In this contribution I will examine Cotnoir’s (2013) solution to the problems that alethic pluralism faces when it comes to logical paradoxes. I will argue that his proposal fails to be a viable option and I will put forward an alternative approach, more Tarskian in spirit, but with the same “pluralist” trait of Cotnoir’s solution. Such an alternative approach is based on the idea that each truth predicate can be associated with an index that fully describes its relation with (...) other truth predicates.I will show how such indexes must be constrained in order to avoid logical paradoxes. (shrink)

I use the principle of truth-maker maximalism to provide a new solution to the semantic paradoxes. According to the solution, AUS, its undecidable whether paradoxical sentences are grounded or ungrounded. From this it follows that their alethic status is undecidable. We cannot assert, in principle, whether paradoxical sentences are true, false, either true or false, neither true nor false, both true and false, and so on. AUS involves no ad hoc modification of logic, denial of the T-schema's validity, or (...) obvious revenge. (shrink)

Recently, several philosophers have proposed fictionalist accounts of truth-talk, as a means for resolving the semantic pathology that the Liar Paradox appears to present. These alethic fictionalists aim to vindicate truth-talk as a kind of as if discourse, while rejecting that the talk attributes any real property of truth. Liggins has recently critically assessed one such proposal, Beall’s constructive methodological deflationist, offering objections to Beall’s proposed alethic fictionalism that potentially generalize to other alethic fictionalist accounts. Liggins further argues that CMD (...) supports a classically consistent response to the Liar Paradox—one that can be extracted from CMD, while leaving its putatively problematic fictionalist elements behind in favor of alethic nihilism. In this paper, after establishing that Liggins’s criticisms of CMD are off base, we show that the classical resolution of the Liar Paradox that he proposes is unworkable. Since his resistance to alethic fictionalism turns out to be unmotivated, we conclude that this approach is still worth considering as a framework for a resolution of the Liar Paradox. (shrink)

A contrary-to-duty obligation (sometimes called a reparational duty) is a conditional obligation where the condition is forbidden, e.g. “if you have hurt your friend, you should apologise”, “if he is guilty, he should confess”, and “if she will not keep her promise to you, she ought to call you”. It has proven very difficult to find plausible formalisations of such obligations in most deontic systems. In this paper, we will introduce and explore a set of temporal alethic dyadic deontic systems, (...) i.e., systems that include temporal, alethic and dyadic deontic operators. We will then show how it is possible to use our formal apparatus to symbolise contrary-to-duty obligations and to solve the so-called contrary-to-duty (obligation) paradox, a problem well known in deontic logic. We will argue that this response to the puzzle has many attractive features. Semantic tableaux are used to characterise our systems proof theoretically and a kind of possible world semantics, inspired by the so-called T× W semantics, to characterise them semantically. Our models contain several different accessibility relations and a preference relation between possible worlds, which are used in the definitions of the truth conditions for the various operators. Soundness results are obtained for every tableau system and completeness results for a subclass of them. (shrink)

The recent, short debate over the alethic undecidability of a Liar Sentence between Stephen Barker and Mark Jago is revisited. It is argued that Jago’s objections succeed in refuting Barker’s alethic undecidability solution to the Liar Paradox, but that, nevertheless, this approach may be revived as the alethic indeterminacy solution to the Liar Paradox. According to the alethic indeterminacy solution, there is genuine metaphysical indeterminacy as to whether a Liar Sentence bears an alethic property, whether truth or falsity. While the (...) alethic indeterminacy solution is presented here, and some revenge cases are considered and addressed, the primary aim of this paper is to revive and defend this underexplored and auspicious approach to solving the Liar Paradox. (shrink)

Jay Newhard (2021) proposes a novel solution to the Liar Paradox, which he calls the alethic indeterminacy solution to the Liar Paradox. Bradley Armour-Garb (2021) raises a pair of objections to the alethic indeterminacy solution. Both objections are based upon the alethic indeterminacy solution’s alleged commitment that the truth conditions for a Liar Sentence are indeterminate, and therefore not true. In this paper, this alleged commitment is shown to be mistaken. The alethic indeterminacy solution is compatible with maintaining that the (...) truth conditions for a Liar Sentence are a non-truth-functional biconditional which is true, and not indeterminate. Logically complex sentences are typically and standardly treated as truth-functional, and the philosophical literature on non-truth-functionality is diffuse. Two independent accounts of non-truth-functional biconditionals are defended. The first account is based on the claim that indicative conditionals express a non-truth-functional dependency relation between consequent and antecedent. The second account is based upon connected sentences having interdependent truth conditions, which can occur with any polyadic connective. These accounts are fully general, not ad hoc measures. Each account solves both of Armour-Garb’s objections. With both objections met, the alethic indeterminacy solution is shown to be a viable solution to the Liar Paradox worth further development. (shrink)

I put forward precise and appealing notions of reference, self-reference, and well-foundedness for sentences of the language of first-order Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically well-motivated semantic theories of truth.

Note: The paper attached here is a "pre-review" version, not the final version that has now been published online first at the link below. -/- In “Nothing is True,” Will Gamester defends a form of alethic nihilism that still grants truth-talk a kind of legitimacy: an expressive role that is implemented via a pretense. He argues that this view has all of the strengths of deflationism, while also providing an elegant resolution of the Liar Paradox and its kin. For the (...) alethic nihilist, Liar and related sentences are not true, and that is the end of the story. No contradiction arises because it does not thereby follow that any of these sentences are also true, since nothing is. Gamester concludes that the simplicity of this response to the semantic paradoxes makes alethic nihilism an attractive approach. We disagree. In addition to providing insurmountable obstacles for his form of alethic nihilism, we contend that a certain form of non-nihilist deflationism is better placed to deal with the paradoxes and to account for truth-talk more generally. (shrink)

Stephen Barker presents a novel approach to solving semantic paradoxes, including the Liar and its variants and Curry’s paradox. His approach is based around the concept of alethic undecidability. His approach, if successful, renders futile all attempts to assign semantic properties to the paradoxical sentences, whilst leaving classical logic fully intact. And, according to Barker, even the T-scheme remains valid, for validity is not undermined by undecidable instances. Barker’s approach is innovative and worthy of further consideration, particularly by those (...) of us who aim to find a solution without logical revisionism. As it stands, however, the approach is unsuccessful, as I shall demonstrate below. (shrink)

I argue that a new solution to the semantic paradoxes is possible based on truth-making. I show that with an appropriate understanding of what the ultimate truth and falsity makers of sentences are, it can be demonstrated that sentences like the liar are alethically undecidable. That means it cannot be said in principle whether such sentences are true, not true, false, not-false, neither true nor false, both true and false, and so on. I argue that this leads to a (...) solution to the semantic paradoxes that appears to be free of revenge problems, allows us to maintain classical logic and the validity of the T-schema. (shrink)

What is the property of being true like? To answer this question, begin with a Canberra-plan analysis of the concept of truth. That is, assemble the platitudes for the concept of truth, and then investigate which property might satisfy them. This project is aided by Friedman and Sheard’s groundbreaking analysis of twelve logical platitudes for truth. It turns out that, because of the paradoxes like the liar, the platitudes for the concept of truth are inconsistent. Moreover, there are so (...) many distinct paradoxes that only small subsets of platitudes for truth are consistent. The result is that there is no property of being true. The failure of the Canberra plan analysis of the concept of truth, points the way toward a new methodology: a conceptual engineering project for the concept of truth. Conceptual engineering is assessing the quality of our concepts, and when they are found defective, offering new and better concepts to replace them for certain purposes. Still, there are many aletheic properties, which are properties satisfied by reasonably large subsets of platitudes for the concept of truth. We can treat these aletheic properties as a guide to the multitude of new aletheic concepts, which are concepts similar to, but distinct from, the concept of truth. Any new aletheic concept or team of concepts might be called on to replace the concept of truth. In particular, the concepts of ascending truth and descending truth are recommended, but the most important point is that we need a full-scale investigation into the space of aletheic properties and new aletheic concepts—that is, we need an Aletheic Principles Project. (shrink)

Thinking about truth can be more dangerous than it looks. Of course, our concept of truth is the source of one of the most frustrating and impenetrable paradoxes humans have ever contemplated, the liar paradox, but that is just the beginning of its treachery. In an effort to understand why one of the most beloved and revered members of our conceptual repertoire could cause us so much trouble, philosophers have for centuries proposed “solutions” to the liar paradox. However, it (...) seems that our concept of truth takes offense to our efforts to understand it because it appears to retaliate against those who propose “solutions” to the liar. It takes its revenge on us by creating new paradoxes from our own attempts to find resolution. That is, most proposed solutions to the liar paradox give rise to new, more insidious paradoxes—often called revenge paradoxes. For our attempts at understanding, truth rewards us with inconsistent theories, untenable logics, and a deep feeling of bewilderment. It is as if our concept of truth lashes out at us because it wants to remain a mystery. After a few run-ins with truth, many philosophers have the good sense to keep their distance. Far from being the serene, profound concept most people take it to be, those of us who think much about the liar paradox know truth to be a vengeful bully—a conceptual misanthrope. (shrink)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)

The non-alethic systems N1 of da Costa and A of Grana are both paraconsistent and paracomplete. Based on them, a multi-agent doxastic logic NADK can be obtained by logical expansion. The soundness and completeness of NADK are proved and its special theorems are also presented. In this logic, the belief version of the laws of contradiction and excluded middle, as well as the principle of explosion are all invalid. Therefore, it may provide a reliable logical basis for any theory which (...) has paraconsistent or paracomplete epistemic conflicts, such as true contradictions, true contrarieties, and belief paradoxes. We also explain in detail how a non-alethic doxastic logic provides a reliable logical basis for tolerating these three types of epistemic conflicts. The present paper is the deepening and development of system N1 and A. (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.

John Mair was an influential post-medieval scholar. This paper focuses on his Tractatus insolubilium, in which he proposed semantic analysis of self-referential phenomena, in particular on his solution to alethic and correspondence paradoxes and his treatment of their general semantic aspects as well as particular applications. His solution to paradoxes is based on the so-called “network evaluation”, i.e. on a semantics which defines the concepts of truth and correspondence with reality in contextual terms. Consequently, the relation between semantic (...) valuation, synonymy and contradiction must be redefined. (shrink)

The Liar paradox raises foundational questions about logic, language, and truth. A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says that it is false.How, (...) then, should we classify Liar sentences? Are they true or false? A natural suggestion would be that Liars are neither true nor false; that is, they fall into a category beyond truth and falsity. This solution might resolve the initial problem, but it beckons the Liar's revenge. A sentence that says of itself only that it is false or beyond truth and falsity will, in effect, bring back the initial problem. The Liar's revenge is a witness to the hydra-like nature of Liars: in dealing with one Liar you often bring about another.JC Beall presents fourteen new essays and an extensive introduction, which examine the nature of the Liar paradox and its resistance to any attempt to solve it. Written by some of the world's leading experts in the field, the papers in this volume will be an important resource for those working in truth studies, philosophical logic, and philosophy of language, as well as those with an interest in formal semantics and metaphysics. (shrink)

This paper motivates and defends alethic nihilism, the theory that nothing is true. I first argue that alethic paradoxes like the Liar and Curry motivate nihilism; I then defend the view from objections. The critical discussion has two primary outcomes. First, a proof of concept. Alethic nihilism strikes many as silly or obviously false, even incoherent. I argue that it is in fact well-motivated and internally coherent. Second, I argue that deflationists about truth ought to be nihilists. Deflationists maintain (...) that the utility of the truth predicate is exhausted by its expressive role, and I argue that the truth predicate can still play this expressive role even if nothing is true. As such, deflationists do not stand to lose anything by accepting nihilism. Since they also stand to gain an elegant solution to the alethic paradoxes, on balance deflationists ought to be nihilists. (shrink)

According to some philosophers, the Liar paradox arises because of a mistaken theory of truth. Its lesson is that we must reject some instances of the naive propositional truth-schema \It is true that \ if and only if \\. In this paper, I construct a novel semantic paradox in which no principle even analogous to the truth-schema plays any role. I argue that this undermines the claim that we ought to respond to the Liar by revising our theory of truth.

John Mair (1467–1550) was an influential post-medieval scholar. This paper focuses on his Tractatus insolubilium, in which he proposed semantic analysis of self-referential phenomena, in particular on his solution to alethic and correspondence paradoxes and his treatment of their general semantic aspects as well as particular applications. His solution to paradoxes is based on the so-called “network evaluation”, i.e. on a semantics which defines the concepts of truth and correspondence with reality in contextual terms. Consequently, the relation between (...) semantic valuation, synonymy and contradiction must be redefined. (shrink)

Kevin Scharp proposes an original theory of the nature and logic of truth on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. He argues that truth is best understood as an inconsistent concept, and proposes a detailed theory of inconsistent concepts that can be applied to the case of truth. Truth also happens to be a useful concept, but its inconsistency inhibits its utility; as such, it should be replaced with consistent concepts that can (...) do truth's job without giving rise to paradoxes. To this end, Scharp offers a pair of replacements, which he dubs ascending truth and descending truth, along with an axiomatic theory of them and a new kind of possible-worlds semantics for this theory. He goes to develop Davidson's idea that truth is best understood as the core of a measurement system for rational phenomena, and offers a semantic theory that treats truth predicates as assessment-sensitive and solves the problems posed by the liar and other paradoxes. (shrink)

This article examines Kevin Scharp’s formal solution to the alethic paradoxes, ADT, which stands for ascending and descending truth. One of the main supposed benefits of ADT over its competitors is that it alone can validate the uses of truth concepts in theoretical contexts, such as truth-theoretic semantics. The appendixes contain a new consistency proof for ADT, and additionally show that it is conservative. As a result of its conservativity, the article argues that ADT faces a problem in accounting (...) for certain mathematical uses of truth. Thus, Scharp’s theory needs to be amended in order to fulfill its aim of replicating all substantive uses of truth. (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)

Kevin Scharp argues that the concept of truth is defective, and is therefore unable to play its intended role in natural language truth-conditional semantics. As such, for this theoretical purpose, Scharp constructs two replacements: ascending truth and descending truth. Scharp applies the resultant theory, AD semantics, to the liar sentence, thereby obtaining a novel solution to the liar paradox. The aim of the present paper is fourfold. First, I show that, contrary to Scharp’s claims, AD semantics in fact yields an (...) inconsistency when applied to standard liar sentences. Second, I diagnose the problem: AD semantics mishandles negation. I propose an alternative treatment, resulting in what I call AD* semantics. Third, I show that AD* semantics gives Scharp the resources required to respond to an alleged revenge paradox that has been raised against his view. Finally, I argue that, these consequences notwithstanding, it remains unclear whether AD* semantics provides an adequate account of alethic paradoxes more generally. (shrink)

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)

Kevin Scharp’s influential work on the alethic paradoxes combines an extensively developed inconsistency theory with a substantial conceptual engineering project. I argue that Scharp’s inconsistency theory is in tension with his conceptual engineering project: the inconsistency theory includes an account of concepts that implies that the conceptual engineering project will fail. I recommend that Scharp revises his account of concepts, and show how doing so allows him to resolve the tension. The discussion is important for ongoing work on conceptual (...) engineering. Firstly, it is important to get clear on whether Scharp’s conceptual engineering project is—or could be—successful. Secondly, the issues discussed herein may generalise to other conceptual engineering projects, such as explication and ameliorative projects. In particular, the discussion has implications for how conceptual engineers can think about concepts and their relation to how we use words. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines 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. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (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} is 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 Elohim's 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. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher 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 two-dimensional 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. Elohim invents 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. Elohim provides a counter-example to epistemic closure for logical deduction. 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)

We discuss four distinct semantic consequence relations which are based on Strong Kleene theories of truth and which generalize the notion of classical consequence to 3-valued logics. Then we set up a uniform signed tableau calculus, which we show to be sound and complete with respect to each of the four semantic consequence relations. The signs employed by our calculus are,, and, which indicate a strict assertion, strict denial, tolerant assertion and tolerant denial respectively. Recently, Ripley applied the strict–tolerant account (...) of assertion and denial to develop a new approach to truth and alethic paradox, which we call the Strict–Tolerant Conceptionof Truth. The paper aims to contribute to our understanding of STCT in at least three ways. First, by developing the strict–tolerant calculus.Second, by developing a semantic version of the strict–tolerant calculus, which informs us about the assertoric possibilities relative to a fixed ground model. Third, by showing that the strict–tolerant calculus and assertoric semantics jointly suggest that STCT's claim that the strict and tolerant can be understood in terms of one another has to be reconsidered. (shrink)

In this paper, we offer a brief, critical survey of contemporary work on truth. We begin by reflecting on the distinction between substantivist and deflationary truth theories. We then turn to three new kinds of truth theory—Kevin Scharp's replacement theory, John MacFarlane's relativism, and the alethic pluralism pioneered by Michael Lynch and Crispin Wright. We argue that despite their considerable differences, these theories exhibit a common "pluralizing tendency" with respect to truth. In the final section, we look at the underinvestigated (...) interface between metaphysical and formal truth theories, pointing to several promising questions that arise here. (shrink)

Deflationists argue that the truth predicate does not express a substantive property, but is only required for expressive purposes. Using the resources of a fully schematic, inferentialist account of higher-order logic, truth predicates are purely logical and indeed eliminable, since they are logically definable, for any reasonable language, when we extend the language by the appropriate higher-order quantifiers. Accordingly, the truth predicate is not required for expressive purposes. Alethic deflationism thus appears to collapse into a redundancy theory of truth. In (...) this chapter, I take first steps into investigating whether such an inferentialist redundancy theory could serve as a philosophically satisfactory account of truth. I investigate the charge that semantic paradoxes are merely avoided rather than solved and the assumption that providing a philosophically satisfactory account of truth must be based on the way truth predicates behave in natural languages. (shrink)

Restrictionism is a response to the Liar and other paradoxes concerning truth. Restrictionists—as I will call proponents of the strategy—respond to these paradoxes by giving up instances of the schema -/- <p> is true iff p. -/- My aim is to show that the current unpopularity of restrictionism is undeserved. I will argue that, whilst cautious versions of the strategy may face serious problems, a radical and previously overlooked version of restrictionism provides a strong and defensible response to (...) the paradoxes. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...) so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

How robust is a contraction-free approach to the semantic paradoxes? This paper aims to show some limitations with the approach based on multiplicative rules by presenting and discussing the significance of a revenge paradox using a predicate representing an alethic modality defined with infinitary rules.

The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds (...) of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking differences. I first consider the role that Tarski gives to supervaluation in first order logic (§2.2), and then, after an interlude that asks whether neither-true-nor-false is itself a truth value (§2.3), I consider sentences with non-denoting terms (§2.4), vague sentences (§2.5), ambiguous sentences (§2.6), paradoxical sentences (§2.7), and future-tensed sentences in indeterministic tense logic (§2.8). I conclude my survey with a look at alethic modal logic considered as a cousin (§2.9), and finish with a few sentences of “advice to supervaluationists” (2.10), advice that is largely negative. The case for supervaluations as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest—as in Tarski’s definition of truth for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit phrases such as “settled true” or “determinately true,” never dropping the qualification. (shrink)

This thesis examines the alethic modal concepts of possibility and necessity. It is argued that one cannot do justice to all our modal talk without possible worlds, i.e., complete ways that a cosmos might have been. I argue that not all of the proposed applications of possible worlds succeed but enough remain to give one good theoretical reason to posit them. The two central problems now are: What feature of reality makes correct alethic modal claims true and What are possible (...) worlds? ;David Lewis makes possible worlds be concretely existing universes. Unfortunately, I show Lewis's account involves set-theoretic, ethical, inductive and probabilistic paradoxes, and commits Lewis to an objectionable form of primitive modality that governs the choice of the counterpart relation. The most promising contemporary alternatives to Lewis's theory have been the worlds of Adams and Plantinga constructed out of Platonic entities such as maximal collections of consistent propositions. However, these approaches fail to provide a satisfactory answer to the question of what makes true modal claims true. I also criticize some alternative accounts. ;Finally, I discuss and combine two historical approaches. The first is an Aristotelian approach that says a non-actual event is possible is to say that some actual substances could have initiated a causal chain that could lead up to the event in question. However, it can be shown that some plausible global possibility claims can be made true on this account only if there is a necessarily existent first cause capable of initiating very different universes. On the other hand, Leibniz made possible worlds be ideas in the mind of an omniscient necessarily existent deity. Leibniz fails to explain what it is that makes these possible worlds possible, but if we were willing to combine his story with the conclusion drawn from the Aristotelian one, we could get the following story: Possible worlds are ideas in the mind of an omniscient deity and what makes them possible is that this deity has the Aristotelian capability of initiating causal chains that can lead to them being actualized. (shrink)

The theme of this special issue is minimalism about truth, a conception which has attracted extensive support since the landmark publication of Paul Horwich's Truth (1990). Many well-esteemed philosophers have challenged Horwich's alethic minimalism, an especially austere version of deflationary truth theory. In part, this is at least because his brand of minimalism about truth also intersects with several different literatures: paradox, implicit definition, bivalence, normativity, propositional attitudes, properties, explanatory power, meaning and use, and so forth. Deflationist sympathizers have introduced (...) a few developments and emendations, while critics and other interlocutors have generated objections that have required further responses. Some of these works appeared in the first few years following the publication of the first edition of Truth. But others have appeared only in the last five or ten years, indicating that interest in the minimalist conception continues to bloom and be a highly fecund source for new ideas. Some of those new ideas are collected here, in a special issue celebrating collectively the 25th anniversary of Horwich's Truth in 2015 and the 20th anniversary of the revised edition in 2018. The intent of the issue is overwhelmingly prospective rather than retrospective; however, it presents original work and fresh perspectives, including a new contribution by Paul Horwich himself, that jointly offer au currant reflections on the current status and future promise of the minimal conception. (shrink)

Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative system or to the system of values (...) under which we predicate the deontic qualifications. By taking this aspect into account, we arrive at a logical system which preserves laws proper to a deontic logic but where the standard paradoxes of deontic logic do not arise. It is a logic of strictly-deontic modalities DR. (shrink)

To qualify the truth of a proposition probabilistically is to place it within the scope of a special type of alethic modality. We expect that, as in other modal contexts, the merely probabilistic truth of an assumption in a valid inference must carry over to whatever conclusions are derived from the assumption. That expectation, however, is not always fulfilled in ordinary reasoning about conditional probabilities. There are simpler ways of illustrating what I shall call the paradoxes of conditional probabilistic (...) reasoning in ordinary language, but the following argument is a colorful example. Consider an apparently deductively valid inference, by an imaginary inmate of a penal institution supervised by a bitterly hated warden who is surrounded by dangerous criminals, including the argument’s author. (shrink)

Taking Joyce’s (1998; 2009) recent argument(s) for probabilism as our point of departure, we propose a new way of grounding formal, synchronic, epistemic coherence requirements for (opinionated) full belief. Our approach yields principled alternatives to deductive consistency, sheds new light on the preface and lottery paradoxes, and reveals novel conceptual connections between alethic and evidential epistemic norms.

This article explains why intercultural communication always should be studied in context and how even though misunderstanding is normally at stake in intercultural communication, one can argue that the promotion of mutual understanding actually is of mutual interest for all of humanity. Studying in context means paying attention to circumstances around the uses of signs as well as to the roles and moods of the users of signs. Promoting mutual understanding means avoiding a state of mind that implies the depreciation (...) of the other. To be intercultural, a communication must not be infected by prejudices. Any real attempt at intercultural communication is a paradoxical procedure. It supposes that human beings who engage in it at one and the same time recognize the stranger as similar and as different. Also, it can lead to acceptance of the other and a better understanding of what communication is about as well as to rejection and obscurantism. In this paper, I argue that even though people always relate in various ways to common and different cultural backgrounds, they still have to relate to common issues that govern their ways, and that focusing on those common issues and studying the various communicative contexts and contents help promoting mutual understanding, as these activities highlight the implicit role of the value of respect in all interpersonal communication. Human beings cannot avoid evaluating situations, contexts, relations, peoples and cultures. How can we establish that mutual respect and open-mindedness are better than disdain and dogmatism? Well, precisely by affirming that human relations commonly build on the inevitability of communicating and contrasting values and norms. Meaning in interaction permanently transforms cultural elements and patterns into something new. Intercultural communication becomes more respectable when it acknowledges the variety of ways humans interact meaningfully and the plurality of their logic of action. It is good and reasonable to value understanding because this variety and this pluralism always have kept the social alive and more than ever in our modern globalized world contribute to the creativity and interactivity of modern life. The interest of pragmatics in user attitudes, its focus on practical rather than on alethic modalities, can contribute to a more nuanced approach to intercultural communication, where the different elements of meaning in interaction can be studied in various bundles rather than in a single strand. (shrink)

This chapter contains sections titled: Introduction Two Interrelated Problems Lewis's Solution Inductive Paradox Identity versus Counterpart Theory Platonism: The Main Realist Alternative to Lewis An Aristotelian Alternative Leibniz's Account A Combined Account.

This paper is about the alethic aspect of epistemic rationality. The most common approaches to this aspect are either normative (what a reasoner ought to/may believe?) or evaluative (how rational is a reasoner?), where the evaluative approaches are usually comparative (one reasoner is assessed compared to another). These approaches often present problems with blindspots. For example, ought a reasoner to believe a currently true blindspot? Is she permitted to? Consequently, these approaches often fail in describing a situation of alethic maximality, (...) where a reasoner fulfills all the alethic norms and could be used as a standard of rationality (as they are, in fact, used in some of these approaches). I propose a function α, which accepts a set of beliefs as inputand returns a numeric alethic value. Then I use this function to define a notion of alethic maximality that is satisfiable by finite reasoners (reasoners with cognitive limitations) and does not present problems with blindspots. Function α may also be used in alethic norms and evaluation methods (comparative and non-comparative) that may be applied to finite reasoners and do not present problems with blindspots. A result of this investigation isthat the project of providing purely alethic norms is defective. The use of function α also sheds light on important epistemological issues, such as the lottery and the preface paradoxes, and the principles of clutter avoidance and reflection. (shrink)

Pavel Cmorej has argued that the existence of unverifiable and unfalsifiable empirical propositions follows from certain plausible assumptions concerning the notions of possibility and verification. Cmorej proves, it the context of a bi-modal alethic-epistemic axiom system AM4, that (1) p and it is not verified that p is unverifiable; (2) p or it is falsified that p is unfalsifiable; (3) every unverifiable p is logically equivalent to p and it is not verifiable that p; (4) every unverifiable p entails that (...) p is unverifiable. This article elaborates on Cmorej’s results in three ways. Firstly, we formulate a version of neighbourhood semantics for AM4 and prove completeness. This allows us to replace Cmorej’s axiomatic derivations with simple model-theoretic arguments. Secondly, we link Cmorej’s results to two well-known paradoxes, namely Moore’s Paradox and the Knowability Paradox. Thirdly, we generalise Cmorej’s results, show them to be independent of each other and argue that results (3) and (4) are independent of any assumptions concerning the notion of verification. (shrink)

The workshop took place in Leuven, Belgium, and was hosted by the KU Leuven's Centre for Logic and Analytic Philosophy. The workshop’s theme was the syntactical treatment of (alethic, epistemic, etc.) modalities. The standard view on modalities nowadays is that they are operators. Syntactic theories, however, treat modalities as predicates, and thus have to assume a background theory which is sufficiently strong to encode its own formulas (usually, one works with some system of arithmetic and Gödel coding). As a consequence, (...) such theories suffer from paradoxes of self-referentiality. For example, just as the liar sentence states of itself that it is false, the knower sentence states of itself that it is unknown. Kaplan and Montague (1960: 'A paradox regained', Notre Dame J. Formal Logic, vol. 1, pp. 79–90) famously showed that any sufficiently strong theory that contains the knower is inconsistent. (shrink)

The concept of information has well-known difficulties. Among the many issues that have been discussed is the alethic nature of a semantic conception of information. Floridi :197–222, 2004; Philos Phenomenol Res 70:351–370, 2005; EUJAP 3:31–41, 2007; The philosophy of information, Oxford University Press, Oxford, 2011) argued that semantic information must be truthful. In this article, arguments will be presented in favor of an alethically neutral conception of semantic information and it will be shown that such a conception can withstand Floridi’s (...) criticism. In particular, it is argued that an alethically neutral conception of semantic information can manage the so-called Bar-Hillel Carnap paradox, according to which contradictions have maximum informational content. This issue, as well as some of Floridi’s other arguments, is resolved by disentangling the property of being information from the property of being informative. The essay’s final conclusion is that although semantic information is alethically neutral, a veridical conception of semantic information can, and should, be retained as a subconcept of semantic information, as it is essential for the analysis of informativity, which, unlike the property of being information, depends on truth. (shrink)

The history of contemporary modal logic dates back to the writings of C. S. Lewis in the early part of this century. Since then, a growing body of literature has attested to professional interest in the area, and in a number of related issues in philosophical logic which have received wide attention. The recent development of powerful formal techniques for modal system building, together with an increasing interest in modal logic as a tool for philosophical analysis, have created a need (...) for an up-to-date text to introduce students to this material. Snyder's book attempts to answer this need. Assuming an understanding of elementary propositional logic, Snyder introduces a reductive technique called cancellation for detecting the theorems of a system of logic. This technique, analogous to the construction of Smullyan trees but more compact, is extended to modal and quantified contexts. Cancellation versions of the systems M and Mn of G. H. von Wright, and S4 and S5 of Lewis are developed. Snyder uses a Hintikka type of semantics, showing how the various formal systems are differentiated at the semantic level by differing conditions which must be imposed on the model systems used as interpretations for them. These model systems, and the conditions imposed upon them, are in turn described by means of a metalanguage which is essentially first-order quantificational logic. The power of this technique stems from the fact that for every object language formula of a system, there is a corresponding formula in the metalanguage which describes the conditions an interpretation must meet in order to satisfy the original formula. The conditions that the interpretations of a given system of logic must meet are reflected in this metalanguage as "antecedent assumptions," and these in turn correspond to cancellation rules for the object language. This correspondence is constructed in such a way that the metalinguistic counterpart of each theorem of the system will be a theorem of first-order logic. Snyder's primary interest is in showing how modal logic can be used, with the help of these techniques, to build a large variety of formal systems and to "tailor" such systems to meet a variety of analytical tasks. Simple modal systems are developed for the articulation of a number of modal concepts, in addition to the classic alethic ones. Examples are taken from temporal, deontic, and epistemic logic to show how specific interpretations of the meanings of the relevant operators lead to the incorporation of appropriate conditions in the formal systems used to articulate them. An entire chapter is devoted to a discussion of the paradoxes of material and strict implication, and to an attempt to articulate the notion of entailment through the development of formal systems which include a dyadic modal operator that is free of these paradoxes. The final chapter discusses such classical issues as proper names, reference, fictional entities, definite descriptions, and existence presuppositions. Appendices deal with such matters as the equivalence of the cancellation systems to more classical axiomatic-deduction systems, and the sketch of a proof of soundness and completeness for all the modal systems presented. While designed as a text, this volume should be of interest to both logicians and those working in metaphysics and language analysis, since the primary concern of the author is to develop techniques that will facilitate the usefulness of modal logic as a tool for philosophical analysis. The instructor's manual contains many suggestions derived from the author's experience in teaching this non-standard treatment of the subject.--K. T. (shrink)