Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support (...) the radical enactivist view. I argue that although more research is needed, it is at least possible to develop the REC position consistently with the state-of-the-art empirical research on the development of arithmetical cognition. After this, I move the focus to the question whether the radical enactivist account can explain the objectivity of arithmetical knowledge. Against the realist view suggested by Hutto, I argue that objectivity is best explained through analyzing the way universal proto-arithmetical abilities determine the development of arithmetical cognition. (shrink)

One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. (...) I will show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge. (shrink)

Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued (...) here that arithmetical knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology. (shrink)

Why would we want to develop artificial human-like arithmetical intelligence, when computers already outperform humans in arithmetical calculations? Aside from arithmetic consisting of much more than mere calculations, one suggested reason is that AI research can help us explain the development of human arithmetical cognition. Here I argue that this question needs to be studied already in the context of basic, non-symbolic, numerical cognition. Analyzing recent machine learning research on artificial neural networks, I show how (...) AI studies could potentially shed light on the development of human numerical abilities, from the proto-arithmetical abilities of subitizing and estimating to counting procedures. Although the current results are far from conclusive and much more work is needed, I argue that AI research should be included in the interdisciplinary toolbox when we try to explain the development and character of numerical cognition and arithmetical intelligence. This makes it relevant also for the epistemology of mathematics. (shrink)

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from (...) the proto-arithmetical ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than (...) 4 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series and quantum (...) information referring to infinite one as both appearing in three “hypostases”: correspondingly, mathematical, physical and ontological, each of which is able to generate a relevant science and area of cognition. Scientific transcendentalism is a falsifiable counterpart of philosophical transcendentalism. The underlying concept of the totality can be interpreted accordingly also mathematically, as consistent completeness, and physically, as the universe defined not empirically or experimentally, but as that ultimate wholeness containing its externality into itself. (shrink)

In early analytic philosophy, one of the most central questions concerned the status of arithmetical objects. Frege argued against the popular conception that we arrive at natural numbers with a psychological process of abstraction. Instead, he wanted to show that arithmetical truths can be derived from the truths of logic, thus eliminating all psychological components. Meanwhile, Dedekind and Peano developed axiomatic systems of arithmetic. The differences between the logicist and axiomatic approaches turned out to be philosophical as well (...) as mathematical. In this paper, I will argue that Dedekind’s approach can be seen as a precursor to modern structuralism and as such, it enjoys many advantages over Frege’s logicism. I also show that from a modern perspective, Frege’s criticism of abstraction and psychologism is one-sided and fails against the psychological processes that modern research suggests to be at the heart of numerical cognition. The approach here is twofold. First, through historical analysis, I will try to build a clear image of what Frege’s and Dedekind’s views on arithmetic were. Then, I will consider those views from the perspective of modern philosophy of mathematics, and in particular, the empirical study of arithmetical cognition. I aim to show that there is nothing to suggest that the axiomatic Dedekind approach could not provide a perfectly adequate basis for philosophy of arithmetic. (shrink)

Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter-argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the (...) account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations. (shrink)

Siyaves Azeri (2020) quite well shows that arithmetical thinking emerges on the basis of specific social practices and material engagement (clay tokens for economic exchange practices beget number concepts, e.g.). But his discussion here is relegated mostly to Neolithic and Bronze Age practices. While surely such practices produced revolutions in the cognitive abilities of many humans, much of the cognitive architecture that allows normative conceptual thought was already in place long before this time. This response, then, is an attempt (...) to sketch the deep prehistory of human cognition in order to show the inter-social bases of normative thought in general. To do this, I will look first to the work of Vygotsky and Leontiev, two often neglected psychologists whose combined efforts culminate in a developmental account of human cognitive origins. Then, I will review some key insights from the contemporary comparative psychologist Michael Tomasello—whose project is admittedly a Vygotskian one—in order to further shed light on the social-practical basis of abstract thought, of which mathematical cognition is surely a part. (shrink)

In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.

While there has been significant philosophical debate on whether nonlinguistic animals can possess conceptual capabilities, less time has been devoted to considering 'talking' animals, such as parrots. When they are discussed, their capabilities are often downplayed as mere mimicry. The most explicit philosophical example of this can be seen in Brandom's frequent comparisons of parrots and thermostats. Brandom argues that because parrots (like thermostats) cannot grasp the implicit inferential connections between concepts, their vocal articulations do not actually have any conceptual (...) content. In contrast, I argue that Pepperberg's work with Alex (and other African grey parrots) provides evidence that the vocal articulations of at least some parrots have conceptual content. Using Frege's insight that numbers assert something about a concept, I argue that Alex's ability to answer the question "How many?" depended upon a prior grasp of conceptual content. Developing this claim, I argue that Alex's arithmetical abilities show that he was capable of using numbers as both concepts and objects. Frege's theoretical insight and Pepperberg's empirical work provide reason to reconsider the capabilities of parrots, as well as what sorts of tasks provide evidence for conceptual content. (shrink)

Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the final analysis. The paper offers a pattern borrowed from the (...) theory of information and quantum information (therefore relating philosophy to both mathematics and physics) to formalize logically a few key concepts of Husserl’s phenomenology such as “epoché” “eidetic, phenomenological, and transcendental reductions” as well as the identification of “phenomenological, transcendental, and psychological reductions” in a way allowing for that identification to be continued to “eidetic reduction” (and thus to mathematics). The approach is tested by an independent and earlier idea of Husserl, “logical arithmetic” (parallelly implemented in mathematics by Whitehead and Russell’s Principia) as what “Hilbert arithmetic” generalizing Peano arithmetics is interpreted. A basic conclusion states for the unification of philosophy, mathematics, and physics in their foundations and fundamentals to be the Husserl tradition both tracked to its origin (in the being itself after Heidegger or after Husserl’s “zu Sache selbst”) and embodied in the development of human cognition in the third millennium. (shrink)

The mind-body problem is one of the important topics in philosophy of mind and cognitive science. Following the analytical tradition of linguistic and logical analysis, we focus on two aspects of the mind- body problem: one is around Gödel's incompleteness theorem, and the other is on cognitive logic, especially on the question of whether Epistemological Arithmetic and machines are private. In the former case, in response to the popular view that the Gödel Incompleteness Theorem supports dualism in the mind-body problem, (...) H. Putnam constructs a counter-argument that defends the computationalist agenda: the equivalence of mind and Turing machine. In this regard, the paper discusses Putnam's line of analysis and then argues that it is unsound. In the latter case, the paper examines in detail the cognitive form of the expression of privateness and concludes, together with recent results in EA, that the existence of privateness in Turing machines is logically untenable and, therefore, we argue that the mind is not equivalent to a machine in terms of cognitive ability and privateness, i.e., the computationalist agenda is not valid. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will (...) argue that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and truth (...) to the compound formulas of PA over N---I_PA(N; SV ) and I_PA(N; SC). We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both I_PA(N; SV ) and I_PA(N; SC). We then show: (a) that if we assume the satisfaction and truth of the compound formulas of PA are always non-finitarily decidable under I_PA(N; SV ), then this assignment corresponds to the classical non-finitary putative standard interpretation I_PA(N; S) of PA over the domain N; and (b) that the satisfaction and truth of the compound formulas of PA are always finitarily decidable under the assignment I_PA(N; SC), from which we may finitarily conclude that PA is consistent. We further conclude that the appropriate inference to be drawn from Goedel's 1931 paper on undecidable arithmetical propositions is that we can define PA formulas which---under interpretation---are algorithmically verifiable as always true over N, but not algorithmically computable as always true over N. We conclude from this that Lucas' Goedelian argument is validated if the assignment I_PA(N; SV ) can be treated as circumscribing the ambit of human reasoning about `true' arithmetical propositions, and the assignment I_PA(N; SC) as circumscribing the ambit of mechanistic reasoning about `true' arithmetical propositions. (shrink)

This paper presents 59 new studies (N = 72,310) which focus primarily on the “bat and ball problem.” It documents our attempts to understand the determinants of the erroneous intuition, our exploration of ways to stimulate reflection, and our discovery that the erroneous intuition often survives whatever further reflection can be induced. Our investigation helps inform conceptions of dual process models, as “system 1” processes often appear to override or corrupt “system 2” processes. Many choose to uphold their intuition, even (...) when directly confronted with simple arithmetic that contradicts it – especially if the intuition is approximately correct. (shrink)

The concept of affordances is rapidly gaining traction in the philosophy of mind and cognitive sciences. Affordances are opportunities for action provided by the environment. An important open question is whether affordances can be used to explain mental action such as attention, counting, and imagination. In this paper, we critically discuss McClelland’s (‘The Mental Affordance Hypothesis’, 2020, Mind, 129(514), pp. 401–427) mental affordance hypothesis. While we agree that the affordance concept can be fruitfully employed to explain mental action, we argue (...) that McClelland’s mental affordance hypothesis contain remnants of a Cartesian understanding of the mind. By discussing the theoretical framework of the affordance competition hypothesis, we sketch an alternative research program based on the principles of embodied cognition that evades the Cartesian worries. We show how paradigmatic mental acts, such as imagination, counting, and arithmetic, are dependent on sensorimotor interaction with an affording environment. Rather than make a clear distinction between bodily and mental action, the mental affordances highlight the embodied nature of our mental action. We think that in developing our alternative research program on mental affordances, we can maintain many of the excellent insights of McClelland’s account without reintroducing the very distinctions that affordances were supposed to overcome. (shrink)

A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as (...) the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the violations of (...) energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)

Metaepistemology may be partly characterized as the study of the nature, aims, methods and legitimacy of epistemology. Given such a characterization, most epistemological views and theories have an important metaepistemological aspect or, at least, a number of more or less explicit metaepistemological commitments. Metaepistemology is an important area of philosophy because it exemplifies that philosophy must serve as its own meta-discipline by continuously reflecting critically on its own methods and aims. Even though philosophical methodology may be regarded as a branch (...) of epistemology, epistemology itself is as much in need of metaphilosophical examination as other core disciplines of philosophy. Moreover, metaepistemology is important because it bears significantly on first-order epistemological questions. Indeed, many of the most prominent contemporary debates in philosophy have a distinctly metaepistemological aspect. For example, the debates between rationalists and empiricists do not only concern the nature of cognition of specific areas – perception, arithmetic, logic and so forth – but also general metaepistemological questions about whether it is realistic and desirable that epistemology be naturalized. Likewise, the debates between epistemic internalists and externalists include metaepistemological debates about whether the proper focus for epistemology should be the cognizer’s rational perspective or some more objective property of the cognizer’s epistemic position. Similarly, the debates concerning the relationship between folk epistemology and epistemological theorizing include metaepistemological debates about how empirical data concerning folk epistemology should impact epistemology itself. Each of these debates provides an example of how first-order epistemological issues are deeply connected, and sometimes inseparable from, metaepistemological considerations. (shrink)

Gottlob Frege abandoned his logicist program after Bertrand Russell had discovered that some assumptions of Frege’s system lead to contradiction (so called Russell’s paradox). Nevertheless, he proposed a new attempt for the foundations of mathematics in two last years of his life. According to this new program, the whole of mathematics is based on the geometrical source of knowledge. By the geometrical source of cognition Frege meant intuition which is the source of an infinite number of objects in arithmetic. (...) In this article, I describe this final attempt of Frege to provide the foundations of mathematics. Furthermore, I compare Frege’s views of intuition from The Foundations of Arithmetic (and his later views) with the Kantian conception of pure intuition as the source of geometrical axioms. In the conclusion of the essay, I examine some implications for the debate between Hans Sluga and Michael Dummett concerning the realistic and idealistic interpretations of Frege’s philosophy. (shrink)

Over 40 years ago I read a small grey book with metaphysics in the title which began with the words “Metaphysics is dead. Wittgenstein has killed it.” I am one of many who agree but sadly the rest of the world has not gotten the message. Shoemaker’s work is nonsense on stilts but is unusual only in that it never deviates into sense from the first paragraph to the last. At least with Dennett, Carruthers, Churchland etc. one gets a breath (...) of fresh air when they discuss cognitive science (imagining they are still doing philosophy). As W showed so beautifully, the confusions that lead to metaphysics are universal and nearly inescapable aspects of our psychology. They occur not only in all thinking on behavior but throughout science as well. It’s easy to find examples in Hawking, Weinberg, Penrose, Green, who of course have no idea they have left science and entered metaphysics, that the statement they just made is not a matter of fact at all but a matter of conceptual (linguistic) confusion. “Law, event, space, time, force, matter, proof, connection, cause, follows, physical”, etc., all have clear uses in certain technical contexts, but these blend insensibly into quite different uses that have little in common but the spelling. Since it is pointless to waste time deconstructing Shoemaker line by line, showing the same errors over and over, I will describe some facts about how our psychology (language) works and with this outline and the references I give it is quite straightforward to give a meaningful description of the world in place of the metaphysical fantasies. If I were to debate Shoemaker we would never get beyond the title. Horwich gives one of the most beautiful summaries of where an understanding of Wittgenstein leaves us that I have ever seen. “There must be no attempt to explain our linguistic/conceptual activity (PI 126) as in Frege’s reduction of arithmetic to logic; no attempt to give it epistemological foundations (PI 124) as in meaning based accounts of a priori knowledge; no attempt to characterize idealized forms of it (PI 130) as in sense logics; no attempt to reform it (PI 124, 132) as in Mackie’s error theory or Dummett’s intuitionism; no attempt to streamline it (PI 133) as in Quine’s account of existence; no attempt to make it more consistent (PI 132) as in Tarski’s response to the liar paradoxes; and no attempt to make it more complete (PI 133) as in the settling of questions of personal identity for bizarre hypothetical ‘teleportation’ scenarios.” Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

In the 17th century, Hobbes stated that we reason by addition and subtraction. Historians of logic note that Hobbes thought of reasoning as “a ‘species of computation’” but point out that “his writing contains in fact no attempt to work out such a project.” Though Leibniz mentions the plus/minus character of the positive and negative copulas, neither he nor Hobbes say anything about a plus/minus character of other common logical words that drive our deductive judgments, words like ‘some’, ‘all’, ‘if’, (...) and ‘and’, each of which actually turns out to have an oppositive, character that allows us, “in our silent reasoning,” to ignore its literal meaning and to reckon with it as one reckons with a plus or a minus operator in elementary algebra or arithmetic. These ‘logical constants’ of natural language figure crucially in our everyday reasoning. Because Hobbes and Leibniz did not identify them as the plus and minus words we reason with, their insight into what goes on in ‘ratiocination’ did not provide a guide for a research program that could develop a +/- logic that actually describes how we reason deductively. I will argue that such a +/- logic provides a way back from modern predicate logic—the logic of quantifiers and bound variables that is now ‘standard logic’—to an Aristotelian term logic of natural language that had been the millennial standard logic. (shrink)

The present paper intends to report two results. It is shown that the formula P(x)=∀y∀z[¬G(x, y)→¬M(z)] provides the logic underlying gauge symmetry, where M denotes the predicate of being massive. For the logic of spontaneous symmetry breaking, by Higgs mechanism, we have P(x)=∀y∀z[G(x, y)→M(z)]. Notice that the above two formulas are not logically equivalent. The results are obtained by integrating four components, namely, gauge symmetry and Higgs mechanism in quantum field theory, and Gödel's incompleteness theorem and Tarski's indefinability theorem in (...) mathematical logic. Gödel numbering is the key for arithmetic modeling applied in this paper. (shrink)

Biogenic approaches investigate cognition from the standpoint of evolutionary function, asking what cognition does for a living system and then looking for common principles and exhibitions of cognitive strategies in a vast array of living systems—non-neural to neural. One worry which arises for the biogenic approach is that it is overly permissive in terms of what it construes as cognition. In this paper I critically engage with a recent instance of this way of criticising biogenic approaches in (...) order to clarify their theoretical commitments and prospects. In his critique of the biogenic approach, Fred Adams uses the presence of intentional states with conceptual content as a criterion to demarcate cognition-driven behaviour from mere sensory response. In this paper I agree with Adams that intentionality is the mark of the cognitive, but simultaneously reject his overly restrictive conception of intentionality. I argue that understanding intentionality simpliciter as the mark of the mental is compatible with endorsing the biogenic approach. I argue that because cognitive science is not exclusively interested in behaviour driven by intentional states with the kind of content Adams demands, the biogenic approach’s status as an approach to cognition is not called into question. I then go on to propose a novel view of intentionality whereby it is seen to exist along a continuum which increases in the degree of representational complexity: how far into the future representational content can be directed and drive anticipatory behaviour. Understanding intentionality as existing along a continuum allows biogenic approaches and anthropogenic approaches to investigate the same overarching capacity of cognition as expressed in its different forms positioned along the continuum of intentionality. Even if all organisms engage in some behaviour that is driven by weak intentional dynamics, this does not suggest that every behaviour of all organisms is so driven. As such, the worry that the biogenic approach is overly permissive can be avoided. (shrink)

Tracing the leading role of emotions in the evolution of the mind, a philosopher and a psychologist pair up to reveal how thought and culture owe less to our faculty for reason than to our capacity to feel. Many accounts of the human mind concentrate on the brain’s computational power. Yet, in evolutionary terms, rational cognition emerged only the day before yesterday. For nearly 200 million years before humans developed a capacity to reason, the emotional centers of the brain (...) were hard at work. If we want to properly understand the evolution of the mind, we must explore this more primal capability that we share with other animals: the power to feel. Emotions saturate every thought and perception with the weight of feelings. The Emotional Mind reveals that many of the distinctive behaviors and social structures of our species are best discerned through the lens of emotions. Even the roots of so much that makes us uniquely human—art, mythology, religion—can be traced to feelings of caring, longing, fear, loneliness, awe, rage, lust, playfulness, and more. From prehistoric cave art to the songs of Hank Williams, Stephen T. Asma and Rami Gabriel explore how the evolution of the emotional mind stimulated our species’ cultural expression in all its rich variety. Bringing together insights and data from philosophy, biology, anthropology, neuroscience, and psychology, The Emotional Mind offers a new paradigm for understanding what it is that makes us so unique. (shrink)

ABSTRACTSilencing is a practice that disrupts linguistic and communicative acts, but its relationship to knowledge and justice is not fully understood. Prior models of epistemic injustice tend to c...

I argue for a new delimitation of what Kant means by ‘cognition [Erkenntnis]’, on the basis of the intermediate, transitional place that Kant gives to cognition in the ‘progression [Stufenleiter]’ of our representations and our consciousness of them. I show how cognition differs from mental acts lying earlier on this progression—such as sensing, intuiting, and perceiving—and also how cognition differs from acts lying later on this progression—such as explaining, having insight, and comprehending. I also argue that (...) cognition should not be confused with ‘knowledge [Wissen]’, insofar as knowledge represents the culmination of a separate orthogonal progression of acts of ‘holding-true’. Along the way, I show how having in focus the specific progression from representation, to consciousness, to cognition allows us to better appreciate the architectonic significance of the progression of Kant’s analysis in the first Critique, and also helps to illuminate the unity of Kant’s account of cognition itself across its variety of forms. (shrink)

The concepts expressed by social role terms such as artist and scientist are unique in that they seem to allow two independent criteria for categorization, one of which is inherently normative. This study presents and tests an account of the content and structure of the normative dimension of these “dual character concepts.” Experiment 1 suggests that the normative dimension of a social role concept represents the commitment to fulfill the idealized basic function associated with the role. Background information can affect (...) which basic function is associated with each social role. However, Experiment 2 indicates that the normative dimension always represents the relevant commitment as an end in itself. We argue that social role concepts represent the commitments to basic functions because that information is crucial to predict the future social roles and role-dependent behavior of others. (shrink)

Experimental research suggests that people draw a moral distinction between bad outcomes brought about as a means versus a side effect (or byproduct). Such findings have informed multiple psychological and philosophical debates about moral cognition, including its computational structure, its sensitivity to the famous Doctrine of Double Effect, its reliability, and its status as a universal and innate mental module akin to universal grammar. But some studies have failed to replicate the means/byproduct effect especially in the absence of other (...) factors, such as personal contact. So we aimed to determine how robust the means/byproduct effect is by conducting a meta-analysis of both published and unpublished studies (k = 101; 24,058 participants). We found that while there is an overall small difference between moral judgments of means and byproducts (standardized mean difference = 0.87, 95% CI 0.67 – 1.06; standardized mean change = 0.57, 95% CI 0.44 – 0.69; log odds ratio = 1.59, 95% CI 1.15 – 2.02), the mean effect size is primarily moderated by whether the outcome is brought about by personal contact, which typically involves the use of personal force. (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...) of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

Discursive cognition of the sort that accompanies the grasp of a natural language involves an ability to self-govern by framing and following rules concerning what reason prescribes. In this essay I argue that the formal features of a planning semantics for the deontic and intentional modalities suggest a picture on which shared intentional mental states are a more primitive kind of cognition than that which accompanies the ability to frame and follow a rule, so that deontic cognition—and (...) the autonomous rationality attending the ability to speak a natural language—might be understood as an evolutionary development out of the capacity to share intentions. In the course of defending this picture, I argue that it is supported by work in social psychology, evolutionary anthropology, and primatology concerning the phylogenetic and ontogenetic development of norm psychology and shared intentionality in human beings. (shrink)

Compatibilism is the view that determinism is compatible with acting freely and being morally responsible. Incompatibilism is the opposite view. It is often claimed that compatibilism or incompatibilism is a natural part of ordinary social cognition. That is, it is often claimed that patterns in our everyday social judgments reveal an implicit commitment to either compatibilism or incompatibilism. This paper reports five experiments designed to identify such patterns. The results support a nuanced hybrid account: The central tendencies in ordinary (...) social cognition are compatibilism about moral responsibility, compatibilism about positive moral accountability, neither compatibilism nor incompatibilism about negative moral accountability, compatibilism about choice for actions with positive outcomes, and incompatibilism about choice for actions with negative or neutral outcomes. (shrink)

The paper explores the idea that some singular judgements about the natural numbers are immune to error through misidentification by pursuing a comparison between arithmetic judgements and first-person judgements. By doing so, the first part of the paper offers a conciliatory resolution of the Coliva-Pryor dispute about so-called “de re” and “which-object” misidentification. The second part of the paper draws some lessons about what it takes to explain immunity to error through misidentification. The lessons are: First, the so-called Simple Account (...) of which-object immunity to error through misidentification to the effect that a judgement is immune to this kind of error just in case its grounds do not feature any identification component fails. Secondly, wh-immunity can be explained by a Reference-Fixing Account to the effect that a judgement is immune to this kind of error just in case its grounds are constituted by the facts whereby the reference of the concept of the object which the judgement concerns is fixed. Thirdly, a suitable revision of the Simple Account explains the de re immunity of those arithmetic judgements which are not wh-immune. These three lessons point towards the general conclusion that there is no unifying explanation of de re and wh-immunity. (shrink)

Human aesthetic practices show a sensitivity to the ways that the appearance of an artefact manifests skills and other qualities of the maker. We investigate a possible origin for this kind of sensibility, locating it in the need for co-ordination of skill-transmission in the Acheulean stone tool culture. We argue that our narrative supports the idea that Acheulian agents were aesthetic agents. In line with this we offer what may seem an absurd comparison: between the Acheulian and the Quattrocento. In (...) making it we display some hidden richness in what counts as an aesthetic response to an artefact. We conclude with a brief review of rival explanations—biological and/or cultural—of how this skills-based sensibility became a regular feature of human aesthetic practices. (shrink)

Kant’s views on animals have received much attention in recent years. According to some, Kant attributed the capacity for objective perceptual awareness to non-human animals, even though he denied that they have concepts. This position is difficult to square with a conceptualist reading of Kant, according to which objective perceptual awareness requires concepts. Others take Kant’s views on animals to imply that the mental life of animals is a blooming, buzzing confusion. In this article I provide a historical reconstruction of (...) Kant’s views on animals, relating them to eighteenth-century debates on animal cognition. I reconstruct the views of Buffon and Reimarus and show that (i) both Buffon and Reimarus adopted a conceptualist position, according to which concepts structure the cognitive experience of adult humans, and (ii) that both described the mental life of animals as a blooming, buzzing confusion. Kant’s position, I argue, is virtually identical to that of Reimarus. Hence Kant’s views on animals support a conceptualist reading of Kant. The article further articulates the historical antecedents of the Kantian idea that concepts structure human cognitive experience and provides a novel account of how the ideas of similarity and difference were conceptualized in eighteenth-century debates on animal cognition. (shrink)

Only our lineage has ever used trackways reading to find unseen and unheard targets. All other terrestrial animals, including our great ape cousins, use scent trails and airborne odors. Because trackways as natural signs have very different properties, they possess an information-rich narrative structure. There is good evidence we began to exploit conspecific trackways in our deep past, at first purely associatively, for safety and orienteering when foraging in vast featureless wetlands. Since our own old trackways were recognizable they were (...) self-mirroring, triggering memories of what we had been up to in the past. Using them to find our way back to the band when temporarily lost or to re-find a resource-rich area discovered the day before enabled optimal foraging. Selection for daily reiteration of one’s own old trackways therefore triggered the evolution of what is distinctive about human cognition: the autobiographical or narrative (episodic) faculty for imaginative self-projection. This faculty enabled us to glean useful social information from the stories “told” by other band members’ old trackways, and created spin-off capacities for fast-track social learning. Resultant increases in socioecological complexity then created positive selective feedback loops for further entrenchment. Incrementally we became the ultra-social narrative-minded ape, capable of creating cumulative culture. (shrink)

Distributed Cognition and Integrational Linguistics have much in common. Both approaches see communicative activity and intelligent behaviour in general as strongly con- text-dependent and action-oriented, and brains as permeated by history. But there is some ten- sion between the two frameworks on three important issues. The majority of theorists of distributed cognition want to maintain some notions of mental representation and computa- tion, and to seek generalizations and patterns in the various ways in which creatures like us couple (...) with technologies, media, and other agents; many also want to offer explanations at subpersonal levels which may undercut the autonomy of personal-level accounts. In contrast, dominant views in integrational linguistics reject all invocation of representation, resist the explanatory search for similarity across contexts and moments, and see linguistics as a lay dis- cipline which should not offer explanations in terms alien to ordinary agents. On each of these issues, I argue that integrationists could move closer to the distributed cognition frame- work without losing the most important aspects of their view: integrationist criticisms of mainstream or classical theories can be respected while alliances with revised cognitivist views about representation, context, and explanation are developed. Ó 2004 Elsevier Ltd. All rights reserved. (shrink)

I argue that in addressing worries about the validity and reliability of implicit measures of social cognition, theorists should draw on research concerning “entitativity perception.” In brief, an aggregate of people is perceived as highly “entitative” when its members exhibit a certain sort of unity. For example, think of the difference between the aggregate of people waiting in line at a bank versus a tight-knit group of friends: The latter seems more “groupy” than the former. I start by arguing (...) that entitativity perception modulates the activation of implicit biases and stereotypes. I then argue that recognizing this modulatory role will help researchers to address concerns surrounding the validity and reliability of implicit measures. (shrink)

My goal in this paper is to show that Kant’s prohibition on certain kinds of knowledge of things-in-themselves is motivated less by his anti-soporific encounter with Hume than by his new view of the distinction between “real” and “logical” modality, a view that developed out of his reflection on the rationalist tradition in which he was trained. In brief: at some point in the 1770’s, Kant came to hold that a necessary condition on knowing a proposition is that one be (...) able to prove that all the items it refers to are either really possible or really impossible. Most propositions about things-in-themselves, in turns out, cannot meet this condition. I conclude by suggesting that the best interpretation of this modal condition is as a kind of coherentist constraint. (shrink)

Within eighteenth-century debates on animal cognition we can distinguish at least three main theoretical positions: (i) Buffon’s mechanism, (ii) Reimarus’ theory of instincts, and (iii) the sensationalism of Condillac and Leroy. In this paper, I adopt a philosophical perspective on this debate and argue that in order to fully understand the justification Buffon, Reimarus, Condillac, and Leroy gave for their respective theories, we must pay special attention to the theoretical virtues these naturalists alluded to while justifying their position. These (...) theoretical virtues have received little to no attention in the literature on eighteenth-century animal cognition, but figure prominently in the justification of the mechanist, instinctive, and sensationalist theories of animal behavior. Through my philosophical study of the role of theoretical virtues in eighteenth-century debates on animal cognition, we obtain a deeper understanding of how theoretical virtues were conceptualized in eighteenth-century science and how they influenced the justification of theories of animal cognition. (shrink)

In this paper, I argue that embodied cognition, like many other research traditions in cognitive science, offers mostly fallible research heuristics rather than grand principles true of all cognitive processing. To illustrate this claim, I discuss Aizawa’s rebuttal of embodied and enactive accounts of vision. While Aizawa’s argument is sound against a strong reading of the enactive account, it does not undermine the way embodied cognition proceeds, because the claim he attacks is one of fallible heuristics. These heuristics (...) may be helpful in developing models of cognition in an interdisciplinary fashion. I briefly discuss the issue of whether this fallibility actually makes embodied cognition vulnerable to charges of being untestable or non-scientific. I also stress that the historical approach to this research tradition suggests that embodied cognition is not poised to become a grand unified theory of cognition. (shrink)

Duas das principais controvérsias que têm ocupado aqueles que se dedicam à teoria aris- totélica do movimento animal são a controvérsia acerca da forma da cognição através da qual um animal irracional apreende um objeto como um objeto de desejo e a controvérsia acerca da função desempenhada pela cognição na explicação aristotélica dos movimentos voluntários de locomoção animal. Neste artigo, eu apresento uma teoria acerca das formas como o desejo e a cognição se articulam na teoria aristotélica segundo a qual (...) um animal irracional apreende um objeto como um objeto de desejo através da percepção incidental deste objeto e, ao contrário do que a maioria parece acreditar, esta percepção não tem sempre a mesma função na produção destes movimentos. Se o que for dito aqui estiver correto, em alguns casos esta percepção é responsável tanto pela geração do desejo quan- to pela sua orientação, mas em outros ela é responsável apenas pela sua orientação. (shrink)

Ronald Giere embraces the perspective of distributed cognition to think about cognition in the sciences. I argue that his conception of distributed cognition is flawed in that it bears all the marks of its predecessor; namely, individual cognition. I show what a proper (i.e. non-individual) distributed framework looks like, and highlight what it can and cannot do for the philosophy of science.

The option of being ‘spiritual but not religious’ deserves much more philosophical attention. That is the aim here, taking the work of Robert Solomon as a starting point, with focus on the particular issues around viewing life as gift. This requires analysis of ‘existential gratitude’ to show that there can be gratitude for things without gratitude to someone for providing things, and also closer attention to the role that metaphor plays in cognition. I consider two main concerns with gift (...) and gratitude thinking, that the nonreligious justification is too instrumentalist in its approach and that viewing life as gift, whether in a religious or nonreligious way, is simply too optimistic. (shrink)