Samuel Alexander was one of the first realists of the twentieth century to defend a theory of categories. He thought that the categories are genuinely real and grounded in the intrinsic nature of Space-Time. I present his reduction of the categories in terms of Space-Time, articulate his account of categorial structure and completeness, and offer an interpretation of what he thought the nature of the categories really were. I then argue that his theory of (...) categories has some advantages over competing theories of his day, and finally draw some important lessons that we can learn from his realist yet reductionist theory of categories. (shrink)

In this article, the authors try to answer the following questions: How can an object/instance seen for the first time extend a category or update a concept? How is it possible to determine the reference of a concept that represents a behaviour? In the first case, the authors discuss the learning of inferential linguistic competence used to update a concept through an approach based on prototype theory. In the second case, the authors discuss the learning of referential linguistic competence (...) used to determine the reference of a concept (i.e., determination of an actual behaviour) through an approach based on embodied cognition. The authors show how combining prototype-based and embodied categorization in Wittgenstein’s rule-following praxis (the individual and community dimension), linguistic learning of a concept (inferential competence), and determination of its reference (referential competence) can be traced back to the same model. Keywords Action, Categorization, Embodied Cognition, Embodiment, Linguistic Inferential Competence, Linguistic Referential Competence, Perception, Prototype Theory, Reference, Sign. (shrink)

It is widely acknowledged that categories play significant roles in the appreciation of artworks. This paper argues that the correct categories of artworks are institutionally established through social processes. Section 1 examines the candidates for determining correct categories and proposes that this question should shift the focus from category membership to appreciative behaviour associated with categories. Section 2 draws on Francesco Guala’s theory of institutions to show that categories of artworks are established as rules-in-equilibrium. (...) Section 3 reviews the explanatory benefits of this institutional theory of the correct category. [Winner of the 2022 Debates in Aesthetics Essay Prize]. (shrink)

This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus that the (...) paradoxes arose from having one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or always the other). (shrink)

This essay critically examines some classic philosophical and legal theories of privacy, organized into four categories: the nonintrusion, seclusion, limitation, and control theories of privacy. Although each theory includes one or more important insights regarding the concept of privacy, I argue that each falls short of providing an adequate account of privacy. I then examine and defend a theory of privacy that incorporates elements of the classic theories into one unified theory: the Restricted Access/Limited Control (RALC) (...) theory of privacy. Using an example involving data-mining technology on the Internet, I show how RALC can help us to frame an online privacy policy that is sufficiently comprehensive in scope to address a wide range of privacy concerns that arise in connection with computers and information technology. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical (...) theory of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

This paper seeks to resolve a fairly simple question in ethics: Why do seemingly reasonable people disagree about ethical problems? My paper seeks both to analyze this question and attempts to find a solution. My premise is that disagreement happens because of differences in hierarchical value ranking, or quite simply because some problems are more important to some people than others. Theories of choice, however, influenced by concepts such as "freedom of choice," conceal the hierarchical nature of our choices, leading (...) to confusion over the nature and degree of our ethical disagreements. I propose then that ethical disagreements can be reduced when we understand hierarchy as an essential element in moral choice theory. (shrink)

This paper argues that we should replace the common classification of theories of welfare into the categories of hedonism, desire theories, and objective list theories. The tripartite classification is objectionable because it is unduly narrow and it is confusing: it excludes theories of welfare that are worthy of discussion, and it obscures important distinctions. In its place, the paper proposes two independent classifications corresponding to a distinction emphasised by Roger Crisp: a four-category classification of enumerative theories (about which items (...) constitute welfare), and a four-category classification of explanatory theories (about why these items constitute welfare). (shrink)

One of the central problems in the philosophy of action is to spell out the distinction between action and what merely happens, e.g., a wink versus an eye twitch. This essay proposes a theory of action offering an account of this distinction. The central claim of the theory is that action is movement that is controlled by the mover, where movement is understood capaciously and control is characterized by a trio of conditions consisting of an aim condition, a (...) modal condition, and an explanatory condition. Importantly, being controlled is shown to be a determinable property of movements, and its determination dimensions are isolated. Paired with the claim that action is movement that is controlled by the mover, this account of control as a determinable illuminates the diversity within the category of action. (shrink)

In this chapter, I consider contemporary consequentialist theories of punishment. Consequentialist theories of punishment look to the consequences of punishment to justify the institution of punishment. Two types of theories fall into this category—teleology and aggregationism. I argue that teleology is implausible as it is based on a problematic assumption about the fundamental value of criminal punishment, and that aggregationism provides a more reasonable alternative. Aggregationism holds that punishment is morally justified because it is an institution that helps society to (...) aggregate important moral values. Several theories fall into this category, including general deterrence theories, specific deterrence theories, and preventionism. I critically evaluate these theories and argue that only one specific deterrence theory, namely, my rights-protection theory, provides the most reasonable consequentialist account of punishment. (shrink)

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into (...) 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory. (shrink)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the claim (...) that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Despite widespread recognition of an emergent politics of data in our midst, we strikingly lack a political theory of data. We readily acknowledge the presence of data across our political lives, but we often do not know how to conceptualize the politics of all those data points—the forms of power they constitute and the kinds of political subjects they implicate. Recent work in numerous academic disciplines is evidence of the first steps toward a political theory of data. This (...) article maps some limits of this emergent literature with an eye to enriching its theoretical range. The literature on data politics, both within political theory and elsewhere, has thus far focused almost exclusively on the algorithm. This article locates a further dimension of data politics in the work of formatting technology or, more simply, formats. Formats are simultaneously conceptual and technical in the ways they define what can even count as data, and by extension who can count as data and how they can count. A focus on formats is of theoretical value because it provides a bridge between work on the conceptual contours of categories and the technology-centric literature on algorithms that tends to ignore the more conceptual dimensions of data technology. The political insight enabled by format theory is shown in the context of an extended interrogation of the politics of racialized redlining. (shrink)

Politicians select their words meticulously, never losing sight of their ultimate communicative goal. Sometimes, their objective may be that of not being fully understood by a large portion of the audience. They can achieve this by means of dogwhistles; linguistic expressions that, in addition to their literal meaning, convey a concealed message to a specific sub-group of the audience. This paper focuses on the distinction between overt and covert dogwhistles introduced by J. Saul (2018). I argue that, even if the (...) distinction successfully captures a genuine divide within the category of dogwhistles, the account proposed by Saul to explain the distinction is unsatisfactory. In response to this state of affairs, I illustrate how the distinction between overt and covert dogwhistle can be refined and illuminated by incorporating it into the 'Simple Theory' of dogwhistles advanced by J. Khoo (2017). (shrink)

Plato’s Theory of Perception This research deals with Plato's perceptual theory, as the perceptual theory in Plato's philosophy represents one of the steps of the Plato’s epistemology. Plato divided knowledge into four categories: Sensory knowledge, presumptive knowledge, mathematical knowledge, and rational knowledge. The theory of sensory perception is in the first place, so this research focuses on the statements, the meaning of perception, the senses, the difference between sensation and mind, the topics of sensory perception, (...) and the nature of the work of sensory perception. (shrink)

The article develops a correctness theory of truth (CTT) for semantic information. After the introduction, in section two, semantic information is shown to be translatable into propositional semantic information (i). In section three, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in section four, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + (...) A]. This completes the reduction of the truth of i to the correctness of A. In sections five and six, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates (in a Fregean sense) Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. The last section draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. (shrink)

I investigate why Frege rejected the theory of types, as Russell presented it to him in their correspondence. Frege claims that it commits one to violations of the law of excluded middle, but this complaint seems to rest on a dogmatic refusal to take Russell’s proposal seriously on its own terms. What is at stake is not so much the truth of a law of logic, but the structure of the hierarchy of the logical categories, something Frege seems (...) to neglect. To come to a better understanding of Frege’s response, I proceed to investigate his conception of the nature of the logical categories, and how it differs from Russell’s. I argue that, for Frege, our grasp of the logical categories cannot be severed from our grasp of the Begriffsschrift notation itself. Russell, on the other hand, attaches no such importance to notation. From Frege’s point of view, Russell has not succeeded in presenting an alternative conception of the logical hierarchy, since such a conception must go in tandem with the development of a notation. Moreover, Frege has good reasons to think that Russell’s proposal does not admit of a suitable notation. (shrink)

The paper seeks to develop an account of indexical phenomena based on the highly general theory of structure and dependence set forth by Husserl in his Logical Investigations. Husserl here defends an Aristotelian theory of meaning, viewing meanings as species or universals having as their instances certain sorts of concrete meaning acts. Indexical phenomena are seen to involve the combination of such acts of meaning with acts of perception, a thesis here developed in some detail and contrasted with (...) accounts of indexicals suggested by Frege, Wittgenstein and by the later Husserl himself in his Ideas I. Implications are drawn also for our understanding of the categorial grammar sketched by Husserl in his 4th Logical Investigation, as also for our understanding of the nature of proper names and other candidate indexical expressions. (shrink)

ABSTRACT: I argue that Sellars’s metaconceptual theory of the categories exemplifies and extends a long line of nominalistic thinking about the nature of the categories from Ockham and Kant to the Tractatus and Carnap, and that this theory is far more central than has generally been realized to each of Sellars’s most famous and enduring philosophical conceptions: the myth of the given, the logical space of reasons, and resolving the ostensible clash between the manifest and scientific (...) images of the human being in the world. Sellars’s distinctive contribution to this longstanding (if currently on the defensive) metaconceptual approach to the nature of ontological categories was to interpret and reconstruct it in terms of his own ‘meaning as use’ or norm-governed inferential role semantics. With these resources Sellars sought to preserve the genuine insights in the ‘realist’ or broadly platonic traditions while simultaneously defending the idea that in the end, as he puts it, “a naturalistic ontology must be a nominalistic ontology” (1980a NAO IV §129). (shrink)

Motivated by Scholze and Fargues' geometrization of the local Langlands correspondence using perfectoid diamonds and Clausen and Scholze's work on the K-theory of adic spaces using condensed mathematics, we introduce the Efimov K-theory of diamonds. We propose a pro-diamond, a large stable (infinity,1)-category of diamonds D^{diamond}, diamond spectra and chromatic tower, and a localization sequence for diamond spectra.

In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness (“n-awareness”). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the (...) mathematical formalism of higher category theory. The beauty of higher category theory lies in its universality. Pluralism is categorical. In particular, we model awareness using the theories of derived categories and (infinity, 1)-topoi which will give rise to our meta-language. We then posit a “grammar” (“n-declension”) which could express n-awareness, accompanied by a new temporal ontology (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? Another question which could be re-conceptualized in our model is one of soteriology related to this pluralism: what is a self in this context? A new model of “personal identity over time” is thus introduced. (shrink)

This note is based on a lecture delivered at the Conference on the Scien- tic Research of the Mathematical Center of Opole, Turawa, May 10-11th, 1980. A somewhat extended version will be published in the Proceedings of the Conference. At the same time it is an abstract of a part of a planned larger paper, which will involve the theory of label-tokens. The theory is included into the author's monograph in Polish "Teorie Językow Syntaktycznie Kategorialnych", PWN, Warszawa-Wrocław 1985 (...) and into its English version: Theory of Language Syntax. Categorial Approach, Kluwer Academic Publishers, Boston-London-Dordrecht 1991. (shrink)

The core idea of A Relational Theory of Justice is that normative political and legal philosophy should be grounded on people’s relational features, in particular their ability to commune with others and be communed with by them. Usually, philosophers of justice in the West have based their views on people’s intrinsic features, ones that make no essential reference to others, such as their autonomy, self-ownership, or well-being. In addition, often critics of basing politics and law on justice, whether in (...) the African, feminist/care, Marxian, or Confucian traditions, have appealed to non-intrinsic values as leverage, roughly contending that relationships are more important than justice. In contrast to both major camps, this book articulates and defends accounts of justice based on the dignity of people’s relational nature. A proper valuation of people’s capacity to be party to communal relationships does not transcend categories of justice, but instead calls for certain sorts that differ in plausible ways from those grounded on intrinsic properties. Applications are discussed in the contexts of political, economic, compensatory, criminal, transitional, and global justice. Available for download is the Table of Contents. (shrink)

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (shrink)

The Research Domani Criteria framework (RdoC) encourages research on specific impairments present across traditional nosological categories and suggests a list of biological and behavioral measures for assessing them. After a description of RdoC, in this article we focus on impairments of the ability of understanding others, specifically in Theory of Mind and empathy. We illustrate recent evidence on brain anomalies correlating with these deficits in Schizophrenia, Addiction Disorders and Mood Disorders populations. In the last section, we zoom out (...) and consider this kind of research vis-à-vis the objection of being reductionistic that is, in favoring mechanistic accounts of mental disorders. We argue that metaphysical reductionism and explanatory reductionism are not conceptually entailed by the RdoC framework. (shrink)

Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing (...) class='Hi'>categories, and it is explicitly shown with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory. (shrink)

Aristotle classifies opposition (ἀντικεῖσθαι) into four groups: relatives (τὰ πρός τι), contraries (τὰ ἐναντία), privation and possession (στρέσις καὶ ἓξις) and affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) His example of relatives are the double and the half. Aristotle’s description of relatives as a kind of opposition is as such: ‘Things opposed as relatives are called just what they are, of their opposites (αὐτὰ ἃπερ ἐστι τῶν ἀντικειμένων λέγεται) or in some other way in relation to them. (...) For example, the double is called just what it is double of the other (οἷον τὸ διπλάσιον, αὐτὸ ὃπερ ἐστίν, ἑτέρου διπλάσιον λέγεται). Again, knowledge and the knowable are opposed as relatives, and knowledge is called just what it is, of the knowable, and the knowable too is called just what it is, in relation to its opposite, knowledge; for the knowable is called knowable by something-by knowledge.’ (Cat., 10, 11b24-30) 2) Senses of relatives In Met., Δ, 1020b26-32 Aristotle distinguishes three senses of relatives: i) That which contains something else many times to that which is contained many times in something else, and that which exceeds to that which is exceeded. E.g. double to half ii) The active to the passive; e.g. that which can heat to that which can be heated iii) The measurable to the measure, e.g. the knowable to knowledge and the perceptible to perception. 3) Relatives and contraries Aristotle’s discussion of relatives is unbelievably ambiguous. While he enumerates relatives besides contraries, privation-possession and affirmation-negation as four types of opposition (Cat., 10, 11b15-23), not only does not he restrict relatives to oppositions but he also does not totally differentiate it from contraries. Aristotle distinguishes between two senses of relatives one of which is contraries: ‘We have distinguished elsewhere the two senses in which relatives are so called-some as contraries (ὡς ἐναντία), others as knowledge to things known, a term being called relative because what is said one to the other is said by the other to itself (τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό). (Met., I, 1056b34-1057a1) It seems that this differentiation is the same as, and maybe the one he himself refers to, the differentiation between the second and the third senses of relatives in Met., Δ, 1021a27-32: ‘Relative terms which imply number or capacity, therefore, are all relative because their very essence includes in its nature a reference to something else, not because something else is related to it (πρός τι πὰντα ἐστὶ πρός τι τῷ ὃπερ ἐστὶν ἄλλου λέγεσθαι αὐτὸ ὃ ἐστιν, ἀλλὰ μὴ τῷ ἄλλο πρὸς ἐκεινο); but that which is measurable or knowable or thinkable is called relative because something else is related to it. For the thinkable implies that there is thought of it, but the thought is not relative to that of which it is the thought; for we should then have said the same thing twice.’ Although Aristotle confirms contrariety in relatives (e.g. virtue to vice and knowledge to ignorance), he denies that there is a contrary ‘to every relative’ as there can be no contrary to what is double or treble. (Cat., 7, 6b15-19) The fact that Aristotle dedicates one sense of relatives to contraries means that the fourfold division of oppositions is not such a strict division without any kind of community between them. In his example of the first sense, however, Aristotle says: ‘One and number are in a sense opposed, not as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the other measurable, they are opposed.’ (Met., I, 1057a4-6) Now, the question is: Is Aristotle’s first sense of relative a contrary or not? Aristotle tells us that the opposition in this sense of relatives is the opposition of measure and measurable. The second sense has two differences with the first one: i) it is not a contrary and ii) what is said by one of the relatives to the other is also said by the latter to the former. To differentiate it from the first sense, when the one is the measure of the other, the latter will be the measure of the former as well: ‘But though knowledge is similarly spoken of as related to the knowable, the relation does not work out similarly for while knowledge might be thought to be the measure, and the knowable the thing measured, the fact is that all knowledge is knowable, but not all that is knowable is knowledge, because in a sense knowledge is measured by the knowable.’ (Met., I, 1057a7-12) Aristotle’s assertion at Met., I, 1057a36-37 that ‘of relative terms, those which are not contrary have no intermediate’ ensures us that we must take the first sense as contraries. Here he mentions a criterion of differentiation between two senses: while the first sense accepts intermediates (as, for example, great and small do), the second one does not. (Met., I, 1057a37-b1) It seems, however, that it is only the second sense that is the essential sense of relatives because the first sense, Aristotle says, is an accidental sense: ‘The one is opposed then to the many in numbers as measure to things measureable; and these are opposed as relatives which are not from their very nature relatives.’ (Met., I, 1056b32-34) 4) Definition of relative Aristotle’s first definition of the category of relative (πρός τι) is as such: ‘We call relative all such things as are said to be just what they are, of or than other things, or in some other way in relation to something else (Πρός τι δὲ τὰ τοιαῦτα λέγεται, ὃσα αὐτὰ ἃπερ ἐστὶν ἓτερων εἶναι λέγεται, ἢ ὁπωσοῦν ἄλλως πρὸς ἓτερον). (Cat., 7, 6a36-37; repeated almost without any change in: Cat., 7, 6b6-8) Aristotle’s examples are larger (because it is what it is than something else (τοῦθ᾿ ὃπερ ἐστὶν ἑτέρου λέγεται) that means it is called larger than something) and double. (Cat., 7, 6a37-b1) Aristotle’s aporia regarding relative is about their relation with substances: whether no substance is spoken of as a relative, or whether this is possible with regard to some secondary substances. (Cat., 7, 8a13-15) In the case of primary substances, it seems that he is confident, at least at first, that neither themselves nor their parts are spoken of in relation to anything: neither an individual man is called someone’s individual man nor an individual hand is called someone’s individual hand (but someone’s hand). (Cat., 7, 8a15-21) Although it is obvious that most of secondary substances are not spoken of as relatives (a man is not called someone’s man) (Cat., 7, 8a21-25), there are some with them there is room for dispute: a head is someone’s head and a hand is called someone’s hand, which seem to be relatives. (Cat., 7, 8a25-28) Aristotle thinks this must be due to the previous definition’s being problematic: with that definition ‘it is either exceedingly difficult or impossible to reach the solution that no substance is spoken of as a relative.’ (Cat., 7, 8a28-32) Thus, Aristotle changes his previous definition to a new one: ‘Those things are relatives for which being is the same as being somehow related to something’ (ἔστι τὰ πρός τι οἷς τὸ εἶναι ταὐτόν ἐστι τῷ πρός τί). (Cat., 7, 8a32-34) Although the first definition does indeed apply to all relations, its problem is that it does not take ‘their own being relative’ (τῷ πρός τι αὐτοῖς εἶναι) the same as ‘their being what they are of other things’ (ἃπερ ἐστὶν ἑτέρων λέγεσθαι). (Cat., 7, 8a34-37) Although this change of definition is to exclude all substances from being relative, what Aristotle says in Topics (To., Z, 8, 146a39- ), seems to ignore this: ‘For of everything relative the substance is relative to something else, seeing that the being of every relative term is identical with being in a certain relation to something.’ 5) Necessary knowledge of the related Knowledge of that in relation to which a relative is spoken of is necessary when one knows the relative: it is impossible to know a relative and at the same time not to know that in relation to which it is spoken of. (Cat., 7, 8a37-b3) To prove this, Aristotle adheres to the definition of relatives: ‘If someone knows of a certain ‘this’ that it is a relative, and being for relatives is the same as being somehow related to something, he knows that also to which this is somehow related.’ (Cat., 7, 8a37-b3; cf. 7, 8b3-15 for Aristotle’s examples) This necessary knowledge of the related, if we call it so, dedicates Aristotle an epistemological reason, besides the ontological one mentioned in his definition, for the exclusion of substances. As we noted in our discussion of Aristotle’s definition of relatives, he changed his first definition to exclude all substances from being relatives. Therefore, it is evident that for him relatives must not include substances, either primary or secondary. Aristotle does have no problem with primary substances simply because it is evident for him that they cannot be relatives. The same can be said about most of the secondary substances as well. The problem for which he changed the definition of substances was about some secondary substances like ‘head’ or ‘hand’: the fact that it is possible to know a hand or head without necessarily knowing definitely that in relation to which it is spoken of proves that they are not relatives. (Cat., 7, 8b15-21) 6) Reciprocation Aristotle regards reciprocation (ἀντιστρέφειν) necessary in all relations: ‘All relatives are spoken of in relation to correlatives that reciprocate.’ (Cat., 7, 6b28-29; cf. Cat., 10, 12b21-24) The sense of reciprocation is clear by his own examples: ‘The slave is called slave of a master and the master is called master of a slave; the double double of a half, and the half half of a double.’ (Cat., 7, 6b29-31) Reciprocation of relatives is so necessary that if there seems that we do not have reciprocation, it must necessarily be due to a mistake and that in relation to which something is spoken of must have not been given properly. (Cat., 7, 6b36-7a1) Aristotle’s example is this: If a wing is given as of a bird, ‘bird of a wing’ does not reciprocate because it has not been given properly: a wing is of a winged and not of a bird; a wing is wing of a winged and a winged is winged with a wing. (Cat., 7, 7a1-5) Even if we do not have a proper name to have a proper reciprocation, Aristotle points, we must invent names. (Cat., 7, 7a5-15 and 7b10-14) Thus, having proper names is the condition of necessary reciprocation: ‘All relatives are spoken of in relation to correlatives that reciprocate, provided they are properly given.’ (Cat., 7, 7a22-23) This condition is also said in another way: there is no reciprocation if a relation is given as related to some chance thing or to something that is accidentally the related thing like when, for example, a slave is given as of a man or a biped instead of being given as of a master. (Cat., 7, 7a25-31) 7) Simultaneity of relatives Aristotle believes that in most cases relatives are simultaneous: double and half or master and slave must exist at the same time: when there is a half, there is a double and when there is a slave, there is a master. (Cat., 7, 7b10-14) However, this receives some exceptions like knowable, which is prior and can, thus, exist before and without knowledge. (Cat., 7, 7b22-27) What approves this non-simultaneousness for Aristotle is that the destruction of knowledge does not carry the knowable to destruction. (Cat., 7, 7b27-31) The same is said about perception and perceptible. (Cat., 7, 7b35-8a9) Aristotle attaches simultaneity to reciprocation. This reciprocation, however, is not a simple reciprocation but ‘reciprocation as to implication of existence’ (ἀντιστρέφει μὲν κατὰ τὴν τοῦ εἶναι) with the condition that neither be in any way the cause of the other’s existence. (Cat., 13, 14b27-29; the same is said also at: Cat., 13, 15a4-11) Aristotle’s examples are the double and the half because when there is a double there is a half and when there is a half there is a double but neither is the cause of the other’s existence. (Cat., 13, 14b29-32) (We have ‘reciprocation as to implication of existence’ also in relation between genus and species but it seems that this has a totally different sense there. 8) Having no independent reality That a relative cannot be a substance, either a primary or a secondary substance, is discussed in our review of both the definition of relatives and their reciprocation. The differentiation of relatives and substances are so deep for Aristotle that after questioning the possibility of any common element or principle for substances and relatives (Met., Λ, 1070a33-36), he asserts that no substance, on the one hand, is the element of relatives and none of the relatives, on the other hand, is the element of substances. (Met., Λ, 1070b3-4) Aristotle does not, however, suffice to this. For him, relatives have the least substantiality, which is, for him, almost the same as reality: ‘The relative is least of all categories a real thing (φύσις τις) or substance, and less than quality and quantity; and the relative is an affection of quantity.’ (Met., M, 1088a22-25) Aristotle believes that an evidence of this least reality (ὄν) and substantiality is that relatives have no proper generation, destruction or movement while each of substance, quality and quantity have them. (Met., M, 1088a29-35) Moreover, neither motion (Phy., E, 1) nor any kind of change is applicable to relatives so that relatives are neither themselves alterations nor the subject of alterations (Phy., Z, 3) and the process of losing and acquiring states cannot be considered as alterations because these are the result of the alterations of non-relative things of which they are states. (Phy., Z, 3) Relative is not even matter but is something different. (Met., M, 1088a24-25) The reason is that the matter is potentially of a nature but relative is neither potentially nor actually of a nature. (Met., M, 1088b1-2) To understand the status of relatives in Aristotle’s world, we have to make a tripartite classification; a classification that though Aristotle himself did not make, his assertions approve it. Based on this division, there are three kinds of being in the world: i) Independent beings: This class includes only substances. ii) Dependent beings: This class includes qualities and quantities. Although they are real, they are ‘in’ substances and cannot exist without them. iii) Super dependent beings: This class includes at least relatives. The fact that relatives must be considered in a third class different from substances, on the one hand, and qualities and quantities, on the other hand, is obvious not only from the previously mentioned texts (Met., M, 1088a22-25, 29-35 and b1-2) in which relatives’ reality is considered less than all substances, qualities and quantities and different from matters but from this text: ‘For there is nothing either great or small, many or few, or, in general, relative which is not something (τι ὄν) different (ἓτερον) [that is also] many or few or great or small’. (Met, N, 1088a27-30) Therefore, super dependent beings are those beings that must necessarily be also something else, i.e. an independent or dependent being. Ackrill (1963, 99) points that some of the words used by Aristotle to exemplify relational entities, e.g. slave, are endowed with a complete sense and do not need to be supplemented by a correlate. (Thus, the linguist criterion of incompleteness would be deficient. Some other instances of relative entities like ‘state,’ ‘knowledge’ and perception are not necessarily followed by the genitive case. 9) Extent of relatives What is the extent of relatives? What are or are not included in relatives either among categories or among other concepts? Which concepts or things Aristotle regard as relative? i) Aristotle includes state (ἓξις) and position (θέσις) among relatives. (Cat., 7, 6b2-6; Cat., 7, 6b11-14; Cat., 8, 11a20-24) ii) Although relative is not matter but is something different (Met., M, 1088a24-25), matter is ‘non-being’ only in virtue of an attribute (Phy., A, 9) and is, thus, a relative term. (Phy., B, 2, 194b9) 10) Property and relativity Aristotle draws a contrast between two types of giving a property, absolute and relative: ‘A property is given either in its own right and for always or relative to something else and for a time.’ (To., E, 1, ^128b15-18) Being a civilized man, for example, is an absolute property for man while to command is a relative property for the soul. The absolute property, however, is considered not only potential to be discussed or observed in relation to many things or periods of time, it in fact ‘belongs to its subject relatively to every single thing that there is, so that if the subject is not distinguished relatively to everything else, the property will not have been given correctly.’ (To., E, 1, 129a18-20) Therefore, an absolute property is a property that ‘is ascribed to a thing in comparison with everything else and distinguishes it from everything else.’ (To., E, 1, 128b33- ) An absolute property is, then, absolutely relative and not conditionally relative, i.e. relative to a specific thing. This is what differentiates it from a relative property, which is relative to a certain thing: ‘A property relative to something else is one which separates its subject off not from everything else but from a particular definite thing.’ (To., E, 1, 128b33- ) One important difference between absolute and relative properties is that while an accident can be a relative property, it can never be an absolute property. (To., I, 5, ^102b20-36) For example, sitting, which is an accident, is also a property relatively to those who are not sitting. (To., I, 5, ^102b20-36) 11) Platonic theories as relatives At least three of Platonic theories Aristotle attaches to relatives: i) Forms ‘It seems that a Form is always spoken of in relation to a Form-this desire itself is for the pleasure itself, and wishing itself is for the good itself.’ (To., Z, 8, 147a^10) Moreover, the theory of Forms takes the relative prior to the absolute as, for example, it takes not the dyad but the number as first. (Met., A, 990b15-17) Aristotle believes that this is against not only the necessities of the case but only the Platonists’ opinion because Forms must be substances only, if they can be shared. (Met., A, 990b27-29) There are, however, things like ‘equal’ which are only relative: they are only in relation to something else. Now the theory that ideas are supposed to be substances only should entail the substantiality of merely relatives. The reason being that Forms are not shared incidentally but each thing shares in that which is not predicated of a subject. (Met., A, 990b29-31) ii) Unequal The Platonic theory of great and small or unequal, which we know more from Aristotle and has, in Platonic philosophy, a role like that of matter in Aristotelian philosophy, is also called relative by Aristole. (Met., M, 1089b4-15) iii) Potentiality Aristotle says that Platonists take what potentially is a ‘this’ and a substance but not actually so a relative because it is ‘neither potentially the one or being, nor the contradictory of the one nor of being, but one among beings.’ (Met., N, 1089b15-20) 12) All things as relative Aristotle attaches the theory that ‘everything is true’ to relativity and thinks the consequence of believing in this theory is that everything is true: ‘He who says all things that appear are true, makes all things relative.’ (Met., Γ, 1011a17-20) 13) Genera and species of relatives There are some genera, Aristotle hints, that are relative but their species are not relative. In such cases, the genera are spoken of in relation to something, but none of the particular cases are so spoken. (Cat., 8, 11a20-36) Aristole’s examples are knowledge and grammar of which the former is a relative but the latter is a quality. The consequence of this is that there is nothing absurd for a thing to be in both genera of relative and quality. (Cat., 8, 11a37- ) However, when the species is a relative, the genera will be a relative too. (To., Δ, 4, 124b15- ) Moreover, Aristotle asserts that ‘the differentiae of relative terms are themselves relative.’ (To., Z, 6, 145a14-16) Things that are called relative are called so, Aristotle says, ‘because the classes that include them are of this sort, e.g. medicine is thought to be relative bcs its genus, knowledge, is thought to be relative,’ (Met., Δ, 1021b4-6) 14) Relatives as indefinite? Fabio Morales takes 1088a29-b1 as a textual evidence supporting the assumption that Aristotle regarded relational terms as indefinite. (shrink)

At the very beginning of On Interpretation (I, 1, 16a3-14) Aristotle distinguishes four levels and discusses their relationships. From this text, we can infer the following: 1. There are four levels: writing, speaking, mental experience and external world. Since writing and speaking can truly be taken as belonging to the same realm, we can reduce Aristotle’s distinction to three realms: language, thought and external world. 2. The realm of language, in both levels of writing and speaking, is different for different (...) people but both of the other realms of thought and external world are the same for them. By this Aristotle must mean that though people of different languages have different writings and speaking words, the things that are in the world and their affections on people’s thought are the same. 3. The relations both between language and thought and in language itself is symbolization: ‘Spoken words are the symbols of mental experience and written words are the symbols of spoken words.’ 4. The relation between external world and thought is similarity: ‘Those things of which our mental experiences are similarities (παθἠματα τῆς ψυχῆς ... ὁμοιώματα).’ (ΟΙ., 16a7) In de Anima (16a8-9; II, 5, 418a4-5; II, 4, 429a10-11; 429a13-16; 429a23) Aristotle describes thoughts as ‘likenesses of objects.’ Paolo Crivelli says that in these addresses Aristotle believe that ‘a thought is of an object just if it is a likeness of it’ and ‘to be a likeness of an object is to be the result of a process of likening of which that object is a cause.’ This, Crivelli believes, is indeed the basis of the sameness of the objects of thoughts: they are results of the same processes of likening by the same objects. 5. There is a correspondence between nouns and verbs on the one hand and objects of thought without co-positing and positing away on the other hand: ‘Nouns themselves and verbs are like objects of thought (νοἠματι) without co-positing and positing away.’ (OI, I, 1, 16a13-14) A. Relationship between external world and thought The following can be inferred from Aristotle’s works about the relationship between thought and external world: 1. ‘The soul is in a way all existing things; for existing things are either sensible or thinkable, and knowledge is in a way what is knowable, and sensation is in a way what is sensible.’ (So., Γ, 8, 431b21-23) In fact, ‘within the soul the faculties of knowledge and sensation are potentially these objects, the one what is knowable, the other what is sensible.’ (So., Γ, 8, 431b26-27) 2. It is the form of the external objects that are in thought (So., Γ, 8, 431b26-29) and the objects of thought are in the sensible forms, viz. both the abstract objects and all the states and affections of sensible things (ἐν τοῖς εἴδεσι τοῖς αἰσθητοῖς τὰ νοητὰ ἐστι, τά τε ἐν ἀφαιρέσει λεγόμενα, καὶ ὃσα τῶν αἰσθητῶν ἓξις καὶ πάθη). (So., Γ, 8, 432a3-6) 3. While external objects are perishable, objects of thought seem to be eternal. (PrA., A, 33, 47b21-22) B. Relationship between language and the external world 1. There is a correspondence between the external world and the true statements about them: ‘If it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white.’ (OI, I, 9, 18a39-b5) 2. While external objects ‘does seem in some way the cause of’ the truth or falsity of lingual statements, ‘the true statement is in no way the cause of the actual thing’s existence.’ (Cat., 12, 14b18-22; cf. OI, I, 9, 18b36-19a6) Thus, the external objects reciprocate as to implication of existence with the corresponding true statement about them and thus are prior to them.’ (Cat., 12, 14b11-23) 3. The opposition between an affirmation and negation corresponds to an opposition in the external world between the objects underlying those statements. (Cat., 10, 12b6-15) 4. The correspondence of the whole structure of the external world and language for Aristotle is so that in analyzing the language he shows himself as analyzing the external world. It is in fact a very crucial and controversial dispute whether Aristotle’s philosophy in its very decisive parts is theorizing about language or about external world. In most of his important theories, he begins with discussing language. In fact, language is where he enters the discussion and, in many cases, where he finishes it. In these cases, he either does not discuss external world at all or only derives some principles or conclusions about it. In some other cases he begins from language but ends in external world. a) Daniel W. Graham thinks that language is Aristotle’s ‘model of the world.’ He refers to ‘subjecthood’ as what formally characterizes primary substance and explains how it bases reality in Aristotle: while to be an absolute subject is equal to be fully real, to be a predicate of a subject is equal to be real. ‘Language is not merely a tool to get around in the world; it reveals the structure of the world … the deep structure of language is isomorphic with the world… In this word, logic can reveal connections between elements because language and the world have a form in common. He lists Trendelenburg (1846, 11-13), Gillespie (1925) and (Ackrill (1963, 78-81) as those who have the same idea. b) Emphasizing on the force of τί in Aristotle’s statement when he says that assertions affirm something (τί) of something (τί) makes Peter Simpson (p. 85) to stress, in his interpretation of Jacob’s theory, on the ontological aspect of Aristotle’s philosophy. Jacob says that in his theory of predication, Aristotle focuses on ‘things’ and not words or concepts and predication is a relationship between extralinguistic entities rather than merely linguistic ones; something extralinguistic and ontological. c) Quoting Ackrill ((1963, 73): ‘the categories classify things, not words’) and Kahn ((1978, 248): ‘Aristotle never regards predication as a grammatical or linguistic relation of word to word, nor does he ever speak of subject and predicate as concepts united in judgment’), Fabio Morales says that Aristotle is not classifying predication in Categories but the attributes or properties these stand for.’ d) Graham thinks that the theory of synonymity-homonimity is not purely linguistic, since it is things rather than words that have these properties. (shrink)

This paper presents affirmation as the central normative category of Nietzsche’s positive ethics. The paper argues in particular for two interpretive claims: first, that from Beyond Good and Evil onwards, we find a new variety of Nietzschean affirmation (‘natural affirmation’), which is crucial to the strategy of his later works; and second, for reasons internal to his own philosophical aims, Nietzsche’s new variety of affirmation is seriously flawed. The author argues for the second claim on the basis that Nietzsche himself (...) requires that affirmation not perform exactly the role he requires that it perform. The author contends that we are thus faced with a major challenge to Nietzsche’s late philosophical project—that (late) Nietzschean affirmation fails by Nietzsche’s own standards. (shrink)

The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; they (...) are connected with- the Ajdukiewicz’s work [1935] which was a continuation of Leśniewski’s idea and further developed and popularized in the research on categorial grammars, by Y. Bar-Hillel [1950,1953,1964]. To assign a suitable syntactic category to each word of the vocabulary is the main idea of syntactically-categorial approach to language. Compound expressions are built from the words of the vocabulary and then a suitable syntactic-category is assigned to each of them. A language built in this way should be decidable, which means that there should exist an algorithm for deciding about each expression of it, whether it is well-formed or is syntactically connected . The traditional, originating from Husserl, understanding of the syntactic category confronts some difficulties. This notion is defined by abstraction using the concept of affiliation of two expressions to the same syntactic category. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the (...) nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of verification and validation ); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of proxy ) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of commutation ); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.

The aim of this paper is make a contribution to the ongoing search for an adequate concept of the a priori element in scientific knowledge. The point of departure is C.I. Lewis’s account of a pragmatic a priori put forward in his "Mind and the World Order" (1929). Recently, Hasok Chang in "Contingent Transcendental Arguments for Metaphysical Principles" (2008) reconsidered Lewis’s pragmatic a priori and proposed to conceive it as the basic ingredient of the dynamics of an embodied scientific reason. (...) The present paper intends to further elaborate Chang’s account by relating it with some conceptual tools from cognitive semantics and certain ideas that first emerged in the context of the category-theoretical foundations of mathematics. (shrink)

Philosophers and psychologists widely hold that artifact categories – just like biological categories – are individuated by their function. But recent empirical findings in psychology question this assumption. My proposal is to suggest a way of squaring these findings with the central role function should play in individuating artifact categories. But in order to do so, we need to give up on the standard account of artifact function, according to which function is fixed by design, and replace (...) it with a more context-sensitive account, according to which function attributions depend on the explanatory context and, as a result, categorization also depends on the explanatory context, just as the empirical findings from psychology suggest. I argue that the recent ‘modal theory of function’ originally proposed to explain biological function, is capable of providing such an account of artifact function. (shrink)

This brief brochure is intended to present a philosophical theory known as re- lational materialism. We introduce the postulates and principles of the theory, ar- ticulating its ontological and epistemological content using the language of category theory. The identification of any existing entity is primarily characterized by its relational, finite, and non-static nature. Furthermore, we provide a categorical con- struction of particularities within the relational materialist onto-epistemology. Our objective is to address and transform a specific perspective prevalent (...) in scientific communities into a productive network of philosophical commitments. (shrink)

In the contemporary biomedical literature, every disease is considered genetic. This extension of the concept of genetic disease is usually interpreted either in a trivial or genocentrist sense, but it is never taken seriously as the expression of a genetic theory of disease. However, a group of French researchers defend the idea of a genetic theory of infectious diseases. By identifying four common genetic mechanisms (Mendelian predisposition to multiple infections, Mendelian predisposition to one infection, and major gene and (...) polygenic predispositions), they attempt to unify infectious diseases from a genetic point of view. In this article, I analyze this explicit example of a genetic theory, which relies on mechanisms and is applied only to a specific category of diseases, what we call “a regional genetic theory.” I have three aims: to prove that a genetic theory of disease can be devoid of genocentrism, to consider the possibility of a genetic theory applied to every disease, and to introduce two hypotheses about the form that such a genetic theory could take by distinguishing between a genetic theory of diseases and a genetic theory of Disease. Finally, I suggest that network medicine could be an interesting framework for a genetic theory of Disease. (shrink)

This brief brochure is intended to present a philosophical theory known as relational materialism. We introduce the postulates and principles of the theory, articulating its ontological and epistemological content using the language of category theory. The identification of any existing entity is primarily characterized by its relational, finite, and non-static nature. Furthermore, we provide a categorical construction of particularities within the relational materialist onto-epistemology. Our objective is to address and transform a specific perspective prevalent in scientific communities (...) into a productive network of philosophical commitments. (shrink)

Millikan’s (1984. Language, Thought, and Other Biological Categories: New Foundations for Realism. MIT Press) selected effects theory of functions states that functions are effects for which the ancestors of a trait were selected for. As the function is an effect a thing’s ancestors produced, only things that are reproductions in some sense can have functions. Against this reproduction requirement, Garson (2019. What Biological Functions Are and Why They Matter. Cambridge University Press) argues that not only processes of differential (...) reproduction but also processes of differential persistence can lead to new functions. Since such “persistence functions” have the same explanatory power as traditional selected effects functions, selected effects theorists should include them in their theory. In this paper, I will defend Millikan’s theory against this argument. I will show that the proponents of the generalized theory have yet to provide a working notion of populations that avoids a liberality problem. Further, I will argue that persistence functions are at best a marginal case of functions due to their restricted explanatory power. (shrink)

The aim of this article is to critically examine what I call Action-Centric Theories of Representation (ACToRs). I include in this category theories of representation that (1) reject construing representation in terms of a relation that holds between representation itself (the representational vehicle) and what is represented, and instead (2) try to bring the function that representations play for cognitive systems to the center stage. Roughly speaking, according to proponents of ACToRs, what makes a representation (that is, what is constitutive (...) of it being a representation) is its being functionally involved in preselecting or guiding the actions of cognitive systems. I intend to argue that while definitely valuable, ACToRs are underconstrained and thus not entirely satisfying, since there exist structures that would count as representations according to ACToRs, but which do not play functional roles that could be nontrivially or in an explanatorily valuable way classified as representing something for a cognitive system. I outline a remedy for this theoretical situation by postulating that a fully satisfying theory of representation in cognitive science should have two factors; i.e., it should combine the pragmatic, action-oriented aspect present in ACToRs with an element that emphasizes the importance of the relation holding between a representational vehicle and what is represented. (shrink)

In her landmark book, Language, Thought, and Other Biological Categories (Millikan1984),1 Ruth Garrett Millikan utilizes the idea of a biological function to solve philosophical problems associated with the phenomena of language, thought, and meaning. Language and thought are activities of biological organisms, according to Millikan, and we should treat them as such when trying to answer related philosophical questions. Of special interest is Millikan’s treatment of intentionality. Here Millikan employs the notion of a biological function to explain what it (...) is for one thing in nature, a bee dance (43), for example, to be about another, in this case, the location of a nectar source. My concern in this paper is to understand whether Millikan’s account of intentionality adequately explains how humans achieve reference, in language or thought, to individuals and groups in their environment. In bringing her theory of intentional content to bear on human activities, Millikan focuses largely on natural language. Thus, in what follows, I begin by laying out the biology-based principles that underlie Millikan’s theory of content, then proceed with an explanation of how the theory is to apply to natural language. As it appears, Millikan’s account of how content is determined for natural language terms and sentences rests on the determinacy of intentional content at the psychological level. This leads me to take a careful look at what Millikan says about the content of mental representations, in hopes of finding a sufficient basis there for the application of Millikan’s theory of content to natural language. Ultimately, I conclude that Millikan’s theory faces a problem of vacuity. If we approach the theory as a theory of intentional content, intended to explain the nature of reference, the theory is lacking in an extremely important respect: Millikan explains how it could be one of the biological functions of a mental or natural language term to refer, without telling us precisely what in the natural order constitutes the reference relation.. (shrink)

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based definitions can (...) be abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions. (shrink)

The representational content or subject matter of a picture is normally distinguished from various non-representational components of meaning involved in artworks, such as expressive, stylistic or intentional factors. However, I show how such non subject matter components may themselves be analyzed in content terms, if two different categories of representation are recognized--aspect indication for stylistic etc. factors, and normal representation for subject matter content. On the account given, the relevant kinds of content are hierarchically structured, with relatively unconceptualized lower (...) level aspectual contents encoding or symbolizing higher level conceptualized representational subject matter. Such an account is strongly supported by the latest findings of cognitive science regarding levels of conceptualization. The paper also demonstrates how the account given is compatible with the actual pictorial competence of normal viewers of visual artworks. (shrink)

This paper examines recent feminist work on Spinoza and identifies the elements of Spinoza’s philosophy that have been seen as promising for feminist naturalism. I argue that the elements of Spinoza’s work that feminist theorists have found so promising are precisely those concepts he derives from Hobbes. I argue that the misunderstanding of Hobbes as architect of the egoist model of human nature has effaced his contribution to Spinoza’s more praised conception of the human individual. Despite misconceptions, I argue that (...) the model of human nature, the view on human emotions and the conception of individual power that Hobbes created and Spinoza developed is an uncommonly useful one for feminist political theory. Through reexamining Hobbes’ model of human nature and the emotions I will argue that Hobbes’ theory of the internal weighing of emotions provides an important mechanism for understanding how the individuals’ affects can be reformed. I will show how we can use this naturalistic model of the human individual to answer contemporary theoretical and practical questions of how to empower women and how to effectively identify, challenge and change social categories, norms and institutions which are disempowering. In particular, I will argue that feminist projects of empowerment need a way to measure empowerment and a way to understand how to understand the power of harmful norms and customs. Understanding the way certain norms and practices disempower women while forming their affects and self‐conceptions provides the first step to reform of these practices. Spinoza and Hobbes provide us with a further tool to reform, and that is their understanding of the role of emotions in human action and power, and the need to reform and reorganize the emotions of individuals in order to escape harmful patterns of behavior. (shrink)

Considering what Kant says with regard to self consciousness, one can question whether Kant is able to claim that his position is substantially different than the positions of David Hume and Rene Descartes. He agrees with Hume that we do not have a permanent perception of ourselves. Conversely, he concurs with Descartes in saying that the "I think" plays a substantival role in experience. He argues that the consciousness involved in judgment must be singular and endure. On the other hand (...) he maintains that one cannot argue successfully from the "I think" to the conclusion that the soul is a simple enduring substance. These views are apparently inconsistent. ;In an examination of the Critique I argue that these positions are consistent. I argue that Kant improves over the position of Hume in that he discovered another route to justification for our belief that there is an identical consciousness at the seat of experience. Where Hume accepted justification of a notion only when he could discover an original impression to account for its logical character, Kant was able to justify the notion of an identical consciousness by reference to arguments concerning the necessary conditions for experience. One can find similar arguments in Hume. When he discusses the notion of independently existing objects, he describes this notion as a fiction which allows us to resolve contradictory experiences. The relationship to Descartes is equally complex. While the Paralogisms section is aimed at dualistic arguments much like those attributed to Descartes, we see, if we examine both philosopher's writings, that their positions are closer in their agnosticism than Kant took them to be. ;In the process of explicating the relationships between these men, I spell out Kant's theory of "empirical self consciousness", according to which we can know a great deal about our own history only if we consider ourselves to be in causal commerce with external bodies. I will argue that this sort of argument lies at the heart of the Deduction of the Categories , and ties that section in with the Analogies of Experience, Refutation of Idealism, and the Principles sections. (shrink)

This essay argues that bullshit art is a meaningful concept that differs from bullshitting about art, although the two may occur in tandem. I defend what I call the social pretense theory of bullshit art. On this view, calling a work of art ‘bullshit’ highlights a discrepancy between the prestige accorded a work of art and its nonsense character. This category of aesthetic criticism plays a unique role that cannot be identified with kitsch but bears only a contingent connection (...) to it. (shrink)

This dissertation argues that a sufficiently worked out concept of habit is crucial for understanding race, and specifically whiteness. It has become common for race theorists to think about white privilege as a matter of habit, but they have yet to realize the potential of this approach. This is in part because the existing accounts of white habit either omit or outright reject an explicitly phenomenological framework. This leads them to think only in terms of discrete habits of racism and (...) white privilege. I agree that racism and white privilege operate through specific habits of perception, cognition, and bodily response. But racism and racial privilege amount to more than individual problematic habits. To fully appreciate the extent to which habit structures racial categories, we need to historicize habit at a more fundamental level. That is to say, we need to understand the ways in which habituation itself––the ability to be oriented in and enabled by certain spaces, and to feel at home in them––tracks race. -/- I do this work through an account of racial habit that combines Merleau-Ponty’s understanding of habit as orientation, a Deweyan-pragmatist ontology of transaction, and a generally Du Boisian approach to race theory. It is not just the kinds of habits that differently racialized subjects acquire that determine their position within a socially and politically hierarchized landscape; it is the very ability to be oriented by and within certain spaces that constitutes one’s racial position. The differential ability to cultivate habits and to accrue the psychological, physiological, and affective benefits of habituation is a phenomenological asymmetry in our lived experience of race that constitutes a harm over and above the harms of individual racist habits. I give the name “anti-social habit” to those individual and collective habits that eventuate in this phenomenological asymmetry. I then draw on the framework of democratic egalitarianism to argue that this constitutes a distinct site of unjust social inequality. Finally, I argue for phenomenological disruption as a necessary form of social praxis and consider what this might look like in terms of political action. (shrink)

Alvin Plantinga’s theory of knowledge, as developed in his Warrant trilogy, has shaped the debates surrounding many areas in epistemology in profound ways. Plantinga has received his share of criticism, however, particularly in his treatment of belief in God as being “properly basic”. There has also been much confusion surrounding his notions of warrant and proper function, to which Plantinga has responded numerous times. Many critics remain unsatisfied, while others have developed alternative understandings of warrant in order to rescue (...) Plantinga’s theory from certain objections. The most promising of such attempts fall under the broad category of “virtue epistemology” or a “virtue-theoretic” approach. The work being done in virtue epistemology is still in its early stages and a consensus on what actually constitutes virtue epistemology has yet to be reached. While some have attempted to structure an entire theory of knowledge based on the virtues possessed by the knower, others have focused more on the role of epistemic virtues as an attempt to supplement existing theories, including Plantinga’s. In this paper, I will offer an analysis of what such an attempt might look like and evaluate the potential success of broadening Plantinga’s original model. -/- My proposal is that certain features of a virtue-theoretic approach (also referred to as “agent-reliabilism”) could improve Plantinga’s model in significant ways. Not only would such a broadened approach be better equipped to handle common objections, but it would also be better suited to contribute an enhanced understanding of the task of epistemology, one that seeks to discover multiple epistemic goods other than what has been traditionally confined to the realm of knowledge. I conclude by applying this approach to Plantinga’s treatment of theistic belief in Warranted Christian Belief and by articulating a few of the ways in which epistemic virtues can increase the degree of warrant enjoyed by such belief. (shrink)

The precondition of any feminist politics – a usable category of ‘woman’ – has proved to be difficult to construct, even proposed to be impossible, given the ‘problem of exclusion’. This is the inevitable exclusion of at least some women, as their lives or experiences do not fit into the necessary and sufficient condition(s) that denotes group membership. In this paper, I propose that the problem of exclusion arises not because of inappropriate category membership criteria, but because of the presumption (...) that categories can only be organised by identity relations or shared properties among their members. This criterion of sameness as well as the characterisation of this exclusion as essentialism attests to a metaphysics that is not conducive to resistance and liberatory projects. Following a strain of hybrid thinking in feminist and post-colonial theory, I outline an alternative pluralist logic that confronts oppressive binaries that impede theory work in gender, sexuality, and race theory, and limit political action and resistance. The problem of exclusion is neither irresolvable nor is it essentialism. Instead it is a denial of subjectivity due to pseudodualistic self/Other dichotomies that can be resisted by adopting a new categorial logic. While this paper focuses on the specific problem of formulating a category of ‘woman’, it has implications for other areas of gender, critical race, and postcolonial theory. Rather than working toward an inclusive category founded on sameness, theorists need to develop independent and positive categories grounded in difference. Our current categorial logic does not permit such a project, and therefore a new metaphysics must be adopted. (shrink)

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in category theory is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of (...) $\Omega$-logical validity, and thus the generic invariance of mathematical truth, modal coalgebras are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (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)