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)
This paper provides an account of Kant's categories of freedom, explaining how they fit together and what role they are supposed to play. My interpretation places particular emphasis on the structural features that the table of the categories of freedom shares with the table of judgements and the table of categories laid out by Kant in the Critique of Pure Reason. In this way we can identify two interpretative constraints, namely (i) that the categories falling under (...) each heading must form a synthetic unity whereby the third one derives from the combination of the other two. and (ii) that the first two categories falling under each heading must be morally undetermined and sensibly conditioned, while the third category is sensibly unconditioned and determined only by the moral law. (shrink)
I describe an account of ontological categories which does justice to the facts that not all categories are ontological categories and that ontological categories can stand in containment relations. The account sorts objects into different categories in the same way in which grammar sorts expressions . It then identifies the ontological categories with those which play a certain role in the systematization of collections of categories. The paper concludes by noting that on my (...) account what ontological categories there are is partially interest-relative, and that furthermore no object can belong essentially to its ontological category. (shrink)
I argue, without offering what Ameriks has called a 'short argument', that idealism follows already from the constraints that the use of the categories, in particular the categories of quality, places on the conceivability of things in themselves. My claim is that, although it is not only possible but also necessary to think things in themselves, it doesn't follow that by merely thinking we have a full grasp of the nature of things in themselves. For support, I look (...) to a much overlooked chapter in the Critique, the Transcendental Ideal, where Kant discusses what it is for a thing to be a thing-in-itself proper, namely something that is thoroughly determined. I claim that the chief reason why, given Kant's view of determinative judgment, we cannot determine a thing-in-itself is because of two connected reasons: (1) a thing-in-itself is already fully determined and therefore not further determinable and (2) we cannot possibly determine all of the thing's possible determinations. (shrink)
James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, and (...) it suggests an interesting reason why the rewriting might have been thought necessary. (shrink)
The discussion of the relation of levels of reality to categories is important because categories have often been interpreted as constituting levels of reality. This article explores whether this view is correct, and argues it is not. Categories as such should not be understood to constitute levels of reality, although particular categories may. The article begins with a discussion of levels of reality and then turns to specific questions about categories and how they are related (...) to these levels. (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. (English translation in progress.). (shrink)
This article argues for two related theses. First, it defends a general thesis: any kind of necessity, including metaphysical necessity, can only be known a priori. Second, however, it also argues that the sort of a priori involved in modal metaphysical knowledge is not related to imagination or any sort of so-called epistemic possibility. Imagination is neither a proof of possibility nor a limit to necessity. Rather, modal metaphysical knowledge is built on intuition of philosophical categories and the structures (...) they form. (shrink)
Much recent work on Aristotle's Categories assumes that there is an ontological theory presented in that work and tries to reconstruct it on the basis of the slender evidence in the book. I claim that this is misguided. Using a distinction made by G.E.L. Owen between theory and the "phaenomena", I argue that the Categories is mainly concerned with setting out the phenomena -- the intuitions that any ontology must explain. This thesis has consequences for the interpretation of (...) Aristotle's ontological writings. I explore some of these. (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)
The concept of an ontological category is central to metaphysics. Metaphysicians argue about which category of existence an object should be assigned to, whether one category can be reduced to another one, or whether there might be different equally adequate systems of categorization. Answers to these questions presuppose a clear understanding of what precisely an ontological category is, and Jan Westerhoff now provides the first in-depth analysis. After examining a variety of attempted definitions, he proceeds to argue for a new (...) understanding of ontological categories, according to which they are systematizations of our knowledge of the world rather than essential characteristics of the world itself. Metaphysicians will find his work highly stimulating. (shrink)
Roderick Chisholm has been for many years one of the most important and influential philosophers contributing to metaphysics, philosophy of mind, and epistemology. This book can be viewed as a summation of his views on an enormous range of topics in metaphysics and epistemology. Yet it is written in the terse, lucid, unpretentious style that has become a hallmark of Chisholm's work. The book is an original treatise designed to defend an original, non-Aristotelian theory of categories. Chisholm argues that (...) there are necessary things and contingent things; necessary things being things that are not capable of coming into being or passing away. He defends the argument from design, and thus includes the category of necessary substance (God). Further contentions of the essay are that attributes are also necessary beings, but not necessary substances, and that human beings are contingent substances but may not be material substances. (shrink)
Dennis Schulting offers a thoroughgoing, analytic account of the first half of the Transcendental Deduction of the Categories in the B-edition of Kant’s Critique of Pure Reason that is different from existing interpretations in at least one important aspect: its central claim is that each of the 12 categories is wholly derivable from the principle of apperception, which goes against the current view that the Deduction is not a proof in a strict philosophical sense and the standard reading (...) that in the Deduction Kant only gives an account of the global applicability of the categories to experience. This novel approach enables a reappraisal of Kant’s controversial claim that transcendental self-consciousness is not only a necessary condition of objective experience but also sufficient for it. The book provides an extensive analysis of Kant’s theory of transcendental apperception and also explains why the argument of the Transcendental Deduction is both a regressive and a progressive argument. (shrink)
I attempt to answer the question of what Aristotle's criteria for 'being a substance' are in the Categories. On the basis of close textual analysis, I argue that subjecthood, conceived in a certain way, is the criterion that explains why both concrete objects and substance universals must be regarded as substances. It also explains the substantial primacy of concrete objects. But subjecthood can only function as such a criterion if both the subjecthood of concrete objects and the subjecthood of (...) substance universals can be understood as philosophically significant phenomena. By drawing on Aristotle's essentialism, I argue that such an understanding is possible: the subjecthood of substance universals cannot simply be reduced to that of primary substances. Primary and secondary substances mutually depend on each other for exercising their capacities to function as subjects. Thus, subjecthood can be regarded as a philosophically informative criterion for substancehood in the Categories. (shrink)
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of (...) a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category . We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics. (shrink)
Residual categories are those which cannot be formally represented within a given classification system. We examine the forms that residuality takes within our information systems today, and explore some silences which form around those inhabiting particular residual categories. We argue that there is significant ethical and political work to be done in exploring residuality.
Facets and general categories used in bibliographic classification have been based on a disciplinary organization of knowledge. However, facets and categories of phenomena independent from disciplines can be identified similarly. Phenomena can be classified according to a series of integrative levels (layers), which in turn can be grouped into the major strata of form, matter, life, mind, society and culture, agreeing with Nicolai Hartmann’s ontology. Unlike a layer, a stratum is not constituted of elements of the lower ones; (...) rather, it represents the formal pattern of the lower ones, like the horse hoof represents the shape of the steppe. Bibliographic categories can now be seen in the light of level theory: some categories are truly general, while others only appear at a given level, being the realization of a general category in the specific context of the level: these are the facets of that level. In the notation of the Integrative Level Classification project, categories and facets are represented by digits, and displayed in a Web interface with the help of colours. (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)
Simplicius in Cat. 12,10-13,12 presents an interesting justification for the study of Aristotle's Categories, based in Neoplatonic psychology and metaphysics. I suggest that this passage could be regarded as a testimonium to Iamblichus' reasons for endorsing Porphyry's selection of the Categories as an introductory text of Platonic philosophy. These Iamblichean arguments, richly grounded in Neoplatonic metaphysics and psychology, may have exercised an influence comparable to Porphyry's.
We explore the possibility and some potential payoffs of using the theory of accessible categories in the study of categories of logics. We illustrate this by two case studies focusing on the category of finitary structural logics and its subcategory of algebraizable logics.
We investigated the understanding of causal systems categories—categories defined by common causal structure rather than by common domain content—among college students. We asked students who were either novices or experts in the physical sciences to sort descriptions of real-world phenomena that varied in their causal structure (e.g., negative feedback vs. causal chain) and in their content domain (e.g., economics vs. biology). Our hypothesis was that there would be a shift from domain-based sorting to causal sorting with increasing expertise (...) in the relevant domains. This prediction was borne out: The novice groups sorted primarily by domain and the expert group sorted by causal category. These results suggest that science training facilitates insight about causal structures. (shrink)
Humans are remarkably proficient at categorizing visually-similar objects. To better understand the cortical basis of this categorization process, we used magnetoencephalography (MEG) to record neural activity while participants learned--with feedback--to discriminate two highly-similar, novel visual categories. We hypothesized that although prefrontal regions would mediate early category learning, this role would diminish with increasing category familiarity and that regions within the ventral visual pathway would come to play a more prominent role in encoding category-relevant information as learning progressed. Early in (...) learning we observed some degree of categorical discriminability and predictability in both the prefrontal cortex and the ventral visual pathway. Predictability improved significantly above chance in the ventral visual pathway over the course of learning with the left inferiortemporal and fusiform gyri showing the greatest improvement in predictability between 150-250msec (M200) during category learning. In contrast, there was no comparable increase in discriminability in prefrontal cortex with the only significant post-learning effect being a decrease in predictability in inferior frontal gyrus between 250-350msec (M300). Thus, the ventral visual pathway appears to encode learned visual categories over the long term. At the same time these results add to our understanding of the cortical origins of previously-reported signature temporal components associated with perceptual learning. (shrink)
Sophist 255c14 distinguishes καθ’ αὑτά and πρὸς ἄλλα (in relation to others). Many commentators identify this with the ‘absolute’ and ‘relative’ category distinction. However, terms such as ‘same’ cannot fit into either category. Several reliable manuscripts read πρὸς ἄλληλα (in relation to each other) for πρὸς ἄλλα. I show that πρὸς ἄλληλα is a palaeographically plausible reading which accommodates the problematic terms. I then defend my reading against objections.
Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered.
The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the bio-mathematician 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 against computational models that since the 1990’s are pervading almost every domain of biology. (shrink)
Mintz (2003) found that in English child-directed speech, frequently occurring frames formed by linking the preceding (A) and succeeding (B) word (A_x_B) could accurately predict the syntactic category of the intervening word (x). This has been successfully extended to French (Chemla, Mintz, Bernal, & Christophe, 2009). In this paper, we show that, as for Dutch (Erkelens, 2009), frequent frames in German do not enable such accurate lexical categorization. This can be explained by the characteristics of German including a less restricted (...) word order compared to English or French and the frequent use of some forms as both determiner and pronoun in colloquial German. Finally, we explore the relationship between the accuracy of frames and their potential utility and find that even some of those frames showing high token-based accuracy are of limited value because they are in fact set phrases with little or no variability in the slot position. (shrink)
A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...) Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)
The merited response argument is an argument in favor of artistic ethicism. According to this view, the interaction between art and morality is such that a moral defect in a work of art negatively influences the work's artistic value (and a moral merit, when relevant, is always an artistic merit). I contend that the argument relies on a criterion of aesthetic and artistic relevance that, when properly understood, fails to constitute a premise that either the artistic contextualist or the autonomist (...) would accept. I then offer a version of the merited response argument that supports artistic contextualism and argue that, given certain controversial assumptions, immoral art in the Western tradition is more common than typically acknowledged in the recent literature on the topic. (shrink)
The present volume makes available for the first time the earliest translation of Aristotle into a Semitic language. It will open the way to a fuller understanding of the transformation of Greek logic in Syriac and Arabic.