This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing iterated epistemic states on the model of fixed points in the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- a hyperintensional epistemic $\mu$-automaton permits fixed points to entrain a principled means by which to iterate epistemic states and account (...) thereby for necessary conditions on self-knowledge. The hyperintensional epistemic $\mu$-calculus is applied to the iteration of the epistemic states of a single agent instead of the common knowledge of a group of agents, and is thus a novel contribution to the literature. (shrink)

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I proffer four novel extensions of the theory, and detail six issues that the theory faces. I provide a counter-example to epistemic closure for reductio proofs.

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (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 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)

This paper argues that the types of intention can be modeled both as modal operators and via a multi-hyperintensional semantics. I delineate the semantic profiles of the types of intention, and provide a precise account of how the types of intention are unified in virtue of both their operations in a single, encompassing, epistemic space, and their role in practical reasoning. I endeavor to provide reasons adducing against the proposal that the types of intention are reducible to the mental states (...) of belief and desire, where the former state is codified by subjective probability measures and the latter is codified by a utility function. I argue, instead, that each of the types of intention -- i.e., intention-in-action, intention-as-explanation, and intention-for-the-future -- has as its aim the value of an outcome of the agent's action, as derived by her partial beliefs and assignments of utility, and as codified by the value of expected utility in evidential decision theory. (shrink)

This paper examines the philosophical significance of the consequence relation defined in the $\Omega$-logic for set-theoretic languages. I argue that, as with second-order logic, the hyperintensional profile of validity in $\Omega$-Logic enables the property to be epistemically tractable. Because of the duality between coalgebras and algebras, Boolean-valued models of set theory can be interpreted as coalgebras. In Section \textbf{2}, I demonstrate how the hyperintensional profile of $\Omega$-logical validity can be countenanced within a coalgebraic logic. Finally, in Section \textbf{3}, the philosophical (...) significance of the characterization of the hyperintensional profile of $\Omega$-logical validity for the philosophy of mathematics is examined. I argue (i) that $\Omega$-logical validity is genuinely logical, and (ii) that it provides a hyperintensional account of formal grasp of the concept of `set'. Section \textbf{4} provides concluding remarks. (shrink)

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The categorical duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The hyperintensional profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal and hyperintensional profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely (...) logical. Second, the foregoing provides a hyperintensional account of the interpretation of mathematical and metamathematical vocabulary. (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)

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)

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in category theory is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of $\Omega$-logical validity, (...) and thus the generic invariance of mathematical truth, modal coalgebras are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (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)

This paper provides a rebuttal to the argument in Elohim (2018) in `Synthese'. Elohim provides a novel hyperintensional, ground-theoretic regimentation of the proposals in the metaphysics of consciousness. He then argues that Chalmers' (2010) intensional two-dimensional conceivability argument against physicalism is unsound, in light of the hyperintensional metaphysics of consciousness. Thus, intensional conceivability cannot be a guide to hyperintensional metaphysics. This paper demonstrates that a multi-hyperintensional version of epistemic two-dimensional semantics can be countenanced, and is sufficient for conceivability (...) to be a guide to metaphysics in the hyperintensional setting such that Chalmers' argument, hyperintensionally construed, is in fact sound. (shrink)

This paper aims to demonstrate that the ontology of consciousness is consistent with both the modal and the metaphysical versions of Haecceitism. I examine the varieties of Haecceitism, and I specify the intended versions that the arguments will vindicate. I define the property of 'being purely qualitative', and examine its relation to the properties of phenomenal consciousness. I draw, inter alia, on Bayesian perceptual psychology, in order to specify the identity-conditions of phenomenal properties in detail. I provide two, abductive arguments (...) for the claim that the identity-conditions on some individuals are metaphysically haecceitistic, in virtue of the relations that hold between those individuals and the phenomenal properties that they instantiate. The first argument is corroborated by empirical results concerning the phenomenological effects of attention. The second argument is corroborated by empirical results from the study of color in vision science. The arguments vindicate a version of Metaphysical Haecceitism, because the individuals are shown to be typed by the phenomenal properties that they instantiate, although quantification over the individuals is an ineliminable condition on their identity and distinctness. I provide, then, a regimentation of the extant proposals in the ontology of consciousness, using the logic of hyperintensional ground, as augmented by the Bayesian probability calculus. The hyperintensional regimentation vindicates a version of Modal Haecceitism, because the probabilistic ontological dependence of the parts of worlds on other parts thereof provides an ineliminable condition on the identity and distinctness of worlds. (shrink)

I argue that the two-dimensional hyperintensions of epistemic topic-sensitive two-dimensional truthmaker semantics provide a compelling solution to the access problem. I countenance an abstraction principle for epistemic hyperintensions based on Voevodsky's Univalence Axiom and function type equivalence in Homotopy Type Theory. I apply, further, modal rationalism in modal epistemology to solve the access problem. Epistemic possibility and hyperintensionality, i.e. conceivability, can be a guide to metaphysical possibility and hyperintensionality, when (i) epistemic worlds or epistemic hyperintensional states are interpreted as being (...) centered metaphysical worlds or hyperintensional states, i.e. indexed to an agent, when (ii) the epistemic (hyper-)intensions and metaphysical (hyper-)intensions for a sentence coincide, i.e. the hyperintension has the same value irrespective of whether the worlds in the argument of the functions are considered as epistemic or metaphysical, and when (iii) sentences are said to consist in super-rigid expressions, i.e. rigid expressions in all epistemic worlds or states and in all metaphysical worlds or states. I argue that (i) and (ii) obtain in the case of the access problem. (shrink)

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation, which is super-rigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a two-dimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...) and their metaphysical possibility or verification. I then generalize the approach to haecceitistic properties, and examine the Julius Caesar problem as a test case. (shrink)

This paper aims to contribute to the analysis of the nature of mathematical modality and hyperintensionality, and to the applications of the latter to absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority (...) and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory, providing two-dimensional hyperintensional formalizations of the modal logic of ZFC, large cardinal axioms, $\Omega$-logic, and the Epistemic Church-Turing Thesis. (shrink)

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and two-dimensional indexing. I examine the significance of the semantics, by developing three, novel interpretations of the framework. The first interpretation provides a characterization of the distinction between fundamental and derivative truths. The second interpretation demonstrates how the elements of decision theory are definable within the semantics, and provides a novel account of the interaction between probability measures and hyperintensional grounds. The third interpretation concerns the contents of the (...) types of intentional action, and the semantics is shown to resolve a puzzle concerning the role of intention in action. Topic-sensitive two-dimensional truthmaker semantics can be interpreted epistemically and metasemantically. (shrink)

This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting the (...) notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. (shrink)

This paper aims to provide two abductive considerations adducing in favor of the thesis of Necessitism in modal ontology. I demonstrate how instances of the Barcan formula can be witnessed, when the modal operators are interpreted 'naturally' -- i.e., as including geometric possibilities -- and the quantifiers in the formula range over a domain of natural, or concrete, entities and their contingently non-concrete analogues. I argue that, because there are considerations within physics and metaphysical inquiry which corroborate modal relationalist claims (...) concerning the possible geometric structures of spacetime, and dispositional properties are actual possible entities, the condition of being grounded in the concrete is consistent with the Barcan formula; and thus -- in the geometric setting -- merits adoption by the Necessitist. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative (...) principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration. (shrink)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised learning (...) methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

David Heyd's study will stimulate philosophers to recognise the importance of the rather neglected topic of the distinctiveness of supererogation and the ...

Extant theoretical work on the political resource curse implies that dependence on resource revenues should decrease autocracies’ likelihood of democratizing but not necessarily affect democracies’ chances of survival. Yet most previous empirical studies estimate models that are ill-suited to address this claim. We improve upon earlier studies, estimating a dynamic logit model that interacts a continuous measure of resource dependence with an indicator of regime type using data from 166 countries, covering the period from 1816-2006. We find that an increase (...) in resource dependence at time t - 1 increases the likelihood of autocratic persistence at t, but has no appreciable effect on democratic survival. We go beyond existing empirical studies to show that increases in resource dependence have persistent and substantial cumulative effects on autocracies' likelihood of becoming democratic over the long-term, showing that the total effect of resource dependence on regime type is much larger than the short-term (one period) effect indicates. (shrink)

According to dispositionalism about modality, a proposition <p> is possible just in case something has, or some things have, a power or disposition for its truth; and <p> is necessary just in case nothing has a power for its falsity. But are there enough powers to go around? In Yates (2015) I argued that in the case of mathematical truths such as <2+2=4>, nothing has the power to bring about their falsity or their truth, which means they come out both (...) necessary and not possible. Combining this with axiom (T), it is easy to derive a contradiction. I suggested that dispositionalists ought to retreat a little and say that <p> is possible just in case either p, or there is a power to bring it about that p, grounding the possibility of mathematical propositions in their truth rather than in powers. Vetter’s (2015) has the resources to provide a response to my argument, and in her (2018) she explicitly addresses it by arguing for a plenitude of powers, based on the idea that dispositions come in degrees, with necessary properties a limiting case of dispositionality. On this view there is a power for <2+2=4>, without there being a power to bring about its truth. In this paper I argue that Vetter’s case for plenitude does not work. However, I suggest, if we are prepared to accept metaphysical causation, a case can be made that there is indeed a power for <2+2=4>. (shrink)

Chapter 20 David Kovacs’ “Essence, Grounding, and Explanation” sets out four different ways in which essence might be taken to relate to the notion of grounding or metaphysical explanation, i.e., the type of connection that is often expressed by means of non-causal “in virtue of” or “because”-claims: (i) Unity: essence and grounding belong to a unified set of explanatory concepts; (ii) Supplementation: essence and grounding both contribute in their own way to a distinctive type of explanation; (iii) Independence: essence (...) is a sui generis notion with no straightforward conceptual links to grounding; and (iv) Irrelevance: essence is not an explanatory notion at all and therefore should not be viewed as connected to explanatory notions like grounding. As Kovacs brings out in the chapter, a wide variety of attitudes are represented in the literature even among philosophers who are sympathetic to the recent “hyperintensional” turn in metaphysics when it comes to the question of how the notions of essence and grounding interact with one another. (shrink)

Fichte-Studien, volume 49 (Leiden: Brill/Rodopi Publishers, 8 April 2021), edited by David W. Wood, 471pp. -/- Presenting new critical perspectives on J.G. Fichte’s Wissenschaftslehre, this volume of articles in English by an international group of scholars addresses the topic of first principles in Fichte’s writings. Especially discussed are the central text of his Jena period, the 1794/95 Grundlage der gesammten Wissenschaftslehre, as well as later versions like the Wissenschaftslehre nova methodo (1796-99) and the presentations of 1804 and 1805. Also (...) included are new studies on the first principles of the particular sub-disciplines of Fichte’s system, such as the doctrines of aesthetics, nature, right, ethics, and history. The volume also contains a number of miscellaneous essays on Fichte research, as well as several book reviews. (shrink)

L'ingegneria concettuale è una branca della filosofia caratterizzata da un approccio normativo nei confronti della rappresentazione. Assunzione fondamentale è che i nostri dispositivi rappresentazionali possano essere difettosi. Si configura dunque come l'attività che consiste nell'identificare i difetti in tali dispositivi e mettere in atto strategie di miglioramento. Verranno illustrate le questioni fondamentali a cui una teoria di ingegneria concettuale deve rispondere: in cosa consiste esattamente questa attività? Come possiamo attuarla? Quali meccanismi regolano la formazione dei dispositivi rappresentazionali? Possiamo influire su (...) tali meccanismi? Verrà inoltre presentata un'obiezione all'ingegneria concettuale e varie risposte. -/- Conceptual engineering is a branch of philosophy characterised by a normative approach towards representation. The fundamental assumption of it is that our representational devices can be defective. Conceptual engineering is then the activity consisting of identifying the defects of such devices and putting in place ameliorative strategies. This paper illustrates the fundamental issues for a theory of conceptual engineering: what does this activity consist of? How can we implement it? What mechanisms regulate the formation of representational devices? Can we have an influence over those mechanisms? Moreover, it will be presented an objection to conceptual engineering and various responses to it. (shrink)

Our aim in this entry is to articulate the state of the art in the moral psychology of personal identity. We begin by discussing the major philosophical theories of personal identity, including their shortcomings. We then turn to recent psychological work on personal identity and the self, investigations that often illuminate our person-related normative concerns. We conclude by discussing the implications of this psychological work for some contemporary philosophical theories and suggesting fruitful areas for future work on personal identity.

In this paper, we present three necessary conditions for morally responsible animal research that we believe people on both sides of this debate can accept. Specifically, we argue that, even if human beings have higher moral status than nonhuman animals, animal research is morally permissible only if it satisfies (a) an expectation of sufficient net benefit, (b) a worthwhile-life condition, and (c) a no unnecessary-harm/qualified-basic-needs condition. We then claim that, whether or not these necessary conditions are jointly sufficient conditions of (...) justified animal research, they are relatively demanding with the consequence that many animal experiments may fail to satisfy them. (shrink)

Truthmaker theory promises to do some useful philosophical work: equipping us to argue against phenomenalism and Rylean behaviourism, for instance, and helping us decide what exists (Lewis 1999, 207; Armstrong 1997, 113-119). But it has proved hard to formulate a truthmaker theory that is both useful and believable. I want to suggest that a neglected approach to truthmakers – that of Ian McFetridge – can surmount some of the problems that make other theories of truthmaking unattractive. To begin with, I’ll (...) outline some of the most prominent accounts of truthmaking in the current literature. Then the second part of the paper will explain McFetridge’s theory and argue for its superiority over these accounts. (shrink)

Conciliationism holds that disagreement of apparent epistemic peers often substantially undermines rational confidence in our opinions. Uniqueness principles say that there is at most one maximally rational doxastic response to any given batch of total evidence. The two views are often thought to be tightly connected. This paper distinguishes two ways of motivating conciliationism, and two ways that conciliationism may be undermined by permissive accounts of rationality. It shows how conciliationism can flourish under certain strongly permissive accounts of rationality. This (...) occurs when the motivation for conciliationism does not come from taking disagreement as evidence of one's own rational failings. However, divorcing the motive for conciliating from worries about rationality does not remove a feature of conciliationism that some find troubling: that conciliationism can lead to cases of “rational toxicity,” in which the most rational response to one's evidence involves violating some rational ideal. (shrink)

In a recent paper, Firt, Hemmo and Shenker argue that Hempel’s dilemma, typically thought to primarily undermine physicalism, is generalizable and impacts mind-body dualism and many other theories equally. I challenge this view and argue that Hempel’s dilemma admits of at least two distinct construals: a general-skeptical construal, underpinned by historically driven arguments such as the pessimistic induction, and a non-skeptical construal, driven by the specific puzzles and volatility of current physics. While the general-skeptical construal applies to all changeable deep-structure (...) theories, the non-skeptical construal primarily targets volatile theories which harbor exclusionary ambitions. As a result, dualism largely evades both construals due to the stability of theories of the mental and their lack of exclusionary ambitions. Conversely, physicalism is uniquely susceptible to both construals due to its strong commitment to deep-structure realism, inherent exclusionary ambitions, and the volatility of certain branches of fundamental physics. The paper ultimately concludes that Hempel’s dilemma is not universally problematic, but presents a unique challenge to physicalism while being relatively congenial to dualism. (shrink)

Recent methodological debates regarding the place of feasibility considerations in normative political theory are hindered for want of a rigorous model of the feasibility frontier. To address this shortfall, I present an analysis of feasibility that generalizes the economic concept of a production possibility frontier and then develop a rigorous model of the feasibility frontier using the familiar possible worlds technology. I then show that this model has significant methodological implications for political philosophy. On the Target View, a political ideal (...) presents a long-term goal for morally progressive reform efforts and, thus, serves as an important reference point for our specification of normative political principles. I use the model to show that we can- not reasonably expect that adopting political ideals as long-term reform objectives will guide us toward the realization of morally optimal feasible states of affairs. I conclude by proposing that political philosophers turn their attention to the analysis of actual social failures rather than political ideals. (shrink)

Longtermism is the thesis that in a large class of decision situations, the best thing we can do is what is best for the long-term future. The scope question for longtermism asks: how large is the class of decision situations for which this is true? In this paper, I suggest that the scope of longtermism may be narrower than many longtermists suppose. I identify a restricted version of longtermism: swamping axiological strong longtermism (swamping ASL). I identify three scope-limiting factors - (...) probabilistic and decision-theoretic phenomena which, when present, tend to reduce the prospects for swamping ASL. I argue that these scope-limiting factors are often present in human decision problems, then use two case studies from recent discussions of longtermism to show how the scope-limiting factors lead to a restricted, if perhaps nonempty, scope for swamping ASL. (shrink)

Many believe that a suitably programmed computer could act for its own goals and experience feelings. I challenge this view and argue that agency, mental causation and qualia are all founded in the unique, homeostatic nature of living matter. The theory was formulated for coherence with the concept of an agent, neuroscientific data and laws of physics. By this method, I infer that a successful action is homeostatic for its agent and can be caused by a feeling - which does (...) not motivate as a force, but as a control signal. From brain research and the locality principle of physics, I surmise that qualia are a fundamental, biological form of energy generated in specialized neurons. Subjectivity is explained as thermodynamically necessary on the supposition that, by converting action potentials to feelings, the neural cells avert damage from the electrochemical pulses. In exchange for this entropic benefit, phenomenal energy is spent as and where it is produced - which precludes the objective observation of qualia. (shrink)

Are demands for equality motivated by envy? Nietzsche, Freud, Hayek, and Nozick all thought so. Call this the Envy Objection. For egalitarians, the Envy Objection is meant to sting. Many egalitarians have tried to evade the Envy Objection.. But should egalitarians be worried about envy? In this paper, I argue that egalitarians should stop worrying and learn to love envy. I argue that the persistent unwillingness to embrace the Envy Objection is rooted in a common misunderstanding of the nature of (...) the charge, what it reveals, and what can be said in response to it. I develop what Bernard Williams might call a vindicatory genealogy of envy, thereby allowing us to see that envy, rather than undermining egalitarian intuitions, can in fact play a distinct justificatory role (when it is fitting), which undermines the Envy Objection. (shrink)

Edgar A. Singer Jr. is largely forgotten. Yet in the early twentieth century he was one of the most persistent proponents for a theory of "mind as behavior." This essay explores Singer's theory of mind as a form of experimentally-definable behavior. This interpretation of mind is derived from Singer's "philosophy of experiment," which delimits the forms of questions that can have meaningful answers. Valid questions, according to Singer's theory, must appeal to phenomena that are public in some sense and which (...) have verifiable effects on our "mechanical images" of nature (which is not to say that such phenomena are themselves solely mechanical). From this perspective, Singer is able to give behavioral criteria for attributing "mind" to organisms and for such "mental faculties" as purpose, sensation, consciousness, and thought. It might be wondered how Singer's experimental concept of mind compares with B. F. Skinner's better-known concept of private events. Although there are difficulties involved in the interpretation of each, it would seem that Singer and Skinner are largely in agreement, although they emphasize different factors in the behavioral interpretation of mind. (shrink)

[This is an edited version of a keynote talk at the conference on Neural Information Processing Systems (NeurIPS) on November 28, 2022, with some minor additions and subtractions.] -/- There has recently been widespread discussion of whether large language models might be sentient or conscious. Should we take this idea seriously? I will break down the strongest reasons for and against. Given mainstream assumptions in the science of consciousness, there are significant obstacles to consciousness in current models: for example, their (...) lack of recurrent processing, a global workspace, and unified agency. At the same time, it is quite possible that these obstacles will be overcome in the next decade or so. I conclude that while it is somewhat unlikely that current large language models are conscious, we should take seriously the possibility that successors to large language models may be conscious in the not-too-distant future. (shrink)

The question of how people change artworks is important for the metaphysics of art. It’s relatively easy for anyone to change a painting or sculpture, but who may change a literary or musical work is restricted and varies with context. Authors of novels and composers of symphonies often have a special power to change their artworks. Mary Shelley revised Frankenstein, and Tchaikovsky revised his Second Symphony. I cannot change these artworks. In other cases, such as those involving jazz standards and (...) folk songs, performers and ordinary folks have more power to change artworks. My preferred explanation of these facts is the created-abstract-simples view, according to which literary and musical works, unlike paintings and sculptures, are created abstract objects that have no parts. On this view, the way to change a literary or musical work is for an individual, empowered by social practices, to change rules about how a literary work should be published or a musical work should be performed. A. R. J. Fisher and Caterina Moruzzi object that the created-abstract-simples view doesn’t allow for literary and musical works to genuinely change, and Nemesio Garcia-Carríl Puy objects that the view doesn’t allow for these artworks to be repeatable. This paper clarifies the created-abstract-simples view and defends the view against these objections. -/- . (shrink)

Several different quantum gravity research programmes suggest, for various reasons, that spacetime is not part of the fundamental ontology of physics. This gives rise to the problem of empirical coherence: if fundamental physical entities do not occupy spacetime or instantiate spatiotemporal properties, how can fundamental theories concerning those entities be justified by observation of spatiotemporally located things like meters, pointers and dials? I frame the problem of empirical coherence in terms of entailment: how could a non-spatiotemporal fundamental theory entail spatiotemporal (...) evidence propositions? Solutions to this puzzle can be classified as realist or antirealist, depending on whether or not they posit a non-fundamental spacetime structure grounded in or caused by the fundamental structure. These approaches place different constraints on our everyday concepts of space and time. Applying lessons from the philosophy of mind, I argue that only realism is both conceptually plausible and suitable for addressing the problem at hand. I suggest a role functionalist version of realism, which is consistent with both grounding and causation, and according to which our everyday concepts reveal something of the true nature of emergent spacetime. (shrink)

Hylomorphists hold that substances are, in some sense, composites of matter and form. The form of a substance is typically taken to play a fundamental role in determining the unity or identity of the whole. Staunch hylomorphists think that this role is of a kind that precludes the ontological reduction of form to the physical and thus take their position to be inconsistent with physicalism. Forms, according to staunch hylomorphism, play a fundamental role in grounding their bearers’ proper parts and (...) that, it seems, rules out the physical grounding of form itself. I shall develop a physicalist version of hylomorphism that treats form as geometric structure and which, I shall argue, entails many of the central theses endorsed by staunch hylomorphists. Based on Shoemaker’s notion of conditional powers, I shall argue that the geometric structures of complex wholes are the conditions on at least some of the conditional powers of their bearers’ proper parts, transforming those powers into powers simpliciter. Thus, forms play a fundamental role in the dynamical evolution of the physical world, but without bestowing causal powers themselves and hence without violating the causal closure of the physical domain. If a substance’s proper parts are taken to be individuated by their powers simpliciter, then they derive their identities from their places in the substantial whole, which thus determines the identities of its proper parts without changing their intrinsic natures. (shrink)

The causal closure of the physical poses a familiar causal exclusion problem for the special sciences that stems from the idea that if closure is true, then fundamental physical properties do all the causal work involved in bringing about physical effects. In this paper I aim to show that the strongest causal closure principle that is not ruled out by some simple physics in fact allows for a certain kind of downward causation, which in turn makes room for robust special (...) science autonomy. I focus on the case of vector composition, arguing that it involves irreducibly multilevel causation. To give a complete causal explanation of what goes on in cases that involve the effects of multiple forces, we need to appeal not only to the fundamental properties that generate those forces, but also to geometric properties that determine how multiple vectors compose. However, if all the causal work involved in such cases were due to fundamental physical properties, there would be a one-level explanation available. Hence, I argue, it cannot be the case that fundamental physical properties do all the causal work. The extra causal work, I suggest, comes from the fact that the causal powers bestowed by fundamental physical properties have irreducibly geometric manifestation conditions. I defend the resulting form of downward causation as a solution to the problem of special science autonomy, and discuss two potential accounts of its source, in terms of the debate between kinematic and dynamic theories of the origins of spacetime symmetries. (shrink)

Two hundred and sixty-three subjects each gave examples for one of five geographic categories: geographic features, geographic objects, geographic concepts, something geographic, and something that could be portrayed on a map. The frequencies of various responses were significantly different, indicating that the basic ontological terms feature, object, etc., are not interchangeable but carry different meanings when combined with adjectives indicating geographic or mappable. For all of the test phrases involving geographic, responses were predominantly natural features such as mountain, river, lake, (...) ocean, hill. Artificial geographic features such as town and city were listed hardly at all for geographic categories, an outcome that contrasts sharply with the disciplinary self-understanding of academic geography. However, geographic artifacts and fiat objects, such as roads, cities, boundaries, countries, and states, were frequently listed by the subjects responding to the phrase something that could be portrayed on a map. In this paper, we present the results of these experiments in visual form, and provide interpretations and implications for further research. (shrink)

Ontology has been proposed as a solution to the 'Tower of Babel' problem that threatens the semantic interoperability of information systems constructed independently for the same domain. In information systems research and applications, ontologies are often implemented by formalizing the meanings of words from natural languages. However, words in different natural languages sometimes subdivide the same domain of reality in terms of different conceptual categories. If the words and their associated concepts in two natural languages, or even in two terminological (...) traditions within the same language, do not have common referents in the real world, an ontology based on word meanings will inherit the 'Tower of Babel' problem from the languages involved, rather than solve it. In this paper we present evidence from a preliminary comparison of landscape terms in English with those in the Yindjibarndi language of northwestern Australia demonstrating that this problem is not just hypothetical. Some possible solutions are suggested. (shrink)

In this paper, I motivate skepticism about the causal efficacy of moral properties in two ways. First, I highlight a tension that arises between two claims that moral realists may want to accept. The first claim is that physically indistinguishable things do not differ in any causally efficacious respect. The second claim is that physically indistinguishable things that differ in certain historical respects have different moral properties. The tension arises to the extent to which these different moral properties are supposed (...) to have different effects on people. I will introduce a class of cases in which this tension arises and suggest that the moral properties in these cases have no causal power. I will also question whether there are differences between the moral properties in these cases and moral properties in other cases that do not involve physically indistinguishable things that could make the latter moral properties causally efficacious. The second way that I motivate skepticism consists in pointing out a unique feature of cases in which moral properties are supposed both to supervene on historical properties and to be causally efficacious. These cases allow us to change moral properties with alleged effects while we hold constant the nonmoral candidates for causal contribution to those effects. This feature of these cases is unique because in most other cases the moral properties supervene on the physical properties in the nonmoral candidates, such that we cannot change the former while holding constant the latter. This way of changing moral properties provides empirical grounds for testing their causal efficacy. (shrink)