We prove the following theorems: (1) If X has strong measure zero and if Y has strong first category, then their algebraic sum has property s 0 . (2) If X has Hurewicz's covering property, then it has strong measure zero if, and only if, its algebraic sum with any first category set is a first category set. (3) If X has strong measure zero and Hurewicz's covering property then its algebraic sum with any (...) set in APC ' is a set in APC '. (APC ' is included in the class of sets always of first category, and includes the class of strong first category sets.) These results extend: Fremlin and Miller's theorem that strong measure zero sets having Hurewicz's property have Rothberger's property, Galvin and Miller's theorem that the algebraic sum of a set with the γ-property and of a first category set is a first category set, and Bartoszynski and Judah's characterization of SR M -sets. They also characterize the property (*) introduced by Gerlits and Nagy in terms of older concepts. (shrink)

We improve results of Marczewski, Frankiewicz, Brown, and others comparing the $\sigma$-ideals of measure zero, meager, Marczewski measure zero, and completely Ramsey null sets; in particular, we remove CH from the hypothesis of many of Brown's constructions of sets lying in some of these ideals but not in others. We improve upon work of Marczewski by constructing, without CH, a nonmeasurable Marczewski measure zero set lacking the property of Baire. We extend our analysis of $\sigma$-ideals to include the completely Ramsey (...) null sets relative to a Ramsey ultrafilter and obtain all 32 possible examples of sets in some ideals and not others, some under the assumption of MA, but most in ZFC alone. We also improve upon the known constructions of a Marczewski measure zero set which is not Ramsey by using a set theoretic hypothesis which is weaker than those used by other authors. We give several consistency proofs: one concerning the relative sizes of the covering numbers for the meager sets and the completely Ramsey null sets; another concerning the size of non; and a third concerning the size of add$. We also study those classes of perfect sets which are bases for the class of always first category sets. (shrink)

We improve results of Marczewski, Frankiewicz, Brown, and others comparing the σ-ideals of measure zero, meager, Marczewski measure zero, and completely Ramsey null sets; in particular, we remove CH from the hypothesis of many of Brown's constructions of sets lying in some of these ideals but not in others. We improve upon work of Marczewski by constructing, without CH, a nonmeasurable Marczewski measure zero set lacking the property of Baire. We extend our analysis of σ-ideals to include the completely Ramsey (...) null sets relative to a Ramsey ultrafilter and obtain all 32 possible examples of sets in some ideals and not others, some under the assumption of MA, but most in ZFC alone. We also improve upon the known constructions of a Marczewski measure zero set which is not Ramsey by using a set theoretic hypothesis which is weaker than those used by other authors. We give several consistency proofs: one concerning the relative sizes of the covering numbers for the meager sets and the completely Ramsey null sets; another concerning the size of non(CRU 0); and a third concerning the size of add(CRU 0). We also study those classes of perfect sets which are bases for the class of always first category sets. (shrink)

In this paper we show that it is consistent with ZFC that for any set of reals of cardinality the continuum, there is a continuous map from that set onto the closed unit interval. In fact, this holds in the iterated perfect set model. We also show that in this model every set of reals which is always of first category has cardinality less than or equal to ω 1.

This is the first in a series of papers on Predicative Algebraic Set Theory, where we lay the necessary groundwork for the subsequent parts, one on realizability [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory II: Realizability, Theoret. Comput. Sci. . Available from: arXiv:0801.2305, 2008], and the other on sheaves [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory III: Sheaf models, 2008 ]. We introduce the notion of a predicative category (...) with small maps and show that it provides a sound and complete semantics for constructive set theories like IZF and CZF. The main technical contribution of this paper is that it shows in detail that such categories can always be conservatively embedded in categories that are exact. These exactness properties play a crucial rôle in showing that predicative categories with small maps contain models of set theory and that they are closed under sheaves and realizability. We will prove the former statement in this paper as well, leaving a proof of the closure properties to the papers on realizability and sheaves as mentioned above. (shrink)

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions . As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that (...) the full axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo-Fraenkel set theory. (shrink)

We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order set theory whose associated categories of sets are exactly the elementary toposes. In addition, we show that (...) the full axiom of Separation is validated whenever the dssi is superdirected. This gives a uniform explanation for the known facts that cocomplete and realizability toposes provide models for Intuitionistic Zermelo—Fraenkel set theory (IZF). (shrink)

Much fuss has been made of the “spatial turn” in recent years, across a range of disciplines. It is hard to know if the attention has been warranted. A confusion of terms has been used—such as space, place, spatiality, location—and each has signified a cluster of often contradictory and confusing meanings. This phenomenon is common to a range of disciplines in the humanities. This means, first, that it is not always easy to recognize what is being discussed under (...) the rubric of space, and second, that over-extended uses of the cultural turn have stymied meaningful engagement with materiality in discussions of space. This article shows how materiality has been marginalized both by a casual vocabulary and a vigorous a priori epistemological holism on the part of scholars, and how the spatial turn has been too closely linked to the cultural turn to allow it to develop its fullest explanatory potential. It demonstrates how historians might profitably theorize the significance of place and space in their work , and sets out some challenges for using space more effectively in explanatory systems. Inspired by environmental history, sociology, and science and technology studies, I propose a way of establishing space as different from conventional historical handling of materiality, and end by identifying some methodological problems that need to be solved if we are to proceed on a surer footing. (shrink)

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, (...) as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models. (shrink)

Drawing on anthropological examples of first contacts between people from different cultures, I argue that non-verbal communication plays a far bigger part in intercultural communication than has been acknowledged in the literature so far. Communication rests on mutually attuning in a large number of judgements. Some sort of structuring principle is needed at this point, and Davidson's principle of charity is a good candidate, provided sufficient attention is given to non-verbal communication. There will always be more and less (...) successful interpretations and translations, and their success will depend on the success of the non-verbal communication at hand. There is no need for cognitive or semantic universals: people understand each other because they share (a) certain form(s) of life. How ever, it is incorrect to treat forms of life as rigid entities with clear boundaries: it is both impossible and unnecessary to determine them in an exact way. Any appeal to cognitive or cultural essences to explain how people communicate successfully is flawed. My critique of essentialism is not a defence of linguistic ‘anything goes' relativism whatsoever. Assumptions underwriting a relativist stance often wrongly issue, in a decidedly non-relativist confidence in one fixed set of categories, values or meanings. S. Afr. J. Philos. Vol.21(2) 2002: 85-96. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory (...) of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

Why do sociological theorists remain uninterested in and resistant to feminist theory? Notwithstanding indications of increasing openness to feminist theory, journals and texts on sociological theory reflect a continuing pattern of neglect. I identify reasons for this pattern, including tensions resulting from the introduction of gender as a central analytical category: Not only does gender challenge the dichotomous categories that define sociology's boundaries and identity, it also displaces the discipline's central problematic of modernity. The significance of this displacement is (...) apparent when the discipline's responses to feminist and postmodernist theory are compared. I discuss the relevance of feminist theoretical work to contemporary issues in sociological theory, with specific attention to the synthetic nature of feminist theorizing, to work on rethinking power, resistance, and oppression, and to efforts to effect a conceptual shift from "either/or" to "both/and" thinking and to establish new grounds for assessing knowledge claims. (shrink)

Three different styles of foundations of mathematics are now commonplace: set theory, type theory, and category theory. How do they relate, and how do they differ? What advantages and disadvantages does each one have over the others? We pursue these questions by considering interpretations of each system into the others and examining the preservation and loss of mathematical content thereby. In order to stay focused on the “big picture”, we merely sketch the overall form of each construction, referring to (...) the literature for details. Each of the three steps considered below is based on more recent logical research than the preceding one. The first step from sets to types is essentially the familiar idea of set theoretic semantics for a syntactic system, i.e. giving a model; we take a brief glance at this step from the current point of view, mainly just to fix ideas and notation. The second step from types to categories is known to categorical logicians as the construction of a “syntactic category”; we give some specifics for the benefit of the reader who is not familiar with it. The third step from categories to sets is based on quite recent work, but captures in a precise way an intuition from the early days of foundational studies. With these pieces in place, we can then draw some conclusions regarding the differences between the three schemes, and their relative merits. In particular, it is possible to state more precisely why the methods of category theory are more appropriate to philosophical structuralism. (shrink)

This paper serves three specific goals. First, it reports the development of an Indian Asian face set, to serve as a free resource for psychological research. Second, it examines whether the use of pre-tested U.S.-specific norms for stimulus selection or weighting may introduce experimental confounds in studies involving non-U.S. face stimuli and/or non-U.S. participants. Specifically, it examines whether subjective impressions of the face stimuli are culturally dependent, and the extent to which these impressions reflect social stereotypes and ingroup favoritism. (...) Third, the paper investigates whether differences in face familiarity impact accuracy in identifying face ethnicity. To this end, face images drawn from volunteers in India as well as a subset of Caucasian face images from the Chicago Face Database were presented to Indian and U.S. participants, and rated on a range of measures, such as perceived attractiveness, warmth, and social status. Results show significant differences in the overall valence of ratings of ingroup and outgroup faces. In addition, the impression ratings show minor differentiation along two basic stereotype dimensions, competence and trustworthiness, but not warmth. We also find participants to show significantly greater accuracy in correctly identifying the ethnicity of ingroup faces, relative to outgroup faces. This effect is found to be mediated by ingroup-outgroup differences in perceived group typicality of the target faces. Implications for research on intergroup relations in a cross-cultural context are discussed. (shrink)

Fate has always existed in life both as a faith issue appearing in most of the religions and as a vital phenomenon. The unknown sides of fate and the uncertainties related to fate have been a factor that always keeps a human’s sense of curiosity alive. The fate perceptions’ potential of affecting life is high. As an individual’s fate perception is one of the factors determining his attitude to life, and it also affects his behaviours. The fate perceptions’ (...) power of influencing human behaviours was effective in specifying the research topic. The subject of the research was determined as “fate perception”, and university students were selected as the sample group. The research was carried out through metaphor analysis technique based on the phenomenological method. The reason for referring this method rather than directly asking questions related to fate is to reach the real thoughts in the depths of youths’ minds. A total of 211 students participated in the study performed with undergraduate students from different departments of different universities, and the analysis was continued with 163 data sets since the inappropriate data were sorted out. First of all, groups that included the same theme according to the meanings attributed to the fate in the metaphors were formed, and rather than the metaphor, the “because…” part that described it was based on in the grouping. The categories and the metaphors collected in the themes under them were again reviewed relationally, and then the research was analysed by two specialists to ensure the validity and reliability. As a result of the research, it was determined that some of the participants tried to clarify equivalents of the problems related to fate in their minds and to conceptually define the fate while producing metaphors. It was seen that some of the participants associated the fate with religious beliefs in forming metaphors while some of them dealt with it separately from the religion. The most frequently repeated metaphor is the "path" metaphor in the study, in which university students were found to have produced 106 metaphors related to the concept of "fate". This is followed by the metaphors "book" and "wheel". "Scenario, pen, map, crossroads, bunker, line, ship" metaphors are among the top ten most preferred metaphors. After the explanations of the metaphors produced in the scope of the research were examined, they were grouped in terms of their common features, themes were formed, and categories were formed by grouping the themes among themselves. Accordingly, the first category was identified as “fate in the context of characteristic” and its sub-themes were “fate as a(n) unchanging/determined phenomenon, fate as a divertible/preferable phenomenon, fate as an unknown/uncontrollable phenomenon, fate as both determined and divertible phenomenon and fate as a defence mechanism”. The second category was “fate in the context of faith/freedom”. The sub-themes of this category were determined as “the phenomenon of fatalist-inclined fate, the phenomenon of pure faith-based fate, the phenomenon of faith-based voluntaristic fate, the phenomenon of faith-based Cebrî fate, the phenomenon of not faith-based voluntaristic fate, fate contrast”. (shrink)

This study examined the representation of women in the world press, through the coverage of two very different events during 1995: The 50th anniversary of the surrender of Nazi Germany and the end of World War II, and the 4th Conference on Women in Beijing. Using the first level of the agenda-setting approach as well as the second level we analyzed the content of more than 10,000 stories which appeared in the news around the world. The findings show that (...) women's presence is still not felt in the world's press, that is, they are not there in great frequency or quantity, regardless of the event, and even when they are present, they are associated more with the private than with the public sphere. Second level agenda-setting research would suggest that this might simply reinforce existing stereotypes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"A Mark ofthe Growing Mind is Veneration of Objects" (Ludwig Wittgenstein) Fay Horton Sawyier Introduction In book 1 of the Treatise,1 Hume directs his attention to two sets of concepts; one of these sets is what I think of as the "basic epistemological set" and the other as the "basic metaphysical or ontological set." Except for the idea of personal identity, the First Inquiry2 addresses the same arrays (...) of concerns. Within the "epistemological set" we find discussions ofknowledge, belief, origin of ideas, etc.; within the "metaphysical set"are seen space, time, identity, cause and effect, uniformity ofnature, external objects and so on.3 For the first (epistemological) set, Hume constructs a mode of analysis which depends crucially on the provenance of an idea or concept. Thatis, asit does forarthistorians today, authenticityortruth depends on how the thingin question came intoyour possession. Hume announces not only that every simple idea depends on and comes from its simple impression, but that the full understandingofa complexidea requires first factoring it into its simple components and then tracing them back to their impressions. Understanding is, so to speak, like displaying the family tree. It turns out that all of the members of the "metaphysical" set have dubious parentage. Even if one grants the accuracy and adequacy of Hume's factoring, we are left facing his demonstrations that for each metaphysical concept there are at least some elements with no clear ancestry from single impressions. In this wayHume directs our attention tohis questforhow suchideas(or such elements withinideas) are ever come by. Why do we attribute identity? Howcanwe assume thereisanecessary connection and apower? What can possibly bring us to imagine, even, that anything can be independent ofour perceptions? And so on. All ofthis is not only at the heart ofthe Humean enterprise inbook 1 ofthe Treatise ami theFirstInquiry butis well-known to anyone even modestly familiar with Hume's writings. The result of his powerful analyses is that these mysterious, illegitimate elements in the metaphysical concepts are generated within subjects exposed to repeated instances of, for example, pairings in time or place, similar sightings after temporal lapses and so on. The processes by which we Volume XVIII Number 2 315 FAY HORTON SAWYIER construct our categories as well as the elements out ofwhich we make them areimportantandin these cases were shown tobe developmental or time-dependent.4 Furthermore, since these processes and these resultant conceptshavebeen shown tohave been generated by us, they are uniquely quaUfied to demonstrate the nature of human nature, which was, after all, the subject ofthe Treatise? Having reminded ourselves ofthese extremely general features of Hume's exposition, I want now to isolate and to highlight some particular and peculiar features. 1.The subject upon whose mind or sensibilities paired and repeated events are presumed to impinge and by whose consequent conditioning these otherwise inexplicable concepts can be understood is always an adult male.6 2.The presentingsituation which is presumed to arise and repeatfor this adult male is always hypothetical and never observed. 3.Thisman'sconstructionofanyoneofthese concepts (like necessary connection) is always as his solution to a logical problem, his way-out ofa mental awkwardness or unease. 4.These adult male concept generators and logical problem solvers neverseem to doanything but sitstill and look around themselves.7 The fundamental character ofmy inquiry can be understood as a search for the (presumably deleterious) consequences of the four particular features noted above. Since the lives and experiences of young children are neglected and since acquisition of the basic metaphysical set is always initiated in early childhood, one may well hypothesize that Hume's results will be damaged or skewed. Intuitively, this would seem to be an obvious inference, but proof is needed that in some cases Hume did indeed misconstrue certain basic concepts and that the central factor in his shortfall was his neglect of the child's experience of concept development and acquisition. By contrast, his contemporary, Thomas Reid, remarked, "Could we obtain a distinct and full history of all that hath passed in the mind ofa child from thebeginning ofUfe and sensation, till it grows to the use ofreason... this would be a treasury of natural history, which would probably give... (shrink)

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental (...) idea of an adjoint pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general­ ized monoid. Chapters VI and VII explore this notion and its generaliza­ tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure lead inter alia to the study of more convenient categories of topological spaces. (shrink)

El poema épico de Ovidio -una historia universal mítico-etiológica- se abre con un relato acerca del origen del mundo, seguido por la creación del hombre. La transformación del caos en cosmos es, por ende, la primera metamorfosis. El texto continúa con una descripción de las Edades decrecientes, puesto que la instauración de un orden armonioso siempre está seguida por su disolución (HOLZBERG 2002: 120). Este trabajo se propone estudiar la cosmogonía y antropogonía ovidianas a partir de las categorías específicas enunciadas (...) por W. BURKERT (1999: 87-106) y explorar las relaciones entre lo que se ha denominado carácter 'tecnomórfico' de dicha cosmogonía y la figura del poeta en cuanto tal. Ovid's epic poem, a mythical and etiologic world history, starts with a story about the origin of the world, followed by the creation of man. Thus, the first metamorphosis is the transformation of chaos into cosmos. The text continues with a description of the decreasing Ages, since the establishment of a harmonious order is always followed by its dissolution (HOLZBERG 2002: 120). This work intends to study ovidian cosmogony and anthropogony starting from specific categories set out by W. BURKERT (1999: 87-106) and explore the relationship between what has been termed technomorphic character of cosmogony and the figure of the poet itself. (shrink)

In _Always More Than One_, the philosopher, visual artist, and dancer Erin Manning explores the concept of the "more than human" in the context of movement, perception, and experience. Working from Whitehead's process philosophy and Simondon's theory of individuation, she extends the concepts of movement and relation developed in her earlier work toward the notion of "choreographic thinking." Here, she uses choreographic thinking to explore a mode of perception prior to the settling of experience into established categories. Manning connects this (...) to the concept of "autistic perception," described by autistics as the awareness of a relational field prior to the so-called neurotypical tendency to "chunk" experience into predetermined subjects and objects. Autistics explain that, rather than immediately distinguishing objects—such as chairs and tables and humans—from one another on entering a given environment, they experience the environment as gradually taking form. Manning maintains that this mode of awareness underlies all perception. What we perceive is never first a subject or an object, but an ecology. From this vantage point, she proposes that we consider an ecological politics where movement and relation take precedence over predefined categories, such as the neurotypical and the neurodiverse, or the human and the nonhuman. What would it mean to embrace an ecological politics of collective individuation? (shrink)

While first-person methods are essential for a science of consciousness, it is controversial what form these methods should take and whether any such methods are reliable. I propose that first-person experiments are a reliable method for investigating conscious experience. I outline the history of these methods and describe their characteristics. In particular, a first-person experiment is an intervention on a subject's experience in which independent variables are manipulated, extraneous variables are held fixed, and in which the subject (...) makes a phenomenal judgement about the target experience of the investigation. I examine historical and contemporary examples of first-person experiments: Mariotte’s demonstration of the visual blind spot, Kanizsa’s subjective contours, the Tse Illusion, and investigations of the non-uniform resolution of the visual field. I discuss the role that phenomenal contrast plays in these methods, and how they overcome typical introspective errors. I argue that their intersubjective repeatability is an important factor in their scientific status, however, it is not the only factor. That they control for extraneous factors and confounds is another factor which sets them apart from pseudoscience (e.g., the perception of auras), and hence another reason for classifying them as genuine experiments. Furthermore, by systematically mapping out the structure of visual experience, these methods make scientific progress. Praises of such first-person experimental approaches may not always be sung by philosophers and psychologists, but they continue to flourish as respectable scientific methods nevertheless. (shrink)

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

Seminal work by Knobe, Prasada, and Newman (2013) distinguished a set of concepts, which they named “dual‐character concepts.” Unlike traditional concepts, they require two distinct criteria for determining category membership. For example, the prototypical dual‐character concept “artist” has both a concrete dimension of artistic skills, and an abstract dimension of aesthetic sensibility and values. Therefore, someone can be a good artist on the concrete dimension but not truly an artist on the abstract dimension. Does this analysis capture people's understanding (...) of cornerstone social categories, such as gender, around which society and everyday life have traditionally been organized? Gender, too, may be conceived as having not only a concrete dimension but also a distinct dimension of abstract norms and values. As with dual‐character concepts, violations of abstract norms and values may result in someone being judged as not truly a man/woman. Here, we provide the first empirical assessment of applying the dual‐character framework to people's conception of gender. We found that, on some measures that primarily relied on metalinguistic cues, gender concepts did indeed resemble dual‐character concepts. However, on other measures that depicted transgressions of traditional gender norms, neither “man” nor “woman” appeared dual‐character‐like, in that participants did not disqualify people from being truly a man or truly a woman. In a series of follow‐up studies, we examined whether moral norms have come to replace gender role norms for the abstract dimension. Implications for the evolution of concepts and categories are explored. (shrink)

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into (...) 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory. (shrink)

The article begins with an effort to clarify and differentiate a variety of terms used by analysts in dealing with mentions of persons in conversation and other forms of talk-in-interaction — such terms as person-reference, identifying, describing, categorizing, and the like. This effort leads to the observation that `reference to persons' and `membership categorization' are quite distinct sets of practices, with most reference to persons not being done by membership categories, and most uses of membership categorization devices being in the (...) service of actions other than referring. Two interactional sequences whose analysis turns on a connection to talk earlier in the occasion are then examined; first, to establish what is going on interactionally without respect to the mentioning of persons, and then as exercises in examining the various ways person-reference and membership categorization can figure in a stretch of interaction. (shrink)

Stimuli that resemble humans, but are not perfectly human-like, are disliked compared to distinctly human and nonhuman stimuli. Accounts of this “Uncanny Valley” effect often focus on how changes in human resemblance can evoke different emotional responses. We present an alternate account based on the novel hypothesis that the Uncanny Valley is not directly related to ‘human-likeness’ per se, but instead reflects a more general form of stimulus devaluation that occurs when inhibition is triggered to resolve conflict between competing stimulus-related (...) representations. We consider existing support for this inhibitory-devaluation hypothesis and further assess its feasibility through tests of two corresponding predictions that arise from the link between conflict-resolving inhibition and aversive response: 1) that the pronounced disliking of Uncanny-type stimuli will occur for any image that strongly activates multiple competing stimulus representations, even in the absence of any human-likeness, and 2) that the negative peak of an ‘Uncanny Valley’ should occur at the point of greatest stimulus-related conflict and not (in the presence of human-likeness) always closer to the ‘human’ end of a perceptual continuum. We measured affective responses to a set of line drawings representing nonhuman animal-animal morphs, in which each continuum midpoint was a bistable image (Exp. 1), as well as to sets of human-robot and human-animal computer-generated morphs (Exp. 2). Affective trends depicting classic Uncanny Valley functions occurred for all continua, including the nonhuman stimuli. Images at continua midpoints elicited significantly more negative affect than images at endpoints, even when the continua included a human endpoint. This illustrates the feasibility of the inhibitory-devaluation hypothesis and the need for further research into the possibility that the strong dislike of Uncanny-type stimuli reflects the negative affective consequences of cognitive inhibition. (shrink)

One of the fundamental ethical concerns about biomedical research is that it frequently exposes participants to risks for the benefit of others. To protect participants’ rights and interests in this context, research regulations and guidelines set out a mix of substantive and procedural requirements for research involving humans. Risk thresholds play an important role in formulating both types of requirements. First, risk thresholds serve to set upper risk limits in certain types of research. Second, risk thresholds serve to demarcate (...) risk categories that streamline risk-adapted systems of ethical oversight. But although risk thresholds play such an important role in research governance, there is a need both to better define the existing risk thresholds and to delineate new thresholds in order to develop more risk-adapted systems of research oversight. The present paper examines the existing minimal risk threshold and the surrounding debates with the goal of deriving a systematic approach to setting thresholds of research risk. (shrink)

Peirce’s method of categorial development reveals the experimental nature of phenomenology, of metaphysics, and of the relation between their respective claims. The phenomenological categories of Firstness, Secondness, and Thirdness come to light as an interrelated set of meanings, abductively generated as a tool for focusing on the richness of experience in order to elicit its illusive, “intangible” but pervasive textures, “traits” “tones or tints”. The move from experiential claims to metaphysical claims is an imaginative extension via analogy. In the development (...) of his metaphysical categories, there is an exaggeration of the experimental method by which we have meaningful everyday experience. There is an exaggeration of the metaphorical, imaginative, creative features of the meanings which arise out of past experience though abductive fixations of experience, and which legislate for the analysis of future experience. Further, there is an exaggerated attentiveness to what appears in experience, to its pervasive features or textures, an attentiveness which both founds the categories and serves to verify their adequacy. The claims of his experimental phenomenology, and hence the claims of the metaphysics which it grounds, are fallibilistic and open to alternative categorial possibilities. (shrink)

It would be useful to have a category of extensive-form games whose isomorphisms specify equivalences between games. Since working with entire games is too large a project for a single paper, I begin here with preforms, where a “preform” is a rooted tree together with choices and information sets. In particular, this paper first defines the category \, whose objects are “functioned trees”, which are specially designed to be incorporated into preforms. I show that \ is isomorphic (...) to the full subcategory of \ whose objects are converging arborescences. Then the paper defines the category \, whose objects are “node-and-choice preforms”, each of which consists of a node set, a choice set, and an operator mapping node-choice pairs to nodes. I characterize the \ isomorphisms, define a forgetful functor from \ to \, and show that \ is equivalent to the full subcategory of \ whose objects are perfect-information preforms. The paper also shows that many game-theoretic entities can be derived from preforms, and that these entities are well-behaved with respect to \ morphisms and isomorphisms. (shrink)

It is assumed that a Kripke–Joyal semantics \({\mathcal{A} = \left\langle \mathbb{C},{\rm Cov}, {\it F},\Vdash \right\rangle}\) has been defined for a first-order language \({\mathcal{L}}\) . To transform \({\mathbb{C}}\) into a Heyting algebra \({\overline{\mathbb{C}}}\) on which the forcing relation is preserved, a standard construction is used to obtain a complete Heyting algebra made up of cribles of \({\mathbb{C}}\) . A pretopology \({\overline{{\rm Cov}}}\) is defined on \({\overline{\mathbb{C}}}\) using the pretopology on \({\mathbb{C}}\) . A sheaf \({\overline{{\it F}}}\) is made up of sections (...) of F that obey functoriality. A forcing relation \({\overline{\Vdash}}\) is defined and it is shown that \({\overline{\mathcal{A}} = \left\langle \overline{\mathbb{C}},\overline{\rm{Cov}},\overline{{\it F}}, \overline{\Vdash} \right\rangle }\) is a Kripke–Joyal semantics that faithfully preserves the notion of forcing of \({\mathcal{A}}\) . That is to say, an object a of \({\mathbb{C}Ob}\) forces a sentence with respect to \({\mathcal{A}}\) if and only if the maximal a-crible forces it with respect to \({\overline{\mathcal{A}}}\) . This reduces a Kripke–Joyal semantics defined over an arbitrary site to a Kripke–Joyal semantics defined over a site which is based on a complete Heyting algebra. (shrink)

This paper addresses the problem of the origin and principle of Aristotle’s distinctions among the categories. It explores the possibilities of reformulating and reviving the “grammatical” theory, generally ascribed first to Trendelenburg. The paper brings two new perspectives to the grammatical theory: that of Aristotle’s own theory of syntax and that of contemporary linguistic syntax and semantics. I put forth a provisional theory of Aristotle’s categories in which (1) I propose that the Categories sets forth a theory of lexical (...) structure, with the ten categories emerging as lexical or semantic categories, and (2) I suggest conceptual links, both in Aristotle’s writings and in actuality, between these semantic categories and certain grammatical inflections. (shrink)

It is a commonplace that, to a great extent, the way we think depends upon the categories we think with. In this paper I propose to introduce a group of related categories which, if they do not obviously lead to new discoveries, at least provide new ways of understanding and interrelating old ideas. The basic category I am concerned with is that of imperceptibles: not particularly a new one, but always previously a confused one because proper definition of (...) it requires specification of the perceiver. I wish to propose a set of definitions which cures such ambiguities, and then to examine some of the uses to which it may be put. (shrink)

This paper addresses the problem of the origin and principle of Aristotle’s distinctions among the categories. It explores the possibilities of reformulating and reviving the “grammatical” theory, generally ascribed first to Trendelenburg. The paper brings two new perspectives to the grammatical theory: that of Aristotle’s own theory of syntax and that of contemporary linguistic syntax and semantics. I put forth a provisional theory of Aristotle’s categories in which (1) I propose that the Categories sets forth a theory of lexical (...) structure, with the ten categories emerging as lexical or semantic categories, and (2) I suggest conceptual links, both in Aristotle’s writings and in actuality, between these semantic categories and certain grammatical inflections. (shrink)

We develop the concepts of recursively nowhere dense sets and sets that are recursively of first category and study closed sets of points in light of Baire's Category Theorem. Our theorems are primarily concerned with exdomains of recursive quantum functions and hence with avoidable points . An avoidance function is a recursive function which can be used to expel avoidable points from domains of recursive quantum functions. We define an avoidable set of points to be an arbitrary (...) subset of the avoidable points of a single avoidance function, and we study an effective union of such sets which we call a piecemeal avoidable set. We note that each of ‘the set of recursive points’ and ‘the set of avoidable points’ is of first category but not recursively of first category. We show an exdomain exists which is recursively nowhere dense, as well as one that is nowhere dense but not recursively nowhere dense. After establishing that every exdomain is recursively of first category, we prove that given any fixed exdomain, there is another exdomain, which while dense in the underlying space, is disjoint from the fixed exdomain. Finally, we show how to build a recursive sequence of recursive quantum functions that have mutually disjoint, dense exdomains. (shrink)

The central problem about the relationship between categories and the real order can be stated very simply: the purpose of categorial predication is to yield a set of necessary truths about things within the world, but the universality of these same truths sometimes seems to subordinate the particularity of the real order to the generality of conceptual understanding. As a result, an apparent conflict arises between the real and the logical orders which quite naturally raises a question about how these (...) two separate realms are to be related. In this paper I will examine this question in typically Aristotelian terms, first by discussing a small cluster of passages in Wilfrid Sellars’s challenging paper about Aristotle’s metaphysics, and then by offering my own interpretation of Aristotle’s position about the issue in question. My fundamental purpose in doing this is to establish an intelligible relationship between categories and the real order and to do so by exploring the logical space between an individual thing and the question “What is it?” I am convinced that within this space form and content meet and that we can at least begin to answer our original question about the real and the logical orders by exploring their interconnection. (shrink)

Context: The use of first-person micro-phenomenological interviews and their productive interaction with third-person physiological data is a challenging and pressing issue in order to offer an effective and fruitful application of Varela’s neurophenomenological hypothesis. Problem: We aim at offering a generative method of analysis of first-person micro-phenomenological interviews using third-person physiological data. Our challenge is to describe this generative first-person analysis with the third-person physiological framework rather than put Varela’s hypothesis into practice in a generative way (as (...) we did in another paper. Method: The present contribution is a first pioneering study as far as the exposition of such an interactive generative methodology is concerned. It is also a new issue insofar as it deals with a case study, surprise in depression, that has not been thoroughly dealt with so far, either in philosophy or in psychopathology. Results: We show that the analysis of first-person data is an intrinsic generative one, insofar as new refined categories and multifarious circular micro- and macro-processes were discovered in the very process of analyzing. They provide the initial structural generic third-person description of surprise inherited both from philosophical phenomenological a priori categories and from the experimental startle setting with a refined micro-segmentation of the dynamic of the experience. Implications: Our article could be of interest to neurophenomenologists looking for an effective application and to researchers in quest of a method of analysis of first-person data. The present limitations are due to the still preliminary data-results we need to complete. Constructivist content: The article is directly linked to Varela’s neurophenomenological program and aims at extending and reforming it with a cardio-phenomenological approach. Keywords: First-person micro-phenomenological interviews, surprise, generative analysis of first-person data, depression, cardio-phenomenology, generative categories. (shrink)

This paper firstly distinguishes between principles of “global justice” that apply the same anywhere and everywhere – Tännsjö’s utilitarianism, egalitarianism, prioritarianism and such like – and principles of “local justice” that apply within the specific sphere of health-care. Sometimes the latter might just be a special case of the former – but not always. Secondly, it discusses reasons, many psychological in nature, why physicians might devote excessive resources to prolonging life pointlessly, showing once again that those reasons might themselves (...) be morally significant. (shrink)

Algebraic Set Theory, a reconsideration of Zermelo-Fraenkel set theory in category-theoretic terms, has been built up in the mid-nineties by André Joyal and Ieke Moerdijk. Since then, it has developed into a whole research program. This paper gets back to the original formulation by Joyal and Moerdijk, and more specifically to its first three axioms. It explains in detail that these axioms set up a framework directly linked to descent theory, a theory having to do with the shift (...) from local data to a global item in modern algebraic geometry. Fibered categories, introduced by Grothendieck, provide a powerful framework for descent theory: They formalize in a very general way the consideration of local data of different kinds over the objects of some base category. The paper shows that fibered categories fit Joyal and Moerdijk’s axiomatization in a natural way, since the latter actually aims to secure a descent condition. As a result, Algebraic Set Theory is shown to accomplish, not only an original and fruitful combination of set theory with category theory, but the genuine graft of a deeply geometric idea onto the usual setting of zfc. (shrink)

It is commonly thought that on Kant’s view of action, ‘everyone always acts on maxims.’ Call this the ‘descriptive reading.’ This reading faces two important problems: first, the idea that people always act on maxims offends against common sense: it clashes with our ordinary ideas about human agency. Second, there are various passages in which Kant says that it is ‘rare’ and ‘admirable’ to firmly adhere to a set of basic principles that we adopt for ourselves. This (...) article offers an alternative: the ‘normative reading.’ On this reading, it is a normative ideal to adopt and act on maxims: it is one of the things Kant thinks we would do if our reason were fully in control of our decision-making. (shrink)

Something has been going wrong on many college campuses in the last few years. Speakers are shouted down. Students and professors say they are walking on eggshells and are afraid to speak honestly. Rates of anxiety, depression, and suicide are rising--on campus as well as nationally. How did this happen? First Amendment expert Greg Lukianoff and social psychologist Jonathan Haidt show how the new problems on campus have their origins in three terrible ideas that have become increasingly woven into (...) American childhood and education: What doesn't kill you makes you weaker; always trust your feelings; and life is a battle between good people and evil people. These three Great Untruths contradict basic psychological principles about well-being and ancient wisdom from many cultures. Embracing these untruths--and the resulting culture of safetyism--interferes with young people's social, emotional, and intellectual development. It makes it harder for them to become autonomous adults who are able to navigate the bumpy road of life. Lukianoff and Haidt investigate the many social trends that have intersected to promote the spread of these untruths. They explore changes in childhood such as the rise of fearful parenting, the decline of unsupervised, child-directed play, and the new world of social media that has engulfed teenagers in the last decade. They examine changes on campus, including the corporatization of universities and the emergence of new ideas about identity and justice. They situate the conflicts on campus within the context of America's rapidly rising political polarization and dysfunction. This is a book for anyone who is confused by what is happening on college campuses today, or has children, or is concerned about the growing inability of Americans to live, work, and cooperate across party lines. (shrink)

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this (...) case 2.In the present work, we generalize the entire arrangement from propositional to first-order logic, using a representation result of Butz and Moerdijk. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed primarily in the form of a contravariant adjunction, is established by homming into a common dualizing object, now Sets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology.The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we give an elementary proof of Butz and Moerdijkʼs result in logical terms. (shrink)

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

In his Categories, Aristotle details the kinds of being that exist, along with what can be understood and predicated of existing things. Most notably within this work, Aristotle advances a set of ten, top-level categories that can be used to classify all kinds of being. Even today, the influence of the Categories is felt in many domains, particularly in knowledge organization (KO). Here, Aristotle’s Categories bear deep, long-standing connections with works examining categorization, subject analysis, and theory of classification. Though its (...) relation to ontology might seem obvious, connections to KO perspectives on knowledge organization systems (KOSs) and ontological modeling are curiously lacking. The aim of this work is to offer a re-examination of the Categories as a KOS, particularly through the lens of the KO field’s understandings of ontology. Utilizing Zeng’s classification of KOSs as a theoretical framework, this study draws parallels between the first two sections of the Categories and the defining features of ontologies and offers an initial ontological model of this work. The results of this re-examination stand to offer a new view of a fundamental work in the KO canon, draw further connections between past and present perspectives in KO, and further contribute to the theoretical grounding of contemporary KOS research and practice. (shrink)

It is shown that a formula of modal propositional logic has precisely the same models as a sentence of the first-order language of a single dyadic predicate iff its class of models is closed under ultraproducts. as a corollary, any modal formula definable by a set of first-order conditions is always definable by a single such condition. these results are then used to show that the formula (lmp 'validates' mlp) is not first-order definable.

This paper pursues two goals. Its first goal is to clear up the “identity problem” faced by the structuralist interpretation of mathematics. Its second goal, through the consideration of examples coming in particular from the theory of permutations, is to examine cases of misunderstandings in mathematics fit to cast some light on mathematical understanding in general. The common thread shared by these two goals is the notion of setting. The study of a mathematical object almost always goes together (...) with the choice of a particular setting, and the understanding of the workings of mathematical settings is an essential component of mathematical knowledge. It is claimed that the recognition of mathematical settings, as features distinct from both mathematical structures and the systems which instantiate those structures, allows one to classify most of understandable misunderstandings in mathematics, and also to solve the identity problem. (shrink)

This study examines processes through which social personae are conveyed by male Japanese students at a public university in Yokohama. Focusing on the frame-setting function of first person pronominals in contexts where there is no intra/inter speaker variation in the choice of FPP, this paper analyzes how speakers manage identity-associated discursive alignments related to a shared Okinawa prefecture background. The common experience of being from Okinawa prefecture and attending university far from home is the primary reason that these speakers (...) are close friends. However, analysis reveals speakers’ continual and active contention and re-formulation of this shared ‘Okinawan-ness’ and the personae to which it is linked. In particular, FPPs are implicated in speakers’ discussion of heterogeneity and/or local differences with respect to their Okinawa prefecture background. Strategic use of FPPs thus emerges as a salient tactic for speakers’ active negotiation of conversation relevant personae categories even in interactional contexts without variation. (shrink)

Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits (...) of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. -/- In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. -/- By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. -/- These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond. (shrink)

The term ‘environment’ is not uniformly defined in the public health sciences, which causes crucial inconsistencies in research, health policy, and practice. As we shall indicate, this is somewhat entangled with diverging pathogenic and salutogenic perspectives (research and policy priorities) concerning environmental health. We emphasise two distinct concepts of environment in use by the World Health Organisation. One significant way these concepts differ concerns whether the social environment is included. Divergence on this matter has profound consequences for the understanding of (...) health and disease, for measures derived from that understanding targeting health promotion and disease prevention, and consequently, for epistemic structures and concept development in scientific practice. We hope to improve the given situation in public health by uncovering these differences and by developing a fruitful way of thinking about environment. Firstly, we side with the salutogenic conception of environment as a _health resource_ (as well as a source of health risks). Secondly, we subdivide the concept of environment into four _health-oriented environmental categories_ (viz., natural, built-material, socio-cultural, and psychosocial) and we link these with other theoretical notions proposed in the health sciences literature. Thirdly, we propose that in public health ‘environment’ should be understood as consisting of all extrinsic factors that influence or are influenced by the health, well-being, and development of an individual. Consequently, none of the four categories should be excluded from the concept of environment. We point out the practical relevance and fruitfulness of the conception of environment as a health source and frame this in causal terms, representing _individual health environments_ as causal networks. Throughout, we side with the view that for the design of human health-promoting settings, increased attention and consideration of environmental resources of salutogenic potential is particularly pressing. (shrink)

The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. (...) In this taxonomy, I distinguish between three taxa, those of family, genus, and species. The family includes all cognitive artifacts without further specifying their informational properties. Two genera are then distinguished: representational and non-representational (or ecological) cognitive artifacts. These genera are further divided into species. In case of representational artifacts, these species are iconic, indexical, or symbolic. In case of ecological artifacts, these species are spatial or structural. Within species, token artifacts are identified. The proposed taxonomy is an important first step towards a better understanding of the range and variety of cognitive artifacts and is a helpful point of departure, both for conceptualizing how different artifacts augment or impair cognitive performance and how they transform and are integrated into our cognitive system and practices. (shrink)