After defining, for each many-sorted signature Σ = (S, Σ), the category Ter ( Σ ), of generalized terms for Σ (which is the dual of the Kleisli category for , the monad in Set S determined by the adjunction from Set S to Alg ( Σ ), the category of Σ -algebras), we assign, to a signature morphism d from Σ to Λ , the functor from Ter ( Σ ) to Ter ( Λ ). Once (...) defined the mappings that assign, respectively, to a many-sorted signature the corresponding category of generalized terms and to a signature morphism the functor between the associated categories of generalized terms, we state that both mappings are actually the components of a pseudo-functor Ter from Sig to the 2-category Cat . Next we prove that there is a functor Tr Σ , of realization of generalized terms as term operations, from Alg ( Σ ) × Ter ( Σ ) to Set , that simultaneously formalizes the procedure of realization of generalized terms and its naturalness (by taking into account the variation of the algebras through the homomorphisms between them). We remark that from this fact we will get the invariance of the relation of satisfaction under signature change. Moreover, we prove that, for each signature morphism d from Σ to Λ , there exists a natural isomorphism θ d from the functor to the functor , both from the category Alg ( Λ ) × Ter ( Σ ) to the category Set , where d * is the value at d of the arrow mapping of a contravariant functor Alg from Sig to Cat , that shows the invariant character of the procedure of realization of generalized terms under signature change. Finally, we construct the many-sorted term institution by combining adequately the above components (and, in a derived way, the many-sorted specification institution), but for a strict generalization of the standard notion of institution. (shrink)

After defining, for each many-sorted signature Σ = (S, Σ), the category Ter(Σ), of generalized terms for Σ (which is the dual of the Kleisli category for $${\mathbb {T}_{\bf \Sigma}}$$, the monad in Set S determined by the adjunction $${{\bf T}_{\bf \Sigma} \dashv {\rm G}_{\bf \Sigma}}$$ from Set S to Alg(Σ), the category of Σ-algebras), we assign, to a signature morphism d from Σ to Λ, the functor $${{\bf d}_\diamond}$$ from Ter(Σ) to Ter(Λ). Once defined the mappings (...) that assign, respectively, to a many-sorted signature the corresponding category of generalized terms and to a signature morphism the functor between the associated categories of generalized terms, we state that both mappings are actually the components of a pseudo-functor Ter from Sig to the 2-category Cat. Next we prove that there is a functor TrΣ, of realization of generalized terms as term operations, from Alg(Σ) × Ter(Σ) to Set, that simultaneously formalizes the procedure of realization of generalized terms and its naturalness (by taking into account the variation of the algebras through the homomorphisms between them). We remark that from this fact we will get the invariance of the relation of satisfaction under signature change. Moreover, we prove that, for each signature morphism d from Σ to Λ, there exists a natural isomorphism θ d from the functor $${{{\rm Tr}^{\bf {\bf \Lambda}} \circ ({\rm Id} \times {\bf d}_\diamond)}}$$ to the functor $${{\rm Tr}^{\bf \Sigma} \circ ({\bf d}^* \times {\rm Id})}$$, both from the category Alg(Λ) × Ter(Σ) to the category Set, where d* is the value at d of the arrow mapping of a contravariant functor Alg from Sig to Cat, that shows the invariant character of the procedure of realization of generalized terms under signature change. Finally, we construct the many-sorted term institution by combining adequately the above components (and, in a derived way, the many-sorted specification institution), but for a strict generalization of the standard notion of institution. (shrink)

This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world.

Category mistakes are sentences such as ‘Colourless green ideas sleep furiously’ or ‘The theory of relativity is eating breakfast’. Such sentences are highly anomalous, and this has led a large number of linguists and philosophers to conclude that they are meaningless (call this ‘the meaninglessness view’). In this paper I argue that the meaninglessness view is incorrect and category mistakes are meaningful. I provide four arguments against the meaninglessness view: in Sect. 2, an argument concerning compositionality with respect (...) to category mistakes; in Sect. 3 an argument concerning synonymy facts of category mistakes; in Sect. 4 concerning embeddings of category mistakes in propositional attitude ascriptions; and in Sect. 5 concerning the uses of category mistakes in metaphors. Having presented these arguments, in Sect. 6 I briefly discuss some of the positive motivations for accepting the meaninglessness view and argue that they are unconvincing. I conclude that the meaninglessness view ought to be rejected. (shrink)

1 Recognition Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Classical Categorial Grammar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Classical (...) Categorial Grammar. Examples . . . . . . . . . . . . . . . . . . . . . 5 4 Logic Grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 Lambek calculus. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 Lambek calculus. Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 7 Lambek calculus. Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 8 Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 9 Residuated and Galois Connected Functions . . . . . . . . . . . . . . . . . . 14 10 Interpretation of the Constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 11 Nonveridical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 12 Dutch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 13 Classification of NPIs in Dutch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 14 Antilicensing Relation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.. (shrink)

Probably colour is the best worked-out example of allegedly neurophysiologically innate response categories determining percepts and percepts determining concepts, and hence biology fixing the basic categories implicit in the use of language. In this paper I argue against this view and I take C. L. Hardin's Color for Philosophers [1988] as my main target. I start by undermining the view that four unique hues stand apart from all other colour shades (Section 2) and the confidence that the solar spectrum is (...) naturally divided into four categories (Section 3). For such categories to be truly universal, they have to be true for all peoples and in Section 4 I show that Berlin and Kay's [1969] widely quoted theory of basic colour categories is not sufficiently supported to lend it any credibility.Having disposed of the view that inspection of language or ‘pure’ perception unveils the universal colour categories. I turn to neurophysiological and psychophysical theories of colour vision to see whether they provide a more solid basis for deciding what the innate response categories are. In Section 5 I show that Hardin's account of the opponent-process theory neither supports his view that ‘colour-coding’takes place early in the visual neural pathway, nor his view that knowledge of colour vision science will help us solve many philosophical mysteries about colour.In Section 6 I give a more detailed review of what is known today about the neurophysiology of colour vision and I show that there's nothing in the brain which could be called a colour module, let alone a module with homunculi for particular basic colour categories. In Section 7 I show that psychophysical models do not support such rigid constraints on category formation either. Hence (Section 8), at least in the case of colour, current science supports a plasticity in the formation of categories that goes far beyond the requirements of those naturalistic philosophers who would like to ground primitive concepts in biology. (shrink)

The logic is rational. The logic is not external or independent of mind.

Gilbert Ryle never pursued research under Edmund Husserl. However, Ryle was indeed Husserl’s student in a broader sense, as much of his own work was deeply influenced by his studies of Husserl’s pre-World War I writings. While Ryle is the thinker whose name typically comes to mind in connection with the concern over category mistakes I argue that (1) Husserl deserves to be known for precisely this concern as well, and (2) the similarity between them is no accident. Developing (...) this reading of Ryle’s Husserlian pedigree forces a broader reevaluation of each of their roles in twentieth-century thought. (shrink)

0. The ancient and honorable role of philosophy as a servant to the learning, development and use of scientific knowledge, though sadly underdeveloped since Grassmann, has been re-emerging from within the particular science of mathematics due to the latter's internal need; making this relationship more explicit (as well as further investigating the reasons for the decline) will, it is hoped, help to germinate the seeds of a brighter future for philosophy as well as help to guide the much wider learning (...) of mathematics and hence of all the sciences. 1. The unity of interacting opposites "space vs. quantity", with the accompanying "general vs. particular" and the resulting division of variable quantity into the interacting opposites "extensive vs. intensive", is susceptible, with the aid of categories, functors, and natural transformations, of a formulation which is on the one hand precise enough to admit proved theorems and considerable technical development and yet is on the other hand general enough to admit incorporation of almost any specialized hypothesis. Readers armed with the mathematical definitions of basic category theory should be able to translate the discussion in this section into symbols and diagrams for calculations. 2. The role of space as an arena for quantitative "becoming" underlies the qualitative transformation of a spatial category into a homotopy category, on which extensive and intensive quantities reappear as homology and cohomology. 3. The understanding of an object in a spatial category can be approached through definite Moore-Postnikov levels; each of these levels constitutes a mathematically precise "unity and identity of opposites", and their ensemble bears features strongly reminiscent of Hegel's Science of Logic. This resemblance suggests many mathematical and philosophical problems which now seem susceptible of exact solution. (shrink)

Language acquisition may be one of the most difficult tasks that children face during development. They have to segment words from fluent speech, figure out the meanings of these words, and discover the syntactic constraints for joining them together into meaningful sentences. Over the past couple of decades, computational modeling has emerged as a new paradigm for gaining insights into the mechanisms by which children may accomplish these feats. Unfortunately, many of these models assume a computational complexity and linguistic knowledge (...) likely to be beyond the abilities of developing young children. This article shows that, using simple statistical procedures, significant correlations exist between the beginnings and endings of a word and its lexical category in English, Dutch, French, and Japanese. Therefore, phonetic information can contribute to individuating higher level structural properties of these languages. This article also presents a simple 2‐layer connectionist model that, once trained with an initial small sample of words labeled for lexical category, can infer the lexical category of a large proportion of novel words using only word‐edge phonological information, namely the first and last phoneme of a word. The results suggest that simple procedures combined with phonetic information perceptually available to children provide solid scaffolding for emerging lexical categories in language development. (shrink)

in a late note, dated 1797, Kant refers to the schematism of the pure understanding as one of the most difficult as well as one of the most important issues treated in the Critique of Pure Reason.1 His treatment of this theme is indeed notorious for its obscurity.2 As I see it, part of the problem is caused by the fact that Kant frames his discussion in terms that he could expect his readers to be familiar with, while he gradually (...) develops ideas that breach any traditional account of cognition. This holds for his references to the power of judgment and the related view that cognition is a matter of subsuming intuitions under concepts3 as well as for the suggestion that there is an initial gap between categories... (shrink)

Our knowledge of natural categories includes beliefs not only about what is true of them but also about what would be true if the categories had properties other than (or in addition to) their actual ones. Evidence about these beliefs comes from three lines of research: experiments on category-based induction, on hypothetical transformations of category members, and on definitions of kind terms. The 1st part of this article examines results and theories arising from each of these research streams. (...) The 2nd part considers possible unified theories for this domain, including theories based on ideals and norms. It also contrasts 2 broad frameworks for modal category information: one focusing on beliefs about intrinsic or essential properties, the other focusing on interacting causal relations. (shrink)

In this paper, I propose to resolve the controversy over the derivation of the categories of quantity by spelling out three claims: (1) the three quantitative functions/forms of judgment (universal-particular-singular), qua synthetic categories of quantity (unity-plurality-totality), lawfully direct the determination of sensible manifolds as singular totalities, which (2) brings to light a specifically categorial type of judgmental activity, distinguishable from but presupposed by empirical judgments. This calls for (3) pairing the category of totality with the singular judgment and the (...) category of unity with the universal judgment (‘Order B’), rather than pairing the singular judgment with unity and the universal judgment with totality (‘Order A’). At stake in this controversy is our understanding of the categories’ normativity, their scope, and the division of labor between intuitions and categories in individuating objects. (shrink)

Verbs and nouns gear θ-dependencies, Case, agreement, or construal relations. Building on Chomsky’s 1974 decomposition of such categories into ±N, ±V features, by translating said features into ±1, ±i scalars that allow for the construction of a vector space, this paper studies the possibility of organizing said features into 2 × 2 square matrices. In the system proposed to explore “head-complement” relations, operating on nouns yields a measurable/observable (Hermitian matrix), which in turn limits other potential combinations with abstract lexical categories. (...) Functional/grammatical categories in the system deploy the same features, albeit organized differently in the matrix diagonal and off-diagonal. The algebraic result is a group with well-defined mathematical properties, which properly includes the Pauli group of standard use in quantum computation. In the system, the presumed difference between categories and interactions—here, in a context of the head-complement sort—reduces to whether the magnitude of the matrix eigenvalue is 1 or not, in the latter instance inducing asymmetric interactions. (shrink)

We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by Baldwin–Eklof–Trlifaj are stable (...) and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický. (shrink)

I defend a one category ontology: an ontology that denies that we need more than one fundamental category to support the ontological structure of the world. Categorical fundamentality is understood in terms of the metaphysically prior, as that in which everything else in the world consists. One category ontologies are deeply appealing, because their ontological simplicity gives them an unmatched elegance and spareness. I’m a fan of a one category ontology that collapses the distinction between particular (...) and property, replacing it with a single fundamental category of intrinsic characters or qualities. We may describe the qualities as qualitative charactersor as modes, perhaps on the model of Aristotelian qualitative (nonsubstantial) kinds, and I will use the term “properties” interchangeably with “qualities”. The qualities are repeatable and reasonably sparse, although, as I discuss in section 2.6, there are empirical reasons that may suggest, depending on one’s preferred fundamental physical theory, that they include irreducibly intensive qualities. There are no uninstantiated qualities. I also assume that the fundamental qualitative natures are intrinsic, although physics may ultimately suggest that some of them are extrinsic. On my view, matter, concrete objects, abstract objects, and perhaps even spacetime are constructed from mereological fusions of qualities, so the world is simply a vast mixture of qualities, including polyadic properties (i.e., relations). This means that everything there is, including concrete objects like persons or stars, is a quality, a qualitative fusion, or a portion of the extended qualitative fusion that is the worldwhole. I call my view mereological bundle theory. (shrink)

Two experiments show that action alters the shape categories formed by 2-year-olds. Experiment 1 shows that moving an object horizontally (or vertically) defines the horizontal (or vertical) axis as the main axis of elongation and systematically changes the range of shapes seen as similar. Experiment 2 shows that moving an object symmetrically (or asymmetrically) also alters shape categories. Previous work has shown marked developmental changes in object recognition between 1 and 3 years of age. These results suggest a role for (...) action in this developmental process. (shrink)

This chapter contains sections titled: Preliminaries 1 The Highly Problematic Status of the Category of Substance 2 A New Approach: Prime State of Affairs (“Pristate”) as the Only Ontological Category at the Fundamental Level 3 Concluding Remarks.

In this essay, I challenge Charles Mills’s use of the category of moral personhood for advancing a robust anti-racist political critique in nonideal circumstances. I argue that the idea of the moral equality of persons is necessary but insufficient for reparative justice. I enrich the normative basis of political critique to include: (1) a clarification of what the public recognition of moral personhood can legitimately entail as a requirement of justice enforceable by the state, especially with respect to economic (...) reforms that advance equal opportunity and (2) a conception of non-alienated labor that assails identity-based occupational segregation in the labor market. These additional components do not exhaust the plausible bases for political critique, but enrich it in a way that the idea of moral equality alone cannot. (shrink)

Cet article examine la doctrine des catégories développée par Emil Lask (1875-1915) au début du xx e siècle (1911). Son objectif est double. 1) Nous entendons proposer une étude historique précise de cette doctrine relativement méconnue qui présente une synthèse inédite entre l’objectivisme sémantique de Bolzano, la théorie des valeurs de l’école de Bade et le formalisme husserlien, dans le contexte de l’héritage de la révolution copernicienne kantienne. Nous montrons que cette doctrine présente un caractère radical en ceci qu’elle considère (...) que la philosophie est eo ipso une doctrine des catégories. 2) Le deuxième objectif de cette étude, plus critique, est d’évaluer la pertinence de la lecture herméneutique, d’inspiration heideggérienne, qui en est souvent proposée. S’il est indéniable que la doctrine de Lask exerça une réelle influence sur la phénoménologie herméneutique du jeune Heidegger, nous entendons également montrer que les intuitions originales de Lask sur la résistance du matériau sont irréconciliables avec toute forme d’herméneutique. (shrink)

El objetivo de este trabajo es dar una mirada a la manera en que Roig opera en los ámbitos categoriales. Nuestro propósito es observar cómo el autor critica, confecciona, articula, utiliza, crea y entrelaza categorías, es decir, hemos querido hacer un alto en los procedimientos estructurales de su filosofar, en sus operaciones. Sostenemos como hipótesis que el rearme categorial al que Roig apela en múltiples pasajes de su obra implica, como operación de base, un cambio en el reconocimiento del lugar (...) de enunciación, y que éste se juega en parte importante en el empadronamiento de las categorías. Distinguimos al menos cinco operaciones categoriales en su trabajo reflexivo, las cuales pueden rastrearse a lo largo de toda su obra: (1) rescate, (2) crítica (3) reemplazo, (4) reelaboración e (5) invención. The aim of this work is to give a glance to the way in which Roig operates at categorical levels. Our intention is to observe how the author criticizes, makes, articulates, uses, creates and interlaces categories, that is to say, we wanted to take a break in the structural procedures of his philosophising, in his processes. We support as hypothesis that the categorical rearmament to that Roig appeals in multiple passages of his work involves, as a base operation, a change in the recognition of the place of enunciation, and that it plays an important part in the registration of the categories. We distinguish at least five categorical operations in his reflective work, which can be traced back throughout all his work: (1) rescue, (2) critique, (3) replacement, (4) re-elaboration and (5) invention. (shrink)

Theories of relational concept acquisition based on structured intersection discovery predict that relational concepts with a probabilistic structure ought to be extremely difficult to learn. We report four experiments testing this prediction by investigating conditions hypothesized to facilitate the learning of such categories. Experiment 1 showed that changing the task from a category-learning task to choosing the “winning” object in each stimulus greatly facilitated participants' ability to learn probabilistic relational categories. Experiments 2 and 3 further investigated the mechanisms underlying (...) this “who's winning” effect. Experiment 4 replicated and generalized the “who's winning” effect with more natural stimuli. Together, our findings suggest that people learn relational concepts by a process of intersection discovery akin to schema induction, and that any task that encourages people to discover a higher order relation that remains invariant over members of a category will facilitate the learning of putatively probabilistic relational concepts. (shrink)

『논리연구』에서 후설이 탐구하는 범주적 직관은 단순히 감성적인 방식으로 이루어지지 않는 직관이다. 그리고 거기에서 등장하는 범주적 재현(Repräsentation) 이론은 범주적 직관이 재현이라는 이론이다. 『논리연구』에서 ‘재현’과 ‘파악(Auffassung)’은 외연이 같은 말이므로, 범주적 재현 이론은 범주적 직관이 파악이라는 이론이 된다. 그런데 20여년 후????논리연구????제2판 제2분책 서문에서 후설은 범주적 재현 이론을 더 이상 인정하지 않는다고 말한다. 하지만 후설이 실제로 이 이론을 포기하는가 하는 점은 논란의 여지가 있다. 나는 후설이 이 이론을 포기하지 않거나, 적어도 포기해서는 안 된다고 주장한다. 범주적 재현 이론은 『경험과 판단』 같은 후기의 저작에서도 채택되는 것처럼 (...) 보이며, 무엇보다도 범주적 직관을 이해하기 위하여 필수적이기 때문이다. 이 논문에서 나는 범주적 직관과 범주적 재현 이론을 자세하게 설명한 후, 범주적 재현 이론이 포기되거나 수정될 필요가 있다고 주장하는 투겐트하트(E. Tugendhat)와 로마(D. Lohmar)의 견해를 각각 비판한다. 이와 더불어 명확해지는 것은, 범주적 재현 이론을 통해 이해된 범주적 직관 개념이 선술어적 경험으로부터 술어적 인식의 발생을 규명하는 데 결정적인 역할을 한다는 점이다. (shrink)

Ontology – the study of the most fundamental categories of being – lies at the very heart of metaphysics. The reason why it appears to be so central is because it takes on the following questions: What sorts of entities are there? What features do those entities have? How do they relate to one another? And so on. Section 1 of this Element presents a fast-paced historical overview of some of the notable approaches to these questions. Section 2 tells the (...) story of how one of the oldest, most disputed, but also most developed ontological categories – universals – got introduced. Section 3 builds on the discussion of universals as it considers the desiderata for a promising system of ontological categories. And Section 4 looks at ways in which philosophers might break with tradition and explore some new ontological categories. (shrink)

In this essay we introduce a new tool for studying the patterns of sentential reference within the framework introduced in [2] and known as the language of paradox $\mathcal {L}_{\mathsf {P}}$ : strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms. In particular, we show that (i) strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms between $\mathcal {L}_{\mathsf {P}}$ constructions preserve paradoxicality, (ii) many (but not all) earlier results regarding the paradoxicality of $\mathcal {L}_{\mathsf {P}}$ constructions can be recast as special cases of our central result regarding (...) strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms, and (iii) that we can use strong $\mathcal {L}_{\mathsf { P}}$ -homomorphisms to provide a simple demonstration of the paradoxical nature of a well-known paradox that has not received much attention in this context: the McGee paradox. In addition, along the way we will highlight how strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms highlight novel connections between the graph-theoretic analyses of paradoxes mobilized in the $\mathcal {L}_{\mathsf {P}}$ framework and the methods and tools of category theory. (shrink)

We examined 11-month-olds’ tendency to generalize properties to category members, an ability that may contribute to the inductive reasoning abilities observed in later developmental periods. Across 3 experiments, we tested 11-month-olds’ (N= 113) generalization of properties within the cat and dog categories. In each experiment, infants were familiarized to animal-sound pairings (i.e., dog-barking; cat-meowing), and tested on this association and the generalization of the sound property to new members of the familiarized categories. After familiarization with a single exemplar, 11-month-olds (...) generalized the sound to new category members that were both highly similar and less similar to the familiarized animal (Expt. 1). When familiarized with mismatched animal-sound pairings (Expt. 2; i.e., dog-meowing; cat-barking), 11-month-olds did not learn or generalize the sound properties, suggesting that infants have pre-existing expectations about the links between the characteristic sound properties and the animal categories. When familiarized with unfamiliar sound-animal pairings (Expt. 3; i.e., dog-unfamiliar sound), 11-month-olds linked the animals with the novel sounds but did not generalize to new category members. Taken together, these findings highlight the conditions under which young infants generalize properties from one exemplar to other category members. (shrink)

ABSTRACT: A general interpretation and close textual analysis of Kant’s theory of the categories of freedom (or categories of practical reason) in his Critique of Practical Reason. My main concerns in the paper are the following: (1) I show that Kant’s categories of freedom have primarily three functions: as conditions of the possibility for actions (i) to be free, (ii) to be comprehensible as free and (iii) to be morally evaluated. (2) I show that for Kant actions, although qua theoretical (...) objects they are always already constituted by means of the theoretical categories, qua practical objects (objects of reason in its practical use, i.e. objects qua possibly good or bad) they are constituted by means of the categories of freedom; and that it is only in this way that actions, qua phenomena, can be a consequence of freedom, and can be understood and evaluated as such. (3) Since Kant's presentation of his theory of the Categories of Freedom is extremely brief, Kant's parallel theory of the theoretical categories in his Critique of Pure Reason is used as a guide for the interpretation of the practical categories and their systematic relevance. (Translation by Alex Worsnip, reviewed and approved by the author.). (shrink)

(2001). Fruits, Apples, and Category Mistakes: On Sport, Games, and Play. Journal of the Philosophy of Sport: Vol. 28, No. 2, pp. 151-159. doi: 10.1080/00948705.2001.9714610.

Stimuli that resemble humans, but are not perfectly human-like, are disliked compared to distinctly human and nonhuman stimuli. Accounts of this “Uncanny Valley” effect often focus on how changes in human resemblance can evoke different emotional responses. We present an alternate account based on the novel hypothesis that the Uncanny Valley is not directly related to ‘human-likeness’ per se, but instead reflects a more general form of stimulus devaluation that occurs when inhibition is triggered to resolve conflict between competing stimulus-related (...) representations. We consider existing support for this inhibitory-devaluation hypothesis and further assess its feasibility through tests of two corresponding predictions that arise from the link between conflict-resolving inhibition and aversive response: 1) that the pronounced disliking of Uncanny-type stimuli will occur for any image that strongly activates multiple competing stimulus representations, even in the absence of any human-likeness, and 2) that the negative peak of an ‘Uncanny Valley’ should occur at the point of greatest stimulus-related conflict and not (in the presence of human-likeness) always closer to the ‘human’ end of a perceptual continuum. We measured affective responses to a set of line drawings representing nonhuman animal-animal morphs, in which each continuum midpoint was a bistable image (Exp. 1), as well as to sets of human-robot and human-animal computer-generated morphs (Exp. 2). Affective trends depicting classic Uncanny Valley functions occurred for all continua, including the nonhuman stimuli. Images at continua midpoints elicited significantly more negative affect than images at endpoints, even when the continua included a human endpoint. This illustrates the feasibility of the inhibitory-devaluation hypothesis and the need for further research into the possibility that the strong dislike of Uncanny-type stimuli reflects the negative affective consequences of cognitive inhibition. (shrink)

The present research examines whether individuation and categorization processes influence trust decisions about strangers at first and across repeated interactions. In a partial replication of the study reported by Cañadas et al. (2015), participants played an adaptation of the multi-round trust game paradigm and had to decide whether or not to cooperate with unknown partners. Gender (Study 1a) and ethnicity (Studies 1b, 2, and 3) served to create distinct social categories among the game partners, whose reciprocation rates were manipulated at (...) group and individual levels. At the group level, two social groups (i.e., ingroup vs. outgroup) were associated with opposite reciprocation rates (i.e., high vs. low reciprocation rate). At the individual level, consistency was manipulated by altering the reciprocation rate of one out of four members of each social group. That is, there was one inconsistent individual in each group showing a pattern of reciprocation opposite to the group reciprocation rate. Our data, contrary to Cañadas et al.’s (2015) findings, suggested that ingroup partners were individuated given that participants made their decisions to cooperate with the trustees according to their individual reciprocation rate and independently of the group reciprocation rate. In contrast, decisions about outgroup partners (i.e., men in Study 1a and Blacks in Studies 1b, 2, and 3) were affected by category-based thinking. At the same time, in comparison with ingroup, greater cooperation was observed with ethnic outgroups but not with gender outgroups. The consistency of our results with the previous literature on social categorization and across the three experiments seems to indicate they are reliable, supporting the hypothesis that categorization and individuation processes guide trust decision-making, promoting individuation mainly for ingroup and categorization among outgroup members. (shrink)

Phillip R. Sloan - Performing the Categories: Eighteenth-Century Generation Theory and the Biological Roots of Kant's A Priori - Journal of the History of Philosophy 40:2 Journal of the History of Philosophy 40.2 229-253 Preforming the Categories: Eighteenth-Century Generation Theory and the Biological Roots of Kant's A Priori Phillip R. Sloan Situating Kant's philosophical project in relation to the natural sciences of his day has been of concern to several scholars from both the history of science and the history of (...) philosophy. Historians of philosophy have displayed an expanded awareness of, and interest in, the importance of the scientific context of the period in which Kant carried out his "Copernican" revolution. Most commonly among philosophers, this interest has been analyzed in relation to Kant's concerns with the foundations of mechanics, matter theory, and the epistemology of Newtonian science, with the central text of interest being the Metaphysische Anfangsgründe. On the other hand, historians of philosophy and historians of science, interested in the issues of the third Critique and in the several papers of Kant dealing with biological and anthropological issues, have emphasized the unified nature of Kant's inquiries into the natural sciences, and the importance of his continued interest in the life and human sciences alongside his interests in the foundations of the physical sciences. The effort to understand the unity of Kant's.. (shrink)

Explicit concepts and sufficiently precise definitions are the basis for further advance of a science beyond a given level. To move toward a situation where the whole population has access to the authentic results of science (italics mine) requires making explicit some general philosophical principles which can help to guide the learning, development, and use of mathematics, a science which clearly plays a pivotal role regarding the learning, development and use of all the sciences. Such philosophical principles have not come (...) from speculation but from studying and concentrating the development of actual mathematical subjects such as algebraic geometry, functional analysis, continuum mechanics, combinatorics, etc. The simplifications in the conceptual relations revealed by such philosophical/mathematical advances are of great value, not only in: (1) clarifying and guiding further research in the mathematical sciences, but also in (2) reforming pedagogy and popularization in ways that will not prove deceptive. (shrink)

The origin of colour categories and their relationship to colour perception have been the prime example for testing the influence of language on perception and thought and more generally for investigating the biological, ecological and cultural determination of human cognition. These themes are central to a broad range of disciplines, including vision research, neuroscience, cognitive psychology, developmental science, cultural anthropology, linguistics, computer science, and philosophy. Unfortunately, though, it has been tacitly taken for granted that the conceptual assumptions and methodological practices (...) from the dawn of empirical research on colour categorisation are the gold standard for current colour category research. Here, we show that these assumptions and practices are obsolete and flawed and have led to four fundamental and widespread misconceptions about colour categorisation: 1.) that colour perception is inherently categorical; 2.) that English Basic Colour Terms correspond to universal categories that are the end point of a fixed evolutionary sequence; 3.) that the prototypes of English basic colour terms are perceptually salient and qualify as focal colours; and 4.) that colour category research essentially revolves around the universalism-realism debate. State-of-the-art research on colour categorisation provides new, more sophisticated approaches and allows for rectifying those four statements. At the same time, some of the questions underlying those statements are not convincingly answered yet and constitute major challenges to future research. The critical considerations on colour categorisation may be transferred to research on other kinds of perceptual categorisation to inspire new, more general research questions. (shrink)

Cognitive Science, Volume 46, Issue 2, February 2022.

There is increasing interest in artifacts among philosophers. The leading edge is the metaphysics of artifacts and artifact kinds. However, an important question has been neglected. What is the ontological status of the category ‘artifact’ itself? Dan Sperber (2007) argues against its theoretical integrity for the purposes of naturalistic social sciences. In Section 2, I lay out Sperber’s argument, which is based on the observed continuum between natural objects and artifacts. I also review the implicit support for this continuum (...) argument in the philosophical literature on artifacts. In Section 3, I diagnose the fatal weakness affecting continuum-based arguments about categories. They fail to take into account recent thinking about classification in philosophy of science, which has been forced to accommodate continua in biology. In Section 4, I focus specifically on the species problem in philosophy of biology, and on pluralism about species concepts as a response to it. I then identify an analogous artifact problem, and argue that pluralism about artifact concepts is an appropriate and defensible response here as well. Finally, in Section 5, I show that just as species pluralism leads to skepticism about the species category, so artifact pluralism leads to skepticism about the artifact category. I thus arrive at Sperber’s conclusion by an alternate route that does not run afoul of the weakness affecting continuum-based arguments about categories. (shrink)

Higher types can readily be added to set theory, Bernays-Morse set theory being an example. A type for each ordinal is added in [2]. Adding higher types to set theory provides a neat solution to the problem of how to handle higher type categories. We give the basic definitions, and prove cocompleteness of some higher type categories. MSC: 14A15.

Grammatical categories of English expressions are shown to differ with regard to the freedom we have in semantically interpreting their lexical (= syntactically simplest) expressions. Section 1 reviews the categories of expression we consider. Section 2 empirically supports that certain of these categories are lexically free, a notion we formally define, in the sense that anything which is denotable by a complex expression in the category is available as a denotation for lexical expressions in the category. Other categories (...) are shown to be not lexically free. Thus for those categories the interpretation of lexical expressions is inherently constrained compared to the interpretation of the full class of expressions in the category. (shrink)

We conducted three studies aimed at showing that one-to-one translations between emotion terms might be comparing independent or barely overlapping categories of emotional experience. In Study 1 we found that the speakers' most accessible features of two supposedly equivalent emotions terms (shame and vergüenza) were very different. In Study 2, American and Spanish speakers' typicality ratings of 25 out of 29 constitutive features of “shame” or “vergüenza” were significantly different. In Study 3, these important differences in the content and internal (...) structure of “shame” and “vergüenza” were also reflected in the affective meaning of their corresponding terms. We conclude that “shame” and “vergüenza” do not share the same cluster of central features, and cannot be treated as identical categories of emotional experience. This finding raises serious questions about the one-to-one translation practices not only of most cross-cultural studies on “shame”, but also of other emotion concepts. We suggest an alternative method of translation based on Diachronic Prototype Semantics (Geeraerts, 1997). (shrink)

The present article discusses the measurement of social class in the social psychology of education research. It was evident that social class experiences are conflated with the socioeconomic status indicators and the subjective measure of the class context was underrepresented. However, this was discussed in Rubin et al about the intersectional nature of social class taking into account both objective and subjective indicators. The derivation of the social class experience from the objective and subjective measures were critically discussed. An effort (...) was made to understand whether these translations are category mistake or not. Three trajectories will be utilized to address the category mistake, that is, 1) subjectivity and objectivity debate in the measurement of social class in social psychology of education, 2) debates encircling around the position of social psychology and its underutilized concept such as social class as scientifically objective facets in social sciences and 3) operationalism of social class and category mistake. (shrink)

[1]. Recently renewed interest in non transformational approaches to syntax [2] suggests that it might be well to take another look at categorial grammars, since they seem to have been neglected largely because they had been shown to be equivalent to context free phrase structure grammars in weak generative capacity and it was believed that such grammars were incapable of describing natural languages in a natural way. It is my purpose here to sketch a theory of grammar which represents a (...) generalization of categorial grammars of the sort invented by Ajdukiewicz (1935) and further elaborated especially by Bar Hillel (1953) and Lambek (1961). (shrink)

We study definable irreducible actions of SL₂(K) on an abelian group of Morley rank ≤ 3rk(K) and prove they are rational representations of the group.

ABSTRACTWe examined whether enhancing the emotionality of a referent public good influences the subsequent valuation of a target public good. We predicted that it would and that the directionality of its impact would depend on a fundamental cognitive process – categorisation. If the target and referent goods belong to the same domain, we expected that the effect on the target would be in the same direction as the emotional enhancement of the referent. However, if the target and referent goods belong (...) to different domains, we expected that the effect on the target would be either negligible or in the opposite direction to that of the emotional enhancement of the referent. In Experiment 1 we examined the impact of emotionally enhancing a referent public good on feelings towards a target public good, whereas in Experiment 2 on the willingness to contribute towards a target public good. The results support the predicted interaction, which was... (shrink)

Discontinuity refers to the character of many natural language constructions wherein signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms which aspire to descriptive adequacy. Pied piping, in particular, is argued by Pollard (1988) to motivate phrase structure-style feature percolation. In the context of categorial grammar, Bach (1981, 1984), Moortgat (1988, 1990, 1991) and others have sought to provide categorial operators suited to discontinuity. These attempts encounter certain difficulties with respect (...) to model theory and/or proof theory, difficulties which the current proposals are intended to resolve.Lambek calculus is complete for interpretation byresiduation with respect to the adjunction operation of groupoid algebras (Buszkowski 1986). In Moortgat and Morrill (1991) it is shown how to give calculi for families of categorial operators, each defined by residuation with respect to an operation of prosodic adjunction (associative, non-associative, or with interactive axioms). The present paper treats discontinuity in this way, by residuation with respect to three adjunctions: + (associative), (.,.) (split-point marking), andW (wrapping) related by the equations 1+s 2+s 3=(s 1,s 3)Ws 2. We show how the resulting methods apply to discontinuous functors, quantifier scope and quantifier scope ambiguity, pied piping, and subject and object antecedent reflexivisation. (shrink)