The distinction between personal level explanations and subpersonal ones has been subject to much debate in philosophy. We understand it as one between explanations that focus on an agent’s interaction with its environment, and explanations that focus on the physical or computational enabling conditions of such an interaction. The distinction, understood this way, is necessary for a complete account of any agent, rational or not, biological or artificial. In particular, we review some recent research in Artificial Life that pretends to (...) do completely without the distinction, while using agent-centered concepts all the way. It is argued that the rejection of agent level explanations in favour of mechanistic ones is due to an unmotivated need to choose among representationalism and eliminativism. The dilemma is a false one if the possibility of a radical form of externalism is considered. (shrink)
Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, (...) and methods of category theory understandable to this broad readership. -/- Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! -/- This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study. (shrink)
Radical Ontic Structural Realism (ROSR) claims that structure exists independently of objects that may instantiate it. Critics of ROSR contend that this claim is conceptually incoherent, insofar as, (i) it entails there can be relations without relata, and (ii) there is a conceptual dependence between relations and relata. In this essay I suggest that (ii) is motivated by a set-theoretic formulation of structure, and that adopting a category-theoretic formulation may provide ROSR with more support. In particular, I consider how (...) a category-theoretic formulation of structure can be developed that denies (ii), and can be made to do work in the context of formulating theories in physics. Keywords: structural realism, category theory, general relativity.. (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)
We provide a full characterization of computational error states for information systems. The class of errors considered is general enough to include human rational processes, logical reasoning, scientific progress and data processing in some functional programming languages. The aim is to reach a full taxonomy of error states by analysing the recovery and processing of data. We conclude by presenting machine-readable checking and resolve algorithms.
The semantic blindness objection to contextualism challenges the view that there is no incompatibility between (i) denials of external-world knowledge in contexts where radical-deception scenarios are salient, and (ii) affirmations of external-world knowledge in contexts where such scenarios are not salient. Contextualism allegedly attributes a gross and implausible form of semantic incompetence in the use of the concept of knowledge to people who are otherwise quite competent in its use; this blindness supposedly consists in wrongly judging that there is genuine (...) conflict between claims of type (i) and type (ii). We distinguish two broad versions of contextualism: relativistic-content contextualism and categorical-content contextualism. We argue that although the semantic blindness objection evidently is applicable to the former, it does not apply to the latter. We describe a subtle form of conflict between claims of types (i) and (ii), which we call différance-based affirmatory conflict. We argue that people confronted with radical-deception scenarios are prone to experience a form of semantic myopia (as we call it): a failure to distinguish between différance-based affirmatory conflict and outright inconsistency. Attributing such semantic myopia to people who are otherwise competent with the concept of knowledge explains the bafflement about knowledge-claims that so often arises when radical-deception scenarios are made salient. Such myopia is not some crude form of semantic blindness at all; rather, it is an understandable mistake grounded in semantic competence itself: what we call a competence-based performance error. (shrink)
We defend the view that belief is a psychological category against a recent attempt to recast it as a normative one. Tamar Gendler has argued that to properly understand how beliefs function in the regulation and production of action, we need to contrast beliefs with a class of psychological states and processes she calls “aliefs.” We agree with Gendler that affective states as well as habits and instincts deserve more attention than they receive in the contemporary philosophical psychology literature. (...) But we argue that it is a serious error to align beliefs with the norm of rationality, while building a contrasting category whose members are characterized primarily by their failure to measure up to that normative standard, since these latter ones cannot constitute a distinct psychological category. First, we demonstrate that Gendler gets unwarranted conclusions about the existence of aliefs from belief-discordant cases. Next, we argue that the concept of alief is insufficiently clear. Aliefs cannot be distinguished from other types of states, such as beliefs. Also, when grouping many states under the category of aliefs, Gendler overlooks important differences between phenomena that are clearly distinct, such as habits and instincts. Aliefs simply do not constitute a legitimate psychological category. (shrink)
This is a translation of an early essay by the German philosopher Nicolai Hartmann (1882–1950). In this 1923 essay Hartmann presents many of the fundamental ideas of his new critical ontology. He summarizes some of the main points of his critique of neo-Kantian epistemology, and provides the point of departure for his new approach in an extensive criticism of the errors of the classical ontological tradition. Some of these errors concern the definition of an ontological category or (...) principle, and others concern the relations among categories themselves. The outline for the new ontology is sketched through the correctives Hartmann appends to the treatment of each error, prefiguring his mature ontological system. (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)
One way in which philosophy of science can perform a valuable normative function for science is by showing characteristic errors made in scientific research programs and proposing ways in which such errors can be avoided or corrected. This paper examines two errors that have commonly plagued research in biology and psychology: 1) functional localization errors that arise when parts of a complex system are assigned functions which these parts are not themselves able to perform, and 2) (...) vacuous functional explanations in which one provides an analysis that does account for the inputs and outputs of a system but does not employ the same set of functions to produce this output as does the natural system. These two kinds of error usually arise when researchers limit their investigation to one type of evidence. Historically, correction of these errors has awaited researchers who have employed the opposite type of evidence. This paper explores the tendency to commit these errors by examining examples from historical and contemporary science and proposes a dialectical process through which researchers can avoid or correct such errors in the future. (shrink)
This article addresses two questions related to colour categorization, to wit, the question what a colour category is, and the question how we identify colour categories. We reject both the relativist and universalist answers to these questions. Instead, we suggest that colour categories can be identified with the help of the criterion of psychological saliency, which can be operationalized by means of consistency and consensus measures. We further argue that colour categories can be defined as well-structured entities that optimally (...) partition colour space. We provide some empirical support for this claim by presenting experimental results, which indicate that internal structure is a better predictor of colour categories than perceptual saliency. (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)
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)
Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in (...) other branches of contemporary mathematics. If such a specification suffices, then a category-theoretical approach will be highly appropriate. But if sets have a richer `nature' than is preserved under isomorphism, then such an approach will be inadequate. (shrink)
The aim of this paper is two-fold: (1) To contribute to a better knowledge of the method of the Argentinean mathematicians Lia Oubifia and Jorge Bosch to formulate category theory independently of set theory. This method suggests a new ontology of mathematical objects, and has a profound philosophical significance (the underlying logic of the resulting category theory is classical iirst—order predicate calculus with equality). (2) To show in outline how the Oubina-Bosch theory can be modified to give rise (...) to a strong paraconsistent category theory; strong enough to be taken as the basis for a paraconsistent mathematics which encompasses all classical mathematical results. (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)
E. J. Lowe, a prominent figure in contemporary metaphysics, sets out and defends his theory of what there is. His four-category ontology is a metaphysical system which recognizes four fundamental categories of beings: substantial and non-substantial particulars and substantial and non-substantial universals. Lowe argues that this system has an explanatory power which is unrivaled by more parsimonious theories and that this counts decisively in its favor. He shows that it provides a powerful explanatory framework for a unified account of (...) causation, dispositions, natural laws, natural necessity and many other related matters, thus constituting a full metaphysical foundation for natural science. (shrink)
Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called "internalization through a universal" based on universal mapping properties. A recently developed "heteromorphic" (...) theory of adjoint functors allows the concepts to be more easily applied empirically. This suggests a conceptual structure, albeit abstract, to model a range of selectionist mechanisms (e.g., in evolution and in the immune system). Closely related to adjoints is the notion of a "brain functor" which abstractly models structures of cognition and action (e.g., the generative grammar view of language). (shrink)
This paper traces the history of uses of the word "gender". It suggests that though "gender" has been recuperated and become commonplace, many issues persist around the way "women" and "men", and the power relations between them, are defined and are evolving. Provided it still allows us to question the meanings attached to the sexes, how they are established and in what contexts, gender remains a useful, because critical, analytical category.
What language allows us to do is to "steal" categories quickly and effortlessly through hearsay instead of having to earn them the hard way, through risky and time-consuming sensorimotor "toil" (trial-and-error learning, guided by corrective feedback from the consequences of miscategorisation). To make such linguistic "theft" possible, however, some, at least, of the denoting symbols of language must first be grounded in categories that have been earned through sensorimotor toil (or else in categories that have already been "prepared" for us (...) through Darwinian theft by the genes of our ancestors); it cannot be linguistic theft all the way down. The symbols that denote categories must be grounded in the capacity to sort, label and interact with the proximal sensorimotor projections of their distal category-members in a way that coheres systematically with their semantic interpretations, both for individual symbols, and for symbols strung together to express truth-value-bearing propositions. (shrink)
As of January 25, 2006, readers have identified the following errors in Darwin's Dangerous Idea. (I have considered other criticisms offered by readers, but decided that they were in error. Further criticisms are, of course, invited.).
J. Angelo Corlett: The errors of atheism Content Type Journal Article Pages 1-5 DOI 10.1007/s11153-010-9285-y Authors C. Robert Mesle, Graceland University, 1 University Ave., Lamoni, IA 50140, USA Journal International Journal for Philosophy of Religion Online ISSN 1572-8684 Print ISSN 0020-7047.
We normally think that public health policy is an important political activity. In turn, we normally understand the value of public health policy in terms of the promotion of health or some health-related good (such as opportunity for health), on the basis of the assumption that health is an important constituent or determinant of wellbeing. In this paper, I argue that the assumption that the value of public health policy should be understood in terms of health leads us to overlook (...) important benefits generated by such policy. To capture these benefits we need to understand the ends of public health policy in terms of the promotion of 'physical safety'. I then go on to argue that the idea that 'health' is an important category for evaluating or estimating individuals' wellbeing in the normative context of social policy is confused. I then clarify the relationship between my arguments and QALY-based accounts of health assessment. In the final section of the paper, I defend this surprising conclusion against various attacks. (shrink)
In “Lifelines” Steven Rose constructs a case against neurogenetic determinism based on experimental data from biology and in favor of a significant degree of self determination. Two philosophical errors in the case favoring neurogenetic determinism are illustrated by Rose: category mistakes and an excessively narrow view of causality restricted to the linear form.
Two classes of argument, logical and moral, are usually offered for the general assumption that racism is inherently irrational. The logical arguments involve accusations concerning stereotyping (category mistakes and empirical errors resulting from overgeneralization) as well as inconsistencies between attitudes and behavior and inconsistencies in beliefs. Moral arguments claim that racism fails as means to well-defined ends, or that racist acts achieve ends other than moral ones. Based on a rationality-neutral definition of racism, it is argued in this (...) article that none of these arguments establish exhaustively that racism is inherently irrational. Ways are suggested to proceed in condemning racism(s) as morally and socially unacceptable, independent of the irrationality claim. (shrink)
Four requirements are suggested for an axiomatic system S to provide the foundations of category theory: (R1) S should allow us to construct the category of all structures of a given kind (without restriction), such as the category of all groups and the category of all categories; (R2) It should also allow us to construct the category of all functors between any two given categories including the ones constructed under (R1); (R3) In addition, S should (...) allow us to establish the existence of the usual basic mathematical structures and carry out the usual set-theoretical operations; and (R4) S should be shown to be consistent relative to currently accepted systems of set theory. This paper explains how all but parts of (R3) can be met using a system S extending NFU enriched by a stratified pairing operation; to meet more of (R3) a stronger system S∗ is introduced, but there are still some real obstacles to meeting this requirement in full. For (R4) it is sketched how both S and S∗ are shown to be consistent. (shrink)
In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, (...) then, as the structuralist sees mathematics as talking about structures and their morphology, I contend that category theory furnishes a framework for mathematical structuralism. (shrink)
is a presentation of mathematics in terms of the fundamental concepts of transformation, and composition of transformations. While the importance of these concepts had long been recognized in algebra (for example, by Galois through the idea of a group of permutations) and in geometry (for example, by Klein in his Erlanger Programm), the truly universal role they play in mathematics did not really begin to be appreciated until the rise of abstract algebra in the 1930s. In abstract algebra the idea (...) of transformation of structure (homomorphism) was central from the beginning, and it soon became apparent to algebraists that its most important concepts and constructions were in fact formulable in terms of that idea alone. Thus emerged the view that the essence of a mathematical structure is to be sought not in its internal constitution, but rather in the nature of its relationships with other structures of the same kind, as manifested through the network of transformations. This idea has achieved its fullest expression in category theory, an axiomatic framework within which the notions of transformation (as morphism or arrow) and composition (and also structure, as object) are fundamental, that is, are not defined in terms of anything else. (shrink)
Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recovering the Grothendieck method of universes. Both topos theory and set theory can be carried (...) out relative to such domains; puzzles about ‘large categories’ and ‘proper classes’ are handled in a uniform way, by relativization, sustaining insights of Zermelo. (shrink)
This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as (...) a “foundation”, or turning meta-mathematical analyses of logical concepts into “philosophical” ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be algebraic structuralists all the way down. (shrink)
Ex ante predicted outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. But error rates have error rates. We reapply measurements of uncertainty about the estimation errors of the estimation errors of an estimation treated as branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error, and lead to fatter tails in the projections than in past realizations. Counterfactuals of error rates always lead to fat (...) tails, regardless of the probability distribution used. A mere .01% branching error rate about the STD (itself an error rate), and .01% branching error rate about that error rate, etc. (recursing all the way) results in explosive (and infinite) moments higher than 1. Missing any degree of regress leads to the underestimation of small probabilities and concave payoffs (a standard example of which is Fukushima). The paper states the conditions under which higher order rates of uncertainty (expressed in spreads of counterfactuals) alters the shapes the of final distribution and shows which a priori beliefs about conterfactuals are needed to accept the reliability of conventional probabilistic methods (thin tails or mildly fat tails). (shrink)
We develop a category theoretical scheme for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The scheme is based on the existence of a categorical adjunction, that provides a theoretical platform for the descriptive analysis of the complex system as a process of functorial information communication.
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)
Åsa Maria Wikforss has proposed a response to Burge's thought-experiments in favour of social externalism, one which allows the individualist to maintain that narrow content is truth-conditional without being idiosyncratic. The narrow aim of this paper is to show that Wikforss' argument against social externalism fails, and hence that the individualist position she endorses is inadequate. The more general aim is to attain clarity on the social externalist thesis. Social externalism need not rest, as is typically thought, on the possibility (...) of incomplete linguistic understanding or conceptual error. I identify the unifying principle that underlies the various externalist thought-experiments. (shrink)
Different accounts of what it is for something to have a social nature have been given. Sociality does not appear to be a category worthy of philosophical focus, given some of these accounts. If sociality is construed as plural subjecthood, it emerges as a category crucial for our understanding of the human condition. Plural subjects are constituted by a joint commitment of two or more persons to do something as a body. Such commitments generate rights and obligations of (...) a special type, and underlie such phenomena as social conventions, agreements, shared action and social groups on one standard understanding of what these are. (shrink)
Recently, Timothy Williamson has argued that considerations about margins of errors can generate a new class of cases where agents have justified true beliefs without knowledge. I think this is a great argument, and it has a number of interesting philosophical conclusions. In this note I’m going to go over the assumptions of Williamson’s argument. I’m going to argue that the assumptions which generate the justification without knowledge are true. I’m then going to go over some of the recent (...) arguments in epistemology that are refuted by Williamson’s work. And I’m going to end with an admittedly inconclusive discussion of what we can know when using an imperfect measuring device. (shrink)
The concept that peope have of themselves as a 'person' is one of the most intimate notions that they hold. Yet the way in which the category of the person is conceived varies over time and space. In this volume, anthropologists, philosophers, and historians examine the notion of the person in different cultures, past and present. Taking as their starting point a lecture on the person as a category of the human mind, given by Marcel Mauss in 1938, (...) the contributors critically assess Mauss's speculation that ntions of the person, rather than being primarily philosophical or psychological, have a complex social and ideological origin. Discussing societies ranging from ancient Greece, India, and China to modern Africa and Papua New Guinea, they provide fascinating descriptions of how these different cultures define the person. But they also raise deeper theoretical issues: What is universally constant and what is culturally variable in people's thinking about the person? How can these variations be explained? Has there been a general progressive development toward the modern Western view of the person? What is distinctive about this? How do one's notions of the person inform one's ability to comprehend alternative formulations? These questions are of compelling interest for a wide range of anthropologists, philosophers, historians, psychologists, sociologists, orientalists, and classicists. The book will appeal to any reader concerned with understanding one of the most fundamental aspects of human existence. (shrink)
The article surveys some past and present debates within mathematics over the meaning of category theory. It argues that such conceptual analyses, applied to a field still under active development, must be in large part either predictions of, or calls for, certain programs of further work.
In this paper I argue for the thesis that Stout's category of abstract particulars (what Husserl calls "moments') has played a role in the transition from Bradleian idealism to British analytic philosophy. That category plays this role as part of a new theory of wholes, parts and relations that Stout develops in opposition to Bradley. In Stout's theory abstract particulars are dependent parts of wholes. The critical remarks that G. E. Moore and Kevin Mulligan have made concerning Stout's (...) identification of abstract particulars and predicates are elaborated in this paper. Notwithstanding the fact that Stout mistakenly identifies abstract particulars with predicates, the category of abstract particulars may be of value in a theory of individuals, universals and truthmakers. (shrink)
Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy : logical, conceptual, and justificatory. We argue that, while a strong case can be made for its logical and conceptual autonomy, its justificatory autonomy turns on whether or not mathematical theories can be justified by appeal to mathematical practice. If they can, a category-theoretical approach will be fully autonomous; (...) if not, the most natural route to justificatory autonomy is blocked. (shrink)
We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with (...) an operation on the hierarchy that expresses the formation of complex theories from simple theories that express first principles. Another operation forms abstractions expressing the shared concepts in an array of theories. The use of categorical model theory makes possible the incremental analysis of possible worlds, or instances, for the theories, and the mapping of instances of a theory to instances of its more abstract parts. We describe the theoretical approach by applying it to the semantics of neural networks. (shrink)
The standpoint of this paper is the distinguished Ode to Sport from Pierre de Coubertin, specifically the second part of the elegy, the one concerning beauty. Starting with ?O Sport, you are Beauty!?, Pierre de Coubertin mentions, beyond beauty, an assemblage of aesthetic categories such as sublime, abject, balance, proportion, harmony, rhythm and grace. He also mentions strength, power and suppleness. Although the first quoted categories are general categories of aesthetics, it seems quite relevant to emphasize the need of the (...) author to introduce specific categories that fits to body movement and sport, such as strength, power and suppleness. There is no doubt that the first group of categories also fits to sport and body movement, but it equally fits to different forms of art, while strength, power and suppleness can only be literally applied to sport and performing arts. The purpose of this paper is to analyze strength as an aesthetic category of sport, developing three main arguments: the feeling of achievement and its conservation, the fight against gravity and the multiple forms of strength?s expression. It is concluded that strength can improve the communicative power of sport and its emotional appeal. In sports such as gymnastics, diving or synchronized swimming, the appreciation of strength exhibited by the athletes communicates to the observer some king of ease and lightness that enhances the aesthetic judgment. In other sports like weightlifting, sumo or rugby, effort and heaviness are stamped on the athlete's faces, what contributes to a sort of communion between the observer and the athlete that can also improve the aesthetic experience. (shrink)
Elementary axioms describe a category of categories. Theorems of category theory follow, including some on adjunctions and triples. A new result is that associativity of composition in categories follows from cartesian closedness of the category of categories. The axioms plus an axiom of infinity are consistent iff the axioms for a well-pointed topos with separation axiom and natural numbers are. The theory is not finitely axiomatizable. Each axiom is independent of the others. Further independence and definability results (...) are proved. Relations between categories and sets, the latter defined as discrete categories, are described, and applications to foundations are discussed. (shrink)
Against the backdrop of eliminitivist versus critical conservationist approaches to the racial category of whiteness, this article asks whether a rehabilitated version of whiteness can be worked out concretely. What might a non-oppressive, anti-racist whiteness look like? Turning to Josiah Royce’s “Provincialism” for help answering this question, I show that even though the essay never explicitly discusses race, it can help explain the ongoing need for the category of whiteness and implicitly offers a wealth of useful suggestions for (...) how to transform it. “Provincialism” is an exercise in critical conservation of the concept of provincialism, and while not identical, provincialism and whiteness share enough in common that “wise” provincialism can serve as a model for “wise” whiteness. Royce’s concept of provincialism thus can be a great help to critical philosophers of race wrestling with questions of whether and how to transformatively conserve whiteness. Exploring similarities and differences between wise provincialism and wise whiteness, I use Royce’s analyses of provincialism to shed light on why whiteness should be rehabilitated rather than discarded and how white people today might begin living whiteness as an anti-racist category. (shrink)
Category-specific impairments of object recognition and naming are among the most intriguing disorders in neuropsychology, affecting the retrieval of knowledge about either living or nonliving things. They can give us insight into the nature of our representations of objects: Have we evolved different neural systems for recognizing different categories of object? What kinds of knowledge are important for recognizing particular objects? How does visual similarity within a category influence object recognition and representation? What is the nature of (...) our semantic knowledge about different objects? We review the evidence on category-specific impairments, arguing that deficits even for one class of object (e.g., living things) cannot be accounted for in terms of a single information processing disorder across all patients; problems arise at contrasting loci in different patients. The same apparent pattern of impairment can be produced by damage to different loci. According to a new processing framework for object recognition and naming, the hierarchical interactive theory (HIT), we have a hierarchy of highly interactive stored representations. HIT explains the variety of patients in terms of (1) lesions at different levels of processing and (2) different forms of stored knowledge used both for particular tasks and for particular categories of object. Key Words: category-specific deficits; functional imaging; hierarchical models; interactive activation models; neuropsychology; object recognition; perceptual and functional knowledge. (shrink)
Giandomenico Sica’s volume is a collection of eleven papers on category theory by philosophers, mathematicians, and mathematical physicists. In addition to papers of direct interest to philosophers of mathematics, the volume contains some introductory expositions of category theory along with a valuable discussion of the relationship between category theory and physics by Bob Coecke. While there are several technically difficult papers, the volume as a whole is reasonably accessible to those with some familiarity with the basics of (...)category theory. The importance of the volume lies in the possibility that it will encourage broader interest in category theory among philosophers. (shrink)
Today there is a thriving 'emotions industry' to which philosophers, psychologists and neuroscientists are contributing. Yet until two centuries ago 'the emotions' did not exist. In this path-breaking study Thomas Dixon shows how, during the nineteenth century, the emotions came into being as a distinct psychological category, replacing existing categories such as appetites, passions, sentiments and affections. By examining medieval and eighteenth-century theological psychologies and placing Charles Darwin and William James within a broader and more complex nineteenth-century setting, Thomas (...) Dixon argues that this domination by one single descriptive category is not healthy. Overinclusivity of 'the emotions' hampers attempts to argue with any subtlety about the enormous range of mental states and stances of which humans are capable. This book is an important contribution to the debate about emotion and rationality which has preoccupied western thinkers throughout the eighteenth and nineteenth centuries and has implications for contemporary debates. (shrink)
Cognitive developmental evidence is sometimes conscripted to support ''naturalized epistemology'' arguments to the effect that a general epistemic stance leads children to build theory-like accounts of underlying properties of kinds. A review of the evidence suggests that what prompts conceptual acquisition is not a general epistemic stance but a series of category-specific intuitive principles that constitute an evolved ''natural metaphysics''. This consists in a system of categories and category-specific inferential processes founded on definite biases in prototype formation. Evidence (...) for this system provides a better understanding of the limited ''plasticity'' of ontological commitments as well as a computationally plausible account of their initial state, avoiding ambiguities about innateness. This may provide a starting point for a ''naturalized epistemology'' that takes into account evolved properties of human conceptual structures. (shrink)
This essay attempts to distinguish and discuss the importance and limitations of different ways of being wrong. At first it is argued that strictly falsifiable knowledge is concerned with simple (instrumental) mistakes only, and thus is incapable of understanding more complex errors (and truths). In order to gain a deeper understanding of mistakes (and to understand a deeper kind of mistake), it is argued that communicative aspects have to be taken into account. This is done in the theory of (...) communicative action, which adds to our knowledge of errors the notion of communicative mistakes: mistakes as obstacles for sincere communication. However, to overcome this still purely negative judgement of errors, two processes are examined in which mistakes are best regarded as developmental steps, that is, steps not only meaningful in their own right (as containing some truth), but also as necessary preconditions for further progress. This would suggest that truth is born out of errors. But if so, one has to understand the wrongness of such errors; how is it that they are erroneous if they (somehow) contain the truth? At the end of this essay, a tentative answer to this question is given. (shrink)
The types of errors that emerge in the development and maintenance of software are essentially different from the types of errors that emerge in the development and maintenance of engineered hardware products. There is a set of standard responses to actual and potential hardware errors, including: engineering ethics codes, engineering practices, corporate policies and laws. The essential characteristics of software errors require new ethical, policy, and legal approaches to the development of software in the global arena.
We summarise and respond to the main points made by the commentators on our target article, which concern: (1) whether structural similarity can play a causal role in normal object identification and in neuropsychological deficits for living things, (2) the nature of our structural knowledge of the world, (3) the relations between sensory and functional knowledge of objects, and the nature of our functional knowledge about living things, (4) whether we need to posit a “core” semantic system, (5) arguments that (...) can be marshalled from evidence on functional imaging, (6) the causal mechanisms by which category differences can emerge in object representations, and (7) the nature of our knowledge about categories other than living and nonliving things. We also highlight points raised in our article that seem to be accepted. (shrink)
Against influential strands of feminist theory, I argue that there is nothing essentialist or homogenising about the category ‘women’. I show that both intersectional claims that it is impossible to separate out the ‘woman part’ of women, and deconstructionist contentions that the category ‘women’ is a fiction, rest on untenable meta-theoretical assumptions. I posit that a more fruitful way of approaching this disputed category is to treat it as an abstraction. Drawing on the philosophical framework of critical (...) realism I elucidate the nature of the vital and inevitable process of abstraction, as a means of finding a way out of the theoretical and methodological impasse that the ‘ban’ on the category ‘women’ has caused. Contrary to many contemporary feminist theorists, I contend that, although the category ‘women’ does not reflect the whole reality of concrete and particular women, it nevertheless refers to something real, namely the structural position as woman. (shrink)
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, and (ii) the idea of a subobject of the coarse-graining presheaf (Section 3).
There is a widespread feeling that health is special; the rules that are usually used in other policy areas are not applied in health policy. Health economists, for example, tend to be reluctant to offer economists’ usual prescription of competition and consumer choice, even though they have largely failed to justify this reluctance by showing that health economics involves special features such as public goods, externalities, adverse selection, poor consumer information, or unusually severe consequences. Similarly, while some philosophers argue for (...) bioethical conclusions based on very general ethical intuitions,1 many others rely on moral intuitions that are specific to health and medicine to draw conclusions that are meant to apply mainly in health and medicine. For example, many authors appear to start from the strong moral intuition that it typically seems wrong to deny poor people access to health care, and then seek moral principles that can both account for such intuitions and justify the claim that people have some sort of right to health care.2 In metaethics, opinions on moral intuitions range from an extreme intuitionism, which accepts all case-specific moral intuitions at face value as reliable moral guides, to an extreme foundationalism, which rejects such intuitions as evidence regarding correct general moral principles. Between these extremes, opinions vary on how severe the errors in our moral intuitions are. The practice of bioethics seems to favor the extreme intuitionist end of this spectrum, and thus implicitly expects mild errors.3 In contrast, this essay will suggest that common practice in bioethics has seriously underestimated the errors in our moral intuitions. In this essay, I consider the evolutionary origin of our moral intuitions, but avoid the extreme positions of moral skepticism and “whatever evolved must be good,” both of which are commonly associated with evolution-. (shrink)
A type theory constructed with reference to a particular language will associate with each monadic predicate P of that language a class of individuals C(P) of which it is categorically significant to predicate P (or which P spans, for short). The extension of P is a subset of C(P), which is a subset of the language’s universe of discourse. The set C(P) is a category discriminated by the language. The relation 'is spanned by the same predicates as' divides the (...) language’s universe of discourse into equivalence classes. These are the types discriminated by the language. This paper criticizes an attempt by Peter Strawson to explain terms peculiar to type theory in terms of other notions not peculiar to type theory. (shrink)
I challenge here the concept of SOC in regard to the question of the consciousness or unconsciousness of logical errors. My commentary offers support for the demonstration of how neuroimaging techniques might be used in the psychology of reasoning to test hypotheses about a potential hierarchy of levels of consciousness (and thus of partial unconsciousness) implemented in different brain networks.
Gilles Deleuze's notion of sense, as developed in Difference and Repetition and The Logic of Sense, is meant to be a fourth dimension of the proposition besides denotation, manifestation and signification. While Deleuze explains signification in inferentialist terms, he ascribes to sense some very unusual properties, making it hard to understand what sense is. The aim of this paper is to improve this situation by confronting Deleuzian sense with a more or less contemporary, but otherwise rather distant philosophical conception: Gilbert (...) Ryle's theory of categories and category mistakes. The leading idea is that to understand the sense of a proposition regarding X is to know the category of the concept X, which requires that one knows which questions may appropriately be asked with regard to X. Thus, sense, category and questions are intimately related to each other. Finally, it seems to be consistent with Deleuze's views to assume that abstract signification is contextually generated by concrete sense. (shrink)
The Principle of Dependent Choice is shown to be equivalent to: the Baire Category Theorem for Čech-complete spaces (or for complete metric spaces); the existence theorem for generic sets of forcing conditions; and a proof-theoretic principle that abstracts the "Henkin method" of proving deductive completeness of logical systems. The Rasiowa-Sikorski Lemma is shown to be equivalent to the conjunction of the Ultrafilter Theorem and the Baire Category Theorem for compact Hausdorff spaces.
A provisional model is presented in which categorical perception (CP) provides our basic or elementary categories. In acquiring a category we learn to label or identify positive and negative instances from a sample of confusable alternatives. Two kinds of internal representation are built up in this learning by "acquaintance": (1) an iconic representation that subserves our similarity judgments and (2) an analog/digital feature-filter that picks out the invariant information allowing us to categorize the instances correctly. This second, categorical representation (...) is associated with the category name. Category names then serve as the atomic symbols for a third representational system, the (3) symbolic representations that underlie language and that make it possible for us to learn by "description." Connectionism is one possible mechainsm for learning the sensory invariants underlying categorization and naming. Among the implications of the model are (a) the "cognitive identity of (current) indiscriminables": Categories and their representations can only be provisional and approximate, relative to the alternatives encountered to date, rather than "exact." There is also (b) no such thing as an absolute "feature," only those features that are invariant within a particular context of confusable alternatives. Contrary to prevailing "prototype" views, however, (c) such provisionally invariant features must underlie successful categorization, and must be "sufficient" (at least in the "satisficing" sense) to subserve reliable performance with all-or-none, bounded categories, as in CP. Finally, the model brings out some basic limitations of the "symbol-manipulative" approach to modeling cognition, showing how (d) symbol meanings must be functionally grounded in nonsymbolic, "shape-preserving" representations -- iconic and categorical ones. Otherwise, all symbol interpretations are ungrounded and indeterminate. This amounts to a principled call for a psychophysical (rather than a neural) "bottom-up" approach to cognition. (shrink)
Crombie's acceptance of the deliberate commission of a category mistake in his defense of the meaningfulness of theological statements raises a pointed challenge to the philosophy of Ryle which seems not to have been specifically addressed in subsequent literature. We review the analysis which leads Crombie into it, including concepts of anomaly, deficiency, affinity, and inadequate notion, noting basic differences in method and attitude from Ryle. We express our own agreements and disagreements in keeping with an overall concern for (...) the preservation of rationality in this sphere of language, finding acceptable distinct contributions to that end from both. (shrink)
Adults have been shown to attribute certain properties more frequently than others to the dead. This category-specific pattern has been interpreted in terms of simulation constraints, whereby it may be harder to imagine the absence of some states than others. Afterlife beliefs have also shown context-sensitivity, suggesting that environmental exposure to different types of information might influence adults? reasoning about post-death states. We sought to clarify category and context effects in adults afterlife reasoning. Participants read a story describing (...) the death of a human protagonist after exposure to a biological prime, an emotional prime, or no prime. Emotions, desires, and epistemic states were more frequently attributed to the dead character than biological, psychobiological, and perceptual states, partially replicating previous findings. The biological prime decreased the attribution of certain post-death states relative to the control condition, whereas the emotional prime had no effect. Simulation theory does not provide a satisfactory explanation of the present findings, which may be better accounted for by conflict between different cognitive systems that are engaged in thinking about the dead. (shrink)
          Despite the fact that the strength of argument is clearly on the pro-life side—nobody except a handful of academics would question the grave wrongness of abortion were pregnancy never inconvenient—somehow ordinary intelligent people, like our students, often remain unconvinced. There are many reasons for this, of course. For instance, a number of students have had their children aborted while many know others who have had abortions, and one does not want (...) to condemn oneself or oneÂ’s friends. I am a philosopher, however, and so I will be interested in intellectual reasons, even though these subjective psychological ones are almost surely more important. Specifically, I will be interested in the fact that the ordinary person subscribes to a number of erroneous big-picture ethical beliefs, each of which, to a different degree, does something to block access to the pro-life arguments. I will not talk about all such erroneous beliefs and I would be grateful in the discussion for more examples.           I will talk about eight errors I have identified, largely through teaching. For each one, I will identify the error, show how it impacts the pro-life message and explain why it is tempting to most of us —there is, after all, something right about five of the errors. For each of these errors is one that we might ourselves be tempted by on occasion. I will then suggest some ways of refuting the error. In some cases, the mere identification of the error should do the trick, as these erroneous beliefs are often not explicitly identified by our interlocutors. My suggested refutations will not always be phrased in the way in which I would phrase them for didactic effectiveness: in this talk, I am mainly trying to convey ideas. (shrink)
Medical error is a leading problem of health care in the United States. Each year, more patients die as a result of medical mistakes than are killed by motor vehicle accidents, breast cancer, or AIDS. While most government and regulatory efforts are directed toward reducing and preventing errors, the actions that should follow the injury or death of a patient are still hotly debated. According to Nancy Berlinger, conversations on patient safety are missing several important components: religious voices, traditions, (...) and models. In After Harm, Berlinger draws on sources in theology, ethics, religion, and culture to create a practical and comprehensive approach to addressing the needs of patients, families, and clinicians affected by medical error. She emphasizes the importance of acknowledging fallibility, telling the truth, confronting feelings of guilt and shame, and providing just compensation. After Harm adds important human dimensions to an issue that has profound consequences for patients and health care providers. (shrink)
Very young children occasionally commit scale errors, which involve a dramatic dissociation between planning and control: A child's visual representation of the size of a miniature object is not used in planning an action on it, but is used in the control of the action. Glover's planning–control model offers a very useful framework for analyzing this newly documented phenomenon.
Four experiments investigated how people judge the plausibility of category-based arguments, focusing on the diversity effect, in which arguments with diverse premise categories are considered particularly strong. In Experiment 1 we show that priming people as to the nature of the blank property determines whether sensitivity to diversity is observed. In Experiment 2 we find that people's hypotheses about the nature of the blank property predict judgements of argument strength. In Experiment 3 we examine the effect of our priming (...) methodology on people's tendency to bring knowledge about causality or similarity to bear when evaluating arguments, and in Experiment 4 we show that whether people's hypotheses about the nature of the blank property were causal predicted ratings of argument strength. Together these results suggest that diversity effects occur because diverse premises lead people to bring general features of the premise categories to mind. Although our findings are broadly consistent with Bayesian and Relevance-based approaches to category-based inductive reasoning, neither approach captures all of our findings. (shrink)
It seems to have been taken for granted that we all know what a human action is. However in attempting to draw from what philosophers have said about actions the necessary clues as to their distinguishing features, one finds little to discourage the idea that there is no way of distinguishing one category of occurrences, human actions, from the complex of different sorts of things which happen. From this I am tempted to conclude that there is no category (...) of human action. But before drawing such a conclusion an ancient but terrible question must be faced: What sorts of things happen in the world ? This ancient question is faced but not answered. It is brought up because the failure to find a satisfactory answer to the question, Is human action a category? is a failure even to find a satisfactory assumption about what kind of reference the term ?human action? is supposed to have. (shrink)
Research in education and cognitive development suggests that explaining plays a key role in learning and generalization: When learners provide explanations—even to themselves—they learn more effectively and generalize more readily to novel situations. This paper proposes and tests a subsumptive constraints account of this effect. Motivated by philosophical theories of explanation, this account predicts that explaining guides learners to interpret what they are learning in terms of unifying patterns or regularities, which promotes the discovery of broad generalizations. Three experiments provide (...) evidence for the subsumptive constraints account: prompting participants to explain while learning artificial categories promotes the induction of a broad generalization underlying category membership, relative to describing items (Exp. 1), thinking aloud (Exp. 2), or free study (Exp. 3). Although explaining facilitates discovery, Experiment 1 finds that description is more beneficial for learning item details. Experiment 2 additionally suggests that explaining anomalous observations may play a special role in belief revision. The findings provide insight into explanation’s role in discovery and generalization. (shrink)
A Study of the History and Philosophy of Category Theory Jean-Pierre Marquis. to say that objects are dispensable in geometry. What is claimed is that the specific nature of the objects used is irrelevant. To use the terminology already ...
Is there not any place in the history of ideas for the imperfect character of human doings (i.e. capability of error) that is repeated for so long until we lately start to think that it had long been wrong? The answer is: In the conventional histories of ideas there is almost none. The importance of the phenomenon,however, is immense. Intellectual history is full of errors. Scholarly errors are among the factors that generate intellectual pathways in which consequences of (...) historical small events feed back up on each other positively and give rise to historical pathologies in the end. Pathways hold the intellectuals dependent on the consequences of errors which interact upon each other and prevent resulting pathologies to disappear fully. As a result, ideas do not converge to a level of perfection. Evolutionary account of errors suggests that errors in the history of ideas matter even though they are often corrected. (shrink)
This paper addresses the problem of the distinction between basic science and applied science. It also explores their differences with regard to technology. For this analysis, as well as a general epistemological and methodological approach, we study a particular case: information science. As the emphasis of the paper is on the category of applied science, it includes a critical analysis of Philip Kitcher's proposal. First, there is an examination of Ph. Kitcher's thought, because he has addressed this issue without (...) offering a clear distinction between the various categories. I then consider the contributions of I. Niiniluoto, which determine in a more genuine way the features that distinguish applied science from basic science. Here, I focus on the ideas of H. A Simon on the science of design, to the extent that it is an applied science. This then allows us to shed light on the disciplinary field of information science, which is characterized as an applied science of design. This is a case that shows the need to distinguish three epistemological and methodological domains: basic science, applied science and technology. (shrink)
Identifying objects as members of ontological domains activates category-specific processes. There is evidence that these processes include particular ways of “tracking” substances and could do all the “tracking” necessary for concept acquisition. There may be no functional need or evolutionary scenario for a general tracking capacity of the kind described by Millikan.
home page other lists my email address Philip Dorrell, 6 September 2005 At talk.origins there is a list of creationist claims with links to accompanying responses. The responses attempt to refute the corresponding claims, but there are errors in some of the refutations. Each item below starts with a link to the section of the talk.origins site that responds to a particular creationist claim.
For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets.We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.
It has been shown in Spirtes(1995) that X and Y are d-separated given Z in a directed graph associated with a recursive or non-recursive linear model without correlated errors if and only if the model entails that ρXY.Z = 0. This result cannot be directly applied to a linear model with correlated errors, however, because the standard graphical representation of a linear model with correlated errors is not a directed graph. The main result of this paper is (...) to show how to associate a directed graph with a linear model L with correlated errors, and then use d-separation in the associated directed graph to determine whether L entails that a particular partial correlation is zero. (shrink)
Working within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call RCA+ 0 and WKL+ 0, and show that RCA+ 0 suffices to prove B.C.T.II. Some model theory of WKL+ 0 and its importance in view (...) of Hilbert's program is discussed, as well as applications of our results to functional analysis. (shrink)
I explore a distinction that is philosophically significant but rarely a cynosure. The distinction is betvveen fallacies and logical errors, and I approach it by advancing overlooked albeit deleterious logical errors that are not fallacies but that fall squarely within the purview of Critical Thinking if not also Informal Logic. One key claim to emerge is that these logical errors -- just as basic and thought-impeding as the fallacies -- demand that we take a hard look at (...) what is and what should be guiding our activity in teaching such courses. Another is that although philosophers appeal to the notion of logical error in their explications of fallacies, the former notion is anything but clear and indeed usually explained in terms of the latter. Yet another is that the distinction illustrates why the oft encountered “false premise or bad inference” account of how thinking can go bad is oversimplified. (shrink)
Humphreys & Forde concentrate on the living/nonliving dissociation. However, further dissociations have been reported, including selective loss or preservation in recognizing body parts and numbers. This commentary outlines the relevance of the number category for understanding the organising principles of semantic memory.
In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both (...) options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents. (shrink)
HIT produces category-specific deficits without category- specific mechanisms by assuming that differences in properties of objects are transparently converted into differences in representational format. A complete model would specify the mechanisms that accomplish this. Such category-specific mechanisms may have evolved because assumptions about the properties of some kinds of objects (e.g., living things) are invalid for others (e.g., artifacts).
A. Karpinski (2004) recently criticized Implicit Association Test (IAT) measures of self-esteem, arguing that their measurements of self-associations are compromised by their contrasting self with a putatively extremely negative second category, the nonspecific other. The present data show, to the contrary, that the nonspecific other category in the self-esteem IAT is near neutral in valence. Validity of the self-esteem IAT is most appropriately assessed by examining its correlations with conceptually related measures. That has been done in several previous (...) studies that are reviewed here. The nonspecific other category is only one of several choices for representing the concept of other in self-esteem IATs. Choice of the appropriate other category to contrast with self in self-esteem IATs should be guided by the needs of the research question being addressed. (shrink)
The present studies tested the hypothesis that strong assumptions about within-category homogeneity impede children’s recognition of the inductive value of diverse samples of evidence. In Study 1a, children (7-year-olds) and adults were randomly assigned to receive a prime emphasizing within-category variability, a prime emphasizing within-category similarities, or to not receive a prime. Only following the variability prime, children demonstrated a reliable preference for evaluating diverse over nondiverse samples to determine whether there is support for a category-wide (...) generalization. Adults demonstrated a robust preference for diverse samples in all conditions. These effects extended beyond the specific categories included in the prime, as well as to multiple types of test questions. Study 1b demonstrated that priming variability leads children to select diverse samples only when doing so is informative for induction. Implications for conceptual development are discussed. (shrink)
In this paper we are going to show that error coping strategies play an essential role in linguistic pragmatics. We study the effect of noisy speaker strategies within a framework of signalling games with feedback loop. We distinguish between cases in which errors occur in message selection and cases in which they occur in signal selection. The first type of errors affects the content of an utterance, and the second type its linguistic expression. The general communication model is (...) inspired by the Shannon–Weaver communication model. We test the model by a number of benchmark examples, including examples of relevance implicatures, quantity implicatures, and presupposition accommodation. (shrink)
Stanovich & West interpret errors in syllogistic reasoning in terms of computational limitations. I argue that the variety of strategies used by reasoners in solving syllogisms requires us to consider also performance errors. Although reasoners' performance from one trial to another is quite consistent, it can be different, in line with the definition of performance errors. My argument has methodological implications for reasoning theories.
The term "false memories" has been used to refer to suggestibility experiments in which whole events are apparently confabulated and in media accounts of contested memories of childhood abuse. Since 1992 psychologists have increasingly used the term "false memory" when discussing memory errors for details, such as specific words within word lists. Use of the term to refer to errors in details is a shift in language away from other terms used historically (e.g., "memory intrusions"). We empirically examine (...) this shift in language and discuss implications of the new use of the term "false memories." Use of the term presents serious ethical challenges to the data-interpretation process by encouraging over-generalization and misapplication of research findings on word memory to social issues. (shrink)
The goal of the present set of studies is to explore the boundary conditions of category transfer in causal learning. Previous research has shown that people are capable of inducing categories based on causal learning input, and they often transfer these categories to new causal learning tasks. However, occasionally learners abandon the learned categories and induce new ones. Whereas previously it has been argued that transfer is only observed with essentialist categories in which the hidden properties are causally relevant (...) for the target effect in the transfer relation, we here propose an alternative explanation, the unbroken mechanism hypothesis. This hypothesis claims that categories are transferred from a previously learned causal relation to a new causal relation when learners assume a causal mechanism linking the two relations that is continuous and unbroken. The findings of two causal learning experiments support the unbroken mechanism hypothesis. (shrink)
Extrapolation of Steels & Belpaeme's (S&B) results show that colour is a culturalist category. Populations will only share the category of colour if it is built into the system. If “left to themselves” different populations may or may not stumble on the colour category. Populations that do not share a colour category may still be able to communicate in a wide variety of environments.
In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken to be at least compact closed, and more often, dagger compact, enforcing a certain self-duality, whereby preparation processes (roughly, states) are interconvertible with processes of registration (roughly, measurement outcomes). This is in contrast to the more concrete “operational” approach, in which the (...) states and measurement outcomes associated with a physical system are represented in terms of what we here call a convex operational model: a certain dual pair of ordered linear spaces–generally, not isomorphic to one another. On the other hand, state spaces for which there is such an isomorphism, which we term weakly self-dual, play an important role in reconstructions of various quantum-information theoretic protocols, including teleportation and ensemble steering. In this paper, we characterize compact closure of symmetric monoidal categories of convex operational models in two ways: as a statement about the existence of teleportation protocols, and as the principle that every process allowed by that theory can be realized as an instance of a remote evaluation protocol—hence, as a form of classical probabilistic conditioning. In a large class of cases, which includes both the classical and quantum cases, the relevant compact closed categories are degenerate, in the weak sense that every object is its own dual. We characterize the dagger-compactness of such a category (with respect to the natural adjoint) in terms of the existence, for each system, of a symmetric bipartite state, the associated conditioning map of which is an isomorphism. (shrink)
The HIT framework accepts a number of assumptions that are widely held as plausible or even well established in the literature on category-specific agnosia. We point out that a number of these elementary conjectures, now almost taken for granted, have received little in the way of convincing empirical support.
In the second part of the Critique of Judgment, Immanuel Kant provides a transcendental analysis of the bases of our right to employ teleological conceptions in biology. A living organism exemplifies the conception of a natural end insofar as the organization of the parts to form a whole is the result of a process in which the organism is both cause and effect of itself. Kant’s analysis of the concept of a natural purpose is guided, in part, by his general (...) theory of logic. By examining the manner in which the logical modes of relation are used as a basis for analyzing the concept of a natural purpose, I hope to accomplish two goals: (1) to compare Kant’s analysis of the category of community to the analysis of the concept of a natural purpose; (2) to evaluate some of the strengths and weaknesses ofKant’s account of community and natural purpose; (3) to consider one criticism of Kant’s use of the logical form of the disjunctive as a basis for the analysis of these conceptions that is developed by Charles Sanders Peirce. Peirce indicates that Darwin’s theory of biological evolution was one of the primary causes that led him revisit Kant’s logic and his analysis of the categories of relation. (shrink)
For academic research outcomes, there is an increasing emphasis on the bibliometric scorings like the journal impact factor and citations when the assessment of the scientific merits of research or researchers is required. Currently, no known study has been conducted to explore the bibliographical trends of the subject category of multidisciplinary sciences as indexed by the annual Journal Citation Reports of the Thomson Scientific. The effect of journal self-citations and intra-citing within a discipline to the bibliometric data computation can (...) be confounding. In this study, six journals were selected from the multidisciplinary sciences subject category where the trend of self-citations and intra-citing were analysed. These journals were chosen as they published more than 450 citable articles in the year 2007 and had available bibliometric data for a 10-year period. The results showed that self-citations rose as much as +23.98% while intra-citing declined up to −5.80% over the observed period. The retrospective impacts and influences of these observations were also discussed in this study. (shrink)
A value statement such as “she is a good teacher” is categoryspecified, i.e., the criteria of evaluation are specified as those that are applicable to a given category, in this case the category of teachers. In this study of categoryspecified value statements, certain categories are identified that cannot be used to specify value aspects. Special attention is paid to categories that are constituted by functional characteristics. The logical properties of value statements that refer to such categories are shown (...) to differ significantly from the corresponding properties in social choice theory. (shrink)
Within the context of an involutive monoidal category the notion of a comparison relation ${\textsf{cp} : \overline{X} \otimes X \rightarrow \Omega}$ is identified. Instances are equality = on sets, inequality ${\leq}$ on posets, orthogonality ${\perp}$ on orthomodular lattices, non-empty intersection on powersets, and inner product ${\langle {-}|{-} \rangle}$ on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with “tame” relations as morphisms. Examples include familiar categories in the foundations (...) of quantum mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions between them, or Hilbert spaces with bounded (continuous) linear maps. Of one particular example of such a dagger category of tame relations, involving sets and bifinite multirelations between them, the categorical structure is investigated in some detail. It turns out to involve symmetric monoidal dagger structure, with biproducts, and dagger kernels. This category may form an appropriate universe for discrete quantum computations, just like Hilbert spaces form a universe for continuous computation. (shrink)
Although Humphreys & Forde's HIT provides a comprehensive account of category-specific deficits, standard models of categorization and identification may also be able to explain many aspects of such deficits. The assumptions of an exemplar-based account of category- specific deficits are presented, and it is argued that exemplar models may be able to explain key findings on impaired object identification and categorization.
This discussion argues that for many word meanings, the child has to assemble a new category, using relatively slow information-sifting processes. This does not cause high semantic errors, because children probably hold off using a word until much such sifting has occurred, rather than producing the new word as soon as they have any information on it.
Let κ B be the least cardinal for which the Baire category theorem fails for the real line R. Thus κ B is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κ B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2 ω 1 be ℵ ω . Similar questions are considered for the ideal of measure zero sets, (...) other ω 1 saturated ideals, and the ideal of zero-dimensional subsets of R ω 1. (shrink)
