I provide an analysis of sentences of the form ‘To be F is to be G’ in terms of exact truth-maker semantics—an approach that identifies the meanings of sentences with the states of the world directly responsible for their truth-values. Roughly, I argue that these sentences hold just in case that which makes something F is that which makes it G. This approach is hyperintensional, and possesses desirable logical and modal features. These sentences are reflexive, transitive and symmetric, and, if (...) they are true, then they are necessarily true, and it is necessary that all and only Fs are Gs. I close by defining an asymmetric and irreflexive notion of analysis in terms of the reflexive and symmetric one. (shrink)

I provide a truthmaker semantics for Angell’s system of analytic implication and establish completeness.

I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true and that q is an analytic part of p, then S knows that q. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox.

This paper is chiefly aimed at individuating some deep, but as yet almost unnoticed, similarities between Aristotle's syllogistic and the Stoic doctrine of conditionals, notably between Aristotle's metasyllogistic equimodality condition and truth-conditions for third type conditionals. In fact, as is shown in §1, Aristotle's condition amounts to introducing in his metasyllogistic a non-truthfunctional implicational arrow '', the truth-conditions of which turn out to be logically equivalent to truth-conditions of third type conditionals, according to which only the impossible follows from the (...) impossible. Moreover, Aristotle is given precisely this non-Scotian conditional logic in two so far overlooked passages of Themistius' Paraphrasis of De Caelo. Some further consequences of Aristotle's equimodality condition on his logic, and notably on his syllogistic, are pointed out and discussed at length. A extension of Aristotle's condition is also discussed, along with a full characterization of truth-conditions of fourth type conditionals. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

Pure mathematical truths are commonly thought to be metaphysically necessary. Assuming the truth of pure mathematics as currently pursued, and presupposing that set theory serves as a foundation of pure mathematics, this article aims to provide a metaphysical explanation of why pure mathematics is metaphysically necessary.

Among contemporary philosophers, there is widespread consensus that begging the question is a grave argumentative flaw. However, there is presently no satisfactory analysis of what this flaw consists of. Here, I defend a notion of question-begging in terms of analyticity. In particular, I argue that an argument begs the question just in case its conclusion is an analytic part of the conjunction of its premises.