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 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 cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-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 μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-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 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 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 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 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 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 Ω-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 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 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 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 the interpretational and objective modalities and 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 while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 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)

A key failing in contemporary philosophy of mind is the lack of attention paid to evolutionary theory in its research projects. Notably, where evolution is incorporated into the study of mind, the work being done is often described as philosophy of cognitive science rather than philosophy of mind. Even then, whereas possible implications of the evolution of human cognition are taken more seriously within the cognitive sciences and the philosophy of cognitive science, its relevance for cognitive science has only been (...) appreciated relatively recently, and the approach still comes in for some major criticism from prominent theorists within the field. This paper explores some of the reasons for this state of affairs and finds that it might have less to do with due consideration and well-founded scepticism about the relevance of evolutionary theory to these disciplines and more to do with historical accident and faulty assumptions on the part of key theorists in these disciplines. It is also noted that where cognitive scientists are taking evolution into account in their work on the mind, they straying more and more into domains that used to fall exclusively under the purview of philosophy of mind as it is traditionally conceived – qualia, consciousness, perception, intentionality and so forth. The point is made that in ignoring the work being done on the evolution of mind, philosophy of mind runs the risk of becoming obsolete. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual engineering for intensions and (...) hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

To explain why, in scientific problem solving, a diagram can be “worth ten thousand words,” Jill Larkin and Herbert Simon (1987) relied on a computer model: two representations can be “informationally” equivalent but differ “computationally,” just as the same data can be encoded in a computer in multiple ways, more or less suited to different kinds of processing. The roots of this proposal lay in cognitive psychology, more precisely in the “imagery debate” of the 1970s on whether there are image-like (...) mental representations. Simon (1972, 1978) hoped to solve this debate by thoroughly reducing the differences between forms of mental representations (e.g., between images and sentences) to differences in computational efficiency; to carry out this reduction, he borrowed from computer science the concepts of data type and of data structure. I argue that, in the end, his account amounted to nothing more than characterizing representations by the fast operations on them. This analysis then allows me to assess what Simon’s approach actually achieves when transported from psychology to the study of scientific representations, as in Larkin and Simon (1987): it allows comparing, not representations in and of themselves, but rather the computational roles they play in particular problem-solving processes—that is, representations together with a particular way of using them. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models.Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

A comprehensive introduction to the Language of Though Hypothesis (LOTH) accessible to general audiences. LOTH is an empirical thesis about thought and thinking. For their explication, it postulates a physically realized system of representations that have a combinatorial syntax (and semantics) such that operations on representations are causally sensitive only to the syntactic properties of representations. According to LOTH, thought is, roughly, the tokening of a representation that has a syntactic (constituent) structure with an appropriate semantics. Thinking thus consists in (...) syntactic operations defined over representations. Most of the arguments for LOTH derive their strength from their ability to explain certain empirical phenomena like productivity, systematicity of thought and thinking. (shrink)

This dissertation concerns the foundations of epistemic modality. 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 dissertation demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The dissertation demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the apriori-aposteriori distinction; to the modal profile of rational propositional intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Examining the nature of epistemic logic itself, I develop a novel approach to conditions of self-knowledge in the setting of the modal μ-calculus, as well as novel epistemicist solutions to Curry's, the liar, and the knowability paradoxes. Solutions to previously intransigent issues concerning the first-person concept; the distinction between fundamental and derivative truths; and the unity of intention and its role in decision theory, are developed along the way. (shrink)

A scientific explanatory project, part-whole explanation, and a kind of science, part-whole science are premised on identifying, investigating, and using parts and wholes. In the biological sciences, mechanistic, structuralist, and historical explanations are part-whole explanations. Each expresses different norms, explananda, and aims. Each is associated with a distinct partitioning frame for abstracting kinds of parts. These three explanatory projects can be complemented in order to provide an integrative vision of the whole system, as is shown for a detailed case study: (...) the tetrapod limb. My diagnosis of part-whole explanation in the biological sciences as well as in other domains exploring evolved, complex, and integrated systems (e.g., psychology and cognitive science) cross-cuts standard philosophical categories of explanation: causal explanation and explanation as unification. Part-whole explanation is itself one essential aspect of part-whole science. (shrink)

I analyze the importance of parts in the style of biological theorizing that I call compositional biology. I do this by investigating various aspects, including partitioning frames and explanatory accounts, of the theoretical perspectives that fall under and are guided by compositional biology. I ground this general examination in a comparative analysis of three different disciplines with their associated compositional theoretical perspectives: comparative morphology, functional morphology, and developmental biology. I glean data for this analysis from canonical textbooks and defend the (...) use of such texts for the philosophy of science. I end with a discussion of the importance of recognizing formal and compositional biology as two genuinely different ways of doing biology – the differences arising more from their distinct methodologies than from scientific discipline included or natural domain studied. Ultimately, developing a translation manual between the two styles would be desirable as they currently are, at times, in conflict. (shrink)

This introduction to a special issue of Topoi introduces and summarises the relationship between three main varieties of 'enactivist' theorising about the mind: 'autopoietic', 'sensorimotor', and 'radical' enactivism. It includes a brief discussion of the philosophical and cognitive scientific precursors to enactivist theories, and the relationship of enactivism to other trends in embodied cognitive science and philosophy of mind.

Ramsey (1997) argues that connectionist representations 'do not earn their explanatory keep'. The aim of this paper is to examine the argument Ramsey gives to support that conclusion. In doing so, I identify two kinds of explanatory need—need relative to a possible explanation and need relative to a true explanation and argue that internal representations are not needed for either connectionist or nonconnectionist possible explanations but that it is quite likely that they are needed for true explanations. However, to show (...) that the latter is the case requires more than a consideration of the form of explanation involved. (shrink)

Ramsey (1997) argues that connectionist representations ‘do not earn their explanatory keep’. The aim of this paper is to examine the argument Ramsey gives to support that conclusion. In doing so, I identify two kinds of explanatory need—need relative to a possible explanation and need relative to a true explanation and argue that internal representations are not needed for either connectionist or non‐connectionist possible explanations but that it is quite likely that they are needed for true explanations. However, to show (...) that the latter is the case requires more than a consideration of the form of explanation involved. (shrink)

According to the dominant computational approach in cognitive science, cognitive agents are digital computers; according to the alternative approach, they are dynamical systems. This target article attempts to articulate and support the dynamical hypothesis. The dynamical hypothesis has two major components: the nature hypothesis (cognitive agents are dynamical systems) and the knowledge hypothesis (cognitive agents can be understood dynamically). A wide range of objections to this hypothesis can be rebutted. The conclusion is that cognitive systems may well be dynamical systems, (...) and only sustained empirical research in cognitive science will determine the extent to which that is true. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

The cross-disciplinary framework of Material Engagement Theory (MET) has emerged as a novel research program that flexibly spans archeology, anthropology, philosophy, and cognitive science. True to its slogan to ‘take material culture seriously’, “MET wants to change our understanding of what minds are and what they are made of by changing what we know about what things are and what they do for the mind” (Malafouris 2013, 141). By tracing out more clearly the conceptual contours of ‘material engagement,’ and firming (...) up its ontological commitments, the main goal of this article is to help refine Malafouris’ fertile approach. In particular, we argue for a rapprochement between MET and the tradition of Cultural-Historical Activity Theory, based on the ‘Vygotskian’ hypothesis of scaffolded and/or distributed cognition. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. (shrink)

Moods have global and profound effects on our thoughts, motivations and behavior. To understand human behavior and cognition fully, we must understand moods. In this paper I critically examine and reject the methodology of conventional ?cognitive theories? of affect. I lay the foundations of a new theory of moods that identifies them with processes of our cognitive functional architecture. Moods differ fundamentally from some of our other affective states and hence require distinct explanatory tools. The computational theory of mood I (...) propose places them within the context of other mental phenomena and is consistent with the empirical data on moods. (shrink)