It has been suggested recently that Heidegger’s philosophy entails a linguistic idealism because it is committed to the thesis that meaning determines reference. I argue that a careful consideration of the relationship between meaning and signification in Heidegger’s work does not support the strong sense of determination required by this thesis. By examining Heidegger’s development of Husserl’s phenomenology, I show that discourse involves a logic that articulates meaning into significations. Further analysis of Heidegger’s phenomenological method at work (...) shows that while meaning serves as a condition of possibility of signification in the sense that all possibilities for a term’s signification are latent in the meaning of that term, meaning under-determines signification and hence reference. Key Words: discourse • language • linguistic idealism • logic • meaning • phenomenology • signification. (shrink)

This book develops a theory of enriched meanings for natural language interpretation that uses the concept of monads and related ideas from category theory. The volume is interdisciplinary in nature, and will appeal to graduate students and researchers from a range of disciplines interested in natural language understanding and representation.

The purpose of this paper is to inquire into the meaning of the troublesome Aristotelian expression ‘Ο λόγοσ τῆσ οὐσίασ as it occurs at the very opening of Categories 1a 1–2, 7. That the passage has presented serious difficulties to commentators and translators alike can be easily ascertained through a survey and comparison of the relevant literature. It would seem from the disagreements among translators that the passage is either vague in the original Greek or that Aristotle did (...) not have a special doctrine to put across at the very opening such that would require technical formulations that would comply with the ontology presented in this treatise. (shrink)

The purpose of this paper is to inquire into the meaning of the troublesome Aristotelian expression ‘Ο λόγοσ τῆσ οὐσίασ as it occurs at the very opening of Categories 1a 1–2, 7. That the passage has presented serious difficulties to commentators and translators alike can be easily ascertained through a survey and comparison of the relevant literature. It would seem from the disagreements among translators that the passage is either vague in the original Greek or that Aristotle did (...) not have a special doctrine to put across at the very opening such that would require technical formulations that would comply with the ontology presented in this treatise. (shrink)

Catholic end-of-life ethics does not contain a principle that prohibits the excessive use of medical treatment for declining and dying patients. This article fills this lacuna by exploring and developing the principle of unreasonable means. Unreasonable means are present when the burdens to the patient and community far outpace the benefits to the patient and when the use of such means directly or indirectly limits another patient’s access to ordinary means. Unreasonable means reinforce the redistribution of limited medical resources from (...) the poor to the wealthy and from the global south to the global north. The principle of unreasonable means guides individual patients and medical proxies to preferentially opt for the morally ordinary medical needs of others before the patient’s own extraordinary medical needs. The principle underscores the need for patients and proxies to incorporate justice and the common good into end-of-life decisions. (shrink)

Among the main concerns of 20th century philosophy was that of the foundations of mathematics. But usually not recognized is the relevance of the choice of a foundational approach to the other main problems of 20th century philosophy, i.e., the logical structure of language, the nature of scientific theories, and the architecture of the mind. The tools used to deal with the difficulties inherent in such problems have largely relied on set theory and its “received view”. There are specific issues, (...) in philosophy of language, epistemology and philosophy of mind, where this dependence turns out to be misleading. The same issues suggest the gain in understanding coming from category theory, which is, therefore, more than just the source of a “non-standard” approach to the foundations of mathematics. But, even so conceived, it is the very notion of what a foundation has to be that is called into question. The philosophical meaning of mathematics is no longer confined to which first principles are assumed and which “ontological” interpretation is given to them in terms of some possibly updated version of logicism, formalism or intuitionism. What is central to any foundational project proper is the role of universal constructions that serve to unify the different branches of mathematics, as already made clear in 1969 by Lawvere. Such universal constructions are best expressed by means of adjoint functors and representability up to isomorphism. In this lies the relevance of a category-theoretic perspective, which leads to wide-ranging consequences. One such is the presence of functorial constraints on the syntax–semantics relationships; another is an intrinsic view of (constructive) logic, as arises in topoi and, subsequently, in more general fibrations. But as soon as theories and their models are described accordingly, a new look at the main problems of 20th century’s philosophy becomes possible. The lack of any satisfactory solution to these problems in a purely logical and set-theoretic setting is the result of too circumscribed an approach, such as a static and punctiform view of objects and their elements, and a misconception of geometry and its historical changes before, during, and after the foundational “crisis”, as if algebraic geometry and synthetic differential geometry – not to mention algebraic topology – were secondary sources for what concerns foundational issues. The objectivity of basic geometrical intuitions also acts against the recent version of structuralism proposed as ‘the’ philosophy of category theory. On the other hand, the need for a consistent and adequate conceptual framework in facing the difficulties met by pre-categorical theories of language and scientific knowledge not only provides the basic concepts of category theory with specific applications but also suggests further directions for their development (e.g., in approaching the foundations of physics or the mathematical models in the cognitive sciences). This ‘virtuous’ circle is by now largely admitted in theoretical computer science; the time is ripe to realise that the same holds for classical topics of philosophy. (shrink)

In this paper I display a general metaphysical assumption that characterizes basic naturalistic views and that is inherited, in a residual form, by their leading teleological rivals. The assumption is that intentional states require identifiable inner vehicles and that to explain intentional properties we must develop accounts that bind specific contents to specific vehicles. I show that this assumption is deeply rooted in representationalist and reductionist theories of content and I argue that it is deeply inappropriate. I sketch the main (...) features of plausible alternatives: such alternatives are either anti-representationalist (Dynamical Systems' models) or anti-reductionist (institution-based approaches), and are not committed to any such metaphysical premise. (shrink)

Linguistic evaluation has become an important area of inquiry in recent years. In the traditions of, e.g., lexical semantics, phraseology, corpus linguistics, and interactional linguistics, a large inventory of linguistic means have been identified by which speakers can express evaluative meanings. However, the class of German sentential idioms, e.g., Das kannst du dir in die Haare schmieren , has not gained much attention. This paper explores how the evaluative meaning of German sentential idioms is constructed syntactically, semantically, and pragmatically. (...) In particular, it is investigated how the meaning of these idioms interacts with the context in which they are used. A context model of evaluation is developed in which the cognitive category of cause plays a central role. The model is applied to contextualized examples, the findings supporting the hypothesis that cause is one of the core categories of evaluation. (shrink)

The paper presents a mode of researching epistemological and conceptual implications of text focused on the category of countertextuality. Parallel to the development of the orality / literacy theory within different areas of humanities and social sciences there runs a thread of various reconceptualization of text and textuality. It implies an increasing awareness of the non-neutral character of text (as a means of communicating knowledge within the academia) for the research results, which appears on both methodological and ethical grounds.In the (...) paper the example of the project of postmodern anthropology is invoked to show how the constraints of the norms of writing texts specific of anthropology in mid-1980’s are articulated and what the proposed ways of writing are that would overcome the perceived flaws of text. The article focuses on the major manifesto of the postmodern turn in anthropology (Writng Culture), some other methodological articles of its authors, as well as some of the actual ethnographic researches. I highlight some of the major charges laid against text in these works and some of the major countertextual writing strategies. (shrink)

This 1994 book develops a way of representing the meanings of linguistic expressions which is independent of any particular language, allowing the expressions to be manipulated in accordance with rules related to their meanings which could be implemented on a computer. It begins with a survey of the contributions of linguistics, logic and computer science to the problem of representation, linking each with a particular type of formal grammar. A system of graphs is then presented, organized by scope relations in (...) which linguistic constituents are sub-graphs whose configuration is determined by their categories. In developing this system, the author extends the notion of scope and argues that anaphoric and relative pronouns are structural signs not linguistic constituents. Certain count nouns are made the basis of this system and an account of proper names relating the count nouns, is given. (shrink)

Review of Timothy Potts, *Structures and Categories for the Representation of Meaning* (CUP).

Duns Scotus's Doctrine of Categories and Meaning is a key text for the origins of Martin Heidegger's concept of "facticity." Originally submitted as a doctoral thesis in 1915, it focuses on the 13th-century philosopher-theologian John Duns Scotus. Heidegger first analyzes Scotus's doctrine of categories, then offers a meticulous explanation of the Grammatica Speculativa, a work of medieval grammar now known to be authored by the Modist grammarian Thomas of Erfurt. Taken together, these investigations represent an early foray (...) into Heidegger's lifelong philosophical concerns, "the question of being in the guise of the problem of categories and the question of language in the guise of the doctrine of meaning." This new and unique translation of one of Heidegger's earliest works offers an important look at his early thinking before the question of being became his central concern and will appeal to readers exploring Heidegger's philosophical development, medieval philosophy, phenomenological interpretations of the history of philosophy, and the philosophy of language. (shrink)

We are women, we are men. We are refugees, single mothers, people with disabilities, and queers. We belong to social categories and they frame our actions, self-understanding, and opportunities. But what are social categories? How are they created and sustained? How does one come to belong to them? Ásta approaches these questions through analytic feminist metaphysics. Her theory of social categories centers on an answer to the question: what is it for a feature of an individual to (...) be socially meaningful? In a careful, probing investigation, she reveals how social categories are created and sustained and demonstrates their tendency to oppress through examples from current events. To this end, she offers an account of just what social construction is and how it works in a range of examples that problematize the categories of sex, gender, and race in particular. The main idea is that social categories are conferred upon people. Ásta introduces a 'conferralist' framework in order to articulate a theory of social meaning, social construction, and most importantly, of the construction of sex, gender, race, disability, and other social categories. (shrink)

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

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)

The general topic of this book is the theory of categories, its sources, meaning and development. The inquiry can be seen to proceed on two levels. On one, the history of the theory is traced from its alleged genesis in Aristotle, through its main subsequent stages of Kant and Hegel, up to a kind of consummation in two of its prominent twentieth century adherents, Alfred North White head and Nicolai Hartmann. Special attention has been paid to that aspect (...) of the Hegelian conception of the categorial analysis from which the principle of coherence emerged. On the second, deeper level, however, everything starts with Whitehead's metaphysical system, the central part of which con sists of a fascinating, though highly intricate, web of categorial notions and propositions. The historical perspective becomes a means for untangling that web. I am indebted to a number of people for advice, comment and criticism of various parts of this book. My greatest thanks go to my teachers and colleagues Nathan Rotenstreich, Nathan Spiegel, Yaakov Fleischman, as well as to the late Shmuel Hugo Bergman and Pepita Haezrachi. of this book was published in 1967 by An earlier, Hebrew version the Bialik Institute of Jerusalem. I am grateful to Mr Yehoshua Perel, Mr Arnold Schwartz and to my wife Varda for their cooperation in rendering the extensively revised text of the book into readable English. I also owe great appreciation to Miss Liat Dawe for an accurate and painstaking word-processing of the text. (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)

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)

A study of Jim Jones and the Peoples Temple. It features a prologue that considers the meaning of the tragedy for a post-Waco, post-9/11 world.

The Lambek-Grishin calculus is a symmetric version of categorial grammar obtained by augmenting the standard inventory of type-forming operations (product and residual left and right division) with a dual family: coproduct, left and right difference. Interaction between these two families is provided by distributivity laws. These distributivity laws have pleasant invariance properties: stability of interpretations for the Curry-Howard derivational semantics, and structure-preservation at the syntactic end. The move to symmetry thus offers novel ways of reconciling the demands of natural language (...) form and meaning. (shrink)

Many commentators have attempted to say, more clearly than Wittgenstein did in his Tractatus logico-philosophicus, what sort of things the ‘simple objects’ spoken of in that book are. A minority approach, but in my view the correct one, is to reject all such attempts as misplaced. The Tractarian notion of an object is categorially indeterminate: in contrast with both Frege's and Russell's practice, it is not the logician's task to give a specific categorial account of the internal structure of elementary (...) propositions or atomic facts, nor, correlatively, to give an account of the forms of simple objects. The few commentators who have hitherto maintained this view have mainly devoted themselves to establishing that this was Wittgenstein's intention, and do not much address the question why Wittgenstein held that it is not the logician's business to say what the objects are. The present paper means to fill this lacuna by placing this view in the context of the Tractatus's treatment of logic generally, and in particular by connecting it with Wittgenstein's treatment of generality and with his reaction to Russell's approach to logical form. (shrink)

The project of Categories We Live By is to offer a metaphysics of social categories. The strategy is to give a theory of social properties of individuals. The main components of the theory are a conferralist framework for properties; an account of social meaning; and an account of social construction; accompanying is also an account of social identity. This theory can be applies to offer concrete conferralist proposals of categories such as sex, gender, race, disability, religion, (...) and LGBTQ categories. This précis describes the main components (conferralist framework, social meaning, social construction, social identity) briefly, but leaves discussions of applications for another time. (shrink)

Most people, including philosophers, tend to classify human motives as falling into one of two categories: the egoistic or the altruistic, the self-interested or the moral. According to Susan Wolf, however, much of what motivates us does not comfortably fit into this scheme. Often we act neither for our own sake nor out of duty or an impersonal concern for the world. Rather, we act out of love for objects that we rightly perceive as worthy of love--and it is (...) these actions that give meaning to our lives. Wolf makes a compelling case that, along with happiness and morality, this kind of meaningfulness constitutes a distinctive dimension of a good life. Written in a lively and engaging style, and full of provocative examples, Meaning in Life and Why It Matters is a profound and original reflection on a subject of permanent human concern. (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.

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

Dominical categories are categories in which the notions of partial morphisms and their domains become explicit, with the latter being endomorphisms rather than subobjects of their sources. These categories form the basis for a novel abstract formulation of recursion theory, to which the present paper is devoted. The abstractness has of course its usual concomitant advantage of generality: it is interesting to see that many of the fundamental results of recursion theory remain valid in contexts far removed (...) from their classic manifestations. A principal reason for introducing this new formulation is to achieve an algebraization of the generalized incompleteness theorem, by providing a category-theoretic development of the concepts and tools of elementary recursion theory that are inherent in demonstrating the theorem.Dominical recursion theory avoids the commitment to sets and partial functions which is characteristic of other formulations, and thus allows for an intrinsic recursion theory within such structures as polyadic algebras. It is worthy of notice that much of elementary recursion theory can be developedwithout referencetoelements.By Gödel's generalized incompleteness theorem for consistent arithmetical systemTwe mean any statement of the following sort: if every recursive set is definable inT, thenTis essentially undecidable [41]; or if all recursive functions are definable inT, thenTis essentially undecidable [41]; or if every recursive set is definable inT, thenT0andR0 are recursively inseparable [39]; or if all re sets are representable inT, thenT0is creative [28], [39]; or ifTis a Rosser theory, thenT0andR0are effectively inseparable [39]. (shrink)

The gradual appearance and relative stabilisation of the names of different kinds of martial activities in different cultures and contexts has led to confusion and to an unhelpful and unjustifiable elision of meanings, which merges different modes of combat and other martial activities. To gain a clearer perspective on this area, we must enquire into the criteria according to which the various kinds of martial activities are classified. Our assessment of the literature suggests that there is no satisfactory and well-justified (...) overall cross-cultural account of the classification of martial activities. This paper provides a revisionary classification and offers an explanation and a justification of the five main categories identified: close combat, warrior arts, martial paths, martial arts and martial sports; as well as some minor ones, such as martial training, martial therapy, martial display, martial games and martial dance. (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 overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a quantum algebra (...) of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an Appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches. (shrink)

The notion of the "impolitical" developed in this volume draws its meaning from the exhaustion of modernity's political categories, which have become incapable of giving voice to any genuinely radical perspective. The impolitical is not the opposite of the political but rather its outer limit: the border from which we might glimpse a trajectory away from all forms of political theology and the depoliticizing tendencies of a completed modernity. The book's reconstruction of the impolitical lineage-which is anything but (...) uniform-begins with the extreme conclusions reached by Carl Schmitt and Romano Guardini in their reflections on the political and then moves through a series of encounters between several great twentieth-century texts: from Hannah Arendt's On Revolution to Hermann Broch's The Death of Virgil, to Elias Canetti's Crowds and Power; from Simone Weil's The Need for Roots to Georges Bataille's Sovereignty to Ernst Junger's An der Zeitmauer. The trail forged by this analysis offers a defiant counterpoint to the modern political lexicon, but at the same time a contribution to our understanding of its categories. (shrink)

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

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

When, for example, we say of something that it ‘is an object’, or ‘is an event’, or ‘is a property’, we are engaging in categorial predication: we are assigning something to a certain ontological category. Ontologicalcategorization is clearly a type of classification, but it differs radically from the types of classification that are involved in thetaxonomic practices of empirical sciences, as when a physicist saysof a certain particle that it ‘is an electron’, or when a zoologist saysof a certain animal (...) that it ‘is a mammal’, or when a meteorologist says of a certain weather‐phenomenon that it ‘is a hurricane’. Classifications of the latter types presuppose that the items being classified have already been assigned to appropriate ontologicalcategories, such as the categories of object, species, or event. What do categorial predications mean? How are their truth‐conditions to be determined, and how can those truth‐conditions be known to be satisfied? Do they have truthmakers? Questions like these are amongst those addressed in the present paper. (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)

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. (...) Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method. (shrink)

Most people, including philosophers, tend to classify human motives as falling into one of two categories: the egoistic or the altruistic, the self-interested or the moral. According to Susan Wolf, however, much of what motivates us does not comfortably fit into this scheme. Often we act neither for our own sake nor out of duty or an impersonal concern for the world. Rather, we act out of love for objects that we rightly perceive as worthy of love--and it is (...) these actions that give meaning to our lives. Wolf makes a compelling case that, along with happiness and morality, this kind of meaningfulness constitutes a distinctive dimension of a good life. Written in a lively and engaging style, and full of provocative examples, Meaning in Life and Why It Matters is a profound and original reflection on a subject of permanent human concern. (shrink)

Even though residuation is at the core of Categorial Grammar (Lambek, 1958), it is not always immediate to realize how standard logical systems like Multi-modal Categorial Type Logics (MCTL) (Moortgat, 1997) actually embody this property. In this paper, we focus on the basic system NL (Lambek, 1961) and its extension with unary modalities NL() (Moortgat, 1996), and we spell things out by means of Display Calculi (DC) (Belnap, 1982; Goré, 1998). The use of structural operators in DC permits a sharp (...) distinction between the core properties we want to impose on the logical system and the way these properties are projected into the logical operators. We will show how we can obtain Lambek residuated triple \, / and of binary operators, and how the operators and introduced by Moortgat (1996) are indeed their unary counterpart.In the second part of the paper we turn to other important algebraic properties which are usually investigated in conjunction with residuation (Birkhoff, 1967): Galois and dual Galois connections. Again, DC let us readily define logical calculi capturing them. We also provide preliminary ideas on how to use these new operators when modeling linguistic phenomena. (shrink)

Western philosophy has been dominated by the concept or the idea—the belief that there is one sovereign notion or singular principle that can make reality explicable and bring all that exists under its sway. In modern politics, this role is played by ideology. Left, right, or center, political schools of thought share a metaphysics of simplification. We internalize a dominant, largely unnoticeable framework, oblivious to complex, plural, and occasionally conflicting or mutually contradictory explanations for what is the case. In this (...) groundbreaking work, Michael Marder proposes a new methodology for political science and philosophy, one which he terms “categorial thinking.” In contrast to the concept, no category alone can exhaust the meaning of anything: categories are so many folds, complications, respectful of multiplicity. Ranging from classical Aristotelian and Kantian philosophies to phenomenology and contemporary politics, Marder's book offers readers a theoretical toolbox for the interpretation of political phenomena, processes, institutions, and ideas. His categorial apparatus encompasses political temporality and spatiality; the revolutionary and conservative modalities of political actuality, possibility, and necessity; quantitative and qualitative approaches to the study of political reality; the meaning of political relations; and various senses of political being. Under this lens, the political appears not as a singular concept but as a family of categories, allowing room for new, plural, and often antagonistic ideas about the state, the people, sovereignty, and power. (shrink)