextricable from the ‘internal’ world of concepts.

In sharp contrast to Dewey, neopragmatism no longer takes experience as an explicit philosophical theme. Rorty began his pre-pragmatist philosophical career as an eliminative materialist, and the view survives in Philosophy and the Mirror of Nature , newly bolstered by Sellarsian concerns about the ‘myth of the given’. On this basis, Rorty declares that ‘Dewey should have dropped the term “experience” rather than redefining it… He should have agreed with Peirce that a great gulf divides sensation and cognition, [and] decided that cognition was possible only for language users…’ (Rorty 1998: 297). Similarly, Brandom focusses his attention exclusively on linguistic meaning (albeit in this case qua rationalist), and has famously ruled that (as ‘blasphemy’ was to Oscar Wilde) ‘experience’ is ‘not one of his words’ (Brandom 2011: 197). This neopragmatist neglect of one of classical pragmatism’s central concepts has become a major point of contention on the part of many New Pragmatists (e.g. Koopman 2007; Levine 2010, 2012; Sachs 2015).

Having discussed pragmatists’ emphases upon the activity of inquiry and the thickness of experience, we turn to their views about the nature of thought. It has been common for philosophers to assume that the ‘content’ of a thought, judgment or proposition is a kind of intrinsic property that it possesses. Perhaps it offers a ‘picture’ or ‘idea’ of some state of affairs, and we can identify this content simply by reflecting upon the item itself, and its structural properties. All pragmatists have rejected this idea as a key driver of an antinaturalistic Cartesian dualism . Instead, they have held that the content of a thought, judgment or proposition is a matter of the role it fills in our activities of inquiry, and is to be explained by reference to how we interpret it or what we do with it. This shall be illustrated by considering three particular pragmatist views.

First, all of the classic pragmatists identified beliefs and other mental states as habits . According to Peirce, our beliefs ‘[g]uide our desires and shape our actions’ (EP1: 114). The content of a belief is determined by its role in determining our actions. This was reflected in Peirce’s formulations of his Pragmatic Maxim. In order to be clear about the content of a concept or hypothesis, we must reflect upon its role in determining what we should do in the light of our desires and our background knowledge. In Robert Brandom’s terminology, the philosopher ‘makes explicit’ aspects of our practice that are implicit in our habits and dispositions. The role of tacit habits of reasoning and acting in fixing our beliefs and guiding our actions is a theme that recurs in the work of the pragmatists, and is now finding strong echoes in recent empirically informed work on ‘4E’ cognition, which is embodied, embedded, enactive and extended. (For an accounts of this research area which explicitly engage classical pragmatism, see Menary 2007 and Gallagher 2017.)

The second illustration concerns a passage in which James defended his account of truth by urging that it was the concept used in successful science. He identified the ‘traditional view’ that, for early scientists, the ‘clearness, beauty and simplification’ provided by their theories led them to think that they had deciphered authentically the eternal thoughts of the Almighty. By contrast, contemporary scientists held that ‘no theory is absolutely a transcript of reality, but that any of them may from some point of view be useful …’. A scientific theory was to be understood as ‘an instrument: it is designed to achieve a purpose—to facilitate action or increase understanding’ (James 1907: 33). For James and Dewey, this holds of all our concepts and theories: we treat them as instruments to be judged by how well they achieve their intended purpose.

The third illustration comes from Peirce’s general theory of signs, or semiotics , which was developed entirely independently of the more well-known semiotics of Ferdinand de Saussure, and is one of the most original areas of his thought. Peirce’s semiotics offers an account of the contents of thoughts as well as language, visual media, music and any other item that can be said to have meaning (for introductions to this area of Peirce’s thought, see Liszka 1996; Short 2007). Unlike Saussure, Peirce insisted that the sign-relation was essentially triadic in structure, comprising a representation, an object and an interpretation. In other words: a sign is ‘about’ some object because it is understood, in subsequent thought, as a sign of that object. This subsequent thought Peirce calls the sign’s interpretant . In understanding or interpreting a sign, we may feel things about it (which at times Peirce called the emotional interpretant ), undertake actions that are rational in the light of the sign and the other information we possess (the dynamic interpretant ), or an indefinite number of inferences may be drawn from it (the logical interpretant ) (Jappy 2016). Interpretation is generally a goal-directed activity and, once again, the content of a sign is determined by the ways in which we use it (or might do so).

A further triadic distinction deriving from Peirce’s theory of signs which has been influential in disciplines from Biology to Media Studies holds between three ways in which a sign may pick out its object :

• by resembling it (or more generally, by possessing the very properties that the sign aims to signify), e.g. a map
• by indicating it in some brute unmediated fashion, e.g. a weather-vane signifying the wind’s direction
• via some arbitrary convention that must be learned, e.g. words in English.

These three kinds of signs Peirce termed: icon , index and symbol respectively. Meanwhile, the three ways in which a sign may give rise to its interpretant were categorised by Peirce as:

• the rheme (essentially: a term)
• the proposition
• the argument

Peirce’s sign theory continued to richly evolve and clarify itself right to the end of his life (Jappy 2016; Bellucci 2017), albeit by means of some rather forbidding special-purpose technical terminology.

5. Further pragmatists

It would be wrong to conclude that pragmatism was restricted to the United States or that the only important pragmatist thinkers were Peirce, James and Dewey. As is documented by Thayer, there were pragmatists in Oxford, in France and, especially, in Italy in the early years of the twentieth century (Thayer 1968, part III, Baldwin 2003: 88–9). Moreover we can mention several other important American pragmatists, for example Josiah Royce. Commonly thought to be an idealist opponent of James and a critic of pragmatism, Royce increasingly came to be influenced by Peirce’s work on signs and on the community of inquirers and was acknowledged as a fellow pragmatist by Peirce himself. C.I. Lewis, the teacher of Quine and of several generations of Harvard philosophers developed a philosophy that was a sort of pragmatist Kantianism. Murray Murphey has identified him as ‘the last great pragmatist’ (Murphey 2005). In books such as Mind and the World Order (1929), he defended a pragmatist conception of the a priori , holding that our choices of laws of logic and systems of classification were to be determined by pragmatic criteria (Lewis 1923, 1929; Murphey 2005: chapters four and five). Of comparable importance was George Herbert Mead, whose contribution to the social sciences has been noted. The work of Frank Ramsey at Cambridge (Ramsey 1926) in the 1920s developed Peirce’s views on statistical reasoning and on inquiry in ways that provided fertile research programmes through much of the century, for example in the work of Isaac Levi at Columbia (Levi 2012). As a number of scholars have documented (Boncompagni 2016; Goodman 2002), Wittgenstein’s later thought acquired a pragmatist flavour through his reading of James’s Varieties of Religious Experience (1902).

Where Peirce and Dewey—and even perhaps James—were engaged in working out systematic philosophical visions, Rorty treated ‘pragmatism’ as a more critical or therapeutic philosophical project. What pragmatists teach us about truth , he tells us, is that there is nothing very systematic or constructive to be said about it. In particular, the concept does not capture any metaphysical relation between our beliefs and utterances, on the one hand, and reality on the other. We can describe what we do with the word ‘true’: we use it to express our endorsement of beliefs and sentences, and sometimes we might find it useful to express our fallibility by saying that some of our beliefs may not be true. (Rorty calls this the ‘cautionary’ use of the term.) But, beyond talking about the rather trivial formal properties of the concept, there is nothing more to be said. He also uses what he describes as a ‘pragmatist’ principle to show that truth cannot be our aim when we inquire. This principle holds that we can only adopt something as an aim when we are able to recognize that it has been achieved. And since we are fallible, we are never in a position to prove that one of our beliefs is actually true—all we can recognize is that it meets standards of acceptance that are endorsed, for the time being, in our community (Rorty 1991a: chapter one; 2000; Hookway 2007). This consequentialist reading of pragmatist ideas is also reflected in his account of how we can criticize and revise our view of the world. We should be free to propose new ‘vocabularies’—systems of classification and description. We do not test these vocabularies by seeing whether they enable us to discover truths or by showing that they can be read off the nature of reality. Instead, we evaluate them by seeing how they enable us to achieve our current goals, formulate better and more satisfying goals, and generally become better at being human (Rorty 1995).

Hilary Putnam has at times denied that he is a pragmatist because he does not think that a pragmatist account of truth can be sustained. Indeed, he shows little sympathy for the pragmatic maxim. However, he has written extensively on James, Peirce, and Dewey—often in collaboration with Ruth Anna Putnam—and has provided insightful accounts of what is distinctive about pragmatism, and what can be learned from it (See Putnam 1994a). He has identified four characteristics of pragmatism: the rejection of skepticism; the willingness to embrace fallibilism; the rejection of sharp dichotomies such as those between fact and value, thought and experience, mind and body, analytic and synthetic etc; and what he calls ‘the primacy of practice’ (1994c). With the turn of the twenty first century, he made ambitious claims for the prospects of a pragmatist epistemology. After surveying the apparent failures of the original enlightenment project, and attributing them to the fact that enlightenment philosophers were unable to overcome the fundamental dichotomies mentioned above, he expresses the hope that the future might contain a ‘pragmatist enlightenment’ (Putnam 2004:89–108). The rich understanding of experience and science offered by pragmatists may show us how to find an objective basis for the evaluation and criticism of institutions and practices. He is particularly struck by the suggestion that pragmatist epistemology, by emphasizing the communal character of inquiry and the need to take account of the experiences and contributions of other inquirers, provides a basis for a defence of democratic values (1993: 180–202). This may be related to Rorty’s suggestion that pragmatists insist upon the priority of democracy over philosophy (Rorty 1991b).

Another symptom of a pragmatist revival is found in the work of Robert Brandom. Brandom’s philosophical interests are rather different from those of the classical pragmatists, of whom he is quite critical (Brandom 2011), and who do not noticeably influence his work. His views owe more to philosophers such as Wilfrid Sellars and Quine, his teacher Richard Rorty, and historical readings in thinkers such as Kant and Hegel. As noted above, his concerns are mostly with semantics and the philosophy of language. By contrast to the representationalism deplored by many neopragmatists, he develops a version of inferentialist semantics in order to construct accounts of our use of words like ‘true’ and ‘refers to’ which are liberated from the idea that the function of thought and language is ‘to provide a transcript of reality’. The connection to pragmatism is that his approach to language is focused upon what we do with our practices of making assertions and challenging or evaluating the assertions of others. What constitutes an assertion is its normative pragmatics : it is the smallest unit of language for which we can take responsibility within a ‘game of giving and asking for reasons’. Logical relations are then explicated in terms of the entitlements to make further moves in this ‘language-game’, which flow from the commitments one has assumed through one’s previous assertions (Brandom 1994; Brandom 2000). Brandom also joins the pragmatists in denying that truth is a substantial metaphysical property that can be possessed by some propositions and not by others, and in seeking to reconstructing an account of reference which makes a difference in practice (his favored strategy is, broadly, explaining language-users’ capacity to perform anaphora). In (Brandom 2008) he goes further to discuss how different vocabularies understood pragmatically might be translated into— or reduced to— one another, thereby constructing an overall account of the relationship between ‘saying’ and ‘doing’ that he hopes will form a basis for reintegrating analytic and pragmatist philosophy.

Another notable recent foray into pragmatist-inspired normative pragmatics is found in the work of Jürgen Habermas, a philosopher from the Frankfurt School who has engaged with unparalleled breadth across the landscape of 20th century philosophy. He manages to combine analytic philosophers’ goal of systematically theorising language with a neo-Marxian and hermeneutic critique of modernity, whilst drawing on Mead’s pragmatist analysis of the self as irremediably social. His central concept of communicative action (Habermas 1981) is advocated as a foil to the instrumentalist rationality that he takes to be rampantly colonising the human ‘lifeworld’ in the West. The discourse ethics which he develops in order to scaffold an authentic communicative action that is free from the distortions of power and ideology owes much to pragmatism’s concept of the community of inquiry, although he is sceptical of Peirce’s inquiry-based analysis of truth as overly idealised (Habermas 2003). With major contributions in political philosophy, ethics, philosophy of law, aesthetics and philosophy of religion, amongst other areas, Habermas’ influence has reached far into the social sciences – something Dewey would likely have approved.

6. Pragmatism’s Contribution in Other Areas of Philosophy

We have noted that a strong motivation for James’ interest in pragmatism was exploring truth in religion. He drew on his dual training in philosophy and psychology for his famous book The Varieties of Religious Experience : a unique compendium of testimonies concerning matters such as prayer, worship and mystical experience. These rich personal observations present an extended example of the ‘radical empiricism’ introduced in 4.3. James thereby sought to trenchantly critique the intellectual methods of contemporary theology (‘the metaphysical monster which they offer to our worship is an absolutely worthless invention of the scholarly mind’ (James 1902: 447)). James also advanced a celebrated argument for religious faith in his paper “The Will to Believe”: that for questions that are living, forced and momentous (though only for those), ‘faith based on desire is certainly a lawful, and possibly an indispensable thing’. He thereby confronted his contemporary William Clifford’s evidentialist claim that, ‘It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence’ (1877), generating a lively discussion which continues today (e.g. Bishop 2007; Aikin 2014).

Despite James’ efforts to tightly circumscribe his argument’s application, Peirce objected to such concessions in epistemology, calling the paper in a letter to James, ‘a very exaggerated utterance, such as injures a serious man very much’ (Misak 2013: 64). Peirce himself evolved from an early positivistic disdain for religious questions to producing his own theistic arguments in later life. In 1893, he published an essay entitled “Evolutionary Love”, which passionately contested the social Darwinism promulgated by many prominent thinkers in his era, most notably Herbert Spencer (Pearce 2020), which he called ‘The Gospel of Greed’. Here Peirce urges that amongst the three ways the Universe may unfold: (i) by chance, (ii) deterministically, (iii) through creative love, the third path is the highest and most likely to endure since ‘…growth comes only from love, from I will not say self-sacrifice, but from the ardent impulse to fulfill another’s highest impulse’ (CP 6.289). In his final years Peirce produced the remarkable essay “A Neglected Argument for the Reality of God”. Here he argued for God’s reality , not existence , to signal an ontological priority of intelligible principles over efficient causes. The piece is structured into three argumentative layers: (i) The Humble Argument (an invitation to a phenomenological experiment) which is enfolded by, (ii) The Neglected Argument (an original version of the Ontological Argument) which is enfolded by, (iii) The Scientific Argument (a prophecy of the fullness of future scientific inquiry). Work is ongoing to draw out this unique piece’s full meaning.

Dewey turned his hand to religious questions in his 1934 book A Common Faith . Here he argued that—contrary to what many believe—removing faith in supernatural entities will not destroy religion, but rather set it free from the many ‘creeds and cults’ reflecting outdated social structures that currently survive fossilised inside religious institutions. Rather than being embodied by any kind of entity , he argued, the sacred is a phase or quality of experience , namely, ‘some complex of conditions that have operated to affect an orientation in life…that brings with it a sense of security and peace’ (LW9:13). Such conditions might equally be found in a forest or art gallery as a church or temple. Despite its sophisticated argumentation and originality, as an explication of religious life Dewey’s approach has been considered abstract and somewhat anodyne.

We’ve seen that philosophical pragmatism seeks to connect theory to practice. In ethics it can seem natural to interpret this as recommending that normative notions be reduced to practical utility. Thus James embraced utilitarian ethics as one of the branches of pragmatism (James 1907). Peirce, however, took a different view. Initially (around 1898) his naturalism led him to advocate a sentimentalism according to which ethical questions should be settled by instinct, as our conscious reasoning is too recently evolved and fallible to determine ‘vitally important matters’. But around 1902 he began to warm towards ethical theorising, as he developed a philosophical architectonic which placed ethics directly prior to logic, since ethics studies what is good in action, and logic studies what is good in thought, which is a species of action. He noted, though, that such a ‘normative science’ should be understood to study what goodness is , not whether particular actions are good (by contrast to much normative ethics today) since, ‘a science cannot have for its fundamental problem to distribute objects among categories of its own creation’ (CP 2.198). Recently scholars have turned with renewed interest to developing Peirce’s ethics (e.g. Massecar 2016; Atkins 2016).

A rich and systematic early contribution to pragmatist value theory was made by Alain Locke, who wrote, ‘the gravest problem of contemporary philosophy is how to ground some normative principle or criterion of objective validity for values without resort to dogmatism and absolutism on the intellectual plane, and without falling into their corollaries, on the plane of social behavior and action, of intolerance and mass coercion’ (Locke 1935: 336). Locke taught that the distinctive feeling-qualities that values give rise to in us are our ultimate guide in studying them, although function has an important secondary role to play. He held the resulting axiology to be pluralist, as well as culturally relativist.

Dewey also sought to steer ethics between the traditional poles of an objectivism derived from some kind of human-transcendent authority, and a subjectivism derived from individual preference. He believed that both views err in granting the moral agent an identity prior to interactions with others. For Dewey, we are more frail beings than this, embedded in a sociality that runs much deeper, and the purpose of moral theory is ultimately to provide constructive methods for addressing human problems of a particular kind: those in which we find ourselves unable to choose between equally valuable ends, with a dearth of salient habits with which to cross the breach. With regard to such questions, much effort is required to clear away traditional ethical theory’s pretensions to deliver a spurious settled certainty. Progress can be made by recognising the inherent uncertainty of moral problems and the complexities of moral experience (Hildebrand 2008: 73), and being willing to inquire anew in every moral context, drawing in data from a variety of scientific disciplines, in order to lay down new intelligent habits. The evolution of Dewey’s ethical thinking across his long career is richly explored in (Welchman 1995).

In recent decades, value theory has arguably been under-addressed by pragmatists, due to neopragmatism’s strong focus on philosophy of language and metaphilosophy. A notable recent attempt to develop a pragmatist metaethics drawing on classical pragmatism is (Heney 2016), which forms part of the so-called New Pragmatism.

When (around 1902) Peirce defined ethics as a normative science directly prior to logic, he also defined aesthetics as a normative science directly prior to ethics (since aesthetics studies goodness in and of itself, which may then be used to understand good action). This focus on the intrinsically good or admirable broadens the purview of aesthetics, which Peirce claims ‘has been handicapped by the definition of it as the theory of beauty’ (CP 2.199, 1902). Aesthetics is one of the least well worked-out areas of Peirce’s philosophy; nevertheless he says some intriguing and suggestive things about it. For instance he argues that the so-called summum bonum (ultimate good) really consists in the growth of ‘concrete reasonableness’ (CP 1.602; 1.615; 2.34; 5.121; 5.433), as the only phenomenon ‘whose admirableness is not due to an ulterior reason’ must be the furthering of Reason itself (CP 1.615, 1903). Recent further development of this framework includes (Kaag 2014; Gava 2014).

James did not make sustained contributions to aesthetics, but Dewey did, particularly in his 1934 book Art as Experience . Dewey viewed aesthetic appreciation as a peak human experience and ‘the greatest intellectual achievement in the history of humanity’ (LW10:31, cited in Hildebrand 2008: 146). Consequently the most important question in this area of philosophy is not how to define necessary and sufficient conditions for Art, but how to enable ordinary people to enjoy more of it, so that their lives might be more meaningful. The way forward, Dewey suggested, is to learn to fetishize professionally-curated contexts and Art objects less, in order to open our eyes to consummatory experiences as they occur in the everyday experience of the ‘live creature’. Examples of such consummations include: ‘[a] piece of work is finished in a way that is satisfactory; a problem receives its solution; a game is played through…’ (LW10:42). In contrast to such integrated completions within experience, both hedonistic dissipation and rigid self-control count as ‘anesthetic’. True art alternates between doing and undergoing. Notable recent work building on Dewey’s aesthetics includes Richard Shusterman’s somaesthetics , which extends pragmatism’s defining interest in agency to exploring the complex role of the human body in aesthetic experience (Shusterman 1992; 2012).

Peirce had some insightful things to say about pedagogy which anticipate today’s ‘inquiry-based learning’ and ‘research-led teaching’, but they are scattered across his writings (Strand 2005). The giant figure in philosophy of education is of course Dewey, who pioneered and established it as a separate sphere of study when he first assumed the chair in Philosophy at University of Chicago in 1894. Dewey’s career coincided with a period in which North America’s population was rapidly growing, industrializing and urbanizing, shifting education delivery out of the home into public institutions, and his ideas had enormous impact. Many of his suggestions derive from his vision of democracy as not merely a system of voting but the idea that every societal institution might be designed to foster maximum flourishing in every citizen. Viewed from this angle, traditional modes of schooling whereby teachers deliver an approved (often employer-sanctioned) set of facts for children to memorise count as despotic. Instead the emphasis should be on enabling children to grow from within, according to their present interests and capabilities, and become lifelong learners, although Dewey equally criticises certain romantic, ‘child-centred’ educational theorists of his day for neglecting to direct or guide the child’s interests in any particular direction (Hildebrand 2008: 127). It’s also worth noting that Dewey sees education as primarily a social not an individual process since, as noted above, he views human identity formation as irremediably social.

The result is a ‘problem-centred pedagogy’ which looks to pragmatist epistemology understood as the theory of inquiry for its structure. The teacher begins by facilitating contact with some phenomenon which proves genuinely puzzling to the students, then guides them through a cycle of inquiry which (if all goes well) resolves the problematic situation to the satisfaction of all present. This cycle of inquiry includes as stages: articulating the problem and questions which might need to be answered in its resolution, gathering data, suggesting hypotheses which might potentially resolve the problem, and testing or otherwise evaluating those hypotheses. Opening up the classroom to such ‘live’ thinking generates unpredictability which can be challenging for the teacher to manage, but if the genuine indeterminacy of the problematic situation can be successfully navigated, the reward will be students who have learned not just how to know , but how to think . In that regard, Dewey claimed that his writings on education summed up his entire philosophical position (Hildebrand 2008: 124). For Dewey, all philosophy was philosophy of education.

As well as identifying some of the primary texts of pragmatism and listing works referred to in the article, the bibliography also contains some books which can be studied to supplement the current article.

For both Peirce and Dewey, references are given to collections of their writings. This is because Peirce’s philosophical writings consist of a great number of papers and manuscripts and because Dewey wrote so many books that it would be impossible to list all of them.

• Dewey, J., 1999. The Essential Dewey (two volumes edited by Hickman, L. and Alexander, T.), Bloomington: Indiana University Press, 1999. (When possible, references to Dewey’s writings are given to this collection. They take the form ED n : m —to page m of volume n )
• –––, 1981–91. John Dewey: The Later Works , Carbondale: Southern Illinois University Press. (References to Dewey’s writings in this collection take the form LW n : m —to page m of volume n )
• James, W., 1890. The Principles of Psychology , Cambridge, MA: Harvard University Press, 1981.
• –––, 1897. The Will to Believe and Other Popular Essays in Philosophy , Cambridge, MA: Harvard University Press, 1979.
• –––, 1902. The Varieties of Religious Experience , Cambridge, MA: Harvard University Press, 1902.
• –––, 1907. Pragmatism: A New Name for some Old Ways of Thinking , Cambridge, MA: Harvard University Press, 1975.
• –––, 1909. The Meaning of Truth , Cambridge, MA: Harvard University Press, 1975.
• Peirce, C.S., 1992 and 1999. The Essential Peirce (two volumes edited by the Peirce Edition Project), Bloomington: Indiana University Press. (References to Peirce’s writings in this collection take the form EP n : m —to page m of volume n )
• –––, 1982–. Writings of Charles S. Peirce (a critical edition of Peirce’s entire oeuvre, arranged chronologically and edited by the Peirce Edition Project. So far 8 volumes have been released, covering the time-period up to 1892), Bloomington: Indiana University Press.
• –––, 1976. New Elements of Mathematics ed. Eisele, C. (Peirce’s writings on mathematics and related topics: four volumes in five books), The Hague: Mouton, Humanities Press (reprinted in 2011 by De Gruyter).
• –––, 1931–1958. Collected Papers, vol. 1–7 ed. Hartshorne, C., and Weiss, P., vol 8 ed. Burks, A.. Cambridge, Mass.: Harvard University Press. (References to Peirce’s writings in this collection take the form CP n . m —to paragraph m of volume n )
• Goodman, R. (ed.), 1995. Pragmatism , London: Routledge.
• ––– (ed.), 2005. Pragmatism: Critical Concepts in Philosophy (four volumes covering: volume one: Pragmatism’s first decade; volume two: metaphysics and epistemology; volume three: moral and political issues; volume four: neopragmatism and aesthetics). London: Routledge.
• Haack, S. and Lane, R. (eds.), 2006. Pragmatism, Old and New: Selected Writings , Amherst NY: Prometheus.
• Menand, L. (ed.), 1998. Pragmatism , New York: Random House.
• Stuhr, J.J. (ed.), 1999. Pragmatism and Classical American Philosophy: Essential Readings and Interpretive Essays , New York: Oxford University Press.
• Talisse, R. and Aikin, S. (eds.), 2011. The Pragmatism Reader: From Peirce through the Present , Princeton: Princeton University Press.
• Thayer, H.S. (ed.), 1982. Pragmatism: The Classic Writings , Hackett.
• Addams, J., 1990. Twenty Years at Hull-House , Chicago: University of Illinois Press.
• –––, 2002. Democracy and Social Ethics , Chicago: University of Illinois Press.
• Aikin, S., 2014. Evidentialism and the Will to Believe , London: Bloomsbury Publishing.
• Alexander, T., 2013. The Human Eros: Eco-ontology and the Aesthetics of Existence , Oxford: Oxford University Press.
• Apel, K.O., 1974. “From Kant to Peirce: The Semiotical Transformation of Transcendental Logic”, in Kant’s Theory of Knowledge , L.W. Beck (ed.), Dordrecht: Springer, pp. 23–37.
• Atkins, R.K., 2016. Peirce and the Conduct of Life: Sentiment and Instinct in Ethics and Religion , Cambridge: Cambridge University Press.
• Bacon, M., 2012. Pragmatism , Oxford: Polity Press.
• Baldwin, T., 2003. Cambridge History of Philosophy 1870–1945 , Cambridge: Cambridge University Press.
• Bellucci, F., 2017. Peirce’s Speculative Grammar: Logic as Semiotics , London: Routledge.
• Bernstein, R., 2010. The Pragmatic Turn , Cambridge: Cambridge University Press.
• Bishop, J., 2007. Believing by Faith: An Essay in the Epistemology and Ethics of Religious Belief , Oxford: Oxford University Press.
• Boler, J.F., 1963. Charles Peirce and Scholastic Realism , Seattle: University of Washington Press.
• Boncompagni, A., 2016. Wittgenstein and Pragmatism: On Certainty in the Light of Peirce and James , London: Palgrave Macmillan.
• Brandom, R., 1994. Making It Explicit , Cambridge MA: Harvard University Press.
• –––, 2000. Articulating Reasons , Cambridge MA: Harvard University Press.
• –––, 2008. Between Saying and Doing: Towards an Analytic Pragmatism , Cambridge: Cambridge University Press.
• –––, 2011. Perspectives on Pragmatism: Classical, Recent, and Contemporary , Cambridge, MA: Harvard University Press.
• ––– (ed.), 2000. Rorty and his Critics , Oxford: Blackwell.
• Clifford, W.K., 1877. “The Ethics of Belief”, reprinted in W. Clifford, Lectures and Essays , London: Macmillan, 1886, 163–205.
• Cook, G.A., 1993. George Herbert Mead: The Making of a Social Pragmatist , Chicago: University of Illinois Press.
• Cooke, E., 2007. Peirce’s Pragmatic Theory of Inquiry: Fallibilism and Indeterminacy , London: Bloomsbury.
• Du Bois, W.E.B., 1903 [2007]. The Souls of Black Folk , Oxford: Oxford University Press.
• Festenstein, M., 1997. Pragmatism and Political Theory , Chicago: University of Chicago Press.
• Fischer, M., Nackenoff, C., & Chmielewski, W. (eds.), 2010. Jane Addams and the Practice of Democracy , Champaign, IL: University of Illinois Press.
• Gallagher, S., 2017. Enactivist Interventions: Rethinking the Mind , Oxford: Oxford University Press.
• Gava, G., 2014. Peirce’s Account of Purposefulness: A Kantian Perspective , London: Routledge Studies in Nineteenth Century Philosophy.
• Goodman, R., 2002. Wittgenstein and William James , Cambridge: Cambridge University Press.
• Haack, S., 1976. “The Pragmatist Theory of Truth”, The British Journal for the Philosophy of Science , 27(3): 231–249.
• –––, 1993. Evidence and Inquiry: A Pragmatist Reconstruction of Epistemology , Oxford: Blackwell.
• Habermas, J., 1981. The Theory of Communicative Action (Volume 1: Reason and the Rationalization of Society; Volume 2: Lifeworld and System: A Critique of Functionalist Reason), T.A. McCarthy (trans.), Boston: Beacon Press.
• –––, 2003. Truth and Justification , B. Fultner (trans.), Cambridge: Polity Press.
• Heney, D., 2016. Toward a Pragmatist Metaethics , London: Routledge.
• Hickman, L., 2001. Philosophical Tools for Technological Culture: Putting Pragmatism to Work , Indianapolis: Indiana University Press.
• Hildebrand, D.L., 2003. Beyond Realism and Anti-Realism : John Dewey and the Neopragmatists , Nashville: Vanderbilt University Press.
• –––, 2008. Dewey: A Beginner’s Guide , Oxford: Oneworld.
• Hookway, C.J., 1997. “Logical Principles and Philosophical Attitudes: Peirce’s Response to James’s Pragmatism” in R.A. Putnam (ed.), 145–165.
• –––, 2004a. “The Principle of Pragmatism: Peirce’s Formulations and Examples”, in Midwest Studies in Philosophy , 28: 119–136.
• –––, 2004b. “Truth, Reality and Convergence”, in Misak (ed.) 2004, 127–150.
• –––, 2005. “The Pragmatist Maxim and the Proof of Pragmatism”, in Cognitio , 9: 25–42.
• –––, 2007. “Fallibilism and the Aim of Inquiry”, in Proceedings of the Aristotelian Society (Supplementary Volume), 81: 1–22.
• –––, 2008. “Peirce and Skepticism” in J. Greco (ed.), Oxford Handbook to Skepticism , Oxford: Oxford University Press, 310–329.
• –––, 2012. The Pragmatic Maxim: Essays on Peirce and Pragmatism , Oxford: Oxford University Press.
• Hoopes, J., 1998. Community Denied: The Wrong Turn of Pragmatic Liberalism , Ithaca: Cornell University Press.
• Jappy, T., 2016. Peirce’s Twenty-Eight Classes of Signs and the Philosophy of Representation: Rhetoric, Interpretation and Hexadic Semiosis , London: Bloomsbury.
• Joas, H., 1997. G.H. Mead: A Contemporary Re-examination of his Thought , Cambridge MA: MIT Press.
• Johnston, M., 2003. “Objectivity Refigured: Pragmatism Without Verificationism”, in J. Haldane and C. Wright (eds.), Reality, Representation and Projection , Oxford: Oxford University Press: 85–130.
• Kaag, J., 2014. Thinking Through the Imagination: Aesthetics in Human Cognition , Oxford: Oxford University Press.
• Kegley, J.A.K., 2008. Josiah Royce in Focus , Indianapolis: Indiana University Press.
• Kitcher, P., 2012. Preludes to Pragmatism: Towards a Reconstruction of Philosophy , Oxford: Oxford University Press.
• Koopman, C., 2007. “Language is a Form of Experience: Reconciling Classical Pragmatism and Neopragmatism”, Transactions of the Charles S. Peirce Society , 43(4): 694–727.
• –––, 2009. Pragmatism as Transition: Historicity and Hope in James, Dewey, and Rorty , New York: Columbia University Press.
• Lachs, J. 2012. Stoic Pragmatism , Bloomington: Indiana University Press.
• Lane, R., 2018. Peirce on Realism and Idealism , Cambridge: Cambridge University Press.
• Legg, C., 2014. “Charles Peirce’s Limit Concept of Truth”, Philosophy Compass , 9(3): 204–213.
• –––, 2017. “Idealism Operationalized: How Peirce’s Pragmatism Can Help Explicate and Motivate the Possibly Surprising Idea of Reality as Representational”, in R.K. Atkins and K. Hull (eds.), Peirce on Perception and Reasoning , London: Routledge: 52–65.
• Levi, I., 2012. Pragmatism and Inquiry , Oxford: Oxford University Press.
• Levine, S., 2010. “Rehabilitating Objectivity: Rorty, Brandom, and the New Pragmatism”, Canadian Journal of Philosophy , 40(4): 567–589.
• –––, 2012. “Brandom’s Pragmatism”, Transactions of the Charles S. Peirce Society , 48(2): 125–140.
• –––, 2019. Pragmatism, Objectivity, and Experience , Cambridge: Cambridge University Press.
• Lewis, C.I., 1923. “A Pragmatic Conception of the A Priori ”, Journal of Philosophy , 20: 169–77.
• –––, 1929. Mind and the World Order , New York: Charles Scribner’s Sons.
• Liszka, J.J., 1996. A General Introduction to the Semeiotic of Charles Sanders Peirce , Indianapolis: Indiana University Press.
• Locke, A.L., 1935. “Values and Imperatives”, in M.K. Horace & S. Hook (eds.), American Philosophy Today and Tomorrow , Freeport, NY: Books for Libraries Press: 313–336.
• –––, 1989. The Philosophy of Alain Locke: Harlem Renaissance and Beyond , L. Harris (ed.), Philadelphia: Temple University Press.
• Malachowski, A., 2013. The New Pragmatism , Durham: Acumen.
• ––– (ed.), 2013. Cambridge Companion to Pragmatism , Cambridge: Cambridge University Press.
• Margolis, J., 2010. Pragmatism’s Advantage , Stanford: Stanford University Press.
• Massecar, A., 2016. Ethical Habits: a Peircean Perspective , New York: Lexington Books.
• Mayorga, R.M., 2007. From Realism to ‘Realicism’: The Metaphysics of Charles Sanders Peirce , Lanham, MD: Lexington Books.
• Mead, G.H., 1934. Mind, Self and Society , Chicago: University of Chicago Press
• Menand, L., 2001. The Metaphysical Club , New York: Farrar, Straus and Giroux
• Menary, R., 2007. Cognitive Integration: Mind and Cognition Unbounded , London: Palgrave.
• Misak, C.J., 1999. Pragmatism , Calgary: University of Calgary Press.
• ––– (ed.), 1999. Truth, Politics, Morality: Pragmatism and Deliberation , London: Routledge.
• ––– (ed.), 2004. The Cambridge Companion to Peirce , Cambridge: Cambridge University Press.
• ––– (ed.), 2007. New Pragmatists , Oxford: Oxford University Press.
• ––– (ed.), 2013. The American Pragmatists , Oxford: Oxford University Press.
• –––, 2018. Cambridge Pragmatism: From Peirce and James to Ramsey and Wittgenstein , Oxford: Oxford University Press.
• Moore, E.C., 1961. American Pragmatism: Peirce, James and Dewey , New York: Columbia University Press.
• Mounce, M., 1997. The Two Pragmatisms , London: Routledge
• Murphey, M.G., 2005. C.I. Lewis: The Last Great Pragmatist , Albany: State University of New York Press.
• Murphy, J.P. 1990. Pragmatism from Peirce to Davidson , Boulder: Westview Press.
• Oppenheim, F.M., 2005. Reverence for the Relations of Life: Re-imagining Pragmatism via Josiah Royce’s interactions with Peirce, James, and Dewey , Notre Dame IN: University of Notre Dame Press.
• Pappas, G.F., 1998. “The Latino Character of American Pragmatism”, Transactions of the Charles S. Peirce Society , 34(1): 93–112.
• Pearce, T., 2020. Pragmatism’s Evolution: Organism and Environment in American Philosophy , Chicago: University of Chicago Press.
• Pratt, S.L., 2002. Native Pragmatism: Rethinking the Roots of American Philosophy , Bloomington: Indiana University Press.
• Price, H., 2013. Expressivism, Pragmatism, and Representationalism , Cambridge: Cambridge University Press.
• Putnam, H., 1993. Renewing Philosophy , Cambridge MA: Harvard University Press
• –––, 1994a. Words and Life , Cambridge MA: Harvard University Press
• –––, 1994b. Pragmatism , Oxford: Blackwell
• –––, 1994c. “Pragmatism and Moral Objectivity”, in Putnam 1994a.
• –––, 2002. Collapse of the Fact/Value Dichotomy and Other Essays , Cambridge MA: Harvard University Press
• –––, 2004. Ethics without Ontology , Cambridge MA: Harvard University Press
• Putnam, H. and Putnam, R.A., 2017. Pragmatism as a Way of Life: The Lasting Legacy of William James and John Dewey , D. Macarthur (ed.), Cambridge MA: Harvard University Press.
• Putnam, R.A., 1997. The Cambridge Companion to William James , Cambridge: Cambridge University Press.
• Quine, W.V.O., 1960. Word and Object , Cambridge, MA: MIT Press.
• Ramsey, F.P., 1926. “Truth and Probability”, The Foundations of Mathematics and other Logical Essays , Ch. VII, 156–198, R.B. Braithwaite (ed.), London: Kegan, Paul, Trench, Trubner & Co., New York: Harcourt, Brace and Company.
• Rorty, R., 1980. Philosophy and the Mirror of Nature , Oxford: Blackwell.
• –––, 1982. The Consequences of Pragmatism , Sussex: Harvester.
• –––, 1991a. Objectivity, Relativism and Truth , Cambridge: Cambridge University Press.
• –––, 1991b. “The Priority of Democracy to Philosophy”, in Rorty 1991a, 175–196.
• –––, 1995, “Feminism and Pragmatism”, in R. Goodman (ed.) 1995: 125–48.
• –––, 1998. Truth and Progress , Cambridge: Cambridge University Press.
• –––, 1999. Philosophy and Social Hope , Harmondsworth: Penguin.
• –––, 2000: “Universality and Truth”, in Brandom (ed.) 2000, 1–30.
• Rosenthal, S.B., 1980. Pragmatism and Phenomenology: A Philosophic Encounter , Amsterdam: John Benjamins Publishing.
• –––, 1986. Speculative Pragmatism , Amherst: University of Massachusetts Press.
• –––, 1994. Charles Peirce’s Pragmatic Pluralism , Albany: SUNY Press.
• Rosenthal, S.B., Hausman C.R., and Anderson, D.R. (eds.), 1999. Classical American Pragmatism: Its Contemporary Vitality , Chicago University of Illinois Press.
• Russell, B., 1939. “Dewey’s New Logic”, in P.A. Schilpp (ed.), The Philosophy of John Dewey, Library of Living Philosophers , Evanston, IL: Northwestern University Press: 135–156.
• –––, 1946. History of Western Philosophy , London: George Allen and Unwin.
• Sachs, C.B., 2015. Intentionality and the Myths of the Given: Between Pragmatism and Phenomenology , London: Routledge.
• Scheffler, I., 1986. Four Pragmatists , London: Routledge.
• Seigfried, C.H., 1996. Pragmatism and Feminism: Reweaving the Social Fabric , Chicago: University of Chicago Press.
• Shook, J. and Margolis, J. (eds.), 2005. A Companion to Pragmatism , Oxford: Blackwell.
• Short, T.L., 2007. Peirce’s Theory of Signs , New York: Cambridge University Press.
• Shusterman, R., 1992. Pragmatist Aesthetics: Living Beauty, Rethinking Art , Oxford: Blackwell.
• –––, 1997. Practicing Philosophy: Pragmatism and the Philosophical Life , New York: Routledge.
• –––, 2012. Thinking through the Body: Essays in Somaesthetics , New York: Cambridge University Press.
• Skagestad, P., 1981. The Road of Inquiry: Charles Peirce’s Pragmatic Realism , New York: Columbia University Press.
• Sleeper, R.W., 1986. The Necessity of Pragmatism: John Dewey’s Conception of Philosophy , New Haven CT: Yale University Press.
• Smith, J.E., 1950. Royce’s Social Infinite: The Community of Interpretation , Hamden CT: Archon Books.
• –––, 1978. Purpose and Thought , Chicago: University of Chicago Press.
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• –––, 1996. Heaven’s Champion: William James’ Philosophy of Religion , Notre Dame: University of Notre Dame Press.
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Addams, Jane | Dewey, John | Dewey, John: aesthetics | Dewey, John: moral philosophy | Dewey, John: political philosophy | Du Bois, W.E.B. | feminist philosophy, approaches: pragmatism | Habermas, Jürgen | Hook, Sidney | James, William | Latinx Philosophy | Lewis, Clarence Irving | Locke, Alain LeRoy | Mead, George Herbert | Peirce, Charles Sanders | Peirce, Charles Sanders: theory of signs | pragmatic arguments and belief in God | Rorty, Richard | Royce, Josiah | Santayana, George | truth: pragmatic theory of | Wright, Chauncey

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Intuitive Thinking: A Revolutionary Approach to Problem-Solving

Introduction.

Welcome to “Intuitive Thinking: A Revolutionary Approach to Problem-Solving”! In this blog, we will explore the power of intuitive thinking and how it can transform the way we tackle challenges and find innovative solutions.

Traditional problem-solving often relies on analytical thinking, which involves a logical and methodical approach to analyzing information, breaking down problems into smaller parts, and applying established frameworks and models. While analytical thinking is undoubtedly valuable, it has its limitations. It is often constrained by existing knowledge and can be slow and cumbersome, especially when faced with complex or ambiguous problems.

Intuitive thinking, on the other hand, offers a different approach. It taps into our subconscious mind, allowing us to access knowledge, insights, and creative ideas that may not be readily available to our conscious mind. It is a form of thinking that is instinctive, spontaneous, and automatic, and many successful individuals credit their achievements to their ability to trust their intuition.

This blog aims to delve into the world of intuitive thinking, exploring its definition, the science behind it, and how it differs from analytical thinking. We will debunk common misconceptions surrounding intuition and provide techniques to develop and strengthen our intuitive thinking skills.

In the following chapters, we will examine how intuitive thinking can be applied to problem-solving. We will explore case studies and examples of successful problem-solving through intuition, and discuss the integration of intuitive thinking with analytical thinking. We will also address the challenges that can arise when relying on intuition, such as biases, prejudices, uncertainty, and doubt, and provide strategies to navigate these hurdles effectively.

Furthermore, we will look into the future and explore the potential of intuitive thinking in various fields. We will examine how intuitive thinking can foster innovation and creativity, and discuss the ethical considerations and limitations of relying on intuition alone.

By the end of this blog, you will have a comprehensive understanding of intuitive thinking and its role in problem-solving. You will have gained valuable insights and techniques that can help you enhance your intuitive thinking skills and apply them in various aspects of your life.

So, let’s embark on this journey of discovery together and unlock the power of intuitive thinking to revolutionize our problem-solving approach!

Chapter 1: Understanding Intuition

Intuition is often described as a “gut feeling,” a hunch, or a sense of knowing without any logical explanation. It is a powerful and often overlooked tool in problem-solving that can lead to innovative and creative solutions.

Defining Intuition

Intuition can be defined as the ability to understand or know something instinctively, without the need for conscious reasoning. It is an instantaneous understanding or insight that arises without conscious thought. Unlike analytical thinking, which relies on logical reasoning and evidence, intuition relies on unconscious knowledge and experiences. It bypasses the limitations of conscious thought and can provide unique perspectives on a problem.

The Science behind Intuitive Thinking

Numerous scientific studies have explored the nature and mechanisms of intuition. It is believed that intuition is a result of our brain’s ability to process information at a subconscious level. Our brains continuously collect, store, and analyze data from our experiences, creating a vast repository of tacit knowledge. Intuition taps into this repository and provides us with insights and solutions that go beyond conscious thought.

Research in neuroscience has shown that intuition involves the interplay between the conscious and unconscious parts of the brain. The unconscious mind processes information, makes connections, and sends signals to the conscious mind when it detects patterns or identifies relevant information. This process happens rapidly and often without our awareness, leading to sudden insights or “lightbulb moments.”

Common Misconceptions about Intuition

There are several common misconceptions about intuition that can hinder its effective use in problem-solving. One misconception is that intuition is purely based on guesswork or irrationality. However, intuition is not random or illogical; it is based on the deep-seated knowledge and experiences that our brain has accumulated over time.

Another misconception is that intuition is a mystical or supernatural phenomenon. While intuition may feel mysterious, it is a natural and inherent human ability. It is a product of our brain’s complex cognitive processes, and its effectiveness can be developed and enhanced through practice.

It is important to recognize that intuition is not infallible. It can be influenced by biases, emotions, and other cognitive limitations. However, by understanding the role of intuition and learning to discern valid intuitive insights from personal biases, we can harness its power and use it as a valuable tool in problem-solving.

In the next chapter, we will explore techniques and strategies that can help develop and strengthen our intuitive thinking skills, allowing us to tap into this powerful resource for finding innovative solutions.

Chapter 2: Developing Intuition

Developing intuition is a crucial step in harnessing the power of intuitive thinking. While some people may naturally have a strong intuition, it is a skill that can be cultivated and honed through practice. In this chapter, we will explore various techniques and strategies to develop and strengthen your intuitive thinking skills.

Tuning into your inner voice

One of the fundamental aspects of developing intuition is learning to listen and trust your inner voice. This inner voice often provides valuable insights and guidance, but it can be easily drowned out by the noise and distractions of everyday life. Here are some techniques to help you tune into your inner voice:

Meditation : Regular meditation practice can help quiet the mind and create space for intuitive thoughts and feelings to surface. Find a quiet and comfortable place, focus on your breath, and allow your thoughts to come and go without judgment. Through meditation, you can learn to distinguish between your inner wisdom and unnecessary mental noise.

Spend time in nature : Nature has a way of calming our mind and connecting us to our innate intuition. Take regular walks in nature, go hiking or camping, or simply sit in a park and observe the beauty of the natural world. Being in nature helps us slow down and tap into our intuitive senses.

Developing your sensory awareness

Intuition often manifests itself through our senses. Developing your sensory awareness can help you become more attuned to your intuition. Here are some techniques to enhance your sensory awareness:

Body scan : Perform a body scan meditation where you focus on each part of your body and observe any sensations or discomfort. This practice helps you develop a deeper connection with your body and enhances your ability to pick up subtle signals and messages.

Practice mindfulness : Engage in activities with heightened awareness of your senses. Whether it’s eating a meal, taking a shower, or going for a walk, consciously pay attention to the sights, sounds, smells, tastes, and sensations you experience. This helps train your brain to be more present and tuned into your surroundings.

Cultivating creativity and imagination

Intuition is closely linked to creativity and imagination. Cultivating these traits can help you tap into your intuitive thinking abilities. Here are some techniques to stimulate your creativity and imagination:

Engage in creative activities : Take up activities that inspire your creativity, such as painting, writing, playing a musical instrument, or dancing. These activities help loosen up your mind and open it to new possibilities.

Visualize and daydream : Set aside time each day to visualize and daydream about the topics or problems you want to gain insights into. Allow your mind to wander freely and see where it takes you. Sometimes, the most innovative solutions can come from these moments of unfocused imagination.

Reflecting and journaling

Reflection and journaling are powerful tools for developing intuition. They allow you to capture your thoughts, feelings, and experiences, making it easier to recognize patterns and insights. Here are some ways to incorporate reflection and journaling into your intuitive development process:

Write in a journal : Set aside time each day to write in a journal. Reflect on your experiences, thoughts, and emotions. This practice helps you gain clarity, process your feelings, and identify recurring themes or patterns.

Review past journal entries : Periodically review your past journal entries to identify any recurring themes, ideas, or insights. This retrospective analysis can give you a deeper understanding of your intuitive guidance and help you trust it more confidently.

In conclusion, developing intuition is a transformative process that requires dedication and practice. By tuning into your inner voice, enhancing your sensory awareness, cultivating creativity and imagination, and reflecting through journaling, you can strengthen your intuitive thinking skills and unlock a powerful tool for problem-solving and decision-making.

Chapter 3: Applying Intuitive Thinking to Problem-Solving

In this chapter, we will explore how to apply intuitive thinking to problem-solving and how it can complement analytical thinking. By combining both approaches, we can maximize our chances of finding innovative solutions to complex problems.

Integrating Intuitive Thinking with Analytical Thinking

Intuitive thinking and analytical thinking are often viewed as opposing approaches, but they can actually work together synergistically. Intuition allows us to tap into our subconscious knowledge and experience, while analytical thinking helps us analyze and structure our thoughts.

To integrate intuitive thinking with analytical thinking, it is important to follow these steps:

Recognize the problem : Identifying a problem is the first step in the problem-solving process. Using analytical thinking, define the problem and break it down into its component parts.

Gather information : Use analytical thinking to gather relevant data, facts, and evidence related to the problem. This information will serve as a foundation for intuitive thinking to build upon.

Engage your intuition : Once you have gathered enough information, allow your intuition to come into play. Disconnect from conscious thinking and let your mind wander. Listen to your gut feelings and pay attention to any insights that arise.

Trust your instincts : Intuitive thinking often provides us with initial ideas or hunches about potential solutions. Trust these instincts and use them as a starting point for further exploration.

Combine intuition and analysis : After trusting your instincts, switch back to analytical thinking to analyze and evaluate the potential solutions generated by your intuition. Use logic, critical thinking, and evidence to validate and refine your ideas.

Iterate and refine : Problem-solving is rarely linear, so be prepared to iterate and refine your ideas based on feedback and new insights. This process of going back and forth between intuitive and analytical thinking allows for creative and dynamic problem-solving.

By integrating intuitive thinking with analytical thinking, we can benefit from the strengths of both approaches, leading to more holistic problem-solving outcomes.

Case Studies and Examples

To illustrate the application of intuitive thinking to problem-solving, let’s explore a few real-life case studies:

Steve Jobs and Apple : Steve Jobs, the co-founder of Apple, famously relied on his intuition to drive innovation. His intuition led to the development of game-changing products like the iPod, iPhone, and iPad, which revolutionized the technology industry.

Albert Einstein and the theory of relativity : Einstein’s breakthroughs in physics were often credited to his intuitive thinking. He would imagine and visualize complex theories, trusting his intuition to guide him towards the correct answers.

Marie Curie and radioactivity : Curie’s discovery of radioactivity was driven by her intuitive thinking. She followed her instincts and pursued unconventional research paths, leading to groundbreaking findings in the field of science.

These examples demonstrate how intuitive thinking can lead to extraordinary breakthroughs and advancements in various fields.

When to Rely on Intuition

While intuitive thinking is a valuable problem-solving tool, it is essential to understand when it is appropriate to rely on it and when to use other methods. Here are some factors to consider:

Complexity of the problem : Intuitive thinking works best when dealing with complex problems that cannot be easily solved through analytical thinking alone. Intuition can offer unique insights and unconventional approaches to such challenges.

Experience and expertise : Intuitive thinking becomes more reliable when individuals have a deep understanding and expertise in a specific domain. The more knowledge and experience one has, the more reliable their intuition becomes.

Time constraints : Intuitive thinking can be a faster approach to problem-solving, making it suitable for situations with tight deadlines. However, it is crucial to balance speed with thoughtful analysis to ensure the validity of the solutions generated.

Supporting evidence : While intuitive insights can be powerful, it is important to critically evaluate them and seek supporting evidence. Analytical thinking can help validate and provide additional context for intuitive ideas.

By considering these factors, one can determine when to rely on intuitive thinking and when to leverage other problem-solving methods.

In conclusion, applying intuitive thinking to problem-solving requires a combination of intuition and analysis. Integrating both approaches allows for a more comprehensive and innovative problem-solving process. By understanding when to rely on intuition and when to use other methods, individuals can harness the power of intuitive thinking to find creative solutions to complex problems.

Chapter 4: Overcoming Challenges in Intuitive Thinking

Addressing biases and prejudices in intuitive thinking.

Intuitive thinking is not immune to biases and prejudices that can cloud our judgment and hinder effective problem-solving. It is important to be aware of these biases and actively work towards mitigating their influence. Here are some key strategies to address biases and prejudices in intuitive thinking:

Recognize your biases : The first step in overcoming biases is to acknowledge their presence. Take the time to reflect on your thought processes and identify any preconceived notions or biases that may be influencing your intuitive thinking.

Seek diverse perspectives : Engage with a diverse group of people, each bringing their unique perspectives and experiences to the table. This can help counteract biases by presenting alternative viewpoints and challenging existing assumptions.

Challenge your assumptions : Question your own beliefs and assumptions. Adopt a critical mindset and actively seek evidence that contradicts your intuitive thoughts. This will help you think more objectively and consider a wider range of possibilities.

Practice empathy : Empathy is a powerful tool in overcoming biases as it allows us to put ourselves in someone else’s shoes, understand their perspective, and empathize with their experience. By practicing empathy, we can broaden our own thinking and overcome biases rooted in our limited viewpoint.

Dealing with uncertainty and ambiguity in problem-solving

Uncertainty and ambiguity are inherent in many problem-solving situations, and they can pose challenges when relying on intuitive thinking. Here are some techniques to help you navigate uncertainty and ambiguity while utilizing intuitive thinking:

Embrace the unknown : Instead of fearing or avoiding uncertainty, embrace it as an opportunity for growth and exploration. Recognize that uncertainty can lead to breakthrough solutions and innovative ideas.

Develop tolerance for ambiguity : Cultivate a mindset that is comfortable with ambiguity. This involves accepting that not all problems have clear-cut solutions and being open to exploring multiple possibilities.

Experiment and iterate : When faced with uncertainty, it can be helpful to approach problem-solving as an iterative process. Test different ideas, gather feedback, and make adjustments along the way. This allows you to adapt to changing circumstances and refine your intuitive thinking over time.

Seek feedback and collaboration : Engage with others and seek their feedback when dealing with uncertainty. Collaborative problem-solving can provide valuable insights and help validate or challenge your intuitive ideas.

Strategies for overcoming fear and doubt when trusting your intuition

Trusting your intuition requires a certain level of confidence and self-assurance. It is common to experience fear and doubt when relying heavily on intuitive thinking. Here are some strategies for overcoming these challenges:

Cultivate self-awareness : Develop a deep understanding of your own strengths, abilities, and limitations. This self-awareness will help you build confidence in your intuitive thinking and navigate doubts more effectively.

Keep a record of successful intuitions : Maintain a journal or log of past instances where your intuition has led to successful outcomes. Reflecting on these successes can help build trust in your intuition and alleviate doubts.

Practice mindfulness and self-reflection : Engage in mindfulness practices that help you tune into your intuition and connect with your inner wisdom. Regular self-reflection can also help you identify patterns and gain insights into the accuracy of your intuitive thinking.

Take calculated risks : Overcoming fear and doubt often requires taking calculated risks. Start by experimenting with smaller decisions or situations and gradually build your confidence in making bolder choices based on intuition.

Remember, intuitive thinking is a skill that can be developed and refined over time. By addressing biases, embracing uncertainty, and building trust in your intuition, you can overcome the challenges that may arise and leverage intuitive thinking as a powerful problem-solving tool.

Chapter 5: The Future of Intuitive Thinking

Intuitive thinking has the potential to revolutionize problem-solving across various fields. As we continue to advance technologically and face increasingly complex challenges, the role of intuition becomes increasingly important. This chapter explores the potential of intuitive thinking in different areas and highlights its significance for innovation and creativity.

Intuitive Thinking in Science and Technology

Intuitive thinking has the power to transform scientific and technological advancements. By tapping into our innate ability to perceive patterns and connections, scientists can make breakthrough discoveries and develop groundbreaking technologies. For example, scientists often rely on their intuition to come up with new hypotheses and design experiments that lead to major scientific advances.

In the field of technology, intuitive thinking allows engineers and designers to create user-friendly and intuitive interfaces. By understanding how users think and interact with technology, intuitive designers can develop products that seamlessly integrate into our lives and enhance our overall experience. This approach has already been applied to the design of smartphones, virtual reality devices, and smart home technologies, among others.

Intuitive Thinking in Business and Entrepreneurship

In the business world, intuitive thinking plays a crucial role in innovation and entrepreneurial success. The ability to identify market trends, anticipate customer needs, and make strategic decisions based on intuition can give companies a significant competitive advantage. Intuitive entrepreneurs often have a natural ability to spot opportunities that others may overlook and can make bold and innovative moves that drive business growth.

Additionally, intuitive thinking can enhance problem-solving within organizations. By encouraging employees to tap into their intuitions, organizations can foster a culture of creativity and innovation, leading to more effective and efficient problem-solving approaches. This can translate into improved products and services, enhanced customer satisfaction, and increased profitability.

Ethical Considerations and Limitations of Intuitive Thinking

While intuitive thinking holds great promise, it is essential to recognize its limitations and the ethical considerations that come with it. Intuition is not infallible and can be influenced by biases and prejudices. Therefore, it is crucial to remain aware of our own biases and actively engage in critical thinking to avoid making biased decisions.

Moreover, intuitive thinking may not always be the best approach in every situation. It is essential to strike a balance between intuitive and analytical thinking, depending on the nature of the problem at hand. Some problems may require logical reasoning and extensive analysis, while others may benefit from a more intuitive and creative approach. Recognizing when to rely on intuition and when to switch to analytical thinking is a crucial skill.

Embracing the Power of Intuitive Thinking

As we enter a future shaped by constant change and increasing complexity, intuitive thinking will become an indispensable tool for problem-solving and innovation. By actively developing and harnessing our intuition, we can unlock our creative potential and find innovative solutions to the challenges we face.

To embrace the power of intuitive thinking, we must be willing to trust ourselves and our abilities. It requires overcoming fear and doubt, as well as cultivating a mindset that values and encourages intuitive thinking. By doing so, we can tap into our innate wisdom and individual experiences to uncover insights and make better decisions.

In conclusion, intuitive thinking is a revolutionary approach to problem-solving that has the potential to transform various fields. By understanding the science behind intuition and developing our intuitive thinking skills, we can leverage this powerful tool to tackle complex challenges and drive innovation. As we navigate the future, let us embrace intuitive thinking and harness its transformative power to create a better world.

In conclusion, intuitive thinking is a revolutionary approach to problem-solving that can lead to innovative and creative solutions. Throughout this guide, we have explored the power of intuition and how it differs from traditional analytical thinking. We have debunked common misconceptions about intuition and provided techniques to develop and strengthen our intuitive thinking skills.

Integrating intuitive thinking with analytical thinking can result in a well-rounded problem-solving approach. By considering both logical analysis and intuitive insights, we can uncover unique perspectives and breakthrough solutions. The case studies and examples provided have demonstrated the effectiveness of intuitive thinking in real-world problem-solving scenarios.

It is important to note that intuitive thinking is not without its challenges. We must address biases and prejudices in order to ensure that our intuitive insights are objective and impartial. Additionally, dealing with uncertainty and ambiguity can be intimidating, but by trusting our intuition, we can navigate through these challenges with confidence.

Looking towards the future, there is great potential for intuitive thinking to revolutionize various fields. From business and technology to the arts and sciences, intuitive thinking can fuel innovation and creativity. However, it is important to recognize the limitations and ethical considerations of intuitive thinking. We must use our intuition responsibly and ethically to ensure that we are making informed decisions.

In conclusion, intuitive thinking is a powerful tool for problem-solving that should not be overlooked. By embracing and cultivating our intuitive thinking skills, we can uncover new possibilities and find innovative solutions to the complex challenges we face. So, let us harness the power of intuition and embark on a journey of intuitive problem-solving.

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Home » Blog » General » Understanding Pragmatic Language Skills: A Checklist for High Schoolers

Understanding Pragmatic Language Skills: A Checklist for High Schoolers

Pragmatic language skills play a crucial role in our everyday interactions. They are the social communication skills that allow us to effectively navigate conversations, understand social cues, and solve problems. For high schoolers, developing strong pragmatic language skills is especially important as they navigate the complexities of academic and social life. In this blog post, we will explore the importance of pragmatic language skills in high school and provide a comprehensive checklist to help high schoolers assess and improve their pragmatic language abilities.

What are pragmatic language skills?

Pragmatic language skills refer to the ability to use language appropriately in social situations. It involves not only verbal communication but also nonverbal communication and social interaction. Let’s break down the components of pragmatic language skills:

• Verbal communication: This includes using appropriate language, maintaining conversations, and asking for clarification when needed.
• Nonverbal communication: Understanding and using body language, maintaining eye contact, and interpreting facial expressions are all important aspects of nonverbal communication.
• Social interaction: Taking turns in conversations, understanding social cues, and respecting personal space are key skills for successful social interactions.
• Problem-solving: Identifying and resolving conflicts, negotiating and compromising, and seeking help when needed are all part of effective problem-solving skills.

Why are pragmatic language skills important for high schoolers?

Pragmatic language skills are essential for high schoolers for several reasons:

• Academic success: Strong pragmatic language skills contribute to effective communication with teachers and peers, leading to better understanding of academic material and improved performance in the classroom.
• Social relationships: High school is a time when social relationships become increasingly important. Good pragmatic language skills help high schoolers build and maintain friendships, navigate social situations, and resolve conflicts.
• Future career prospects: In the professional world, effective communication and social skills are highly valued. Developing strong pragmatic language skills in high school sets the foundation for success in future careers.

The pragmatic language checklist for high schoolers

Now that we understand the importance of pragmatic language skills, let’s dive into the pragmatic language checklist for high schoolers. This checklist is designed to help high schoolers assess their pragmatic language abilities and identify areas for improvement. Here is an overview of the checklist:

• Verbal communication skills: Understanding and using appropriate language, maintaining conversations, and asking for clarification.
• Nonverbal communication skills: Understanding and using body language, maintaining eye contact, and interpreting facial expressions.
• Social interaction skills: Taking turns in conversations, understanding social cues, and respecting personal space.
• Problem-solving skills: Identifying and resolving conflicts, negotiating and compromising, and seeking help when needed.

Each of these categories contains specific items that high schoolers can assess themselves on. For example, under verbal communication skills, they can evaluate their ability to understand and use appropriate language, maintain conversations, and ask for clarification when needed. Similarly, under nonverbal communication skills, they can assess their understanding and use of body language, eye contact, and facial expressions.

How to use the pragmatic language checklist

The pragmatic language checklist can be used in various ways to support high schoolers in improving their pragmatic language skills:

• Self-assessment: High schoolers can use the checklist to assess their own pragmatic language skills. By honestly evaluating their abilities, they can identify areas for improvement and set goals for themselves.
• Seeking professional guidance: If high schoolers are struggling with certain aspects of pragmatic language skills, it may be helpful to seek guidance from a speech-language pathologist or social-emotional learning expert. These professionals can provide targeted strategies and interventions to support skill development.
• Collaborating with teachers and parents: Teachers and parents can also play a crucial role in supporting high schoolers’ pragmatic language skills. By sharing the checklist with them, high schoolers can collaborate with their support network to work on specific areas of improvement.

Developing strong pragmatic language skills is essential for high schoolers as they navigate academic and social environments. By using the pragmatic language checklist, high schoolers can assess their abilities and work towards improving their communication and social skills. Remember, effective communication and social interaction are not only important for high school but also for future success in careers and relationships. Start your journey towards improving your pragmatic language skills today by using the pragmatic language checklist!

Start your EverydaySpeech Free trial and gain access to a wide range of resources and activities designed to support pragmatic language skills in high schoolers. Sign up now and take the first step towards enhancing your communication and social abilities!

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Improved multi-strategy adaptive Grey Wolf Optimization for practical engineering applications and high-dimensional problem solving

• Open access
• Published: 05 September 2024
• Volume 57 , article number  277 , ( 2024 )

Cite this article

You have full access to this open access article

• Mingyang Yu 1 ,
• Jing Xu 1 ,
• Weiyun Liang 1 ,
• Sixu Bao 1 &
• Lin Tang 2  

The Grey Wolf Optimization (GWO) is a highly effective meta-heuristic algorithm leveraging swarm intelligence to tackle real-world optimization problems. However, when confronted with large-scale problems, GWO encounters hurdles in convergence speed and problem-solving capabilities. To address this, we propose an Improved Adaptive Grey Wolf Optimization (IAGWO), which significantly enhances exploration of the search space through refined search mechanisms and adaptive strategy. Primarily, we introduce the incorporation of velocity and the Inverse Multiquadratic Function (IMF) into the search mechanism. This integration not only accelerates convergence speed but also maintains accuracy. Secondly, we implement an adaptive strategy for population updates, enhancing the algorithm's search and optimization capabilities dynamically. The efficacy of our proposed IAGWO is demonstrated through comparative experiments conducted on benchmark test sets, including CEC 2017, CEC 2020, CEC 2022, and CEC 2013 large-scale global optimization suites. At CEC2017, CEC 2020 (10/20 dimensions), CEC 2022 (10/20 dimensions), and CEC 2013, respectively, it outperformed other comparative algorithms by 88.2%, 91.5%, 85.4%, 96.2%, 97.4%, and 97.2%. Results affirm that our algorithm surpasses state-of-the-art approaches in addressing large-scale problems. Moreover, we showcase the broad application potential of the algorithm by successfully solving 19 real-world engineering challenges.

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• Artificial Intelligence

Avoid common mistakes on your manuscript.

1 Introduction

The rapid advancement of science, technology, and industry has given rise to a multitude of intricate optimization problems. These problems frequently entail numerous variables, constraints, and objectives. Their solution spaces are huge and complex, and it is difficult for traditional deterministic optimization methods to obtain satisfactory solutions in acceptable time (Deng et al. 2022 ; Guo et al. 2023 ; Zhou et al. 2022 ). To cope with these challenges, researchers in the field of computational intelligence have started to search for new approaches. Among them, metaheuristic algorithms have attracted much attention due to their high efficiency, universal applicability and powerful global search capability (Aldosari et al. 2022 ; Chauhan et al., 2024; Chen et al. 2023 ).

When dealing with engineering problems, constraints are a crucial consideration. Constraints may be physical limitations or requirements and restrictions of the project. In the field of engineering, there are various techniques available for handling these constraints to ensure that projects proceed as expected and achieve their intended goals. One common technique for constraint handling is optimization algorithms. Optimization algorithms assist engineers in finding the best solution given certain constraints. These algorithms can be mathematical optimization methods such as linear programming, integer programming, or nonlinear programming, or they can be heuristic algorithms such as genetic algorithms, simulated annealing, or particle swarm optimization. By leveraging these algorithms, engineers can find the optimal design or decision solution while taking into account various constraints (Fu et al. 2024b ; Li et al. 2023 ).

MH algorithms are inspired by certain phenomena in nature, such as PSO (Kennedy and Eberhart 1995b ), Firefly Algorithm (FA) (Yang 2009 ), Sine Cosine Algorithm (SCA) (Mirjalili 2016 ), Wind Driven Optimization (WDO) (Bayraktar et al. 2010), Fruit Fly Optimization Algorithm (FOA) (Pan 2012 ), Competitive Swarm Optimizer (Chauhan et al. 2024 ), Fox optimizer(FOX) (Mohammed and Rashid 2023 ), Fitness Dependent Optimizer(FDO) (Abdullah and Ahmed 2019 ) and so on. These algorithms often do not rely on the specific nature of the problem, but instead draw on nature's strategies for stochastic search, which can effectively avoid falling into local optima (Abdel-Basset et al. 2023 ). With the development of deep learning, neural networks and other machine learning techniques, researchers have begun to try to combine these techniques with metaheuristic algorithms to further improve the efficiency of solving complex optimization problems (Garg et al. 2023 ). In recent years, with the wide application of heuristic intelligent optimization algorithms in numerical optimization solving, various swarm intelligence algorithms have been proposed (Fu et al. 2022 ).

The popularity of MH algorithms has four distinct advantages: practicality, generalizability, non-leading properties and avoidance of local optima (Fu et al. 2023a ). First, based on their natural theoretical framework, these strategies are relatively intuitive to construct and deploy, thus allowing engineers and researchers to rapidly integrate them into concrete applications (Havaei & Sandidzadeh 2023 ). Next, since these algorithms treat the problem as an unknown mechanism, they can be applied to a wide range of different tasks such as selection (Said, Elarbi, Bechikh, Coello Coello, & Said, 2023), shop visit balancing (Xia et al. 2023 ) and engineering problems (Nadimi-Shahraki et al. 2022 ). Further, these methods do not rely on derivative information and are particularly good for dealing with nonlinear problems (Aldosari et al. 2022 ). Ultimately, with the help of a global search strategy and a stochastic strategy for updating the location, they can efficiently jump out of the local optimum, which is particularly effective for those scenarios where there are multiple locally optimal solutions.

The existing MH algorithm mainly include: Physics-based algorithms (PhA), Swarm Intelligence Algorithms (SI), Natural Evolutionary Algorithms (EA), and Human-based algorithms (Abualigah et al. 2021 ). In the course of evolution, cooperative behavior between individuals has been gradually formed through natural selection over a long period of time. For example, Trojovský and Dehghani, 2022 proposed a pelican optimization algorithm (POA) inspired by pelican predation. The Genetic Algorithm (GA) is a method of optimization based on the principles of natural evolution. It was proposed by John Holland and his colleagues. is a typical example inspired by Darwinian evolution (Bäck & Schwefel 1993 ). Differential Evolution (DE), based on the concepts of natural selection and reproduction in Darwinian evolution(Storn and Price 1997 ); Genetic Programming (GP), inspired by biological evolution processes; and Evolution Strategies (ES) (Wei 2012 ). Among these, Genetic Algorithms (GA) and Differential Evolution (DE) are widely considered to be the most popular evolutionary algorithms, having garnered significant attention and being applied in numerous applications. Physical method is the result of the interaction of physical law and chemical variation. For example, the Chernobyl Disaster Optimizer (CDO) is an optimization algorithm inspired by the core explosion at the Chernobyl nuclear power plant. (Shehadeh 2023 ). The Galaxy Swarm Optimization (GSO) (Muthiah-Nakarajan and Noel 2016 ) algorithm, inspired by the motion of galaxies; the Firefly Algorithm (FFA), drawing inspiration from soil fertility in agriculture (Shayanfar and Gharehchopogh 2018 ); the Firefly Algorithm (FFA), drawing inspiration from soil fertility in agriculture (Eskandar et al. 2012 ); and the Gravitational Search Algorithm (GSA), derived from Newton's law of universal gravitation and kinematic laws (Rashedi et al. 2009 ).In sharp contrast, a variety of human behaviors are simulated based on human behavior patterns, such as the "Alpine skiing Optimization (ASO)" proposed by Professor Yuan, a new idea influenced by the competitive behavior of athletes. Each of these different Metaheuristic algorithms has its own characteristics. According to different problems and requirements, appropriate algorithms can be selected to solve the optimal problems (Yuan et al. 2022 ). Particle Swarm Optimization (PSO) (Kennedy and Eberhart 1995a ) is inspired by the foraging behavior of bird flocks and fish schools. The Ant Colony Optimization (ACO) algorithm (Dorigo et al. 2006 ) is inspired by the social behavior of ant colonies during foraging. The Pathfinder Algorithm (PFA) (Yapici & Cetinkaya 2019 ) is inspired by the collective action of animal populations in finding optimal food areas or prey. The Harris Hawk Optimization algorithm (HHO)(Heidari et al. 2019 ) is based on the predatory process of Harris hawks hunting rabbits. The Sparrow Search Algorithm (SSA) (Xue and Shen 2020 ) is inspired by the foraging and anti-predatory behavior of sparrows. The Dung Beetle Optimization algorithm (DBO) (Xue and Shen 2022 ) is inspired by the rolling, dancing, foraging, stealing, and reproductive behaviors of dung beetles. The Remora Optimization Algorithm (ROA) (Jia et al. 2021 ) is inspired by the behavior of remoras adhering to different-sized hosts to facilitate foraging. The Black Widow Optimization algorithm (BWO) (Hayyolalam and Kazem 2020 ) is inspired by the unique reproductive behavior of black widow spiders. Dikshit Chauhan et al. proposed the Artificial Electric Field Algorithm (AFFEA) based on a series of learning strategies (Chauhan and Yadav 2024a , b ). Additionally, the Secretary Bird Optimization Algorithm (SBOA) was introduced based on the survival behavior of secretary birds in their natural environment (Fu et al. 2024b ), while the Red-Billed Blue Magpie Optimizer (RBMO) was proposed by simulating the search, chase, prey attack, and food storage behaviors of red-billed blue magpies (Fu et al. 2024a ).

Generally, the optimization process of the MH algorithm can be divided into two main steps (Saka et al. 2016 ): exploration and exploitation. In the exploration phase, the algorithm mainly focuses on searching all corners of the solution space to ensure that no possible optimal solution area is missed; while in the exploitation phase, the algorithm will focus on known high-quality solutions and further deepen the search in order to find the real the optimal solution. These two phases complement each other and ensure that the algorithm has both breadth and depth. GWO is inspired by the hunting behavior of grey wolves (Mirjalili et al. 2014 ). GWO effectively balances the two stages of exploration and exploitation by combining the social behavior of grey wolves with a dynamically adjusted location update strategy, thereby ensuring good global and local search capabilities.

Since its introduction in 2014, GWO has received widespread attention from scholars at home and abroad for its simplicity and efficiency, and has become an important tool for solving complex optimization problems (Fan and Yu 2022 ). However, similar to other optimization algorithms, the GWO algorithm does have some limitations although it has shown quite good performance in many optimization problems. In particularly, it is prone to suffer from prematurity and local optimality when dealing with multimodal function problems. As the iterative process of the GWO progresses, the inherent social hierarchy mechanism within the wolf population leads to a decrease in diversity. This mechanism prioritizes the positions and decisions of the leading wolves (Alpha, Beta, and Delta), influencing the entire pack's movement. As a result, the population tends to converge towards the leaders’ positions. However, this strong convergence driven by the social hierarchy can also lead to a drawback. The population may start to aggregate too closely or blindly around the leaders’ current positions. This phenomenon, often referred to as premature convergence, limits the algorithm’s ability to thoroughly explore the solution space. Consequently, the algorithm might struggle to escape local optima, as the current best solutions (guided by the leading wolves) might not always represent the global optimum. The pack, following the leaders too closely, can get trapped in these local optima, lacking the diversity or exploratory behavior needed to venture out and discover better solutions elsewhere in the search space. (Wang et al. 2018 ). In addition, when global exploration transitions to local mining, the algorithm may lose the ability to explore a wider solution space and overly concentrate on a specific region for detailed search. Such a centralized strategy, although helpful in finding the optimal solution in the local region accurately, may also lead the algorithm to ignore other promising regions (Wolpert and Macready 1997 ). Despite there has been various GWO variants, such as Advanced Grey Wolf Optimizer (AGWO) (Meng et al. 2021 ), Exponential Neighborhood Grey Wolf Optimization (EN-GWO) (Mohakud and Dash 2022 ), Hybrid Grey Wolf Optimizer with Mutation Operator (DE-GWO) (Gupta and Deep 2017 ), and others (Ambika et al. 2022; Biabani et al. 2022 ). These improved versions do not break through in solving the large-scale global optimization problems of CEC 2022 and CEC 2013. Moreover, their performance in dealing with complex problems remains unsatisfactory.

To improve the performance of the GWO, this study incorporates several key enhancements. Firstly, the search mechanism from PSO is employed to increase population diversity. This addition helps in broadening the search scope of the algorithm. Secondly, the IMF is used to adjust inertia weights, a strategy that aids in fine-tuning the balance between exploration and exploitation. Lastly, an adaptive mechanism based on the Sigmoid function is introduced for updating the positions of individuals within the population. This adaptive update strategy strengthens the group's ability to escape local optima, enhancing the overall effectiveness of the GWO algorithm in finding optimal solutions.

An improved adaptive grey wolf optimization (IAGWO) is proposed to address the shortcomings of the GWO algorithm. The main contributions are as follows.

The PSO search mechanism is introduced to enhances the algorithm's search efficiency and robustness by updating grey wolf positions early in each iteration. Additionally, the dynamic adjustment of inertia weights through the IMF boosts global search capability initially and local search effectiveness later.

Adaptive position updating strategy based on Sigmoid function to balance the exploration and exploitation of IAGWO.

To evaluate the exploration and exploitation capabilities of IAGWO, extensive experimentation is conducted using a suite of 67 test functions, which includes benchmarks from the CEC 2014, CEC 2017, CEC 2020, CEC 2022, and CEC 2013 for large-scale global optimization problems.

The effectiveness and accuracy of IAGWO in solving practical engineering design challenges are thoroughly assessed through its application to 19 diverse engineering design challenges.

The paper is organized as follows: Sect.  2 provides a brief review of the previous enhancements and potential application directions of the GWO. Section  3 details the original GWO algorithm and the proposed improvement strategy. Section  4 evaluates IAGWO performance through relevant experiments and in-depth analysis. Finally, Sect.  5 concludes this paper with a summary of the results and an outlook on future research directions.

2 Related work

In recent years, there has been a significant focus among researchers on enhancing the GWO. These improvements are aimed at boosting the algorithm's search performance and effectiveness. Scholars have explored various approaches to achieve this, including aspects such as adjusting the algorithm parameters, improving the speed and position equations, and combining it with other algorithms.

Yu et al. ( 2023 ) adopted a new update search mechanism, improved control parameters, mutation driven strategy and greedy selection strategy to improve GWO in the search process. (Singh and Bansal 2022a ) proposed a hybrid GWO and Differential Evolution (HGWODE) algorithm and applied it to UAV path planning. (Cuong-Le et al. 2022 ) introduced an equation to control the moving strategy of the algorithm in each iteration and proposed New Balance Grey Wolf Optimizer (NB-GWO), which was used to optimize the hyperparameters of the deep neural network for damage detection of two-dimensional concrete frames. Liu et al. ( 2023 ) proposed a hybrid differential evolution GWO (DE-GWO) algorithm and applied it to gas emission identification and localization. Luo et al. ( 2023 ) introduced butterfly optimization algorithm and opposition-based learning method based on elite strategy, adaptive nonlinear inertia weight strategy and random walk law to improve the shortcomings of slow convergence speed and low accuracy of GWO algorithm when dealing with high-dimensional complex problem. To address the issue of premature convergence encountered by the classic GWO in some situations due to the stagnation of sub-optimal solutions, Gupta et al. introduced an enhanced leadership-inspired grey wolf optimizer for global optimization problems (GLF-GWO)(Gupta and Deep 2020 ), Addressing the issues of slow convergence speed and insufficient global exploration in GWO, which can lead to settling in local optimal states and failure to achieve global optimal solutions, Singh et al. proposed a novel mutation-driven modified grey wolf optimizer (MDM-GWO) (Singh and Bansal 2022b ). MDM-GWO integrates new update search mechanisms, modified control parameters, mutation-driven schemes, and greedy selection methods into the search process of GWO. Addressing the issues of slow convergence speed and susceptibility to local optima in the Grey Wolf Optimizer (GWO) algorithm, Zhang et al. proposed a nonlinear control parameter strategy based on a sinusoidal function (GWO-SIN) and a nonlinear control parameter combination strategy (GWO-COM) (Zhang et al. 2019 ).

Soliman et al. ( 2022 ) proposed a novel hybrid African vultures–grey wolf optimizer (AV–GWO) approach to precisely estimate the electrical parameters of such TDM. Nadimi-Shahraki et al. ( 2021 ) introduced an enhanced variant of the Grey Wolf Optimization algorithm, termed I-GWO. The algorithm, based on a dimensionally learned hunting and searching (DLH) strategy, uniquely constructs hunting domains for each Wolf and enables them to share information about neighboring domains with each other. This enhances the algorithm's local and global search capabilities for more balanced performance, while also helping to maintain population diversity. A. Abushawish and A. Jarndal (Abushawish and Jarndal 2021 ) jointly proposed a new hybrid algorithm named GWO-CS that combines the advantages of Cuckoo Search (CS) algorithm and GWO algorithm. This algorithm primarily incorporates the position update equation from the CS to further refine the global search process of the GWO. Aimed at solving the problems of poor stability and easily falling into the local optimal solution in the grey wolf optimizer (GWO) algorithm, Liu et al. proposed an improved GWO algorithm based on the differential evolution (DE) algorithm and the OTSU algorithm is proposed (DE-OTSU-GWO) (Liu, Sun, Yu, Wang, & Zhou, 2020). The multithreshold OTSU, Tsallis entropy, and DE algorithm are combined with the GWO algorithm. The multithreshold OTSU algorithm is used to calculate the fitness of the initial population. The population is updated using the GWO algorithm and the DE algorithm through the Tsallis entropy algorithm for crossover steps. Multithreshold OTSU calculates the fitness in the initial population and makes the initial stage basically stable. Tsallis entropy calculates the fitness quickly. The DE algorithm can solve the local optimal solution of GWO. To address the issues of GWO's susceptibility to local optima and its low exploration capabilities, Hardi Mohammed et al. proposed the Enhanced GWO (EGWO) (Mohammed et al. 2024 ). EGWO employs diverse methods to improve the performance of GWO, utilizing gamma, z-position, and the golden ratio.

Liu et al. ( 2022 ) introduced a novel improvement strategy for the GWO algorithm, known as the exponential convergence factor improvement strategy. This strategy is designed to more accurately simulate the actual search process of grey wolves. It incorporates dynamic weighting factors and enhances control parameters to reduce the likelihood of the GWO algorithm getting stuck in local optima. However, despite these improvements, experimental findings indicate that GWO still faces challenges in accurately handling high-dimensional functions. Şenel et al. ( 2019 ) integrated a differential disturbance operator into the GWO algorithm. This addition brought an element of exploration into the exploitation phase, thereby enhancing the GWO algorithm's overall optimization capabilities. Jangir and Jangir ( 2018 ) proposed a multi-objective version of the GWO algorithm, named NSGWO. This algorithm utilizes a crowding distance mechanism to select the optimal solution from a set of Pareto optimal solutions. This approach helps guide the search towards the dominant region in multi-objective search spaces. NSGWO was tested on a variety of standard unconstrained, constrained, and engineering design challenges, demonstrating its efficiency and effectiveness in diverse optimization scenarios.

3 Methodology Overview: Standardized GWO and Proposed Enhancements

This section offers an overview of the hunting behavior and the mathematical model that forms the foundation of the original GWO. Additionally, we introduce the IAGWO, our proposed enhancement to GWO. IAGWO integrates the PSO search mechanism, the IMF strategy for inertia weighting, and an adaptive strategy for updating positions. These additions aim to refine and boost the efficiency of the original GWO algorithm.

3.1 The standardized GWO

3.1.1 inspiration of grey wolf packs’ hunting activity behavior.

The GWO algorithm draws inspiration from the hunting behavior of grey wolf packs. It mathematically simulates the way a group of grey wolves hunts, encircles, and targets their prey while adhering to a well-defined social hierarchy. In this hierarchy, the pack is led by three primary wolves: the Alphas ( α ), Betas ( β ), and Deltas ( δ ), each playing a crucial role in guiding the pack's movements and decisions. These wolves are considered the leaders, showcasing significant leadership abilities. Below them are the Omega ( w ) wolves, who occupy a subordinate role and follow the directives of the leading wolves. This hierarchical structure, integral to the functioning of the GWO algorithm, is depicted in Fig.  1 .

Hierarchy of the grey Wolf Pack

3.1.2 Mathematical model: GWO

GWO simulates grey wolf leadership and hunting mechanisms by dividing grey wolves based on their characteristics into a leader, α , who rules over the entire grey wolf; a facilitator, β , who helps α to make decisions and replaces α when α dies; and an enforcer, δ , who follows α 's and β 's orders (Fan and Yu 2022 ). GWO searches for excellence by modeling the wolf hunting process. In addition to the social hierarchy of wolves, group hunting is another interesting social behavior of grey wolves. The main phases of grey wolf hunting are as follows: The Grey Wolf Optimizer algorithm mimics the hunting behavior of grey wolf packs. Initially, in the "tracking, chasing, and approaching prey" phase, each wolf searches for potential solutions in the solution space and adjusts its position through certain search strategies to get closer to possible candidate solutions. Subsequently, in the "chasing, surrounding, and harassing prey until it stops moving" phase, the wolf pack collaborates to try to corner the prey into a smaller area and prevent its escape, involving behaviors such as encircling and harassing the prey to prevent its escape. Finally, in the "attacking prey" phase, once the prey is cornered and unable to escape, the wolves concentrate their attack on the prey, gradually optimizing the position of candidate solutions through strategies such as linear or leap searches until finding the optimal solution or meeting specific optimization criteria. These three phases represent the Grey Wolf Optimization algorithm's process of searching, chasing, and optimizing in the solution space, analogous to the behavior of a grey wolf pack during hunting, progressing from search to attack, gradually optimizing and approaching the optimal solution.

Now, this paper shows the calculation steps of the basic grey Wolf Optimization algorithm and the pseudo-code as follows (Algorithm 1). The GWO algorithm process is as follows:

1) Each member is initialized using Eq. ( 1 ), determine the population size N , the maximum number of iterations M , the single grey wolf dimension dim , and ɑ , A and C ;

where, LB and UB are the lower and upper boundaries of the solution space, respectively. X represent the positions of the current solution. phi is a random number between [0,1].

2) Calculate the fitness value of each individual using the test function. Then, based on the magnitude of the fitness values, select the best-fit individual as the α -wolf, the second-best individual as the β -wolf, and the third-best individual as the δ -wolf;

3) The mathematical model of Wolf pack leader tracking prey is shown in Eq. ( 2 ), which calculates the traction direction of the entire pack according to the distance difference between the Wolf leader and the pack, that is, the movement direction information of the pack, can be calculated as shown in Eqs. ( 3 ) and ( 4 ). Update the current grey wolf position according to Eqs. ( 2 )– ( 4 ).

where D α , D β , and D δ denote the distance difference between α -wolf, β -wolf, and δ -wolf and other individuals, respectively. X α , X β , and X δ indicate the current positions of α -wolf, β -wolf, and δ -wolf respectively, X indicate the current positions C 1 , C 2 , and C 3 satisfy the constraints of Eq. ( 6 ). A 1 , A 2 , and A 3 are random vectors satisfying the constrain of Eq. ( 5 ); X 1 , X 2 and X 3 are the traction directions of the three leading wolves; and X ( t  + 1) represents the next collective movement position of the wolf pack. As shown in Fig.  2 , the final orientation of the wolves in the search space will be randomly positioned within a circle defined by the locations of the α , β , and δ in the search space. This graphical representation illustrates how the wolves’ positions influence the movement and direction of the entire pack in the pursuit of their prey.

Position update of wolf groups in GWO algorithm

4) Update ɑ , A and C according to Eqs. ( 5 )–( 7 );

where, the parameter ɑ plays a crucial role in balancing global search and local exploration. Its value is set to decrease linearly from 2 to 0 over the course of the algorithm's iterations. Initially, a higher value of ɑ aids in the global convergence of the algorithm, guiding the wolf pack swiftly towards the region where the optimal solution might be found. As the algorithm progresses through its later iterations, the gradual decrease in the value of ɑ facilitates more refined exploration in the area of the optimal solution. This helps improve the convergence accuracy of the GWO algorithm, ensuring a more precise final result. r 1 and r 2 are random vectors and r 1 , r 2  ∈ [0, 1].

5) Update the positions of other individuals, calculate the updated fitness value based on the new position, and update the α -wolf, β -wolf, δ -wolf and global optimal solution, \(R\) represents the position vector of the optimization target;

6) Judge whether the specified stopping condition is reached (e.g., the maximum number of iterations is reached), if not, repeat steps 2 to 5. Otherwise, output the optimal result: the position of the α -wolf obtained at the end is the optimal solution, and the corresponding fitness value is the degree of superiority or inferiority of the optimal solution.

3.2 Improved grey wolf optimization algorithm

3.2.1 pso search mechanism.

The GWO (Grey Wolf Optimizer) exhibits a weak exploratory capability in its early stages and lacks diversity within the population, consequently resulting in suboptimal solution quality. In order to enhance exploration capabilities, improve population diversity (Hu et al. 2022 ), and increase the quality of solutions (Hakli and Kiran 2020 ), this study integrates the PSO, introducing a velocity concept to provide a new search mechanism for the GWO. The individual grey wolves are updated in terms of position during the early iterations, and the application in the velocity update introduces additional randomness. This prevents the algorithm from converging prematurely and encourages exploration of new areas, thereby increasing population diversity. By dynamically adjusting the velocity and position of each individual, this method may help in more effectively balancing global exploration and local exploitation. Leading to a wider search in the early stage of the iteration, this assists in identifying potential high-quality solutions. The computation Eq. ( 8 ) is as follows:

where t represents the current number of iterations, X and \({X}_{best}\) represent the positions of the current solution and the best-performing solution, respectively. \({v}_{rand}\left(t\right)\) is the velocity vector of the current solution at time t of iteration. phi is a random number between [0,1]. \({X}_{selfbest}\) is the best position vector in the history of the current solution.

In this study, at the start of each iteration, a PSO updating strategy is employed, along with the addition of extra randomness to stimulate a more extensive global search. This approach helps avoid local optimization and increases population diversity. This approach not only accumulates a more diverse and high-quality search experience for the GWO but also more effectively balances global exploration and local exploitation by dynamically adjusting the search behavior.

3.2.2 IMF inertia weighting strategy

Inverse Multiquadric Function is a decreasing function based on the principle of inverse multiple squares. It is often used as a regularization method in neural networks, such as a kernel function in support vector machines (Hu et al. 1998 ; Rathan et al. 2023). In accordance with the characteristics of the IMF, this paper incorporates it into the population position update mechanism within the framework of the GWO as delineated in Eq. ( 3 ). The IMF inertia weight ω , along with the revised formulae for the wolf pack updating process, are elucidated in Eqs. ( 9 )–( 10 ).

where, the parameter groups [a, b, c, d] are taken as [0.6, 0.02, 0.05, 0.3] and the graph of ω is shown in Fig.  3 . As indicated by Fig.  3 , during the early to mid-phases of the algorithm's iteration, the inertia weight ω is set to a higher value. This larger influence of the α -wolf, β -wolf, and δ -wolf on the updated positions is beneficial for the pack to quickly converge towards the optimal solution, effectively preventing the waste of search resources due to blind searching and thus enhancing the quality of the pack. As the development progresses to the mid and late stages and the pack becomes densely concentrated, if the higher-ranking wolves get trapped in a local optimum, the lower-ranking wolves led by them are also unable to escape this local optimum. At this juncture, the value of ω should be reduced to a lower level, thereby enlarging the pack's autonomous search capability and avoiding premature convergence.

IMF Inertia Weight Graph

3.2.3 Adaptive updating mechanism

The population updating mechanism based on IMF inertia weight effectively reduces the density of population clustering to a certain extent. However, due to the intrinsic dynamics of the GWO, the newly generated wolf packs are still inevitably concentrated and migrate towards the positions directed by the α -wolf, β -wolf, and δ -wolf during the iterative process. In response to this, the present study defines the aggregation coefficient as the ratio of an individual's fitness value to the average population fitness value, which serves to quantify the degree of divergence between the current solution and the optimal solution. In minimization problems, the smaller the fitness value, the better the solution. A smaller aggregation coefficient indicates a more favorable current solution, thus allowing for minor updates in the vicinity of the individual's current position. Conversely, a larger aggregation coefficient suggests a poor location of the individual, warranting a significant perturbation to facilitate a jump to other positions. Based on this analysis, this paper introduces a Sigmoid function to construct the adaptive updating amplitude of the population under different aggregation coefficients, as depicted in Eqs. ( 11 )-( 12 ).

where f i represents the fitness value of the i th individual, and f ave denotes the average fitness value of the population. θ is the exponential coefficient, which is taken as 0.5 in this paper.

In comparison to the standard GWO, the IAGWO brings several significant advancements. Firstly, it introduces a novel search mechanism by incorporating velocity concepts. This addition helps in preventing premature convergence and allows for a more thorough exploration of the search space. The integration of velocity updates also adds an element of randomness, which in turn increases the diversity within the population of solutions. Moreover, the implementation of the IMF inertia weight strategy in IAGWO improves the balance between exploring the global search space and exploiting local solutions. This strategic enhancement significantly boosts the convergence speed of the algorithm. Furthermore, IAGWO differentiates itself from the standard GWO through its adaptive updating mechanism. This mechanism combines the aggregation coefficient with the Sigmoid function, enhancing the algorithm's ability to switch between broad search patterns and detailed solution refinement. This results in improved performance in maintaining diversity and achieving faster convergence rates. This adaptive approach enables IAGWO to search and optimize more efficiently within the solution space of the problem. For an in-depth comprehension of the workings of IAGWO, the procedural flow is visually depicted in Fig.  4 , its pseudocode is meticulously detailed in Algorithm 2, and the proposed IAGWO workflow(Chauhan & Yadav 2023b ) is shown in Fig.  5 .

Implementation Process for IAGWO

Working procedure of the proposed IAGWO algorithm

3.3 Time complexity analysis

CEC17 (Competition on Evolutionary Computation) defines algorithm complexity as a measure of the computational resources required by an algorithm to solve a given problem instance. This section explains the computational complexity of IAGWO. The complexity of IAGWO is primarily influenced by two main factors: the initialization of solutions and the execution of the algorithm's core functions. These core functions involve calculating fitness functions and updating solutions. The computational complexity is determined by considering several variables: the count of solutions \(\left(N\right)\) , the upper limit of iterations \((T)\) , and the problem's dimension \((D)\) being tackled. Specifically, the complexity of initializing solutions in the IAGWO algorithm can be represented as \(O(N)\) , indicating the order of complexity in relation to the number of solutions. This gives an understanding of the computational resources required for the initial setup phase of the algorithm. This means that as the number of solutions \(N\) increases, the computational complexity of the initial solution of the algorithm will also increase accordingly. This represents the order of complexity for the initial setup phase of the algorithm. The time complexity of the original GWO algorithm is \(O(T\times N\times D)\) . IAGWO modifies this with Eqs. ( 8 ), ( 9 ), and ( 10 )–( 11 ), including enhancements to population diversity using the PSO position updating strategy, integration of IMF weights to reduce the excessive influence of higher-level wolves on lower-level ones, and the introduction of a population adaptive update based on the sigmoid function. The PSO position updating strategy requires calculations for each individual and each dimension, with a complexity of \(O(T\times N\times D)\) . The update from Eq. ( 10 ) is independent of population size and search dimensions, correlating only with the maximum number of iterations, resulting in a time complexity of \(O(T)\) . The time complexity for Eq. ( 11 ) is \(O(N\times D)\) . Consequently, the overall time complexity of IAGWO is \(O(\text{IAGWO})=O\left(T\times N\times D\right)+O\left(T\right)+O\left(N\times D\right)=O(T\times N\times D)\) , consistent with the original algorithm.

4 Results and comprehensive analysis

The simulation for this study was carried out on a Windows 11 platform, operating on a 64-bit system. The analysis was performed using MATLAB 2023b, running on a machine equipped with an AMD Ryzen 7 4800H CPU at 2.30 GHz and 16 GB of RAM.

4.1 Test functions and parameter settings

In this paper, the CEC 2017 (Dim = 30) (Mallipeddi and Suganthan 2010 ), CEC 2020 (Dim = 10 and 20) (Liang et al. 2019 ), and CEC 2022 (Dim = 10 and 20) (Ahrari et al. 2022) test suites were employed to evaluate the performance of the proposed IAGWO algorithm. The test suite for evaluating algorithms covers four different functional types: single-modal, multimodal, mixed, and combined. These different types of test suites are designed to comprehensively evaluate the performance and applicability of algorithms. Additionally, for assessing the scalability of the IAGWO algorithm, we employed the CEC 2013 Large-scale Global Optimization suite (800-dimensional) for simulation analysis (Li et al. 2013 ). The suite contains 15 highly complex reference functions that are grouped into four groups: fully separable, partially additively separable, overlapping, and completely indivisible. These different types of benchmark functions provide a comprehensive experimental framework for evaluating the scalability of optimization algorithms, so that we can more accurately evaluate the performance of IAGWO algorithm on different types of problems.

4.2 Comparison with other algorithms and parameter settings

The performance of the Improved Adaptive Grey Wolf Optimization (IAGWO) is benchmarked against 12 well-known algorithms, grouped into three categories for comparison:

High-citation algorithms: These include the Gravitational Search Algorithm (GSA) (Rashedi et al. 2009 ), Dolphin Echolocation Optimization (DMO) (Kaveh and Farhoudi 2013 ), Whale Optimization Algorithm (WOA) (Mirjalili and Lewis 2016 ), and Harris Hawks Optimization (HHO) (Tripathy et al. 2022 ).

Advanced algorithms: This category includes Combined Particle Swarm Optimization and Gravitational Search Algorithm (CPSOGSA), Crow Optimization Algorithm (COA) (Jia et al. 2023 ), African Vulture Optimization Algorithm (AVOA) (Abdollahzadeh et al. 2021 ), Optical Microscope Algorithm (OMA) (Cheng and Sholeh 2023 ), and Adaptive Artificial Electric Field Algorithm (iAEFA) (Chauhan and Yadav 2023a ).

GWO and its variants: This includes the original Grey Wolf Optimization (GWO), the Adaptive GWO (AGWO) (Meidani et al. 2022 ), the Enhanced GWO (ENGWO)(Mohammed et al. 2024 )and the Revised GWO (RGWO) (Banaie-Dezfouli et al. 2021 ).

Table 1 offers a comprehensive summary of the parameters for 14 different MH algorithms. For each of these algorithms, 30 independent runs were conducted, with each run limited to a maximum of 500 iterations and population size is set to 30 and a maximum of 30,000 evaluations. The outcomes of these runs were meticulously recorded, capturing the average values (denoted as Ave) and the standard deviations (Std) for each algorithm. To facilitate an easy comparison of their performance, the table highlights the best results among these 14 algorithms by formatting them in bold text. This highlighting method provides a clear visual indicator of which algorithms performed most effectively under the given testing conditions.

4.3 Qualitative assessment of IAGWO

4.3.1 exploring convergence patterns.

To verify the convergence performance of IAGWO, we plotted its convergence performance evaluation on the 30-dimensional CEC2017 test functions, as shown in Fig.  6 . It presents the corresponding results of different test functions in the form of nine images involving three instances selected from the same suite. In the presentation of images, the first column distinctly illustrates the two-dimensional profiles of the reference functions being analyzed. The visuals presented in the first column accurately depict the characteristics and contours of each function being optimized. These graphical representations offer a clear understanding of the challenges and intricacies of each function. In the second column, images depict the final positions of the search agents at the end of the optimization process. Within these visuals, the optimal solution's location is distinctly marked with a red dot. This not only illustrates the end point of the search agents' journey but also visually highlights the spot where they successfully identified the most favorable solution. This layout effectively communicates the results of the optimization process, making it easier to comprehend the behavior and efficacy of the search agents in navigating the solution space. This layout offers a clear and informative view of both the nature of the functions and the outcomes of the optimization process. By observing the second column of images, we can clearly find that the search agent is close to the optimal solution in most cases, which fully reflects the powerful ability of IAGWO algorithm in the process of exploration and development. In addition, the third column image accurately tracks the change of the average fitness value during the iteration. Initially high, these values decrease and stabilize after 100 iterations, albeit with minor fluctuations. These fluctuations are normal in complex optimization problems, indicate ongoing detailed searches for improvement and the maintenance of population diversity to prevent premature convergence to local optima. The fourth column reveals the search agents' trajectories in the first dimension, there were marked fluctuations in the early iterations, which then leveled off, and then fluctuations again at intervals, which leveled off again, signifying a balance between exploration and exploitation. Finally, the convergence curve, smooth for unimodal functions, suggests optimal values are achievable through iteration. For multimodal functions, however, the step-like curve reflects the need for continual avoidance of local optima to reach global optima. These four metrics collectively affirm IAGWO's robust convergence.

The convergence behavior of IAGWO

4.3.2 Analyzing the diversity of population

In optimization algorithms, the importance of population diversity is a matter of balance. Moderate population diversity can help the algorithm avoid falling into local optima, thereby increasing search space coverage and global search capability, improving convergence speed, and the quality of optimization results. However, excessive population diversity may lead to overly dispersed search, making it difficult for the algorithm to explore local regions deeply, thereby reducing convergence speed and the quality of final solutions. Therefore, when designing optimization algorithms, it is necessary to consider a balance between population diversity and search efficiency. This can be achieved through appropriate parameter settings or suitable strategies to maintain population diversity, thus effectively solving optimization problems. A population with high diversity indicates significant differences among individuals, allowing for broader exploration in the search space and avoiding premature convergence to local optima. Hence, maintaining good population diversity is a crucial objective in metaheuristic algorithms. Typically, we use Eq. ( 13 ) and Eq. ( 14 ) to measure the population diversity of the algorithm. This calculation method was proposed by Morrison in 2004. Where, \({I}_{C}\) represents the moment of inertia, \({x}_{id}\) denotes the ith search agent's value in the \({d}^{th}\) dimension at iteration t . Furthermore, \({c}_{d}\) represents the spread of the population from its center of mass, denoted by ' c ', in every iteration, as illustrated in Eq. ( 14 ) (Fu et al. 2023a , b).

Figure  7 displays the comparative experimental outcomes regarding population diversity for both IAGWO and GWO. The measurement of population diversity is conducted through \({I}_{C}\) . Observations from Fig.  7 reveal that IAGWO demonstrates an initial marked increase in diversity during the early phases of iteration, which then transitions to a state of relative stability at an elevated level. This indicates an increase in the variance among individuals within the IAGWO population during the early iterations, effectively exploring a vast search space. As iterations progress, the population diversity tends to stabilize, which aids in averting premature convergence to local optima. The minor fluctuation are normal and beneficial for the algorithm to adapt to dynamically changing search spaces and prevent premature convergence. In contrast, GWO shows insufficient population diversity, highlighting IAGWO’s effectiveness in maintaining diversity, crucial for exploring complex search spaces and avoiding local optima. These experimental outcomes demonstrate IAGWO's substantial potential in optimization.

The population diversity of IAGWO and GWO

4.3.3 Exploration and exploitation analysis

In optimization algorithms, managing the balance between exploration and exploitation is key for optimal performance (Saka et al. 2016 ). Exploration involves searching through the solution space, while exploitation focuses on refining known good solutions. This section deals with quantifying the extent of exploration and exploitation in the algorithm. To do this, we use Eq. ( 15 ) to calculate the percentage of exploration and Eq. ( 16 ) for the percentage of exploitation. Additionally, the parameter \(Div\left(t\right)\) used for measuring dimension diversity is calculated using Eq. ( 17 ). The parameter \({\rm Div}_{max}\) reflects the peak diversity noted throughout the entire course of iterations,, which is essential for understanding how broadly and effectively the algorithm explores the solution space(Li et al. 2023 ) (Nadimi-Shahraki et al. 2023 ).

Figure  8 depicts the results of the experiments conducted. It shows that for various function types, as the number of iterations progresses, GWO consistently demonstrates a higher rate of exploration and a comparatively lower rate of exploitation. In contrast, IAGWO shows a changing pattern, with exploration decreasing and exploitation increasing as iterations progress. This observation suggests that GWO tends towards a broad search across the entire space, with less focus on local search and weaker performance in thoroughly exploiting the optimal regions found. In comparison, IAGWO demonstrates the ability to dynamically adjust its search strategy. This implies that the algorithm initially identifies potential good solution areas through extensive exploration and then finely tunes these solutions in the later stages through focused exploitation, potentially enhancing both the efficiency of the algorithm and the quality of solutions. Overall, while GWO shows commendable exploration capabilities, it lacks effective exploitation. In contrast, IAGWO effectively strikes a balance between exploration and exploitation. This balance is well-maintained across a variety of benchmark functions, showcasing IAGWO's adaptability and efficiency in different optimization scenarios. This attribute is particularly important as it ensures the algorithm can thoroughly search the solution space while also honing in on the most promising solutions.

The exploration and exploitation of IAGWO and GWO

4.3.4 Ablation experiments

In this section, a detailed analysis is conducted on the impact of three proposed improvement strategies on the GWO. These strategies include the PSO position updating mechanism, the introduction of IMF inertia weight strategy, and the adoption of a Sigmoid adaptive updating strategy. Based on these improvements, three new algorithm variants are named: PGWO for the PSO search mechanism, IGWO for the IMF inertia weight, and SGWO for the Sigmoid adaptive updating strategy. According to the experimental results in Fig.  9 , all three strategies significantly enhance the convergence accuracy and speed of GWO, with IAGWO showing particularly notable performance.

Comparison of different improvement strategies

Specifically, when dealing with unimodal and multimodal functions, the results of PGWO and IAGWO are relatively consistent, showing a more significant improvement over GWO compared to SGWO and IGWO. However, when dealing with more complex hybrid modal functions, the enhancement of PGWO on GWO diminishes, while the IAGWO algorithm, integrating all three strategies, continues to exhibit exceptional optimization performance. Overall, the IAGWO algorithm successfully overcomes challenges of local optima and premature convergence, significantly boosting the algorithm's convergence speed and accuracy. These findings provide valuable insights for the further development and application of the GWO.

4.4 Quantitative evaluation

In this section, the efficacy of IAGWO is scrutinized using a series of test suites: CEC 2017, CEC 2020, and CEC 2022. Moreover, its proficiency in handling large-scale problems is assessed with the CEC 2013 suite. To clearly compare performance, the best results among the algorithms are highlighted in bold in the tables. The parameters are standardized with a population size of 100, a maximum iteration limit of 500, and a total of 30 independent runs. The performance outcomes are systematically presented in Tables  2 to 7 , which illustrate the average values (Ave) and the standard deviations (Std) for each competing algorithm. A thorough statistical analysis is conducted to highlight the superiority of IAGWO. This includes an initial evaluation represented by three indicators (W|T|L) in the first line of the results, denoting the algorithms' performance as best (win), comparable (tie), or least effective (loss) for specific functions. The second row compiles the mean performance of all algorithms, while the third row offers insights into the overall standings through the final Friedman ranking. The tables distinctly highlight the top results, emphasizing their significance. Furthermore, the comparative analysis of the convergence curves for each algorithm is depicted in Fig.  10 . This visual representation aids in understanding the progression and efficiency of each algorithm in finding optimal solutions over the course of iterations. This detailed evaluation underscores the robustness and adaptability of IAGWO in varied optimization contexts.

Convergence curves of different algorithms

4.4.1 Assessing performance with CEC 2017 test suite

This section examines the efficacy of IAGWO using the CEC 2017 test suite with a dimensionality of 30, as detailed in Table  2 . The results are quite telling: IAGWO recorded the highest number of best performances, leading in 16 out of the 30 functions tested. Notably, it did not register as the least effective in any of the functions. In terms of statistical standing, IAGWO's Friedman mean ranking is 3.00, earning it the top position. Further, a diverse range of functions from CEC 2017 (Dim = 30) were chosen for a more comprehensive evaluation. The comparative analysis of the convergence trends, depicted in Fig.  10 , reveals that IAGWO consistently achieved the quickest convergence rate and maintained the highest level of accuracy in convergence. These results underscore IAGWO's exceptional proficiency in both global exploration and local exploitation. Collectively, these findings solidify the effectiveness and superiority of IAGWO as an optimization tool.

4.4.2 Assessing performance with CEC 2020 test suite

This section is dedicated to evaluating 13 algorithms with the utilization of the CEC 2020 test suite, which includes tests with dimensions of 10 and 20. The outcomes of this evaluation are systematically presented in Table  3 and Table  4 . On the CEC 2020 tests, IAGWO mirrors the impressive results observed in the CEC 2017 suite, achieving the highest number of best performances while not being the least effective in any function. To provide a visual representation of these results, representative functions are chosen to illustrate the convergence curves, as depicted in Fig.  10 . IAGWO consistently shows the quickest convergence speed and the highest accuracy in convergence, reaffirming its efficiency. Additionally, it's important to note the contrasting performance of GWO on the CEC 2020 suite. Despite its lower ranking in the Friedman rankings, indicating a comparatively poor performance, its improved variants, namely AGWO, ENGWO, and RGWO, show marked improvements. Remarkably, RGWO secures the second-highest ranking, closely following IAGWO, underscoring the substantial research value in enhancing the GWO algorithm. A comprehensive statistical analysis among the 13 algorithms tested places IAGWO at the forefront in the Friedman rankings. This achievement highlights its superiority not only over the original GWO but also over other well-regarded algorithms. These results collectively demonstrate the robustness and effectiveness of IAGWO in a competitive algorithmic landscape.

4.4.3 Assessing performance with CEC 2022 test suite

This section is dedicated to a thorough evaluation of the proposed IAGWO and 12 other comparative algorithms, utilizing the CEC 2022 test suite. The primary objective of this evaluation is to gauge the exploration and exploitation capabilities of these algorithms and assess their proficiency in avoiding local optima traps. The experiments are conducted under 10-dimensional and 20-dimensional scenarios, with corresponding results displayed in Tables  5 and 6 , respectively. IAGWO ranks first in Friedman mean ranking in both dimensional settings, with ranking values of 1.75 and 2.25 respectively. Similarly, while GWO shows subpar performance, its variants enhance GWO's performance, emphasizing the research significance of GWO. The analysis of results depicted in Fig.  10 leads to a conclusive observation that IAGWO successfully evades getting stuck in local optima and avoids premature convergence. These findings serve not just as a testament to the excellence and robustness of IAGWO, but they also highlight its substantial performance benefits and the capability to yield enhanced solutions. This analysis underscores IAGWO's effectiveness in navigating complex optimization landscapes, further establishing its potential as a superior tool in optimization tasks.

4.4.4 Scalability evaluation using the CEC 2013 test suite

In real-world scenarios, solving optimization problems often requires adjusting multiple parameters at once. To test the scalability of the IAGWO for high-dimensional problems, we utilized the CEC 2013 suite for large-scale global optimization. The results of this testing are detailed in Table  7 . This suite includes 15 highly complex test functions, each with up to 1000 dimensions, providing a robust challenge for assessing algorithmic performance. In our experiments, IAGWO was compared with 12 other algorithms. The population size was fixed at 100, and we limited the maximum number of iterations to 10 for each run. After conducting 30 independent runs for each algorithm, IAGWO achieved a Friedman mean rank value of 2.63. This score signifies a higher level of performance relative to the other algorithms in the competition. The findings from these experiments demonstrate that the IAGWO algorithm has significant scalability, effectively handling complex, high-dimensional optimization challenges. This capability distinguishes IAGWO from other algorithms, highlighting its suitability for practical, large-scale optimization applications.

4.5 Wilcoxon rank sum test

This study utilizes the non-parametric Wilcoxon rank sum test (Wilcoxon 1945 ) to conduct comparative performance assessments of various algorithms, setting the significance level at 0.05. To succinctly represent the performance of IAGWO relative to its competitors, the symbols “ + / = /-” are used to denote whether IAGWO is superior to, equivalent to, or inferior to the competing algorithms. As shown in Table  8 , these statistical results clearly indicate significant performance differences between IAGWO and other competing algorithms in most cases. Specifically, the statistical data show the following comparative results: 344/0/46、119/0/11、111/13/6、150/0/6、152/0/4 and 175/0/5. The analysis presented above demonstrates that the IAGWO method, as introduced in this study, shows exceptional overall performance when compared to the traditional GWO and other rival algorithms, thereby underscoring its distinct advantages.

4.6 Time comparison analysis of IAGWO and GWO

Building on the findings from previous chapters, it's clear that IAGWO significantly surpasses the original GWO in terms of overall performance. In this section, we focus on a more detailed comparison, specifically looking at the computational costs of both algorithms, with a particular emphasis on the differences in computational time. To facilitate this comparison, we standardized the settings for both IAGWO and GWO. For this evaluation, the population size was configured to 50, the maximum iterations were limited to 1000, and each algorithm underwent 30 independent runs. Table 9 presents the total time (in seconds) each algorithm took to complete all 30 runs. This data provides a clear basis for comparing the efficiency of the two algorithms in terms of how long they take to execute, offering insights into their time-based performance efficiency.

Analysis of the experimental data on the CEC 2017 test suit (Dim = 30) indicates that under the same experimental parameters, IAGWO and GWO perform almost equally in terms of execution time on unimodal functions and some simpler multimodal functions, but when dealing with more complex multimodal and hybrid functions, IAGWO generally consumes significantly less computational time than GWO. This suggests that in handling highly complex problems, IAGWO demonstrates greater computational efficiency. Compared to the original GWO, IAGWO's improved search strategies are more efficient, possessing better global search capabilities or faster local convergence speeds. Overall, IAGWO not only excels in benchmark tests but also exhibits higher computational efficiency and better adaptability when addressing more complex optimization problems that may arise in practical applications.

However, on the CEC 2020 test suite (Dim = 10 and 20) and CEC 2022 test suite (Dim = 10 and 20), IAGWO generally exhibits higher computational times compared to GWO. This may indicate that the types of problems or characteristics included in CEC 2020 are not entirely compatible with the strategies of IAGWO, leading to a higher computational load.

4.7 Evaluating performance against CEC 2014 and CEC 2017 competition-winners

This section evaluates the performance of the proposed IAGWO using the CEC 2014 test suite with a dimensionality of 30 (Liang et al. 2013 ) and CEC 2017 (Dim = 30) test suites. Additionally, we compare the performance of IAGWO with the competition-winners of these two suites in previous CEC competitions, including L-SHADE (Tanabe & Fukunaga 2014 ) and AL-SHADE (Li et al. 2022 ) from CEC 2014, and LSHADE-SPACMA (Mohamed, Hadi, Fattouh, & Jambi, 2017) and LSHADE-cnEpSin (Awad, Ali, & Suganthan, 2017) from CEC 2017. In the experimental setup, the population size is fixed at 30, the maximum iterations are limited to 500, and a total of 30 independent runs are performed.

Table 10 presents the results from testing IAGWO using the CEC 2014 suite. In these tests, IAGWO surpassed other algorithms in six different scenarios, though it showed slightly weaker performance in one. Notably, IAGWO achieved a Friedman mean ranking value of 1.71, which places it second after L-SHADE but ahead of AL-SHADE. Table 11 focuses on the performance of IAGWO in the CEC 2017 suite. Here, IAGWO showed strong results in 8 of the test cases, but its performance was less impressive in 10 others. In terms of the Friedman mean ranking, IAGWO scored 1.99, which is slightly better than LSHADE-SPACMA, but not quite as good as LSHADE-cnEpSin. These results provide a detailed comparison of IAGWO's performance relative to other algorithms in these specific test environments.

Combining experimental outcomes, IAGWO can be positioned as a high-performing optimizer in test functions. These results not only demonstrate IAGWO's strong capability in handling different types of optimization problems but also indicate its competitive standing against existing top-tier algorithms. These findings emphasize the potential application value of IAGWO in the field of evolutionary computing and optimization. This simultaneously demonstrates the effectiveness of the three improvement strategies we introduced: the PSO Search Mechanism, the IMF Inertia Weighting Strategy, and the Adaptive Updating Mechanism, enhancing the optimization performance of the algorithm.

4.8 IAGWO for 19 engineering design challenges

The specific constrained handling technique used in engineering design challenges is called "constraint relaxation." Constraint relaxation involves temporarily easing or loosening certain constraints within the design problem to explore alternative solutions. This allows designers to generate a wider range of potential solutions without being overly restricted by strict constraints. Once various solutions have been identified, designers can then reintroduce and refine the constraints to ensure that the final design meets all necessary requirements. Intelligent optimization algorithms can efficiently explore the design space and uncover potential solutions. By integrating constraint relaxation techniques, these algorithms can dynamically handle constraints during the search process, allowing for a broader exploration of the design space and enhancing the efficiency of finding optimal solutions.

In this section, the proficiency of IAGWO is meticulously evaluated through a set of 19 engineering design challenges (EDC) sourced from the CEC 2020 real-world optimization benchmarks, as outlined by Kumar et al., 2020., 2020. A concise summary of these engineering challenges is presented in Table  12 , which includes key details such as their dimensions ( D ), the count of inequality constraints ( g ), equality constraints ( h ), and the known optimal cost ( f min ). The evaluation parameters are defined as follows: a population size of 50, a maximum of 1000 iterations, and 30 independent runs for each challenge.

Table 13 is dedicated to enumerating the performance metrics of IAGWO. This table encompasses various metrics including the best cost achieved (Best), the average cost (Ave), the cost's standard deviation (Std), and performance symbols (W|T|L), representing the number of wins, ties, and losses, respectively. Additionally, the evaluation includes a comprehensive analysis of the mean performance of all the algorithms involved in the testing. It also presents a ranking of these methods, providing a clear and structured comparison of their overall effectiveness and highlights instances where IAGWO achieves optimal results.

The statistical analysis drawn from these results clearly demonstrates IAGWO's superior ability in solving these real-world engineering design challenges, effectively outshining other methods. In terms of overall effectiveness, other algorithms like OMA, DMO, RGWO, and ENGWO trail behind IAGWO. This comprehensive analysis accentuates the robustness and efficacy of IAGWO.

5 Summary and future directions

In this study, we introduced an enhanced version of the GWO, aiming to tackle its inherent limitations and elevate its efficacy for addressing contemporary optimization challenges. The original GWO, while promising, exhibited deficiencies, notably in its convergence speed and its adaptability to intricate, high-dimensional problem landscapes. To fortify its capabilities, we embarked on an innovative path, culminating in the birth of an enhanced variant dubbed the Improved Adaptive Grey Wolf Optimizer (IAGWO). Central to our enhancement strategy was the infusion of concepts borrowed from Particle Swarm Optimization (PSO), introducing a velocity component to expedite convergence. This integration of velocity mechanics injected dynamism into the algorithm, enabling it to traverse solution spaces with greater agility. Moreover, a novel search mechanism was devised, augmenting the algorithm's exploration and exploitation capabilities to navigate complex problem domains more efficiently. In addition to these fundamental alterations, we devised novel strategies for Inertia Weighting and Position Updating, leveraging Nonlinear Inertia Weighting for Intermediary Fitness (IMF) and employing Sigmoid adaptive techniques. These refinements were meticulously crafted to synergize with the core algorithm, amplifying its prowess in navigating diverse optimization landscapes with finesse.

To validate the prowess of IAGWO, rigorous experimentation ensued, wherein 52 test functions sourced from prestigious benchmark suites were scrutinized. Comparative analysis against eight prominent Metaheuristic (MH) algorithms, including the original GWO and three of its variants, underscored IAGWO's supremacy in terms of convergence speed and solution precision. Furthermore, the algorithm's mettle was tested against 15 formidable large-scale global optimization challenges, affirming its adeptness in grappling with high-dimensional complexities. The litmus test for IAGWO's efficacy extended to competitive arenas, where it stood toe-to-toe against previous champions of the renowned CEC competitions across various iterations. Notably, IAGWO's performance surpassed expectations, firmly establishing its dominance and resilience in the face of formidable adversaries. Beyond the realm of academia, the real-world applicability of IAGWO was validated through its deployment in 19 diverse engineering design challenges. Here, its versatility and competitive edge shone brightly, outperforming established algorithms and offering tangible solutions to practical problems.

Despite its commendable achievements, the journey of IAGWO is far from over. While it has emerged as a potent force in the optimization landscape, ongoing efforts are directed towards fine-tuning its computational efficiency. Time comparison analyses have revealed areas for optimization, particularly concerning computational overhead in certain test suites. Future endeavors will thus focus on streamlining computational complexity without compromising search efficacy, ensuring that IAGWO remains at the forefront of optimization methodologies. Looking ahead, the horizon for IAGWO is brimming with promise. Beyond academic benchmarks, its utility extends to a myriad of real-world applications, ranging from feature extraction to operations research, classification, and logistical challenges. As we embark on this journey, our aim is clear: to harness the full potential of IAGWO in unraveling the complexities of the modern world, one optimization problem at a time.

Availability of data and materials

Enquiries about data availability should be directed to the authors.

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This work was supported by Natural Science Foundation of Tianjin Municipality (21JCYBJC00110) and China Postdoctoral Science Foundation (2023M731803).

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College of Artificial Intelligence, Nankai University, Tianjin, 300350, China

Mingyang Yu, Jing Xu, Weiyun Liang, Yu Qiu & Sixu Bao

Department of Biological and Chemical Sciences, New York Institute of Technology, New York, 11568-8000, USA

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MY: conceptualization, methodology, writing—original draft, formal analysis, data curation, writing—review & editing, software. WL: visualization, formal analysis, writing—review & editing. JX: conceptualization, resources, supervision, formal analysis. YQ: software, writing—review & editing, resources. SB: methodology, visualization resources, software. LT: visualization resources.

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Yu, M., Xu, J., Liang, W. et al. Improved multi-strategy adaptive Grey Wolf Optimization for practical engineering applications and high-dimensional problem solving. Artif Intell Rev 57 , 277 (2024). https://doi.org/10.1007/s10462-024-10821-3

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DOI : https://doi.org/10.1007/s10462-024-10821-3

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