This thesis describes two classes of Dialectica categories. Chapter one introduces dialectica categories based on Goedel's Dialectica interpretation and shows that they constitute a model of Girard's Intuitionistic Linear Logic. Chapter two shows that, with extra assumptions, we can provide a comonad that interprets Girard's !-course modality. Chapter three presents the second class of Dialectica categories, a simplification suggested by Girard, that models (classical) Linear Logic and chapter four shows how to provide modalities (...) ! and ? for this second class of construction. (shrink)

Processes are occurrents that were, are, or will be happening. They endure or they perdure, i.e. they are either “fully” present at every time they happen, or they rather have temporal parts. According to Stout (2016), they endure. His argument assumes that processes may change. Then, Stout argues that, if something changes, it endures. As I show, Stout’s Argument misses its target. In particular, it makes use of a notion of change that is either intuitive but illegitimate or technical but (...) question-begging. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 42.2 (2004) 219-220 [Access article in PDF] Jack Zupko. John Buridan: Portrait of a Fourteenth-Century Arts Master. Notre Dame: University of Notre Dame Press, 2003. Pp. xix + 446. Cloth, $70.00. Paper, $40.00. What does the name "John Buridan" call to mind? For many, including medievalists, not much at all—at best, perhaps, a set of apparently unrelated ideas: nominalism; an impetus theory of (...) projectile motion; and a peculiar account of the will (although "Buridan's ass," the indecisive donkey caught between two equally appetizing bales of hay, is not found in Buridan's writing). In correcting this ignorance—an injustice to arguably the most famous and influential philosopher of the early-to-mid-fourteenth century—the temptation might have been to articulate Buridan's "positions" on "the big questions," allowing readers to fit Buridan into received categories. Thankfully, the present work, the first book-length study of Buridan in any language, resists this temptation. The John Buridan that emerges from Jack Zupko's skillful "exercise in philosophical portraiture" doesn't serve to simply fill gaps in our awareness of the historical record, but to enlighten and challenge our understanding of the practice of philosophy and the study of its history.Zupko emphasizes throughout that Buridan was a teacher, a master of arts in Paris. Buridan's pedagogical concerns help make sense of his central work in logic. As the basis for his arts lectures, Buridan chose Peter of Spain's Summulae Logicales, but in commenting on Peter, Buridan moves beyond creative exegisis to comprehensive renovation. Buridan (c. 1300-c. 1361) naturally wanted to accommodate terminist or via moderna supposition theory; but more importantly, he wanted a logic text that would set out a general plan of philosophical inquiry, "a compendium of methods, a 'how-to' book for the philosopher" (135). Buridan thus designed his own Summulae de Dialectica as a new authoritative logic text, and Zupko persuasively argues that its "nominalism" should be understood as less a set of doctrines in theoretical logic, than a program of logical practice, an education in logic as the ars artium, the universal intellectual tool.Zupko's portrait of "Buridan's vision of the philosophical enterprise" is thus appropriately divided into two parts. The first summarizes Buridan's method as described in the individual treatises of his Summulae. The second displays the method in practice, rehearsing and evaluating some of Buridan's arguments on various subjects. Many scholars will gravitate first to the latter part, where Zupko offers important interpretations and clarifications of Buridan's views. In these chapters, Zupko helps us to appreciate, among other things: how the problem of universals served to help Buridan define the scope of philosophy (ch. 10); the philosophical modesty of Buridan's account of the intellectual soul's presence in the body (ch. 11); the relationship between Buridan's epistemology and the skepticism of his Parisian contemporary Nicholas of Autrecourt (ch. 12); the sense in which Buridan is an "empiricist," viz an epistemic naturalist and reliabilist (ch. 13); how Buridan regarded moral psychology as applied physics, treating virtue as a kind of impetus (ch. 14); how Buridan's account of freedom can be regarded as a "perfection" of Thomistic intellectualism (ch. 15).Throughout these discussions, Zupko always keeps in sight his larger purpose of illustrating Buridan's conception of philosophical inquiry. Zupko makes much of the fact that [End Page 219] Buridan never wrote as a theologian, remaining his entire career in the arts faculty, where he wanted logic to organize secular inquiry. As Zupko notes, in this way Buridan's scholastic project seems to prefigure the "modern." But Buridan seems modern in another way as well. As Zupko points out in his "Introduction," though a cleric, Buridan never joined a religious order, so that his ideas developed independently of the Franciscan and Dominican traditions. He was, then, a teacher without a tradition—at least without deliberate allegiance to tradition, although he was in many ways the product of traditional scholastic intellectual discipline.Perhaps this... (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)

El trabajo, escrito a modo de prólogo para el libro Contribuciones a la epistemología crítica de la complejidad dialéctica en el siglo XXI, busca poner en relación los conceptos de dialéctica, complejidad y epistemología crítica. En tal sentido, se analiza la relación entre las ideas de Karl Marx y las de Edgar Morin. Se muestra cómo hay mucho de complejidad en el pensamiento de Marx y mucho de dialéctica en el de Morin. A pesar de que también hay diferencias importantes (...) entre ellos, nos interesa más aquí mostrar lo que de común y/o complementario existe entre sus respectivos pensamientos, como nutrientes necesarios para una epistemología crítica. (shrink)

Dialectica, un proces care ne conduce la cunoașterea formelor și în final la cea mai înaltă formă a Binelui, prin discuție, raționament, chestionare și interpretare, a preocupat filosofii încă din antichitate. Socrate a practicat dialectica prin metoda dialogului oral, ceea ce el numea arta „nașterii sufletelor” (o metodă numită și maieutică, sau metoda lui Elenchus), care putea duce, în funcție de intenția lui Socrate, la confirmarea sau infirmarea unor afirmații, sau la așa-numitele „aporii” în care nu se ajungea (...) la o concluzie definitivă. La Platon, dialectica este un tip de cunoaștere, cu rol rol ontologic și metafizic, la care se ajunge prin confruntarea mai multor poziții pentru a depăși opinia (doxa), o deplasare din lumea aparențelor (sau a „sensibilului”) către cunoașterea intelectuală (sau „inteligibilul”) până la primele principii. Ea implică și ordonarea conceptelor în genuri și specii prin metoda divizării, și îmbrățișează multiplicitatea în unitate, fiind folosită pentru a înțelege „procesul total al iluminării, prin care filozoful este educat astfel încât să realizeze cunoașterea binelui suprem, a Formei Binelui”. -/- DOI: 10.13140/RG.2.2.22933.60641. (shrink)

Foundational ontologies, central constructs in ontological investigations and engineering alike, are based on ontological categories. Firstly proposed by Aristotle as the very ur- elements from which the whole of reality can be derived, they are not easy to identify, let alone partition and/or hierarchize; in particular, the question of their number poses serious challenges. The late medieval philosopher Dietrich of Freiberg wrote around 1286 a tutorial that can help us today with this exceedingly difficult task. In this paper, I (...) discuss ontological categories and their importance for foundational ontologies from both the contemporary perspective and the original Aristotelian viewpoint, I provide the translation from the Latin into English of Dietrich's De origine II with an introductory elaboration, and I extract a foundational ontology–that is in fact a single-category one–from this text rooted in Dietrich's specification of types of subjecthood and his conception of intentionality as causal operation. (shrink)

Reflexión sobre los desafíos que enfrenta el pensamiento crítico a propósito del 30 aniversario de la fundación de la revista Dialéctica. Se destaca la capacidad permanente de la revista para pulsar lo mejor del pensamiento crítico de cada etapa por la que ha pasado. Fiel a aquella sentencia clásica de una filosofía y un pensamiento social como «crítica radical de todo lo existente», la revista ha sabido al mismo tiempo conservar clarividencia sobre el horizonte de sentido desde donde habría de (...) realizarse la crítica que sus páginas albergaba. El rigor teórico que la ha acompañado no ha sido mella para su compromiso con la praxis liberadora en sus más variadas manifestaciones. Ha sido dinámica, abierta en todo momento a los nuevos signos epocales, pero al mismo tiempo capaz de no cejar ante modismos intelectuales que dieran al traste con el designio que le dio origen. El principal desafío que enfrenta Dialéctica sigue siendo el mismo, su destino continúa asociado al del pensamiento crítico. Y éste, a su vez, necesita una reevaluación permanente acorde a su propia naturaleza. La celebración del 30 aniversario de Dialéctica constituye, pues, una excelente ocasión para reflexionar sobre la situación actual y perspectivas del pensamiento crítico. (shrink)

Reflexión sobre los desafíos que enfrenta el pensamiento crítico a propósito del 30 aniversario de la fundación de la revista Dialéctica. Se destaca la capacidad permanente de la revista para pulsar lo mejor del pensamiento crítico de cada etapa por la que ha pasado. Fiel a aquella sentencia clásica de una filosofía y un pensamiento social como «crítica radical de todo lo existente», la revista ha sabido al mismo tiempo conservar clarividencia sobre el horizonte de sentido desde donde habría de (...) realizarse la crítica que sus páginas albergaba. El rigor teórico que la ha acompañado no ha sido mella para su compromiso con la praxis liberadora en sus más variadas manifestaciones. Ha sido dinámica, abierta en todo momento a los nuevos signos epocales, pero al mismo tiempo capaz de no cejar ante modismos intelectuales que dieran al traste con el designio que le dio origen. El principal desafío que enfrenta Dialéctica sigue siendo el mismo, su destino continúa asociado al del pensamiento crítico. Y éste, a su vez, necesita una reevaluación permanente acorde a su propia naturaleza. La celebración del 30 aniversario de Dialéctica constituye, pues, una excelente ocasión para reflexionar sobre la situación actual y perspectivas del pensamiento crítico. (shrink)

El trabajo aborda, desde una perspectiva marxista, un importante y complejo problema teórico asociado a la supuesta falsedad de toda ideología. Se trata del problema de la veracidad de la valoración, calificado más de una vez como de imposible solución, dado el vínculo de los juicios valorativos con las necesidades, intereses y otros fenómenos subjetivos de la conciencia humana. La negación de la existencia de la verdad valorativa conduce inevitablemente a su negación en la ideología, compuesta fundamentalmente por juicios valorativos (...) y, por lo tanto, sirve de sustento gnoseológico a las diversas variantes de la teoría de la desideologización. El enfoque crítico de estas consideraciones se desarrolla en el artículo sobre la base del análisis de la dialéctica de lo general y lo particular en la verdad valorativa, haciendo énfasis, ante todo, en la especificidad de esta última en comparación con cualquier otra verdad del conocimiento. (shrink)

El trabajo aborda, desde una perspectiva marxista, un importante y complejo problema teórico asociado a la supuesta falsedad de toda ideología. Se trata del problema de la veracidad de la valoración, calificado más de una vez como de imposible solución, dado el vínculo de los juicios valorativos con las necesidades, intereses y otros fenómenos subjetivos de la conciencia humana. La negación de la existencia de la verdad valorativa conduce inevitablemente a su negación en la ideología, compuesta fundamentalmente por juicios valorativos (...) y, por lo tanto, sirve de sustento gnoseológico a las diversas variantes de la teoría de la desideologización. El enfoque crítico de estas consideraciones se desarrolla en el artículo sobre la base del análisis de la dialéctica de lo general y lo particular en la verdad valorativa, haciendo énfasis, ante todo, en la especificidad de esta última en comparación con cualquier otra verdad del conocimiento. (shrink)

Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based induction based on distances on conceptual spaces. We show how this model can predict most of the properties of (...) this kind of reasoning while providing a solid theoretical foundation for it. We also show that it subsumes some of the previous models proposed in the literature and that it generates new predictions. (shrink)

In these pages the author intends to examine the idea, quite widespread among Aristotle’s recent scholars, that the method of metaphysics were mainly dialectical. This problem is investigated in Aquinas, who decidedly denies that metaphysics uses dialectics because it just provides probability. Metaphysics, unlike dialectics, is not only based on the being of reason but also on the natural being. Therefore, it does not simply constitute a rational game about quiddities, but it studies things in their real actuality and must (...) therefore be supported by evidence. Although Aquinas agrees with Aristotle in affirming that not every science enjoys the same certainty, this fact is due to different reasons. First, all things do not possess the same stability and constancy. Secondly, there is not always a perfect match between the studied matter and the human faculty to ascertain. This match between the object and the subject is the most decisive factor for the certainty of sciences. (shrink)

This paper is an essay in what Austin (_Proc Aristotel Soc_ 57: 1–30, 1956–1957) called "linguistic phenomenology". Its focus is on showing how the grammatical features of ordinary causal verbs, as revealed in the kinds of linguistic constructions they can figure in, can shed light on the nature of the processes that these verbs are used to describe. Specifically, drawing on the comprehensive classification of English verbs founds in Levin (_English verb classes and alternations: a preliminary investigation_, University of Chicago (...) Press, Chicago, 1993), I divide the forms of productive causal processes into five classes, corresponding to Aristotle's ontological categories: there are processes that cause change in location, in state, and in quantity; and that lead to the creation and destruction of substances. These broader categories are then subdivided into other ones, corresponding to different Levin classes, according to further differences in the causal processes they involve. I conclude by discussing the relevance of this argument to research in metaphysics and experimental philosophy. (shrink)

Since it is only five years since the publication of our paper, "Geographical categories: An ontological investigation" (Smith and Mark 2001), it seems somewhat strange to be making retrospective comments on the piece. Nevertheless, the field is moving quickly, and much has happened since the article appeared. A large number of papers have already cited the work, which suggests that there is a seam here that people find worthy of being mined. In this short essay, we first review the (...) paper and attempt to assess its significance from the perspective of our current work. We then put the paper in the context of our individual and joint works, which led up to it, and summarize our research trajectories since the paper appeared, pointing out what some of this reveals about spatial ontology in general. We conclude with some remarks on the future of ontological research in geographical information science. (shrink)

Analytical categories of scientific cultures have typically been used both exclusively and universally. For instance, when styles of scientific research are employed in attempts to understand and narrate science, styles alone are usually employed. This article is a thought experiment in interweaving categories. What would happen if rather than employ a single category, we instead investigated several categories simultaneously? What would we learn about the practices and theories, the agents and materials, and the political-technological impact of science (...) if we analyzed and applied styles, paradigms, and models simultaneously? I address these questions in general and for a specific case study: a brief history of systematics. (shrink)

This paper investigates some classical oppositional categories, like synthetic vs. analytic, posterior vs. prior, imagination vs. grammar, metaphor vs. hermeneutics, metaphysics vs. observation, innovation vs. routine, and image vs. sound, and the role they play in epistemology and philosophy of science. The epistemological framework of objective cognitive constructivism is of special interest in these investigations. Oppositional relations are formally represented using algebraic lattice structures like the cube and the hexagon of opposition, with applications in the contexts of modern color (...) theory, Kantian philosophy, Jungian psychology, and linguistics. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial (...) languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

There is growing support for the view that social categories like men and women refer to “objective types” (Haslanger 2000, 2006, 2012; Alcoff 2005). An objective type is a similarity class for which the axis of similarity is an objective rather than nominal or fictional property. Such types are independently real and causally relevant, yet their unity does not derive from an essential property. Given this tandem of features, it is not surprising why empirically-minded researchers interested in fighting oppression (...) and marginalization have found this ontological category so attractive: objective types have the ontological credentials to secure the reality (and thus political representation) of social categories, and yet they do not impose exclusionary essences that also naturalize and legitimize social inequalities. This essay argues that, from the perspective of these political goals of fighting oppression and marginalization, the category of objective types is in fact a Trojan horse; it looks like a gift, but it ends up creating trouble. I argue that objective type classifications often lack empirical adequacy, and as a result they lack political adequacy. I also provide, and in reference to the normative goals described above, several arguments for preferring a social ontology of natural kinds with historical essences. (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.

One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial (...) languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functor-function defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

Kendall Walton’s “Categories of Art” (1970) is one of the most important and influential papers in twentieth-century aesthetics. It is almost universally taken to refute traditional aesthetic formalism/empiricism, according to which all that matters aesthetically is what is manifest to perception. Most commentators assume that the argument of “Categories” applies to works of literature. Walton himself notes a word of caution: “The aesthetic properties of works of literature are not happily called ‘perceptual’ … (The notion of perceiving a (...) work in a category … is not straightforwardly applicable to literary works)” (335 n.5). However, he goes on to say that although he focuses “on visual and musical works … the central points I make concerning them hold, with suitable modifications, for novels, plays, and poems as well” (335 n.5). Here I consider what “suitable modifications” are required to extend the account to literature. (shrink)

Kimberlé Williams Crenshaw ends her landmark essay “Mapping the Margins: Intersectionality, Identity Politics, and Violence against Women of Color” with a normative claim about coalitions. She suggests that we should reconceptualize identity groups as “in fact coalitions,” or at least as “potential coalitions waiting to be formed.” In this essay, I explore this largely overlooked claim by combining philosophical analysis with archival research I conducted at the Gay, Lesbian, Bisexual and Transgender Historical Society Archive in San Francisco about Somos Hermanas, (...) the solidarity project of the Alliance Against Women’s Oppression, based in the San Francisco Women’s Building (1984–90). I extend my analysis into the present by drawing on the oral history and published works of Carmen Vázquez, a key organizer in both Somos Hermanas and the Women’s Building. I argue that conceptualizing identities as in fact coalitions—as complex, internally heterogeneous unities constituted by their internal differences and dissonances and by internal as well as external relations of power—enables us to organize effective political coalitions that cross existing identity categories and to pursue a liberatory politics of interconnection. (shrink)

It will be the thesis of this paper that there are among our mental acts some which fall into the category of real material relations. That is: some acts are necessarily such as to involve a plurality of objects as their relata or fundamenta. Suppose Bruno walks into his study and sees a cat. To describe the seeing, here, as a relation, is to affirm that it serves somehow to tie Bruno to the cat. Bruno's act of seeing, unlike his (...) feeling depressed, his putative thinking-about-Santa-Claus or his musing, abstractedly, about the tallest spy, has at least two fundamenta: it is, as a matter of necessity, dependent for its existence upon both Bruno himself and the cat that he sees. This idea will naturally raise echoes of Russell's doctrine of knowledge by acquaintance. 'I am acquainted with an object', Russell tells us, 'when I have a direct cognitive relation to that object, i. e. when I am directly aware of the object itself' (1918, p. 209). And indeed a distinction in many ways like that between acquaintance and description will find a place within the theory here projected, but there are crucial differences. (shrink)

Arguing first that the best way to understand what a continuant is is as something that primarily has its properties at a time rather than atemporally, the paper then defends the idea that there are occurrent continuants. These are things that were, are, or will be happening—like the ongoing process of someone reading or my writing this paper, for instance. A recently popular philosophical view of process is as something that is referred to with mass nouns and not count nouns. (...) This has mistakenly encouraged the view that the only way to think of process is as the stuff of events, and has obscured the possibility of thinking of processes as individual continuants. (shrink)

In this paper it is shown how simple texts that can be parsed in a Lambek Categorial Grammar can also automatically be provided with a semantics in the form of a Discourse Representation Structure in the sense of Kamp [1981]. The assignment of meanings to texts uses the Curry-Howard-Van Benthem correspondence.

In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...) semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)

Proponents of cognitive penetration often argue for the thesis on the basis of combined intuitions about categorical perception and perceptual learning. The claim is that beliefs penetrate perceptions in the course of learning to perceive categories. I argue that this "diachronic" penetration thesis is false. In order to substantiate a robust notion of penetration, the beliefs that enable learning must describe the particular ability that subjects learn. However, they cannot do so, since in order to help with learning they (...) must instruct learners to employ previously existing abilities. I argue that a better approach recognizes that we can have sophisticated causal precursors to perceptual learning, but that the learning process itself must operate outside of cognitive influence. (shrink)

In this paper an Artificial Neural Network (ANN) model, for predicting the category of a tumor was developed and tested. Taking patients’ tests, a number of information gained that influence the classification of the tumor. Such information as age, sex, histologic-type, degree-of-diffe, status of bone, bone-marrow, lung, pleura, peritoneum, liver, brain, skin, neck, supraclavicular, axillar, mediastinum, and abdominal. They were used as input variables for the ANN model. A model based on the Multilayer Perceptron Topology was established and trained using (...) data set which its title is “primary tumor” and was obtained from the University Medical Centre, Institute of Oncology, Ljubljana, Yugoslavia Test data evaluation shows that the ANN model is able to correctly predict the tumor category with 76.67 % accuracy. (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 (...) class='Hi'>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)

Language exists because human subjects define themselves in the circumstance they are in. This is possible because they are able to know, not directly through their senses only, but adding something new to the construct they create in their conscience. The main thing they add to the construct created is categories, something invented or fabricated by the human subject at the moment of speaking.

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)

Anyone who tries to understand categories soon runs into the problem of giving an account of the unity of a category. Call this the “unity problem.” In this essay, I describe a distinctive and under-studied version of the unity problem and discuss how it might be solved. First, I describe various versions of the unity problem. Second, I focus on one version and argue that it is best dealt with by thinking of at least some categories as “norm-constituted,” (...) in a sense that I try to make clear. Third, I discuss some objections to my proposal. Fourth, I compare norm -constituted categories to categories that are normative in a different sense. Fifth, I briefly discuss the possibility of grounding the normativity of norm-constituted categories. Finally, I raise a few questions for further research. (shrink)

Images of species, sets, and containers, combined with an obsolete positivist theory of meaning and a curiously illogical interpretation of a structuralist understanding of meaning, together have driven feminists and their critics to find unavoidable essentialism and binary totalism in feminist theorists' use of the category WOMEN. This paper explores an enriched imagination for how categories can be structured internally and in relations to other categories, and proposes that we need to think categories simultaneously through multiple and (...) mixed metaphors, including the metaphors of a spun thread and family resemblance, and the image of correlational densities in multidimensional quality spaces. (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)

Wrong beliefs, known by some as ‘alternative facts’, have proliferated lately in important areas of human life, including social, political, and public health domains. This can be and has been damaging. This brief article proposes an epistemological category classification of these wrong beliefs, with the following mappings: a) ‘No-Information’ marked by willful blindness produces ‘Empty Beliefs’; b) ‘Mis-Information’ yields ‘Mis(taken) Beliefs’; and c) ‘Dis-Information’ predicated on blatant distortions produces ‘Dis(torted) Beliefs’. This simple classification system, is perhaps epistemologically satisfying, and moreover (...) could have positive policy implications. (shrink)

This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.

We introduce the category of mereotopology Mtop as an alternative category to that of topology Top, stating ontological consequences throughout. We consider entities such as boundaries utilizing Brentano’s thesis and holes utilizing homotopy theory with a rigorous proof of Hausdorff Spaces satisfying [GEM]TC axioms. Lastly, we mention further areas of study in this category.

Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different (...) categories, on the one hand, and the way in which the realm of Bedeutungen stratifies into logical categories, on the other hand. A proper understanding of this internality reveals how Frege's conception of the relation between language and the world is neither a form of realism nor a form of linguistic idealism. To come to understand Frege's conception of the logical categories, is to come to understand both these forms of internality by coming to understand how they hang together. (shrink)

This paper outlines an Husserlian, phenomenological account of the first stages of the acquisition of empirical knowledge in light of some aspects of Wilfrid Sellars’ critique of the myth of the given. The account offered accords with Sellars’ in the view that epistemic status is attributed to empirical episodes holistically and within a broader normative context, but disagrees that such holism and normativity are accomplished only within the linguistic and conceptual confines of the space of reasons, and rejects the limitation (...) of the relevant normativity to the cognitive domain. Attention to the phenomenological notion of motivations in our mapping of the structure and acquisition of empirical knowledge reveals a form of weak categoriality given in experience, one outside exclusive mediation by language and concepts but also not merely causal. Section 1 outlines some basic aspects of Sellars’ account of empirical knowledge in Empiricism and the Philosophy of Mind, including a regress objection that arises due to his claim that empirical knowledge presupposes knowledge of general facts about perception. Section 2 examines Sellars’ later revisiting of the objection, via his critique of Roderick Firth, in “The Lever of Archimedes,” focusing on his analysis of the “Myth of the Categorial Given” and his use of the notion of ur-concepts. Section 3 looks at Sellars’ psychological nominalism and his rejection of the explanatory primacy of experience in light of the strict dichotomy between the space of causes and the space of reasons, and shows how Firth’s account aligns with phenomenology in its advocating for an irreducible and non-inferential role for experience. It also raises an important objection to Sellars’ account concerning the categorial givenness of causality. Section 4 turns to Husserl, arguing that his conception of motivation in the Logical Investigations and Ideas II reveals a third explanatory or logical space “between” that of causes and that of reasons. Section 5 further develops this account with regard to the explanatory role of lived experience. Section 6 revisits the regress objection to Sellars from the phenomenological standpoint developed earlier in the paper, and argues that an Husserlian account of empirical knowledge offers a viable alternative to Sellars’ that overcomes the regress objection and gives proper explanatory weight to the evidence of lived experience vis-à-vis scientific presuppositions about causality. (shrink)

Categories We Live by: The Construction of Sex, Gender, Race, and Other Social Categories, by Ásta. Oxford: OUP, 2018. Pp. 160.

The aim of the Schematism chapter of the Critique of Pure Reason is to solve the problem posed by the “inhomogeneity” of intuitions and categories: the sensible properties of objects represented in intuition are of a different kind than the properties represented by categories. Kant's solution is to introduce what he calls “transcendental schemata,” which mediate the subsumption of objects under categories. I reconstruct Kant's solution in terms of two substantive premises, which I call Subsumption Sufficiency (i.e., (...) that subsuming an object under a transcendental schema is sufficient to subsume it under the corresponding category) and Real Possibility (i.e., that it is really possible to subsume objects under each of the transcendental schemata). These two principles, together with a trivial modal one (the Subsumption-Possibility Link), entail that it is possible to subsume objects under categories; in other words, the argument of the Schematism is valid. The main work of the paper consists in reconstructing Kant's arguments for, and explanations of, these premises. I argue that they hinge on Kant's claim that transcendental schemata are “time-determinations,” which I interpret to mean: rules for reflexively representing the temporal relations among our own representational states. On the basis of this reading, I reconstruct Kant's argument for Subsumption Sufficiency, category by category. I also explain why Real Possibility follows almost immediately. Granting Kant the argument up to this point in the Critique, the argument of the Schematism is sound. (shrink)

This article uses sim-max games to model perceptual categorization with the goal of answering the following question: To what degree should we expect the perceptual categories of biological actors to track properties of the world around them? I argue that an analysis of these games suggests that the relationship between real-world structure and evolved perceptual categories is mediated by successful action in the sense that organisms evolve to categorize together states of nature for which similar actions lead to (...) similar results. This conclusion indicates that both strongly realist and strongly antirealist views about perceptual categories are too simple. (shrink)

Platon s-a inspirat din activitatea filosofică a unora dintre predecesorii săi, în special a lui Socrate, dar și Parmenide, Heraclit și Pitagora, pentru a-și dezvolta propria filosofie, care explorează majoritatea domeniilor importante, inclusiv metafizica, etica, estetica și politica.Împreună cu profesorul său Socrate și elevul său Aristotel, a pus bazele gândirii filosofice occidentale. Platon este considerat ca unul dintre cei mai importanți și influenți filosofi din istoria omenirii, fiind unul dintre fondatorii religiei și spiritualității occidentale. Filosofia dezvoltată de el, cunoscută sub (...) numele de platonism, se bazează pe teoria Formelor cunoscută prin rațiune pură ca soluție la problema universalelor. Filosofia lui Platon se înscrie pe linia presocraticilor, a sofiștilor și a tradițiilor artistice care stau la baza educației grecești, într-un cadru nou, definit de dialectică și teoria ideilor. Cunoașterea este pentru Platon o activitate a sufletului, afectată de obiectele sensibile, și de procesele interne. În Republica, forma cea mai înaltă este considerată ca fiind Forma Binelui, sursa tuturor celorlalte Forme care ar putea fi cunoscute prin rațiune. Tema centrală a cărții este dreptatea, argumentată cu ajutorul mai multor teorii platonice, inclusiv mitul alegoric al peșterii, doctrina ideilor, dialectica, teoria sufletului și proiectul unui oraș ideal. Dialectica lui este un tip de cunoaștere, cu rol rol ontologic și metafizic, la care se ajunge prin confruntarea mai multor poziții pentru a depăși opinia (doxa), o deplasare din lumea aparențelor (sau a „sensibilului”) către cunoașterea intelectuală (sau „inteligibilul”) până la primele principii. Modelul educațional al lui Platon (paidèia) diferențiază nivelul educației în funcție de aptitudinile elevilor. Conform principiilor socratice, pentru a face dreptate trebuie să se știe ce este bine, iar aceasta o știe cel mai bine filosoful. Platon a detaliat acest concept, evidențiind distincția dintre filosof (care caută principiile adevărului fără a pretinde că îl posedă) și sofist (care se lasă ghidat de opinie ca singurul parametru valid al cunoașterii). -/- CUPRINS -/- Platon - Biografie - Călătoriile lui Platon - Socrate - Academia - Lucrările lui Platon - - Clasificări ale lucrărilor - - - Cronologic - - - Tetralogii - - - Trilogii - - - Grupări lexicale Filosofia lui Platon - Sufletul - Funcția mitului - Idei - Teoria formelor - Ontologia - Epistemologia - Etica - Politica - Statul filosofic - Arta - Doctrinele nescrise: Unu și Diada Republica - Personaje - Conținut - Temele Republicii - - Justiția și dreptatea (Cartea I) - - Statul ideal (Cărțile II-III) - - Analogia oraș-suflet. Armonia părților (Cărțile IV-V) - - Teoria Formelor (Metafora liniei și mitul peșterii) (Cărțile VI-VII) - - Familia și statul (Cărțile VIII-IX) - - Mitul lui Er (Cartea X) Dialectica Educația Filosoful-rege Bibliografie -/- DOI 10.13140/RG.2.2.27534.23361 . (shrink)

There are many ways of construing the claim that some categories are more “natural" than others. One can ask whether a system of categories is innate or acquired by learning, whether it pertains to a natural phenomenon or to a social institution, whether it is lexicalized in natural language or requires a compound linguistic expression. This renders suspect any univocal answer to this question in any particular case. Yet another question one can ask, which some authors take to (...) have a bearing on the issue of the naturalness of categories, is whether a system of categories constitutes a unique way of organizing a particular set of entities or phenomena, or whether there are other legitimate classification schemes that can coexist with it. Another way of putting this is by asking whether systems of categories can cut across one another, and if so, under what circumstances. Some philosophers have claimed that crosscutting systems of categories cannot exist as genuine natural kinds. This paper examines that claim and puts forward some counterexamples, concluding that this notion of natural kind is not in tune with scientific classification and ought to be rejected in favor of an alternative. (shrink)

Introduction to a symposium in The Journal of Aesthetics and Art Criticism on the 50th anniversary of Kendall Walton's "Categories of Art." Featuring papers by Madeleine Ransom, Stacie Friend, David Davies and Kendall Walton.

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