This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines (...) of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

Foucault found the starting point of modern European philosophy to be the construction of “man” as both an empirical fact and a transcendental operator. The aim is to show how this construction was made possible by an underlying strategical handling of the concept of matter. Some restrictions imposed on the materiality of knowledge-contents became key in explaining how actual men could gain access to transcendental knowledge. The paper focuses on Husserl and Kant as meaningful turning points of this transcendental (...) discourse. However, the relevance of their dematerializing strategies will be shown to lay beyond their historic-cultural meaning, since they can also provide a way of dealing with knowledge experiences that can be critical even towards modernity’s characteristic anthropocentrism. (shrink)

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility (...) quantifies over some point on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the two-dimensional (...) semantics for attitude ascriptions developed in Chalmers (2011a) has no trouble accommodating certain forms of the nesting problem that involve factive verbs such as “know” or “establish”. A certain form of the nesting problem involving apriority and necessity operators does raise an interesting puzzle, but we show how a generalized version of the nesting problem arises independently of two-dimensional semantics—it arises, in fact, for anyone who accepts the contingent a priori. We, then, provide a two-dimensional treatment of the apriority operator that fits the two-dimensional treatment of attitude verbs and apply it to the generalized nesting problem. We conclude that two-dimensionalism is not seriously threatened by cases involving the nesting of epistemic and modal operators. (shrink)

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I (...) also describe some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (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)

I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris paribus counterfactual (...) conditionals, the closest worlds are relevantly closest belief-worlds: closest to how things are believed to be, rather than to how they are. Also, closeness takes into account apriority and the opacity of intentional contexts. (shrink)

What are the objects of knowledge, belief, probability, apriority or analyticity? For at least some of these properties, it seems plausible that the objects are sentences, or sentence-like entities. However, results from mathematical logic indicate that sentential properties are subject to severe formal limitations. After surveying these results, I argue that they are more problematic than often assumed, that they can be avoided by taking the objects of the relevant property to be coarse-grained (“sets of worlds”) propositions, and that (...) all this has little to do with the choice between operators and predicates. (shrink)

Two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and (...) class='Hi'>apriority that captures the relevant ideas of two-dimensional semantics. I use this to show that some criticisms of two-dimensional semantics that claim that the theory is incoherent are not justified. I also axiomatize the logic, and compare it to the most important proposals in the literature that define similar logics. To indicate that two-dimensional semantics is a plausible semantic theory, I give an argument that shows that all theorems of the logic can be philosophically justified independently of two-dimensional semantics. (shrink)

This paper takes up the question as to what has primacy within Merleau-Ponty’s existential phenomenology as a way to provide insight into the relation between empirical science and transcendental philosophy within his account of embodiment. Contending that this primacy necessarily pertains to methodology, I show how Kurt Goldstein’s conception of biology provided Merleau-Ponty with a scientific model for approaching human existence holistically in which primacy pertains to the transcendental practice of productive imagination that generates the eidetic organismic Gestalt in terms (...) of which sense is made of empirical facts. Considering the analogous role played by imagination in Merleau-Ponty’s account of perceptual synthesis in the form of what he called projection, I argue that his account of embodiment is, parallel to Goldstein, grounded methodologically on the projection of an organismic Gestalt, and that as a form of operative-intentional praxis projection is the site of primacy in his phenomenology overall. In terms of the relation between natural science and transcendental philosophy in Merleau-Ponty’s account of embodiment, while the theoretical dimension of the latter—the eidetic apriority of the organismic Gestalt—is coupled dialectically with empirical facts on an epistemically coeval basis, these are jointly subordinated to the normative commitments implied by the imaginative projection of that Gestalt. The primacy of the latter is transcendental but in a distinctly practical sense, such that any substantive discrepancy between natural science and Merleau-Pontian phenomenology reflects metaphilosophical, not theoretical, disagreement. (shrink)

Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles.

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 cognitivism and modal 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 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 \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)

The paper presents Husserl’s conception of the relation between science and the living world, i.e. the world of everyday experience and communication. In Husserl view, science, or, more precisely, its basic aprioric structure is founded on the primal, essential core of the living world from which it obtains its sense. Science modifies, idealizes, and mathematizes the primal aprioric Lebenswelt. Due to those operations scientific theories can represent empirical reality.

This book 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 book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of rational (...) intuition; and to the types of intention, when the latter is interpreted as a modal 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. Chapter 3 provides an abstraction principle for epistemic intensions. Chapter 4 advances a 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 $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4. 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 epistemic two-dimensional truthmaker semantics developed in chapter 4 is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapter 8 examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter 9 examines the modal profile of $\Omega$-logic in set theory. Chapter 10 examines the interaction between epistemic two-dimensional semantics and absolute decidability. Chapter 11 avails of modal coalgebraic automata to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. The hyperintensional, epistemic two-dimensional truthmaker semantics developed in chapter 4 is applied in chapters 8, 10, and 11. Chapter 12 provides a modal logic for rational intuition. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Based on the philosophy of Martin Heidegger the article presents the possibility of actualizing Heidegger’s main question about the meaning of Being in the context of the analysis of so-called “a priori perfect.” During the development of fundamental ontology in the second half of the 1920s, Heidegger ponders the approach to Being in the history of philosophy and identifies such a feature of Being as a priori, a kind of antecedence of Being in relation to being. Although tradition invariably understands (...) Being in this way, in it, according to Heidegger, the question is no longer raised either about the sense of such antecedence, or about the temporal basis of this sense, and therefore a priori as the essential character of Being is left in total oblivion. We suggest that it is the problematization of apriority in its temporal origin that can contribute to resolving Heidegger’s fundamental philosophical question of time as the transcendental horizon of any concept of Being that precedes being. In this precedence there is a cherished temporal moment, the comprehension of which allows us to develop the “basic question of metaphysics” about the relationship of Being and time in a more concrete way than Heidegger’s four main themes of the question of Being: the ontological difference; the basic articulation of Being ); the truth-character of Being; the possible modifications of Being and the unity of Being’s variety. Revealing a priori question as the central question of all Heideggers thinking before the “Turn” we attempt to update this question and justify the need for its renewal on the basis of a fundamental ontology. With this task we relate the question of the essence of philosophy in general in its existential-temporal concept since philosophy appears as a temporality-based possible of the questioning return to the “earlier”: to the essential structures of being, knowledge, Being, Dasein. Our analysis is based on the following decisions: Being in relation to being is always pre-understood as “earlier,” and in this understanding a temporal definition operates, hence the main question of fundamental ontology about the relation of Being and time can be developed or at least clarified through the problem of meaning of a priori. The question of the meaning of the “earlier” and of the temporal basis for understanding Being as “earlier,” a priori, is concretized into the question of the conditions for the possibility of any ontology, including the fundamental ontology, which raises the question of the earlier in relation to Being and therefore “lives” in the light of the understanding of the “earlier” as such. This reflexive foundation of the fundamental ontology from itself is a necessary stage on the way of developing its project, if we remember that the main “duty” of the philosopher is to clarify “our inner nature” for the sake of opening the boundaries and conditions of the possibility of philosophy. The conclusion is that the possibilities of fundamental ontology in making sense of Being, time, and philosophy in general are far from exhausted, but await the questions that actualize them and new readings that allow to see the hidden richness of Heidegger’s thought. (shrink)

Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, strong modal force, generality, (...) topic neutrality, basicness, and (quasi-)apriority, (v) the veridicality of logic and its applicability to science, (v) the normativity of logic, (vi) error, revision, and expansion in/of logic, and (vii) the relation between logic and mathematics. The high explanatory power of the truth-theoretic approach does not rule out an equal or even higher explanatory power of the proof-theoretic approach. But to the extent that the truth-theoretic approach is shown to be highly explanatory, it sets a standard for other approaches to logic, including the proof-theoretic approach. (shrink)

In this paper, I argue against the view there are contingent a priori truths, and against the related view that there are contingent logical truths. I will suggest that in general, predicates ›a priori‹ and ›contingent‹ are implicitly relativized to circumstances, and argue that apriority entails necessity, whenever the two are relativized to the same circumstance. I will then criticize the idea, inspired by David Kaplan's framework, of contingent contents "knowable under a priori characters." I will also argue, against (...) Kaplan, that sentences of the form »The actual F is F« do not deserve the status of logical truths, since what they express is neither necessary nor a priori. (shrink)

This paper offers a response to William’s Hanson’s criticism of Sher’s formal-structural conception of logical consequence and logical constants.

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 cognitivism and modal 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 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 \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)

After briefly expositing some fundamental issues in current debates about apriority, I go on to critically examine meaning-based explanations of how we acquire apriori justification.

In this article, I present a novel account of a priori warrant, which I then use to examine the relationship between a priori and a posteriori warrant in mathematics. According to this account of a priori warrant, the reason that a posteriori warrant is subordinate to a priori warrant in mathematics is because processes that produce a priori warrant are reliable independent of the contexts in which they are used, whereas this is not true for processes that produce a posteriori (...) warrant. Following this, I show how this difference explains why a priori warranting processes, such as proof (and mathematical intuition) can, and a posteriori warranting processes cannot, definitively establish mathematical results. I then show why, in the event of a conflict between a priori and a posteriori warranting processes, the former undermine, and cannot be undermined by, the latter. Finally, I explain the connection between apriority and mathematical necessity, but do so in a way that allows for the existence of contingent a priori knowledge. (shrink)

In the 17th and 18th centuries, mathematics was understood to be the science that systematized our knowledge of magnitude, or quantity. But the mathematical notion of magnitude and the methods used to investigate it underwent a period of radical transformation during the modern period, which forced philosophers of mathematics to confront a changing mathematical landscape. In this context, the modern philosopher of mathematics had to provide an account of the apriority and applicability of mathematical reasoning, as such reasoning was (...) then understood. Early modern mathematical reasoning and the accounts of such reasoning offered by Newton, Descartes, Leibniz, and Kant are explained and discussed. (shrink)

The paper raises two questions, which seem central to understanding Kant's transcendental epistemology in the first Critique. First, Kant claims that the conditions for the possibility of experience are also conditions for the possibility of the objects of experience (A158/B197). Here the notion of an object is not conceived from the divine standpoint ('the view from nowhere') and is in some sense relativized to experience. But in what sense? Is the notion of an object relativized to one specific kind of (...) experience, human experience? Or is it relativized only to any possible experience? Second, in what sense is Kant's transcendental epistemology a priori? Is it a priori in the strong sense that its starting-point - the notion of experience in the question 'How is experience possible?' - is a priori? Or is it a priori only in the weak sense that, while the notion of experience is obtained empirically, a priori reasoning is required to establish how experience is possible? It has recently been argued (by Patricia Kitcher, Kant's Transcendental Psychology) that (a) the results that Kant wants to establish transcenden-tally about objects are relative to one specific kind of experience, human experience, and (b) Kant's transcendental epistemology is a priori only in the weak sense that the reasoning is a priori, while the starting-point is empirical. These claims are indeed crucial to Kitcher's overall aim of naturalizing Kant's transcendental epistemology. The aim of the paper is to resist both claims. I argue that Kant's notion of an object of experience is the notion of an object of any possible experience, not the notion of an object of one specific kind of experience, human experience. It follows, I argue, that Kant's transcendental epistemology is a priori in the strong sense that its starting-point is a priori. If we deny strong apriority, we fail to account for Kant's move from the nature of experience to the nature of empirical reality: empirical reality as such, not empirical reality as experienced by a particular variety of creatures capable of experience. The upshot is that, for better or worse, Kant's transcendental epistemology cannot be naturalized. (shrink)

There is a line of thought, neglected in recent philosophy, according to which a priori knowable truths such as those of logic and mathematics have their special epistemic status in virtue of a certain tight connection between their meaning and their truth. Historical associations notwithstanding, this view does not mandate any kind of problematic deflationism about meaning, modality or essence. On the contrary, we should be upfront about it being a highly debatable metaphysical idea, while nonetheless insisting that it be (...) given due consideration. From this standpoint, I suggest that the Finean distinction between essence and modality allows us to refine the view. While liberal about meaning, modality and essence, the view is not without bite: it is reasonable to suppose that it is able to ward off philosophical confusions stemming from the undue assimilation of a priori to empirical knowledge. (shrink)

According to the modal account of propositional apriority, a proposition is a priori if it is possible to know it with a priori justification. Assuming that modal truths are necessarily true and that there are contingent a priori truths, this account has the undesirable consequence that a proposition can be a priori in a world in which it is false. Epistemic two-dimensionalism faces the same problem, since on its standard interpretation, it also entails that a priori propositions are necessarily (...) a priori. In response to this problem, Chalmers and Rabern propose an alternative conception of propositional apriority as well as two-dimensional truth-conditions for apriority statements. Their proposal is also supposed to avoid another problem for the modal account, namely that it entails the existence of false instances of ‘φ iff actually φ’. I discuss Chalmers and Rabern’s account and point out a number of problems with it. I then develop my own account of propositional apriority that solves the problems in question, that can be accepted by friends and foes of two-dimensionalism alike, and that is also neutral with respect to the question of how one construes the objects of propositional apriority. (shrink)

In interpretations of the "Transcendental Aesthetic" section of the first Critique, there is a widespread tendency to present Kant as establishing that the representation of space is a condition for individuating or distinguishing objects, and to claim that it is on this basis that Kant establishes the apriority of this representation. The aim of this paper is to criticize this way of interpreting the "Aesthetic," and to defend an alternative interpretation. On this alternative, questions about the formation of the (...) representation of space figure more centrally, and the anti-Leibnizian character of Kant 's argument can be properly appreciated. (shrink)

If the a priori is the proper subject matter of transcendental philosophy, then the problems of the a priori are also problems for transcendental philosophy. the idea that defines transcendental philosophy is the idea that there are stable general structures which are discernible in experience, provide the foundations of our knowledge of it, and collectively constitute an a priori which transcends experience and informs it. the a priori is traditionally conceived as a nexus of relations which is held to be (...) logically/temporally prior to experience and responsible for its organization. in this essay, i challenge this traditional (kantian) understanding of the a priori and set forth an alternative to it based on the writings of maurice merleau-ponty. the intent is to provide a new conception of transcendental philosophy. (shrink)

One of the more visible recent developments in philosophical methodology is the experimental philosophy movement. On its surface, the experimentalist challenge looks like a dramatic threat to the apriority of philosophy; ‘experimentalist’ is nearly antonymic with ‘aprioristic’. This appearance, I suggest, is misleading; the experimentalist critique is entirely unrelated to questions about the apriority of philosophical investigation. There are many reasons to resist the skeptical conclusions of negative experimental philosophers; but even if they are granted—even if the experimentalists (...) are right to claim that we must do much more careful laboratory work in order legitimately to be confident in our philosophical judgments— the apriority of philosophy is unimpugned. The kinds of scientific investigation that experimental philosophers argue to be necessary involve merely enabling sensory experiences. Although they are not enabling in the sense of permitting concept acquisition, they are enabling in another epistemically significant way that is also consistent with the apriority of philosophy. (shrink)

The first major section of the Critique of Pure Reason, the Transcendental Aesthetic, is concerned with the nature of space and time, and with the nature of our representation of them. In interpretations of this part of the Critique, there is a very widespread tendency to present Kant’s discussion of space as attempting to establish that the representation of space is a condition for individuating or distinguishing objects, and that it is on this basis that Kant establishes the apriority (...) of this representation. I believe that this way of interpreting the Aesthetic is wholly misguided. The interpretive tendency I have in mind takes a number of different forms. On one approach, the role of space is to allow us to distinguish objects even if they are qualitatively identical. This represents Kant as making a certain kind of anti-Leibnizian point, one that concerns Leibniz’s principle of the identity of indiscernibles. On another approach, space—or something closely analogous to space—is regarded as essential on account of its role in allowing us to re-identify objects over time. Interpretations of Kant that follow the second approach are largely inspired by Strawson’s discussions of these matters in chapter 2 of Individuals. (shrink)

In this paper we suggest the use of ontological structures as an appropriate tool for describing the foundations of reality. Every vertex of this structure, representing a fundamental entity in the universe, is completely and solely characterized by its connections to the other vertices in the structure. The edges of this structure are binary compounds of the FEs, and are identified with the elementary particles. The combinations including more than 2 connected vertices correspond to composite particles. The principles according to (...) which the OSs are designed Philosophy of the natural sciences, VHP Tempsky, Vienna, 1989; Shoshani in Phys Essays 4:566–576, 1991; Shoshani in Phys Essays 11:512–520, 1998) are discussed in Sect. 2, and the simplest OSs having the minimal number of vertices, and thus represent the simplest universe, are given in Sect. 3. This section also describes an OS that includes an infinite number of vertices that might represent the space–time points. This structure imparts a new meaning to space–time, detached from their intuitive grasp :285–292, 2010). Section 4 is devoted to show how to ascribe intrinsic properties to the fundamental entities by using their inter-connections in the OS. The predictive power and explanatory capacity of this theory, named Apriorics :126–130, 2014) are briefly described in Sects. 3 and 4. (shrink)

In the 1960s and 1970s, Hilary Putnam articulated a notion of relativized apriority that was motivated to address the problem of scientific change. This paper examines Putnam’s account in its historical context and in relation to contemporary views. I begin by locating Putnam’s analysis in the historical context of Quine’s rejection of apriority, presenting Putnam as a sympathetic commentator on Quine. Subsequently, I explicate Putnam’s positive account of apriority, focusing on his analysis of the history of physics (...) and geometry. In the remainder of the paper, I explore connections between Putnam’s account of relativized a priori principles and contemporary views. In particular, I situate Putnam’s account in relation to analyses advanced by Michael Friedman, David Stump, and William Wimsatt. From this comparison, I address issues concerning whether a priori scientific principles are appropriately characterized as “constitutive” or “entrenched”. I argue that these two features need to be clearly distinguished, and that only the constitutive function is essential to apriority. By way of conclusion, I explore the relationship between the constitutive function of a priori principles and entrenchment. (shrink)

The classical view of the relationship between necessity and apriority, defended by Leibniz and Kant, is that all necessary truths are known a priori. The classical view is now almost universally rejected, ever since Saul Kripke and Hilary Putnam discovered that there are necessary truths that are known only a posteriori. However, in recent years a new debate has emerged over the epistemology of these necessary a posteriori truths. According to one view – call it the neo-classical view – (...) knowledge of a necessary truth always depends on at least one item of a priori knowledge. According to the rival view – call it the neoempiricist view – our knowledge of necessity is sometimes broadly empirical. In this paper I present and defend an argument against the neo-empiricist view. I argue that knowledge of the necessity of a necessary truth could not be broadly empirical. (shrink)

The apriority of moral feeling is an indispensable part of Kant's insistence on moral certainty as a foundation for ethics. Even though the moral feeling of respect cannot be the source of our knowledge of the authority of the moral law, moral feeling is a catalyst to self-criticism and moral self-confidence. It is argued that moral feeling reveals a nonempirical object, one's moral character. In fact, moral feeling plays a representational role that parallels sense experience, but does not derive (...) from sense experience. His general remarks on sensibility and representations and his specific discussion of moral sensibility make it hard to take feeling as central to his ethics, but this paper explains how they in no way preclude a representational function for moral sense. (shrink)

Logical structure may explain the necessity and a priori knowability of such truths as that if A is red then A is either red or green. But this explanation cannot be extended to sentences that, while necessary and knowable a priori, do not wear the appropriate logical structure on their sleeves – sentences like ''''if A is a point and A is red, then A is not green,'''' or ''''if A is a sphere, then A is not a cube.'''' The (...) real origin of these sentences'' necessity and a priori knowability is a relationship between the meanings of their component atomic sentences – a relationship which cannot be systematically reduced to logical structure by translating those atomic sentences into any kind of ''''ideal'''' language. Moreover, this kind of relationship is one to which any atomic sentences are susceptible if they have a classifying, or comparison-implying, content. Arguably, then, all atomic sentences are capable of being related to others in ways that are necessary and knowable a priori. (shrink)

In this paper, I defend the compatibility of externalism and privileged access and argue that the warrant transmission succeeds in cases of armchair knowledge, but that it does not have the anti-sceptical consequences that it is typically thought to have.

In this essay I discuss Fichte's changing understanding of the a priori/a posteriori distinction from the earliest writings on the Wissenschaftslehre to the System of Ethics. I argue that Fichte moves decisively away from the Kantian conception of the a priori, due to his development of the ideal/real distinction in his elaboration of the Wissenschaftslehre. Since Fichte's conception of apriority is not Kant's, we can only understand his claim that the System of Ethics can provide an answer a priori (...) to the question: what is our duty? (shrink)

Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two (...) types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)