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)

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.

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)

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)

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)

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)

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)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic (...) treatment of concrete universals along with a new concept to abstractly model the functions of a brain. (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 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)

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)

The following text is divided in four parts. The first presents the inner relation between the phenomenological concept of intentionality and space in a general mathematical sense. Following this train of though the second part brie_ly characterizes the use of the geometrical concept of manifold (Mannigfaltigkeit) in Husserl’s work. In the third part we present some examples of the use of the concept in Husserl’s analyses of space, time and intersubjectivity, pointing out some dif_iculties in his endeavor. In the fourth (...) and _inal part we offer some points of coincidence between phenomenology and category theory suggesting that the latter can work as a formal frame for ontology in the former. Our thesis is that intentionality operates in different levels as a morphism, functor and natural transformation. (shrink)

The following text is divided in four parts. The first presents the inner relation between the phenomenological concept of intentionality and space in a general mathematical sense. Following this train of though the second part brie_ly characterizes the use of the geometrical concept of manifold (Mannigfaltigkeit) in Husserl’s work. In the third part we present some examples of the use of the concept in Husserl’s analyses of space, time and intersubjectivity, pointing out some dif_iculties in his endeavor. In the fourth (...) and _inal part we offer some points of coincidence between phenomenology and category theory suggesting that the latter can work as a formal frame for ontology in the former. Our thesis is that intentionality operates in different levels as a morphism, functor and natural transformation. (shrink)

Notions such as Sunyata, Catuskoti, 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 Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata 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. Catuskoti refers to the claim (...) that four truth values, along with 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 which 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 Sunyata. 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 Catuskoti. 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)

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)

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.

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 paper, I explore a line of argument against one form of realism about fictional characters : abstract artifact theory, the view according to which fictional characters like Harry Potter are part of our reality, but, they are abstract objects created by humans, akin to the institution of marriage and the game of soccer. I will defend artifactualism against an objection that Mark Sainsbury considers decisive against it: the category-mistake objection. The objection has it that artifactualism attributes (...) to people who produce and process sentences and thoughts about Harry Potter massive error, indeed, a category mistake about what kind of thing Harry Potter is; for an abstract object isn’t the sort of thing that can wear glasses, ride a double-decker bus, attend school. Given problems with this objection, artifactualism, I shall conclude, remains a tenable contender. (shrink)

The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the biomathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of “category” and the correlative concept of “natural equivalence” in mathematical modeling applied to living beings. Our questions are the following: According to Rosen, to what extent does the mathematical notion of category give access to more “natural” formalisms in the modeling of living (...) beings? Is the so -called “naturalness” of some kinds of equivalences (which the mathematical notion of category makes it possible to generalize and to put at the forefront) analogous to the naturalness of living systems? Rosen appears to answer “yes” and to ground this transfer of the concept of “natural equivalence” in biology on such an analogy. But this hypothesis, although fertile, remains debatable. Finally, this paper makes a brief account of the later evolution of Rosen’s arguments about this topic. In particular, it sheds light on the new role played by the notion of “category” in his more recent objections to the computational models that have pervaded almost every domain of biology since the 1990s. (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 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 describes a method for the analysis of the evolutionary path of a complex, dynamic, and contingent social phenomenon in an empirical setting. Given empirical evidence of a surprising or anomalous fact, which contradicts the prediction of the wide-acknowledged theory, the goal is to formulate a plausible explanation based on the context of occurrence, taking a holistic and historical point of view. The procedure begins by translating theoretical propositions into grammar rules to describe patterns of either individual action (...) or interaction that may occur within the hypothesized social system. The result is a category of social process in which the objects are types of decision-making events carried by a stable community of actors over time, and the relationships between them are state transitions revealed in the sequences of event outcomes. Therefore, structural comparison between pairs of representative instances result in an extension of the category of social processes, relying on the configurations of contextual conditions that enable the occurrence of the new event outcome in specific empirical settings. (shrink)

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.

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 idea of a responsible cosmopolitan state (RCS) represents a recent attempt to reconcile the utopianism of cosmopolitan political theory and the practical constraints arising from the current realities of politics among territorial and largely self-interested states. I show in the chapter that the neorealist and/or geopolitical challenge rests on a misconception about what cosmopolitanism is meant to provide, because immediate practical advice is only a part of what normative political theory may bring to the table. Besides the (...) notion of self-interest which can be interpreted in different ways, it is mainly the action-modifying role of norms (especially international/supranational law) which may gradually change the game. Since the sustenance of state capacities is often preconditioned by events which take place beyond state borders, shared rules of conduct allow for more effective coordination in cases where collective action is required. Although the idea of a RCS primarily targets foreign policy priorities of smaller/weaker states (not-great-powers), it may turn out that collective action problems arising from empirical realities of the 21st century increasingly put great powers under pressure to accept such self-imposed constraints and comply with them. In the final part of the paper, however, I explain why this ‘cosmopolitan optimism’ needs to be aware of its own limitations, singling out the problems of internal motivation of actors in world politics and the deeper meaning of sovereignty which precludes an easy switch to the language of dispersed, pooled, or relational sovereignty. I conclude by arguing that if we are to take cosmopolitan ideals seriously, the RCS most likely represents a transitional stage on the route towards a centralised global political authority. (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)

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)

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)

This article focuses on the reception of Aristotle’s Categories by the first three representatives of Greek Neoplatonism: Plotinus (204/205–270 CE), Porphyry (ca. 234–ca. 305 CE), Iamblichus (ca. 242–ca. 325 CE). The first section argues that Plotinus’ acquaintance with Aristotle’s treatises marked a fresh start vis-à-vis the previous Platonist tradition. Aristotle’s views, arguments and vocabulary are ubiquitous in Plotinus writings (the Enneads) and they must be considered an essential part of his philosophical project. Plotinus, however, does not share some of Aristotle’s (...) key theories and is critical of them. The second section focuses on Plotinus’ discussion of Aristotle’s Categories in the tripartite treatise On the Genera of Being (6.1–3). There he rejects the Peripatetic division into ten categories as providing an incomplete account of the genera of being that unduly omits “those which are most authentically beings”, i.e. Plato’s separate Forms. While drawing on earlier Platonist objections to Aristotle, Plotinus’ approach is original insofar as he criticizes Aristotle and his followers not only for omitting intelligible beings in the division of categories, but also for being unable, for this very reason, to work out an adequate division of sensible beings themselves. The third section is devoted to Porphyry, a student of Plotinus’ and the editor of his works. Porphyry worked intensively on Aristotle’s Categories, which he regarded as an introduction not only to logic, but to philosophy as a whole. Unlike Plotinus, Porphyry aimed to integrate Aristotle into Platonism and his engagement with the Categories was a key part of his project after Plotinus’ in-depth criticism. Porphyry’s approach is connected to his view of the subject-matter of the Categories, which he sees as focusing on words insofar as they signify beings, and not on beings as such. The fourth section focuses on some parallels between Plotinus’ Genera of Beings and Porphyry’s works, which may reflect the debate within Plotinus’ school. The fifth section focuses on Iamblichus of Chalcis. Both in theology and in the interpretation of Aristotle’s Categories, Iamblichus aimed to both continue and supplant Porphyry’s work. While Plotinus criticizes Aristotle’s categories for omitting intelligible beings, and while Porphyry accepts Aristotle’s categories insofar as they focus on words signifying sensible things, Iamblichus incorporates his Neoplatonist and Pythagorizing metaphysics into the interpretation of the Categories. (shrink)

Response-dependence theories have historically been very popular in aesthetics, and aesthetic response-dependence has motivated response-dependence in ethics. This chapter closely examines the prospects for such theories. It breaks this category down into dispositional and fittingness strands of response-dependence, corresponding to descriptive and normative ideal observer theories. It argues that the latter have advantages over the former but are not themselves without issue. Special attention is paid to the relationship between hedonism and response-dependence. The chapter also introduces two aesthetic properties (...) that lead to wrong kinds of reasons problems for aesthetic response-dependence: insightfulness and the capacity to change one’s perspective. These properties do not have obvious parallels in the ethical domain, and so present an obstacle for response-dependence even in aesthetics. The chapter ends by examining replies on behalf of the response-dependence theorist, ultimately suggesting that a restricted form of response-dependence is the most promising way forward for fans of such theories. (shrink)

In this paper, I present a categorial theory of meaning which asserts that the meaning of a sentence is the function from the actualization of some potentiality or the potentiality of some actuality to the truth of the sentence. I argue that it builds on the virtues of David Lewis’s Possible World Semantics but advances beyond problems that Lewis’s theory faces with its distinctly Aristotelian turn toward actuality and potentiality.

This paper seeks to carve out a distinctive category of conspiracy theorist, and to explore the process of becoming a conspiracy theorist of this sort. Those on whom I focus claim their beliefs trace back to simply trusting their senses and experiences in a commonsensical way, citing what they take to be authoritative firsthand evidence or observations. Certain flat Earthers, anti-vaxxers, and UFO conspiracy theorists, for example, describe their beliefs and evidence this way. I first distinguish these conspiracy theorists (...) by contrasting them with another group that has recently received a lot of attention from the media, philosophers, and academics more broadly. I then dig more deeply into the nature of these conspiracy theorists’ epistemic self-understanding, in order to give an account of the process by which one becomes such a conspiracy theorist. I conclude with some takeaways and implications: first, I explore the implications of my account for whether these conspiracy theorists’ beliefs are rational; then, I argue that my account has practical takeaways about counteracting beliefs in misinformation, since strategies appropriate to this kind of conspiracy theorist may not be the same ones that are appropriate for other kinds. (shrink)

After coining the term “philopsychy” to describe a “soul-loving” approach to philosophical practice, especially when it welcomes a creative synthesis of philosophy and psychology, this article identifies a system of geometrical figures (or “maps”) that can be used to stimulate reflection on various types of perspectival differences. The maps are part of the author’s previously established mapping methodology, known as the Geometry of Logic. As an illustration of how philosophy can influence the development of psychology, Immanuel Kant’s table of twelve (...) categories and Carl Jung’s theory of psychological types are shown to share a common logical structure. Just as Kant proposes four basic categories, each expressed in terms of three subordinate categories, Jung proposes four basic personality functions, each having three possible manifestations. The concluding section presents four scenarios illustrating how such maps can be used in philosophical counseling sessions to stimulate philopsychic insight. (shrink)

Is it possible to get by with just one ontological category? We evaluate L.A. Paul's attempt to do so: the mereological bundle theory. The upshot is that Paul's attempt to construct a one category ontology may be challenged with some of her own arguments. In the positive part of the paper we outline a two category ontology with property universals and kind universals. We will also examine Paul's arguments against a version of universal bundle theory (...) that takes spatiotemporal co-location instead of compresence or coinstantiation as the feature by which we can identify genuine bundles. We compare this novel theory, bundle theory with kinds, and Paul's mereological bundle theory and apply them to a case study concerning entangled fermions and co-located bosons. (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)

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)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While (...) STT, understood as a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

Thomas Polger and Laurence Shapiro argue that Carl Gillett's much publicized dimensioned theory of realization is incoherent, being subject to a reductio. Their argument turns on the fact that Gillett's definition of realization makes property instances the exclusive relata of the realization relation, while his belief in multiple realization implies its denial, namely, that properties are the relata of the realization relation on occasions of multiple realization. Others like Sydney Shoemaker have also expressed their view of realization in terms (...) of property instances, yet they too have accepted the multiple realizability of properties. Thus I am interested in the more general issue raised by Polger and Shapiro's argument. Specifically, I show how to supplement a theory of realization with a category-inclusive auxiliary assumption, which avoids the stated reductio. I then offer a few reasons to justify the proposed category-inclusive view of realization, making some comparisons to supervenience and causation along the way. (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 (...) class='Hi'>theory, Kantian philosophy, Jungian psychology, and linguistics. (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)

John Hick’s theory concerning plurality of religions is an ontologic pluralism according to which all religions are authentic ways for man to attain the "real an sich". Gods of religions are real as perceived and veridical hallucinations; while the “real an sich” has ineffable substantial and trans-categorical properties. Hick’s view suffers from several problems. As a second order analysis of religions, Hick’s view is not a correct one. To reject naturalism, it falls into an epistemological circle, where distinction between (...) formal and substantial properties fades away. It seems that Hick is captured by a category mistake in the presentation of his own theory concerning authenticity of all religions to attain the "real an sich". (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)

After a short sketch of Lowe’s account of his four basic categories, I discuss his theory of formal ontological relations and how Lowe wants to account for dispositional predications. I argue that on the ontic level Lowe is a pan-categoricalist, while he is a language dualist and an exemplification dualist with regard to the dispositional/categorical distinction. I argue that Lowe does not present an adequate account of disposition. From an Aristotelian point of view, Lowe conflates dispositional predication with hôs (...) epi to poly statements about what is normally or mostly the case. (shrink)

Although a considerable degree of precision has been introduced both into the formulation and the discussion of ontological theories by the use of formal methods there is still a remarkable indefiniteness about foundational issues. In particular it is not clear what an ontological category is and why we regard something as an ontological category. This is amazing given that the notion of ontological category is in fact the most basic of the whole of ontology: it is what (...) this discipline is about. (shrink)

There have been attempts to get some logic out of belief dynamics, i.e. attempts to define the constants of propositional logic in terms of functions from sets of beliefs to sets of beliefs. It is interesting to see whether something similar can be done for ontological categories, i.e. ontological constants. The theory presented here will be a (modest) expansion of belief dynamics: it will not only incorporate beliefs, but also parts of beliefs, so called belief fragments. On the basis (...) of this we will give a belief-dynamical account of the ontological categories of states of affairs, individuals, properties of arbitrary adicities and properties of arbitrary orders. (shrink)

Embodied cognitive theories predict that linguistic conceptual representations are grounded and continually represented in real world, sensorimotor experiences. However, there is an on-going debate on whether this also holds for abstract concepts. Grammar is the archetype of abstract knowledge, and therefore constitutes a test case against embodied theories of language representation. Former studies have largely focussed on lexical-level embodied representations. In the present study we take the grounding-by-modality idea a step further by using reaction time (RT) data from the linguistic (...) processing of nominal classifiers in Chinese. We take advantage of an independent body of research, which shows that attention in hand space is biased. Specifically, objects near the hand consistently yield shorter RTs as a function of readiness for action on graspable objects within reaching space, and the same biased attention inhibits attentional disengagement. We predicted that this attention bias would equally apply to the graspable object classifier but not to the big object classifier. Chinese speakers (N = 22) judged grammatical congruency of classifier-noun combinations in two conditions: graspable object classifier and big object classifier. We found that RTs for the graspable object classifier were significantly faster in congruent combinations, and significantly slower in incongruent combinations, than the big object classifier. There was no main effect on grammatical violations, but rather an interaction effect of classifier type. Thus, we demonstrate here grammatical category- specific effects pertaining to the semantic content and by extension the visual and tactile modality of acquisition underlying the acquisition of these categories. We conclude that abstract grammatical categories are subjected to the same mechanisms as general cognitive and neurophysiological processes and may therefore be grounded. (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) (...) class='Hi'>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)

This essay aims at an analysis of Stumpf’s doctrine of categories. In Erkenntnislehre Stumpf argues that all categories empirically stem from outer and inner perception. Although Stumpf champions an empiricist explanation of the matter, he firmly rejects associationism. In his conception of the origin of categories, including substance, Stumpf builds on the assumption that human perception behaves dynamically. Sensory experience consists indeed essentially of perceptual wholes. The analysis of Stumpf’s theses is of great importance for our thorough understanding of his (...) philosophy. His theory regarding this crucial philosophical topic diverges considerably from Brentano’s. (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)