JOURNAL OF PHILOSOPHICAL LOGIC最新文献

In the last decades, scientific laws and concepts have been increasingly conceptualized as a patchwork of contextual and indeterminate entities. These patchwork constructions are sometimes claimed to be incompatible with traditional views of scientific theories and concepts, but it is difficult to assess such claims due to the informal character of these approaches. In this paper, we will show that patchwork approaches pose a new problem of theoretical terms. Specifically, we will demonstrate how a toy example of a patchwork structure might trivialize Carnap’s semantics for theoretical terms based upon epsilon calculus. However, as we will see, this new problem of theoretical terms can be given a neo-Carnapian solution, by generalizing Carnap’s account of theoretical terms in such a way that it applies also to patchwork constructions. Our neo-Carnapian approach to theoretical terms will also demonstrate that the analytic/synthetic distinction is meaningful even for patchwork structures.

This paper investigates two intuitionistic mereological systems based on Tarski’s axiomatisation of general mereology. These systems use two intuitionistically non-equivalent formalisations of the notion of fusion. I study extensionality and supplementation properties as well as some variants of these systems, and defend parthood as a suitable primitive notion for intuitionistic mereology if working with Tarski’s axiomatisation. Furthermore, I arrive at an equi-interpretability result for one of the atomistic variants with intuitionistic plural logic. I discuss to what extent these results support the philosophical pertinence of the mereological systems under investigation as intuitionistic theories of parthood, thereby reacting to a conceptual challenge that we are confronted with when engaging in intuitionistic mereology.

It has long been known that in the context of axiomatic second-order logic (SOL), Hume’s Principle (HP) is mutually interpretable with “the universe is Dedekind infinite” (DI). In this paper, we offer a more fine-grained analysis of the logical strength of HP, measured by deductive implications rather than interpretability. Our main result is that HP is not deductively conservative over SOL + DI. That is, SOL + HP proves additional theorems in the language of pure second-order logic that are not provable from SOL + DI alone. Arguably, then, HP is not just a pure axiom of infinity, but rather it carries additional logical content. On the other hand, we show that HP is (Pi ^1_1) conservative over SOL + DI, and that HP is conservative over SOL + DI + “the universe is well ordered” (WO). Next, we show that SOL + HP does not prove any of the simplest and most natural versions of the axiom of choice, including WO and weaker principles. Lastly, we discuss other axioms of infinity. We show that HP does not prove the Splitting or Pairing principles (axioms of infinity stronger than DI).

Within the context of general relativity, the Heraclitus asymmetry property requires that no distinct pair of spacetime events have the same local structure Manchak and Barrett (2023). Here, we explore Heraclitus-maximal worlds – those which are “as large as they can be” with respect to the Heraclitus property. Using Zorn’s lemma, we prove that such worlds exist and highlight a number of their properties. If attention is restricted to Heraclitus-maximal worlds, we show senses in which observers have the epistemic resources to know which world they inhabit.

We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a general soundness and completeness theorem.

Abstractionist programs in the philosophy of mathematics have focused on abstraction principles, taken as implicit definitions of the objects in the range of their operators. In second-order logic (SOL) with predicative comprehension, such principles are consistent but also (individually) mathematically weak. This paper, inspired by the work of Boolos (Proceedings of the Aristotelian Society 87, 137–151, 1986) and Zalta (Abstract Objects, vol. 160 of Synthese Library, 1983), examines explicit definitions of abstract objects. These axioms state that there is a unique abstract encoding all concepts satisfying a given formula (phi (F)), with F a concept variable. Such a system is inconsistent in full SOL. It can be made consistent with several intricate tweaks, as Zalta has shown. Our approach in this article is simpler: we use a novel method to establish consistency in a restrictive version of predicative SOL. The resulting system, RPEAO, interprets first-order PA in extensional contexts, and has a natural extension delivering a peculiar interpretation of PA (^2).

We introduce a basic intuitionistic conditional logic (textsf{IntCK}) that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that (textsf{IntCK}) stands in a very natural relation to other similar logics, like the basic classical conditional logic (textsf{CK}) and the basic intuitionistic modal logic (textsf{IK}). As for the basic intuitionistic conditional logic (textsf{ICK}) proposed in Weiss (Journal of Philosophical Logic, 48, 447–469, 2019), (textsf{IntCK}) extends its language with a diamond-like conditional modality (Diamond hspace{-4.0pt}rightarrow ), but its ((Diamond hspace{-4.0pt}rightarrow ))-free fragment is also a proper extension of (textsf{ICK}). We briefly discuss the resulting gap between the two candidate systems of basic intuitionistic conditional logic and the possible pros and cons of both candidates.

Strict-Tolerant Logic ((textrm{ST})) underpins naïve theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical sequent calculus without Cut is sometimes advocated as an appropriate proof-theoretic presentation of (textrm{ST}). Unfortunately, there is only a partial correspondence between its derivability relation and the relation of local metainferential (textrm{ST})-validity – these relations coincide only upon the addition of elimination rules and only within the propositional fragment of the calculus, due to the non-invertibility of the quantifier rules. In this paper, we present two calculi for first-order (textrm{ST}) with an eye to recapturing this correspondence in full. The first calculus is close in spirit to the Epsilon calculus. The other calculus includes rules for the discharge of sequent-assumptions; moreover, it is normalisable and admits interpolation.

In his Formalization of Logic (1943) Carnap pointed out that there are non-normal interpretations of classical logic: non-standard interpretations of the connectives and quantifiers that are consistent with the classical consequence relation of a language. Different ways around the problem have been proposed. In a recent paper, Bonnay and Westerståhl argue that the key to a solution is imposing restrictions on the type of interpretation we take into account. More precisely, they claim that if we restrict attention to interpretations that are (a) compositional, (b) non-trivial and (c) in the case of the quantifiers, invariant under permutations of the domain, Carnap’s Problem is avoided. This paper has two goals. The first is to show that Bonnay and Westerståhl’s solution to Carnap’s Problem doesn’t work. The second is to argue that something similar to their proposal seems to do the job. The problems with Bonnay and Westerståhl’s approach trace back to issues concerning the (un)definability of subsets of the domain of first-order structures, as well as to the compositionality of first-order languages. After expanding on these problems, I’ll propose a way to modify Bonnay and Westerståhl’s account and solve Carnap’s Problem.

Around the turn of the 20th century, Keynes and Johnson extended the well-known square of opposition to an octagon of opposition, in order to account for subject negation (e.g., statements like ‘all non-S are P’). The main goal of this paper is to study the logical properties of the Keynes-Johnson (KJ) octagons of opposition. In particular, we will discuss three concrete examples of KJ octagons: the original one for subject-negation, a contemporary one from knowledge representation, and a third one (hitherto not yet studied) from deontic logic. We show that these three KJ octagons are all Aristotelian isomorphic, but not all Boolean isomorphic to each other (the first two are representable by bitstrings of length 7, whereas the third one is representable by bitstrings of length 6). These results nicely fit within our ongoing research efforts toward setting up a systematic classification of squares, octagons, and other diagrams of opposition. Finally, obtaining a better theoretical understanding of the KJ octagons allows us to answer some open questions that have arisen in recent applications of these diagrams.