This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially (...) developed as exact mathematical constructions. Therefore, they are legitimate components of the theory and the pictures of Cayley graphs are a part of practical mathematical procedures. (shrink)

Prototype theory emerged out of two main sources. First, research on perceptual category learning suggested that people spontaneously abstract representations of the statistical central tendency when they are exposed to a range of similar images. The abstracted representation corresponds to the average or prototype for a range of training images and can be used to classify future examples. The second source was philosophical. On some versions, the prototype features are organized into structured lists, which divide into such (...) subheadings as physical attributes, means of locomotion, and perhaps diet. In a connectionist framework, a prototype might be a collection of weighted feature-representing nodes, or, more graphically, points in a multidimensional space, whose dimensions correspond to nodes in the network. On an empiricist approach, prototype features might be interpreted as components of structured mental images, and imagistic simulations of prototype activities. (shrink)

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

The theory of mind debate has reached a “hybrid consensus” concerning the status of theory-theory and simulation-theory. Extant hybrid models either specify co-dependency and implementation relations, or distribute mentalizing tasks according to folk-psychological categories. By relying on a non-developmental framework these models fail to capture the central connection between simulation and theory. I propose a “dynamic” hybrid that is informed by recent work on the nature of similarity cognition. I claim that Gentner’s model of (...) class='Hi'>structure-mapping allows us to understand simulation as a process in which psychological representations are aligned, causing the spontaneous abstraction of theoretical generalizations about the psychological domain. (shrink)

The aim of the paper is to assess the relative merits of two formal representations of structure, namely, set theory and category theory. The purpose is to articulate ontic structural realism. In turn, this will facilitate a discussion on the strengths and weaknesses of both concepts and will lead to a proposal for a pragmatics-based approach to the question of the choice of an appropriate framework. First, we present a case study from contemporary science—a comparison of (...) the formulation of quantum mechanics in the language of Hilbert spaces and abstract C* algebras. It is then shown how the method of structural representation can be determined based on the pragmatics of goal-oriented research, not a dogmatic choice. We investigate a hypothesis stating that the use of the interplay between the powers of abstraction and detail of different representational methods results in adopting a pluralistic, as opposed to standard, unificatory, perspective on the role of structural representation in OSR. (shrink)

The aim of the study is to contribute to a better understanding of some aspects of the structure of biological knowledge and to make clearer to what extent the methods of reasoning may be useful in this field when only qualitative information is available. A fragment of biological knowledge (theory of cell motility) is analysed from the logico-methodological point of view as a coherent system and the possibility of its formal representation is investigated. The analysis (...) is based on distinguishing the main objects and their features (attributes) of which a given piece of knowledge is composed and on the values which these features may display. The features are interconnected by relations (in which various number of arguments appear) and these relations constitute the main (general, higher level) laws of a given fragment of knowledge (theory). Values of attributes are also mutually connected and these relations correspond to the detailed (lower level) laws. A computer system (in which Prolog language was used) enables to perform inference operations of progressive as well as regressive type. The main categories of reasoning procedures are described and illustrated by examples, namely a) search for conclusions which may be confronted with the actual knowledge in order to verify the system as a whole, b) formation of working hypotheses in the process of their empirical verification and explanation of facts and laws. The problem of development and modification of the system is also discussed. (shrink)

DP hypothesis of Abney (1987), the syntactic unit that had formerly been known as noun phrase should in fact be analyzed as a phrase headed by a determiner, hence the label DP. Quite independently of this syntactic development, Partee (1987) proposed a type shifting paradigm for the semantic analysis of nominals (now called DPs). In Partee's proposal DPs are ambiguous between a referential reading of type e, a predicative reading of type et and a quantificational reading of type (et)t. DP (...) meanings can flexibly move between their different readings due to covert application of semantic operators. The present paper proposes some strong relationships between these syntactic and semantic paradigms. It is argued that the structure of the DP affects its semantics in that the NP level within the DP is purely predicative and the DP level itself is purely quantificational. However, the intermediate D' level is flexible between the predicate/quantifier semantic categories, due to the covert application of semantic operators at this level. Partee's assumption, adopted from Discourse Representation Theory and more traditional approaches in philosophical logic, that some DPs need to have a (discourse) referential reading, is withdrawn. Instead of Partee's type shifting operators between the three semantic categories she assumes, two operators are used between predicates and quantifiers. The choice function operation of Reinhart (1997) and Winter (1997) is used as a general operator from predicates to quantifiers. The minimum operator of Winter (1996) is used as a general operator from quantifiers to predicates. These two operations, referred to as category shifting operators , account for most of the Partee data and substantially extend the theory of flexibility to treat some intricate phenomena in the domains of coordination, plurality and scope. (shrink)

Walter Benjamin foreshadowed many of the aesthetic theories, currently playing a fundamental role in the production and interpretation of art. By emphasising the role of the expressive character of art, or rather the category of expressivity itself, Benjamin defined art as a language. His aesthetics was characterised by the continuous interaction of two almost reciprocal projects: the theoretical critique of art which is based on an understanding of historical processes, and the understanding of historical processes which is formed by (...) the critical experience of art. We find a fundamental similarity between Benjamin’s dialectical character of the aesthetic sign and Lotman’s double-sidedness of the artwork. In classifying the system of art as a language, both theoreticians space out the structure ofart and determine it as the intersection of the synchronic and the diachronic aesthetic discourse. The paper follows the traces of the transition of modern painting from its representational status to an autonomous signification, that is, from being a symbolic expression to a discourse in the grammatological meaning of écriture. Parallel to this transition which resulted into the process of abstraction in painting, there can be observed a shift in the cultural values of art which had its critical bearing upon the world secured not by connections of likeness, but by virtue of the very independence of its values. The abstract form of the modern painting has been the declaration of the language of art as an exemplary realm. What must be expressed and experienced within this realm was (1) the critical reflection on the human condition, and (2) representing the society in so far as art maintained a moral independence from those conditions. This dialectic between the autonomous and social character of art has left deep impacts on the language of painting, a complexity, which has been made transparent through the various semiotic analytic approaches of the aesthetic sign. The paper discusses the processual character of the modern painting and demonstrates briefly the deficiency in the structural analysis of the painting language, encouraging its synthesis with the dynamical character of cultural products as we find it in the Lotmanian culture theory. (shrink)

Chapter 1 First Person Access to Mental States. Mind Science and Subjective Qualities -/- Abstract. The philosophy of mind as we know it today starts with Ryle. What defines and at the same time differentiates it from the previous tradition of study on mind is the persuasion that any rigorous approach to mental phenomena must conform to the criteria of scientificity applied by the natural sciences, i.e. its investigations and results must be intersubjectively and publicly controllable. In Ryle’s view, philosophy (...) of mind needs to adopt an antimentalist stance to achieve this aim. Antimentalism not only definitively rejects the idea that mind is a substance separated from the body, it also denies that mental phenomena radically differ from physical phenomena by virtue of several unique features. Most problematically, mental phenomena have a conscious character (mental states are related to specific qualitative feelings) and are accessible only to the first-person (only the subject knows directly what s/he is experiencing inside his/her mind). Ryle takes a strong stance on antimentalism going so far as to maintain that an approach to mind which aims to meet the criteria of scientificity set by the natural sciences must avoid any reference to internal, unobservable mental states. In his view (which is considered a specifically philosophical version of psychological behaviorism and also addresses questions put forward in psychological research), mental states can be redescribed in terms of behavioral dispositions. In this chapter, we address the historical roots of the antimentalist view and analyze its relation to the later tradition of research on mind. We show that, compared to the antimentalist stance, functionalism and cognitivism take a step back when they maintain that direct reference to mental states is necessary since mental states cause and therefore explain human behavior. This step backwards is often interpreted as a return to mentalism. However, this is only partially true. Indeed, we suggest that these later traditions retain one important element of Ryle’s antimentalism, i.e. the idea that mental states must be uniquely identified using external and publicly observable criteria, while excluding any reference to introspection and those qualitative dimensions of a mental state, which are accessible only to the first-person. According to the perspective we put forward, this epistemological stance has continued to influence contemporary research on mind and current philosophical and psychological theories which both tend to exclude the subjective qualities of human experience from their accounts of how the mind works. The issue we raise here is whether this is legitimate or whether subjective qualities do play a role with respect to the way our mind works. The conclusion of this chapter anticipates the argument the book makes in in favor of this latter position, starting from a particular angle, i.e. the problem of how we categorize concepts related to our internal states. -/- Chapter 2 The Misleading Aspects of the Mind/Computer Analogy. The Grounding Problem and the Thorny Issue of Propriosensitive Information -/- Abstract. After the crisis of behaviorism, cognitivism and functionalism became the predominant models in the field of psychology and of philosophy, respectively. Their success is mainly due to the new key they use for interpreting mental processes: the mind/computer analogy. On the basis of this analogy, mental operations are seen as cognitive processes based on computations, i.e. on manipulations of abstract symbols which are in turn understood as informational unities (representations). This chapter identifies two main problems with this model. The first is how these symbols can relate to and communicate with perception and thus allow us to identify and classify what we perceive through the senses. Here we limit ourselves to presenting this issue in relation to the classical symbol grounding problem originally put forward by Harnad on the basis of Searle’s Chinese room argument. An attempt to address the problem raised here will be made in chap. 3. The second point we discuss in relation to the mind/computer analogy concerns the idea of information it fosters. Indeed, following this analogy, information is something available in the external world which can be captured by the senses and transmitted to the central system without being influenced or modified by the procedures of transmission. This perspective does not take into account that – unlike computers – in living beings information is acquired by means of the body. As Ulric Neisser has already pointed out, the body is itself an informational source that provides us with additional sensory experience that influences (modifies or complements) the information extracted from the external world by the senses. To develop this line of analysis and to determine exactly what information is provided by the body and how this might influence cognition, we examine Sherrington’s and Gibson’s positions. Moving on from their views, we qualify bodily information in terms of ‘proprioception’. We use ‘proprioception’ in a broad sense to describe any kind of experience we have of our internal states (including postural information as well as sensations related to the general state of the body and its parts). Following Damasio’s and Craig’s studies, we further elaborate this position, arguing that living beings are equipped with an internal propriosensitive monitoring system which maps all the changes that constantly occur in our body and that give us perceptual (‘proprioceptive’ or propriosensitive) information about what happens inside us. Moreover, relying on Goldie’s and Ratcliffe’s view, we show that emotional information can also be considered as a form of ‘proprioception’ which contributes to determining everything we perceive. This analysis leads us to the second main thesis of this book: ‘proprioception’ is a form of internal perception and it is an essential component of the sensory information we can access and use for all cognitive purposes. -/- Chapter 3 Semantic Competence from the Inside: Conceptual Architecture and Composition -/- Abstract. Concepts are essential constituents of thought: they are the instruments we use to categorize our experience, i.e. to classify things and group them together in homogeneous sets. Here we define concepts as the internal mental information (representations) that allows us, among other things, to master words in natural language. By analyzing the way in which individuals master word meanings we explore a number of hypotheses regarding the nature of concepts. Following Diego Marconi’s research, we differentiate between two kind of abilities that underpin lexical competence – so-called ‘referential’ and ‘inferential competence’ – and we suggest that, in order to support these abilities, concepts must also include two corresponding kinds of information, i.e. inferential and referential information. We point out that the most widely used and acknowledged theories of concepts do not make this distinction, instead broadly characterizing the information used for categorization in terms of propositionally described feature lists. However, we show that while feature lists can explain inferential competence, they do not account for referential competence. To address the issue of referential competence we examine Ray Jackendoff’s hypothesis that to account for the possibility of linking perceptual and conceptual information we need to assume the existence of a (visual) representation that encodes the geometric and topological properties of objects and bridges the gap between the percept and the concept. Furthermore, we analyze the extension of this work by Jesse Prinz who introduced the notion of a proxytype, a perceptual representation of a class of objects that incorporates structural and parametric information related to their appearance. However, as we point out, proxytypes can only explain the relationship between perception and concepts with respect to instances that can be perceived through the senses and that belong to the same class by virtue of their physical similarity. We suggest that this notion be extended to include larger conceptual classes. To accomplish this, we further develop Mark Johnson, George Lakoff and Jean Mandler’s idea of a schematic image and argue that conceptual representations include a perceptual schema. Perceptual schemata are non-linguistic, structured experiential gestalts (patterns or maps) that make use of information taken from all sensory modalities, including body perception. They accomplish a quasi-conceptual function: they allow us to recognize and to classify different instances. In this work, we hypothesize that perceptual schemata are an essential component of concepts, but not identical to them. Instead, we suggest that concepts include both perceptual and propositional information with perceptual schemata providing the ‘perceptual core concept’ that grounds related propositional information. -/- Chapter 4 In the Beginning There Were Categories. The Bodily Origin of Prelinguistic Categorical Organization: The Example of Folkbiological Taxonomies -/- Abstract. Studies of categorization in psychology and the cognitive sciences have made use of the notions of ‘category’ and ‘concept’ without precisely defining what is meant by either; in fact, often these terms have been used as synonyms, making it difficult to address specific issues related to conceptual development. This chapter begins by discussing the definitions of, as well as the distinctions between, ‘categories’ and ‘concepts’ in the classical philosophical tradition (Aristotle, Kant and Husserl). We introduce our view of categories with reference to Husserl. Categorization is defined as the way in which our experience is originally (pre-linguistically) organized in a passive and fully unconscious manner on the basis of universal structuring principles. Conceptualization is explained as a later process in which the earlier categorical macro-classes are further subdivided into more specific and detailed sets; this later process also relies on linguistic learning and exposure to culture. On the basis of Ray Jackendoff, Jean Mandler, George Lakoff and Mark Johnson’s work, we hypothesize that categorization is a two-step process that begins with the formation of homogeneous sets of entities partitioned into regions that describe the ontological boundaries of the objects that humans perceive (categories) and continues at a later stage with the development of more specific classifications (concepts). In this chapter, we mainly address three related issues: Why should we assume that there is categorical organization which precedes the development of a conceptual system? How do categories and concepts relate to each other? Shall we hypothesize that categories are innate or that they are formed before concepts on the basis of information and organizational structure available at a very early developmental stage? We show that categorical partitions are necessary for categorization and, following Mandler, that the general categories we form at an early age do not match our adult superordinate concepts. As for the third issue, we argue that there might be no need to assume that categories are innately present in the human mind, since their formation can be explained – at least in certain cases – by basic mechanisms that work on body (propriosensitive) information. This hypothesis will not be discussed in general, but in relation to a particularly relevant example of categorical partition, i.e. the folk-biological dichotomy between ANIMATE/INANIMATE. This is compared with other dichotomies that derive from it, but are not directly categorical such as LIVING/NON-LIVING and BIOLOGICAL/NON-BIOLOGICAL. -/- Chapter 5 Internal States: From Headache to Anger. Conceptualization and Semantic Mastery -/- Abstract. Here we ask if we can also apply the distinction between referential and inferential competence we introduced in Chapter 3 to words that do not refer to things that are perceived using the external senses, especially to words/concepts that denote bodily experiences (such as pain, thirst, hunger, etc.) or emotions. We introduce and discuss the hypothesis that – even though such words/concepts do not refer to intersubjectively identifiable entities in the external world – they do have a kind of referent that can be accessed via direct perception, more specifically ‘proprioception’, as we have defined it in terms of all propriosensitive information we can consciously access. In the first part of the chapter, we specifically consider terms denoting bodily experiences such as ‘pain’ or ‘hunger’ and argue that their referents are identified and classified from a first-personal point of view on the basis of four main characteristics: their specific intensity, their localization in the body, their co-occurrence with other signals and above all their specific qualitative sensations. Emotions are addressed in the second part of the chapter. We suggest that there is a continuity between bodily experiences and emotions. In particular, we argue for a perceptual theory of emotions in line with that proposed by James and Lange at the end of the 19th century and developed more recently by authors such as Damasio (see also chap. 2§5, §6). The hypothesis we put forward is that the referential information that supports the categorization of emotions and therefore also our mastery of terms referring to emotions consists in the perception (i.e. the ‘proprioception’) of those bodily states and changes in bodily states which constitute our emotional experience. In the context of this discussion we examine some objections to this line of reasoning that arise from a cognitivist perspective and following authors such as Oatley, Johnson-Laird and Frijda, we distinguish between basic emotions that can be identified and classified solely on the basis on how they feel and complex emotions whose identification and classification additionally depends on cognitive factors. To describe how emotions are identified and classified on the basis of how they feel, we rely on Marcel and Lambie’s distinction between an ‘emotion state’ and an ‘emotion experience’. Both notions indicate kinds of feelings that we consciously experience. However, they describe first-order and second order emotion awareness respectively. The emotion state is the feeling we have of the bodily states and changes that occur when we are experiencing an emotion, while the emotion experience is the fully developed and integrated emotion we both experience and are, with reflection, aware of experiencing. On the basis of this differentiation, we also show that the same characteristics that aid in the identification and classification of bodily experiences (specific qualitative sensations; somatic localization; specific intensity; presence/absence of specific concomitant sensations) can also be used for the identification and classification of emotions – at least basic emotions. In the last two sections of the chapter we present some clinical evidence on the semantic competence of people who suffer from Alexithymia and Autism Spectrum Disorder which supports the conclusions of our preceding analyses. -/- Chapter 6 The ‘Proprioceptive’ Component of Abstract Concepts -/- Abstract. In this chapter, we address the issue of whether the mastery of abstract words requires only inferential knowledge and thus, if the concepts that support the mastery of abstract words include only linguistic information. We start by differentiating the notions of ‘abstract’ and ‘general’ which are often erroneously confused. We then identify a strict definition of abstract, as contrasted with ‘concrete’, that applies to words or concepts whose referent cannot be experienced by the senses. We argue that abstract words/concepts would be better described as theoretical, because they are usually conceived as structured sets of inferential knowledge expressed linguistically; that is, as small theories. Pointing out parallels with Carnap’s analysis of this issue in philosophy of science, we hypothesize that words/concepts denoting non-observable entities are not all ‘equally theoretical’, because their link to sensory experience can be stronger or weaker. We revive the distinction, inspired by Quine, between theoretical and intertheoretical concepts/words. This distinction relies on the fact that the former – unlike the latter – retains a strong, although indirect, connection with perception. In Quine’s discussion, perception is understood uniquely in terms of observability, i.e. of external sensory experience. Here we argue, however, that bodily, ‘proprioceptive’ (i.e. propriosensitive) experience can also serve to referentially ground theoretical (i.e. abstract) concepts/words. We frame this issue using the example of the theoretical concept ‘freedom’ and Lakoff’s hypothesis that this concept is developed on the basis of bodily information. We contrast this with the example of ‘democracy’ which more closely resembles an intertheoretical concept/word. Furthermore, we show that one of the classical views put forward in psycholinguistic research to explain how abstract concepts are mentally represented – i.e. Paivio’s Dual Coding Theory – points in the same direction as our analysis. The same is true of Barsalou’s work suggesting that we use internal information to understand at least some abstract words. To sustain this position, we put forward two lines of evidence: the first comes from psycholinguistic studies while the second examines deficits of semantic competence exhibited by people with Autism Spectrum Disorder. On the basis of our analysis, we put forward a classification that distinguishes between different kinds of concreteness and different degrees of abstraction: concepts/words referring to body experiences and basic emotions are described as analogous to concrete concepts/words because they are grounded in perceptual (i.e. propriosensitive) experience, while abstract concepts/words are considered more or less abstract depending on whether they are intratheoretical (and rely entirely on inferential information) or theoretical (and are partially grounded in perceptual – or more often in propriosensitive perceptual – information). In the last section of the chapter we consider two scales that have been used in psycholinguistic research to measure the degree of concreteness vs. abstractness of words and we show that – used conjointly – they can provide a measure of the internal vs. external grounding of specific words. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 33.3 (2000) 259-285 [Access article in PDF] The Personal, the Political, and Others: Audre Lorde Denouncing "The Second Sex Conference" 1 Lester C. Olsen Those of us who stand outside the circle of this society's definition of acceptable women; those of us who have been forged in the crucibles of difference--those of us who are poor, who are lesbians, who are Black, who are older--know that (...) survival is not an academic skill. It is learning how to stand alone, unpopular and sometimes reviled, and how to make common cause with those others identified as outside the structures in order to define and seek a world in which we can all flourish.--Audre Lorde, Sister Outsider 112Fifty years ago, in 1949, Simone de Beauvoir's book entitled The Second Sex was published in France. She did not consider herself a philosopher because, to her, a philosopher was "someone who has built a great system" (Simons and Benjamin 1979, 338). Her book, nonetheless, became a milestone in feminist philosophy, for it synthesizes elements of existentialism, phenomenology, and socialism in an account of women's situation in society. Central to this account is Beauvoir's concentration upon representations of "self" and "other." For example, Beauvoir affirmed, "The category of the Other is as primordial as consciousness itself. In most primitive societies, in the most ancient mythologies, one finds the expression of a duality--that of the Self and the Other. This duality was not originally attached to the division of the sexes; it was not dependent upon any empirical facts" (1993, xl). In an interview, Beauvoir stressed, "I believe that the Other is not simply an idealist relationship, it is a materialist relationship" (Simons and Benjamin 1979, 345). To develop her analysis, Beauvoir drew upon another binary, "master" and "slave." However, she concentrated on how women, as a category, had been subordinated as men's "other."Twenty years ago, in 1979, Audre Lorde delivered her best-known speech, "The Master's Tools Will Never Dismantle the Master's House," at an international conference held in honor of the thirtieth anniversary of [End Page 259] Beauvoir's book. According to conference organizer Jessica Benjamin and reporter Lilly Rivlin, writing together in Ms. magazine, "[M]ore than 800 women from all over the world gathered at a conference on feminist theory, 'The Second Sex--Thirty Years Later,' sponsored by the New York Institute for the Humanities" (1980, 48). Like most of the conference participants, Lorde was a woman, a feminist, a socialist, a public intellectual, and an activist scholar. Lorde may have participated in the conference as a "consultant," a poet at a public reading, and a speaker at a plenary session 2 because her feminist philosophy is of resonance to Beauvoir's. Both women rejected biology as the basis for women's situation, believing instead that material conditions are most fundamental. Both commented upon the power of symbolism, especially myths about others, in perpetuating social inequalities and failing to differentiate categories for others. Both saw the relationship between "self" and "other" as a vital and creative tension.To understand this tension, Beauvoir drew explicitly on Hegel's ideas as they were treated in Sartre's oeuvre (Lloyd 1983). In contrast, Lorde may have drawn upon conceptions of double consciousness among black public intellectuals in the United States (Henderson 1989, 17-21). Unlike Beauvoir, Lorde was a lesbian, a mother, and a black woman for whom Beauvoir's analogies between the status of women and the status of "Negroes" were problematic. Confronting the conference participants on the last day, during the last panel entitled "The Personal and the Political," Lorde condemned the conference for its limited range of speakers, its substance, its very structure. Lorde examined the ramifications of failing to include others as equals. For in failing to do so, the conference had employed the same tools of oppression over others that the participants deplored in the politics of patriarchy. Lorde challenged the conference participants, who presumably understood that Beauvoir had represented woman as... (shrink)

Four experiments investigated the extent to which abstract quantitative information can be conveyed by basic visual features. This was done by asking observers to estimate and discriminate Pearson correlation in graphical representations where the first data dimension of each element was encoded by its horizontal position, and the second by the value of one of its visual features; perceiving correlation then requires combining the information in the two encodings via a common abstract representation. Four visual features were examined: (...) luminance, color, orientation, and size. All were able to support the perception of correlation. Indeed, despite the strikingly different appearances of the associated stimuli, all gave rise to performance that was much the same: just noticeable difference was a linear function of distance from complete correlation, and estimated correlation a logarithmic function of this distance. Performance differed only in regards to the level of noise in the feature, with these values compatible with estimates of channel capacity encountered in classic experiments on absolute perceptual magnitudes. These results suggest that quantitative information can be conveyed by visual features that are abstracted at relatively low levels of visual processing, with little representation of the original sensory property. It is proposed that this is achieved via an abstract parameter space in which the values in each perceptual dimension are normalized to have the same means and variances, with perceived correlation based on the shape of the joint probability density function of the resultant elements. (shrink)

Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing new strategies for treating diseases (...) such as cancers, is pointed out. The roles played by multiple metastable states in the “continuous uphill flow of Life” supported through internal bioenergetic processes that are coupled to essential inflows are also discussed in relation to dynamic realizations of (M,R)-systems. Furthermore, the roles played by the underlying, many-valued, quantum logics and symbolic computations for ultra-complex biological systems are also briefly discussed. (shrink)

Biologists depend on visual representations, and their use of diagrams has drawn the attention of philosophers, historians, and sociologists interested in understanding how these images are involved in biological reasoning. These studies, however, proceed from identification of diagrams on the basis of their spare visual appearance, and do not draw on a foundational theory of the nature of diagrams as representations. This approach has limited the extent to which we under- stand how these diagrams are involved in (...) class='Hi'>biological reasoning. In this paper, I characterize three different kinds of figures among those previously identified as diagrams. The features that make these figures distinctive as representational types, furthermore, illuminate the ways in which they are involved in biological reasoning. (shrink)

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to (...) covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)

The paper introduces mathematical encoding for subjective experience and meaning in natural cognition. The code is based on a quantum-theoretic qubit structure supplementing classical bit with circular dimension, functioning as a process-causal template for representation of contexts relative to the basis decision. The qubit state space is demarcated in categories of emotional experience of animals and humans. Features of the resulting spherical map align with major theoreties in cognitive and emotion science, modeling of natural language, and semiotics, suggesting (...) several generalizations and improvements. The developed model bridges psychological, quantum-theoretic, and semiotic perspectives, allowing for an integrative account of subjectivity, agency, and meaning in living Nature.Graphical abstract. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 33.3 (2000) 259-285 [Access article in PDF] The Personal, the Political, and Others: Audre Lorde Denouncing "The Second Sex Conference" 1 Lester C. Olsen Those of us who stand outside the circle of this society's definition of acceptable women; those of us who have been forged in the crucibles of difference--those of us who are poor, who are lesbians, who are Black, who are older--know that (...) survival is not an academic skill. It is learning how to stand alone, unpopular and sometimes reviled, and how to make common cause with those others identified as outside the structures in order to define and seek a world in which we can all flourish.--Audre Lorde, Sister Outsider 112Fifty years ago, in 1949, Simone de Beauvoir's book entitled The Second Sex was published in France. She did not consider herself a philosopher because, to her, a philosopher was "someone who has built a great system" (Simons and Benjamin 1979, 338). Her book, nonetheless, became a milestone in feminist philosophy, for it synthesizes elements of existentialism, phenomenology, and socialism in an account of women's situation in society. Central to this account is Beauvoir's concentration upon representations of "self" and "other." For example, Beauvoir affirmed, "The category of the Other is as primordial as consciousness itself. In most primitive societies, in the most ancient mythologies, one finds the expression of a duality--that of the Self and the Other. This duality was not originally attached to the division of the sexes; it was not dependent upon any empirical facts" (1993, xl). In an interview, Beauvoir stressed, "I believe that the Other is not simply an idealist relationship, it is a materialist relationship" (Simons and Benjamin 1979, 345). To develop her analysis, Beauvoir drew upon another binary, "master" and "slave." However, she concentrated on how women, as a category, had been subordinated as men's "other."Twenty years ago, in 1979, Audre Lorde delivered her best-known speech, "The Master's Tools Will Never Dismantle the Master's House," at an international conference held in honor of the thirtieth anniversary of [End Page 259] Beauvoir's book. According to conference organizer Jessica Benjamin and reporter Lilly Rivlin, writing together in Ms. magazine, "[M]ore than 800 women from all over the world gathered at a conference on feminist theory, 'The Second Sex--Thirty Years Later,' sponsored by the New York Institute for the Humanities" (1980, 48). Like most of the conference participants, Lorde was a woman, a feminist, a socialist, a public intellectual, and an activist scholar. Lorde may have participated in the conference as a "consultant," a poet at a public reading, and a speaker at a plenary session 2 because her feminist philosophy is of resonance to Beauvoir's. Both women rejected biology as the basis for women's situation, believing instead that material conditions are most fundamental. Both commented upon the power of symbolism, especially myths about others, in perpetuating social inequalities and failing to differentiate categories for others. Both saw the relationship between "self" and "other" as a vital and creative tension.To understand this tension, Beauvoir drew explicitly on Hegel's ideas as they were treated in Sartre's oeuvre (Lloyd 1983). In contrast, Lorde may have drawn upon conceptions of double consciousness among black public intellectuals in the United States (Henderson 1989, 17-21). Unlike Beauvoir, Lorde was a lesbian, a mother, and a black woman for whom Beauvoir's analogies between the status of women and the status of "Negroes" were problematic. Confronting the conference participants on the last day, during the last panel entitled "The Personal and the Political," Lorde condemned the conference for its limited range of speakers, its substance, its very structure. Lorde examined the ramifications of failing to include others as equals. For in failing to do so, the conference had employed the same tools of oppression over others that the participants deplored in the politics of patriarchy. Lorde challenged the conference participants, who presumably understood that Beauvoir had represented woman as... (shrink)

Emergent phenomena are quite interesting and amazing, but they present two main scientific obstacles: to be rationally understood and to be mathematically modelled. In this paper we propose a powerful mathematical tool for modelling emergent phenomena by applying category theory. Furthermore, since great part of biological phenomena are emergent, we present an essay of how to access an emergence from observational data. In the mathematical perspective, we utilize constructs (categories whose objects are structured sets), their operations and (...) their corresponding generalized underlying functor (which are not necessarily faithful) to define emergence. From this definition, we elaborate several results concerning homomorphism between emergences, representability, pull-back, push-out, equalizer, product and co-product of emergences among other results. After we have presented such mathematical model, we utilize a hierarchical structure as example—from molecules to a flatworm—, in order to understand the relation between biological systems and its underlying emergence in a hierarchical model. (shrink)

Biological sciences have strived to adopt the conceptual framework of physics and have become increasingly quantitatively oriented, aiming to refute the assertion that biology appears unquantifiable, unpredictable, and messy. But despite all effort, biology is characterized by a paucity of quantitative statements with universal applications. Nonetheless, many biological disciplines—most notably molecular biology—have experienced an ascendancy over the last 50 years. The underlying core concepts and ideas permeate and inform many neighboring disciplines. This surprising success is probably not so (...) much attributable to mathematical and statistical approaches in molecular biology, but rather to the preponderance of qualitative approaches, especially visualization. Visualizations can be afforded by quantitative research, but usually they rely on both, quantitative and qualitative research. I claim the following three features to be responsible for the unceasing zeal for using visualizations: visual representations facilitate reasoning, images can be cognitively processed in a “fast” manner, and abstractions of visual representations prompt conceptual advances. In summary, visualizations have largely contributed to the success of molecular biology by conveying its concepts to other disciplines, and at the same time, eclipsing mere quantitative approaches. However, visualizations also bear the risk of misinterpretation when traversing neighboring disciplines and even more so when pervading nonscientific domains. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, (...) it is basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctions-based (...) definitions can be abstracted in purely arrow-theoretic way for abstract category theory. In short, the language of elements & distinctions is the conceptual language in which the category of sets is written, and abstract category theory gives the abstract arrows version of those definitions. (shrink)

The distinction between abstract and concrete concepts is fundamental to cognitive linguistics and cognitive science. This distinction is commonly operationalized through concreteness ratings based on the aggregated judgments of many people. What is often overlooked in experimental studies using this operationalization is that ratings are attributed to words, not to concepts directly. In this paper we explore the relationship between the linguistic properties of English words and conceptual abstractness/concreteness. Based on hypotheses stated in the existing linguistic literature we select a (...) set of variables and verify whether they are statistically associated with concreteness ratings. We show that English nouns are rated as more concrete compared to other parts of speech, but mass nouns are rated as less concrete than count nouns. Furthermore, a more complex morphological structure is associated with abstractness, and as for etymology, French- and Latin-derived words are more abstract than words of other origin. This shows that linguistic properties of words are indeed associated with the degree of concreteness that we attribute to the underlying concepts, and we discuss the implications that these findings have for linguistic theory and for empirical investigations in the cognitive sciences. (shrink)

I this paper, I draw on recent research on the radically embodied and perceptual bases of conceptualization in linguistics and cognitive science to develop a new way of reading and evaluating abstract concepts in social theory. I call this approach Sociological Idea Analysis. I argue that, in contrast to the traditional view of abstract concepts, which conceives them as amodal “presuppositions” removed from experience, abstract concepts are irreducibly grounded in experience and partake of non-negotiable perceptual-symbolic features from which a (...) non-propositional “logic” naturally follows. This implies that uncovering the imagistic bases of allegedly abstract notions should be a key part of theoretical evaluation of concepts in social theory. I provide a case study of the general category of “structure” in the social and human sciences to demonstrate the analytic utility of the approach. (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)

Stem cell biology and systems biology are two prominent new approaches to studying cell development. In stem cell biology, the predominant method is experimental manipulation of concrete cells and tissues. Systems biology, in contrast, emphasizes mathematical modeling of cellular systems. For scientists and philosophers interested in development, an important question arises: how should the two approaches relate? This essay proposes an answer, using the model of Waddington’s landscape to triangulate between stem cell and systems approaches. This simple abstract model represents (...) development as an undulating surface of hills and valleys. Originally constructed by C. H. Waddington to visually explicate an integrated theory of genetics, development and evolution, the landscape model can play an updated unificatory role. I examine this model’s structure, representational assumptions, and uses in all three contexts, and argue that explanations of cell development require both mathematical models and concrete experiments. On this view, the two approaches are interdependent, with mathematical models playing a crucial but circumscribed role in explanations of cell development. (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)

Body part terms (BPTs) are used extensively in Mesoamerican languages to name object parts. The process through which BPTs might be extended to refer to a part of an object and further serve as a relator in describing the relation between objects in space has often been attributed to metaphorical processes. This study proposes an alternative analysis following a Structure–Mapping Theory approach (Gentner, 1983, inter alia), based on data from Diidxazá (Isthmus Zapotec, Otomanguean) obtained through elicitation and experimental (...) tasks. The data show that structure mapping does not depend on a 1:1 match of attributes; frequency of use shed light on principles that constrain the semantic extension of most BPTs; a core set of six BPTs are extended by abstraction of the set of intersecting axes of the body. The detailed nature of this study enables an analysis of the mental representations underlying the semantic extension of BPTs. This in turn elucidates on aspects of the relation between spatial language and spatial cognition. In addition, this study allows us to address questions about the categorial status of BPTs in Diidxazá and their lexicographic representation. (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)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. I provide a counter-example to epistemic closure for reductio proofs. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

It has become commonplace within feminist theory to claim that women’s lives are constructed by multiple, intersecting systems of oppression. In this thesis, I challenge the consensus that oppression is aptly captured by the theoretical model of “intersectionality.” While intersectionality originates in Black feminist thought as a purposive intervention into US antidiscrimination law, it has been detached from that context and harnessed to different representational aims. For instance, it is often asserted that intersectionality enables a representational politics that overcomes (...) legacies of exclusion within hegemonic Anglo-American feminism. I argue that intersectionality reinscribes the political exclusion of racialized women as a feature of their embodied identities. That is, it locates the failure of political representation in the “complex” identities of “intersectional” subjects, who are constructed as unrepresentable in terms of “race” or “gender” alone. Further, I argue that intersectionality fails to supplant race- and class-privileged women as the normative subjects of feminist theory and politics. In Chapter One, I demonstrate that intersectionality illicitly imports unitary concepts of “race,” “gender,” and “class.” In Chapter Two, I argue that intersectionality lacks a theory of hierarchy: it is a “flat geography” which cannot capture vertical and horizontal lines of power. In Chapter Three, I explore the role of analogical reasoning in rendering racialized women invisible both as gendered and as racialized subjects in twentieth-century social movements. To concretize this argument, I turn to Simone de Beauvoir’s use of race-sex analogies to describe (white, bourgeois) “women’s” situation in The Second Sex. In Chapter Four, I advance a programmatic unified account of oppression. I suggest that the possibility of a unified theory (as opposed to an intersectional one) is intimated in the concrete articulation of race, class, and gender. My point of departure is a phenomenology of capitalism, which reveals that these are all fundamentally modes of exploitation and appropriation. In Chapter Five, I theorize how they are made visible (and invisible) on the body. I extend Frantz Fanon’s account of “epidermalization,” drawing upon the marxian concepts of “fetishism” and “mode of appearance” to elaborate four structures of gendered racialized perception: first, the “miscegenation taboo” structures perceptions of the “purity” of whiteness and the “polluting” effects of blackness. Whiteness, theorised as a “possessive investment” and as “property” is defined by the right to exclude. Second, the “episteme of tellable differences” produces the conviction that we can automatically “tell the difference” between a body placed in one “racial” or gender category, and another—while bodies that temporarily confound classification cause fear and consternation. Third, the “race/reproduction bind” names the axiomatic assumption that “race” is reproduced through (heterosexual) procreation and that “race” is, therefore, biologically inheritable. Finally, the “fear/criminalisation reflex” refers to the bidirectional equation of particular racialised-gendered bodies with crime, and of crime with those bodies; this a function of the discursive use of ‘crime’ as an alibi for “race’” the systemic racialisation of punitive carceral institutions, and the historical origins of “race” in transatlantic chattel slavery, which shaped perceptual-cognitive associations of freedom with whiteness and captivity with blackness. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Theories of Emotion: Expressing, Feeling, Acting by Pia CAMPEGGIANISabrina B. LittleCAMPEGGIANI, Pia. Theories of Emotion: Expressing, Feeling, Acting. New York: Bloomsbury Publishing, 2023. xiv + 199 pp. Cloth, $80.89; paper, $21.60In Theories of Emotion, Pia Campeggiani provides a philosophical introduction to the emotions. The book is multidisciplinary and empirically informed. It is organized around three “groundbreaking intuitions” of emotion theory—(1) expression, (2) subjectivity, and (3) action. Each (...) section corresponds to a different thinker—Charles Darwin, William James, and John Dewey, respectively—and each section concludes with a discussion of relevant debates. This book is outstanding. It is clearly written, well organized, and impressive in its scope. In what follows, I outline key ideas and raise questions generated by each section, then conclude with general reflections on the text.Campeggiani begins with the “scandal” of emotion research: There is no agreement about what an emotion is. In part, this lack of consensus is due to the imprecise ways we employ concepts like feelings, emotions, affect, and passions in ordinary discourse. In part, it is due to empirical difficulties. For example, Campeggiani describes how implicit assumptions and a forced-choice format compromised an experiment about expression universality.Additionally, Campeggiani points out that the category “emotions” has an internal structure that lacks clear-cut boundaries. There are paradigmatic examples of emotions, such as fear and anger, but there are also ambiguous phenomena, such as respect and modesty, which we may or may not recognize as such. Throughout the text, Campeggiani introduces and evaluates numerous accounts of emotions, drawing our attention to the strengths, limitations, and empirical adequacy of each.Part 1 begins with Charles Darwin’s contributions to emotion theory—an emphasis on the biological origins of emotions and a focus on expression. This section examines emotions in connection to adaptive fitness, exploring phenomena such as blushing when we are ashamed and the biological bases of emotions. A highlight of this section is an exploration of the social or communicative character of the emotions, which Darwin described as “only a secondary effect” of expression. Campeggiani examines emotional contagion and imitation, as well as the [End Page 141] phenomenon of feeling more pain when we express pain on our faces. There is also a rich discussion about constructionism as an alternative to basic emotions theory.Part 2 opens with William James on subjective experience. Campeggiani describes the limitations of James’s position—of understanding emotions to be reducible to feelings. For starters, this position is not empirically well supported. Campeggiani cites Walter Cannon’s observation that “many of the autonomic changes that are symptomatic of a given emotion can also occur in its absence.” Additionally, James fails to “properly flesh out the link between emotions and evaluations.” Campeggiani then describes the cognitive turn in emotion theory that emerged in response to the lack of attention paid to evaluation. Cognitive accounts of emotion deemphasize the bodily dimensions of emotional experiences in favor of the intentional properties, or “aboutness,” of emotions. Emotions see things as things.From my vantage, this was the best part of the book. Campeggiani highlights Damasio’s point that decision-making depends on having a “correct affective perception of the values at stake in a given situation.” For instance, feeling outsized or misdirected fear may undermine our decision-making. Campeggiani also introduces debates about whether emotions are appraisals, and whether emotions entail judgments or make judgments more likely. In the introduction, she mentions that “decision-making processes are always and inevitably underpinned by emotions, for good and for ill.” We see what she means in this section. Emotions participate in reason, impede reason, and have cognitive content themselves.That emotions involve or participate in our judgments raises two kinds of concerns—epistemic and normative. The epistemic worry is that inaccurate appraisals may undermine our understanding of the world. This is especially worrisome for the class of emotions Campeggiani calls “recalcitrant,” or closed off to other mental states, and for the emotions she says are “heavily influenced by our needs and goals.” Emotions are imperfectly truth-tracking, as was made clear earlier, in part 1, regarding their adaptive nature. The normative worry is that certain emotional... (shrink)

Neuroconstructivism postulates the progressive complexity of mental representation over the course of cognitive development and the role of the graphic representation of movement in the transformation of mental schemas, cognitive flexibility, and representational complexity. This study aims to: understand children’s resources in the drawing of movement ; and verify whether there are differences in the graphic representation of movement as an indicator of cognitive flexibility. The participants were N = 240 children aged 5–8 years; 1,440 drawings were (...) collected representing 2,880 characters from six stories. The analysis consisted: data quality control, using the kappa coefficient, and Generalizability Theory to test the instrument’s validity and reliability; Multivariate General Analysis and Mixed Linear Analysis of the factors ; Multivariate General Analysis of the graphic components: categories and microcategories, as well as the elements that make up the macrocategories: “Static,” “Indication,” and “Movement”; and calculation of the generalizability coefficient. The results show that: age best explains variability, with a high effect size across all components, thus increasing its complexity and at ages 6 and 7, “Indication” appears as a modulator of “Static” toward “Movement”. The generalizability coefficient is optimal. It is concluded that changes in the initial graphic representation of movement may interactively transform mental representation, thus increasing cognitive flexibility and prompting teaching applications to optimize such changes. (shrink)

In this paper, I wish to challenge theory-biased approaches to scientific knowledge, by arguing for a study of theorizing, as a cognitive activity, rather than of theories, as abstract structures independent from the agents’ understanding of them. Such a study implies taking into account scientists’ reasoning processes, and their representational practices. Here, I analyze the representational practices of geneticists in the 1910s, as a means of shedding light on the content of classical genetics. Most philosophical accounts of classical genetics (...) fail to distinguish between the purely genetic, or Mendelian level, and the cytological one. I distinguish between them by characterizing them in terms of their respective associated representational practices. I then present how the two levels were articulated within Morgan’s theory of crossing-over, and I describe the representational technique of linkage mapping, which embodies the “merging” of the Mendelian and cytological levels. I propose an analysis of the mapping scheme, as a means of enlightening the conceptual articulation of Mendelian and cytological hypotheses within classical genetics. Finally, I present the respective views of three opponents to Morgan in the 1910s, who had a different understanding of the articulation of cytology and Mendelism, and entertained different views concerning the role and proper interpretation of maps. I propose to consider these diverging perspectives as instantiating what I call different “versions” of classical genetics. (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. Cuts................................................................................................ ..............39 2.4. Humean Events............................................................................................43 2.5. (...) Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams............................................................................................ ..454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)

The aim of this article is to critically examine what I call Action-Centric Theories of Representation (ACToRs). I include in this category theories of representation that (1) reject construing representation in terms of a relation that holds between representation itself (the representational vehicle) and what is represented, and instead (2) try to bring the function that representations play for cognitive systems to the center stage. Roughly speaking, according to proponents of ACToRs, what makes a (...) class='Hi'>representation (that is, what is constitutive of it being a representation) is its being functionally involved in preselecting or guiding the actions of cognitive systems. I intend to argue that while definitely valuable, ACToRs are underconstrained and thus not entirely satisfying, since there exist structures that would count as representations according to ACToRs, but which do not play functional roles that could be nontrivially or in an explanatorily valuable way classified as representing something for a cognitive system. I outline a remedy for this theoretical situation by postulating that a fully satisfying theory of representation in cognitive science should have two factors; i.e., it should combine the pragmatic, action-oriented aspect present in ACToRs with an element that emphasizes the importance of the relation holding between a representational vehicle and what is represented. (shrink)

The work reported here is of two sorts. One the one hand, we attempt to consolidate a lot of recent work on situation theory into a workable version, one that researchers can use and add to in ways that might be suitable for various applications. On the other, we attempt to solve a representational problem with situation theory: how can we represent complicated situation-theoretic objects in a way that is perspicuous. Our way in to the latter problem comes (...) from an on-going project aimed at bringing insights from Discourse Representation Theory and Situation Theory to bear on one another. In terms of this project, this paper represents a rather modest contribution. Our goal is to design a language for representing situationtheoretic objects that is based on Kamp's discourse representation structures. This was where we started but we found that working on the notation and its semantics led us to clari cations of various aspects of situation theory. A major part of the clari cation in the theory comes from our use of the work on parameters and abstraError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapError: Illegal entry in bfrange block in ToUnicode CMapction by Aczel and Lunnon AL]. (shrink)

This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially (...) developed as exact mathematical constructions. Therefore, they are legitimate components of the theory (combinatorial and geometric group theory) and the pictures of Cayley graphs are a part of practical mathematical procedures. (shrink)

The relational structure of RNA, DNA, and protein bears an interesting similarity to the determination problem in category theory. In this paper, we present this deep-structure similarity and use it as a springboard for discussing some abstract properties of coding in various systems. These abstract properties, in turn, may shed light on the evolution of the DNA world from a semiotic perspective. According to the perspective adopted in this paper, living systems are not information processing systems (...) but “meaning-making” systems. Therefore, what flows in the genetic system is not “information” but “value.” We define meaning, meaning-making, and value and then use these terms to explain the abstract dynamics of coding, which can illuminate many forms of sign-mediated activities in biosystems. (shrink)

The overwhelming majority of the attempts in exploring the problems related to quantum logical structures and their interpretation have been based on an underlying set-theoretic syntactic language. We propose a transition in the involved syntactic language to tackle these problems from the set-theoretic to the category-theoretic mode, together with a study of the consequent semantic transition in the logical interpretation of quantum event structures. In the present work, this is realized by representing categorically the global structure of a (...) quantum algebra of events (or propositions) in terms of sheaves of local Boolean frames forming Boolean localization functors. The category of sheaves is a topos providing the possibility of applying the powerful logical classification methodology of topos theory with reference to the quantum world. In particular, we show that the topos-theoretic representation scheme of quantum event algebras by means of Boolean localization functors incorporates an object of truth values, which constitutes the appropriate tool for the definition of quantum truth-value assignments to propositions describing the behavior of quantum systems. Effectively, this scheme induces a revised realist account of truth in the quantum domain of discourse. We also include an Appendix, where we compare our topos-theoretic representation scheme of quantum event algebras with other categorial and topos-theoretic approaches. (shrink)

According to one influential view, model-building in science is primarily a matter of simplifying theoretical descriptions of real-world target systems using abstraction and idealization. This view, however, does not adequately capture all types of models. Many contemporary models in the natural and social sciences – from physics to biology to economics – stand in a more tenuous relationship with real-world target systems and have a decidedly stipulative element, in that they create, by fiat, ‘model worlds’ that operate according to (...) some set of specified rules. While such models may be motivated by an interest in actual target phenomena, their validity is not – at least not primarily – to be judged by whether they constitute an empirically adequate representation of any particular empirical system. The present paper compares and contrasts three such types of models: minimal models, toy models, and exploratory models. All three share some characteristics and thus overlap in interesting ways, yet they also exhibit significant differences. It is argued that, in all three cases, modal considerations have an important role to play: by exploring the modal structure of theories and phenomena – that is, by probing possibilities in various ways – such models deepen our understanding and help us gain knowledge not only about what there is in the world, but also about what there could be. (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)

The current essay introduces the guidance theory of representation, according to which the content and intentionality of representations can be accounted for in terms of the way they provide guidance for action. The guidance theory offers a way of fixing representational content that gives the causal and evolutionary history of the subject only an indirect role, and an account of representational error, based on failure of action, that does not rely on any such notions as proper functions, (...) ideal conditions, or normal circumstances. Moreover, because the notion of error is defined in terms of failure of action, the guidance theory meets the “meta-epistemological requirement” that representational error should be potentially detectable by the representing system itself. In this essay, we offer a brief account of the biological origins of representation, a formal characterization of the guidance theory, some examples of its use, and show how the guidance theory handles some traditional problem cases for representation: the representation of fictional and abstract entities. Being both representational and actiongrounded, the guidance theory may provide some common ground between embodied and cognitivist approaches to the study of the mind. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. I provide a counter-example to epistemic closure for reductio proofs. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Many cognitive and evolutionary theories of religion argue that supernatural explanations are byproducts of our cognitive adaptations. An influential argument states that our supernatural explanations result from a tendency to generate anthropomorphic explanations, and that this tendency is a byproduct of an error management strategy because agents tend to be associated with especially high fitness costs. We propose instead that anthropomorphic and other supernatural explanations result as features of a broader toolkit of well-designed cognitive adaptations, which are designed for explaining (...) the abstract and causal structure of complex, unobservable, and uncertain phenomena that have substantial impacts on fitness. Specifically, we argue that (1) mental representations about the abstract vs. the supernatural are largely overlapping, if not identical, and (2) when the data-generating processes for scarce and ambiguous observations are complex and opaque, a naive observer can improve a bias-variance trade-off by starting with a simple, underspecified explanation that Western observers readily interpret as “supernatural.” We then argue that (3) in many cases, knowledge specialists across cultures offer pragmatic services that involve apparently supernatural explanations, and their clients are frequently willing to pay them in a market for useful and effective services. We propose that at least some ethnographic descriptions of religion might actually reflect ordinary and adaptive responses to novel problems such as illnesses and natural disasters, where knowledge specialists possess and apply the best available explanations about phenomena that would otherwise be completely mysterious and unpredictable. (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory (...) domain. The role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

In her landmark book, Language, Thought, and Other Biological Categories (Millikan1984),1 Ruth Garrett Millikan utilizes the idea of a biological function to solve philosophical problems associated with the phenomena of language, thought, and meaning. Language and thought are activities of biological organisms, according to Millikan, and we should treat them as such when trying to answer related philosophical questions. Of special interest is Millikan’s treatment of intentionality. Here Millikan employs the notion of a biological function to (...) explain what it is for one thing in nature, a bee dance (43), for example, to be about another, in this case, the location of a nectar source. My concern in this paper is to understand whether Millikan’s account of intentionality adequately explains how humans achieve reference, in language or thought, to individuals and groups in their environment. In bringing her theory of intentional content to bear on human activities, Millikan focuses largely on natural language. Thus, in what follows, I begin by laying out the biology-based principles that underlie Millikan’s theory of content, then proceed with an explanation of how the theory is to apply to natural language. As it appears, Millikan’s account of how content is determined for natural language terms and sentences rests on the determinacy of intentional content at the psychological level. This leads me to take a careful look at what Millikan says about the content of mental representations, in hopes of finding a sufficient basis there for the application of Millikan’s theory of content to natural language. Ultimately, I conclude that Millikan’s theory faces a problem of vacuity. If we approach the theory as a theory of intentional content, intended to explain the nature of reference, the theory is lacking in an extremely important respect: Millikan explains how it could be one of the biological functions of a mental or natural language term to refer, without telling us precisely what in the natural order constitutes the reference relation.. (shrink)

Even the simplest known living organisms are complex chemical processing systems. But how sophisticated is the behaviour that arises from this? We present a framework in which even bacteria can be identified as capable of representing information in arbitrary signal molecules, to facilitate altering their behaviour to optimise their food supplies, for example. Known asion/Representation theory, this framework makes precise the relationship between physical systems and abstract concepts. Originally developed to answer the question of when a physical system (...) is computing, AR theory naturally extends to the realm of biological systems to bring clarity to questions of computation at the cellular level. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Beyond Heaven and Earth: A Cognitive Theory of Religion by Gabriel LevyKevin SchilbrackBeyond Heaven and Earth: A Cognitive Theory of Religion. Gabriel Levy. Cambridge, MA: The MIT Press, 2022. 249 pp. $45.00 paperback; open access.The interdisciplinary field of religious studies includes both the humanities and social sciences in a tricky detente. Some religion scholars focus on interpreting texts, teachings, and rituals in an effort to grasp (...) what religious practitioners understand themselves to be doing. Other scholars want to move beyond the the practitioners’ views to create explanatory accounts of religion in terms of social power, psychological benefits, and modules in the evolved brain—causal accounts of which the practitioners might not be aware or that they might deny. Gabriel Levy argues that to develop consilience between the divergent efforts of the humanities and the sciences, the academic study of religion would be well served by developing a more adequate metaphysics that can do justice simultaneously to human behavior as moved both by subjective reasons and by material forces. Specifically, he recommends the “anomalous monism” of Donald Davidson. [End Page 98]According to this view, there is only one kind of reality, and this is a monist metaphysics that includes no nonmaterial or supernatural entities. However, this one kind of reality is “anomalous” in that the world we experience together permits two irreducible vocabularies, one that is physical and deterministic and another that is mental and includes free will. Davidson considered this two-sided approach Spinozistic (169), and Levy notes its similarities to Thomas Nagel’s “neutral monism” (8, 35, 50–51). In short, then, Levy is proposing to scholars of religion a non-reductive but science-friendly “pragmatist monism” (8) that would be congenial to many readers of this journal. Such a metaphysics would also be in line with the methodological naturalism that, for many, defines the legitimate scope of the academy. We might therefore consider this book an example of a philosophy of religious studies, or even a metaphysics for religious studies.An important feature of Davidson’s approach is that, on his account, semantic content is necessarily intersubjective and therefore non-nomological and irreducible to the physical. Imagine a parent offering their prelinguistic child a doll while asking, “Do you want your doll?” or pulling the child away from a neighbor’s dog while telling them, “You have to be careful around dogs.” Davidson argues that human beings learn the meaning of words and sentences in social exchanges like these as the listener makes an educated guess about the entities to which the other person is referring, a process that Davidson calls “triangulation.” The generation of meaning on this model depends on the human capacity for shared intentionality about things in the world. Davidson argues that having meaningful thoughts, even when alone, then requires that one has had intersubjective, “triangulated” experiences like these. As Levy says, “semantic content arises in immanent, contextual, enacted dialogue and conversation with other agents” (182). It follows that this Davidsonian approach insists on irreducible, non-eliminable mental categories such as meaning, belief, and reasons, now recast in terms of practical engagement with things rather than inner representations of them. Many in religious studies are critical of the field’s focus on subjective categories like these, but, as Levy points out, the meaning-generating and reason-giving subject on a Davidsonian model is necessarily a socially embedded self and not the free-floating, disembodied, or ahistorical self that is critiqued by post-structuralists like Michel Foucault (169–70).Levy introduces this model (ch. 1) and then explores several topics in its light. He proposes that beliefs about religious entities are a subset of imagining fictional entities, so that Mickey Mouse, Santa Claus, and Zeus are in the same cognitive category (ch. 2). He argues that there is a continuum between the human ability to interpret language and the ability of human beings and [End Page 99] other animals to interpret information in their natural environments (ch. 3). In the last three chapters, he connects his discussion to the Sefer Yitzirah, a medieval Jewish mystical “book of creation” that describes the cosmos as structured by language (ch. 4), to... (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational (...) structures that emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Idealism and Objectivity: Understanding Fichte’s Jena Project by Wayne M. MartinJanet RoccanovaWayne M. Martin. Idealism and Objectivity: Understanding Fichte’s Jena Project. Stanford: Stanford University Press, 1997. Pp. xvii + 177. Cloth, $45.00.This text claims to present a new interpretation of Fichte’s Jena system. Toward this end the author presents a primary thesis and several secondary theses as alternatives to standard or recent Fichte interpretations. Martin’s main thesis is (...) that the central and guiding project of Fichte’s Jena Wissenschaftslehre is to develop an idealist theory of objectivity. Most controversial of the subordinate theses will certainly be Martin’s claim that Fichte is a realist.The text is symmetrically divided into two parts, each composed of three chapters. Part I addresses the “Parameters of the Jena Project,” while Part II focuses on the “Elements of a Theory of Objectivity.”In section one of the first chapter Martin sides against the long-standing interpretation of Fichte’s Wissenschaftslehre as speculative metaphysics and with the more recent epistemological (and anthropological) reading of the Wissenschaftslehre, but warns against taking Fichte as a “classic epistemologist,” whose anti-skeptical project is to “provide a rational justification of our claims to empirical knowledge” (15). Rather, Martin contends, Fichte’s main goal in the Wissenschaftslehre is to develop a theory of the “objectivity” or “referential character” of consciousness, which is a concern more with the structure, rather than with the justification, of knowledge.Section two is where Martin lays out his particular notion of objectivity, according to which a conscious state is objective if it is “ ‘of’ or ‘about’ something that I take to exist independently of that conscious state” (18). The author emphasizes that objectivity, as [End Page 634] he understands it, is “less a function of [the] immediate content [of a conscious state] than of how I interpret or ‘take up’ that content” (19).The arguments of Chapters 2 and 3 are intended to lend support to Martin’s thesis that Fichte could, without inconsistency, be counted as a realist. In Chapter 2 Martin argues that Fichte’s rejection of dogmatism should not necessarily be interpreted as a rejection of realism. According to the author, Fichte indeed rejects any synthesis of idealism and dogmatism, although there is textual support for the claim that Fichte might support a synthesis of idealism and realism.In Chapter 3 Martin argues that the standard interpretation that Fichte utterly rejects things-in-themselves is incorrect, and proposes that the concept of things-in-themselves must necessarily be used by Fichte “to state the epistemological implications of [his] idealist theory of objectivity” (75). Martin’s ultimate goal in these chapters is to counter-balance the standard caricature of Fichte’s idealism by arguing that Fichte does not deny the possibility of a reality independent of the I.Part II is where Martin actually begins his interpretation of the Grundlage, especially sections four and five of the same, which, according to Martin, is where “Fichte tries to carry out the task of providing a theory of the objectivity of consciousness” (81). In Chapter 4 Martin examines the Fichtean concepts of (self-) positing and op-positing and determines that these are pre-representational cognitive acts that establish the schema of subject-object opposition, which is a condition for the possibility of conscious representation.Chapter 5 is a study of Fichte’s methodology, which Martin claims is an unsuccessful, but nonetheless “strikingly original,” “dialectical category theory,” or method of contradiction (5). Martin compares Fichte’s method to the ancient mathematical method of “regula falsi,” and concludes that the positive impact of Fichte’s method is to force a conceptual expansion. Fichte, in other words, uses contradiction to retain, rather than to reject (as in a reductio) the source of contradiction.Finally, in what is the most intriguing chapter of the text (Chapter 6) Martin examines Fichte’s striving doctrine in light of his attempt to develop an idealist theory of objectivity. Using ontogenetic analogies based on how an infant comes to experience an independent world, Martin argues here for the primacy of practice, and more specifically that there is a kind of striving that “is independent... (shrink)