Ludovica Conti (Pavia)
Metaphysical Assumptions in Russell’s Paradox
In this talk, I propose an argument in support of the thesis that classical first-order logic has an existential commitment in a non-empty domain of individual entities. This argument consists of an explanation of Russell’s paradox in Frege’s Grundgesetze that focuses on the role of first-order logic in the definition of the domain of the extensionality function. This explanation blames the inconsistency on the un-restricted formulation of first-order quantification and identity rules and, from a metaphysical point of view, on the correlated assumption that every singular term denotes an existing individual object in the first-order domain.
Michał Tomasz Godziszewski (Warsaw)
Axiomatic Theories of Truth and Metaphysical Commitments in Philosophy of Set Theory
Øystein Linnebo (Oslo)
What explains a true universal generalization? This paper distinguishes two kinds of explanation. While an instance-based explanation proceeds via each instance of the generalization, a generic explanation is independent of each instance, relying instead on completely general facts about the properties or operations involved in the generalization. This distinction is illuminated by means of a truthmaker semantics, which is also used to show that instance-based explanations support classical logic, while generic explanations support only intuitionistic logic.
Lavinia Picollo (UCL) and Daniel Waxman (Lingnan)
Mathematical Internal Realism and the Problem of Determinacy
In recent work, Button and Walsh introduce a position they call mathematical internal realism, which, they suggest, explains how we can acquire precise and determinate mathematical concepts without performing semantic ascent (i.e. without talking about models) but rather appealing to internal categoricity results (i.e. deductive proofs within second-order logic to the effect that any structures satisfying the axioms of arithmetic/set theory are isomorphic). In this talk, we critically examine the merits of mathematical internal realism. We contend that an analogue of the challenge of acquiring mathematical concepts re-emerges without semantic ascent, in terms of the notion of determinacy, and argue that this challenge severely threatens internalism.
Lorenzo Rossi (Salzburg)
Contextualist theories of truth have a number of virtues – they offer a uniform, elegant, and fully classical treatment of both ‘standard’ and ‘revenge’ paradoxes. However, standard contextualist theories of truth are incompatible with absolute generality, the view that one can successfully quantify over everything whatsoever. Far from being a minor side effect, this makes it impossible for contextualist theories to correctly interpret arguably absolutely general truths, such as ‘everything is self-identical’. In this paper, I develop a contextualist theory of truth that is compatible with absolute generality, while retaining the virtues of standard contextualism, including its treatment of revenge paradoxes.
Maria Paola Sforza Fogliani (Pavia)
What Logic Could Not Be: Anti-Exceptionalism & the Ontology of Logical Laws
The aim of my talk is to assess the relationships between notable positions in the ontology of logic and various versions of anti-exceptionalism – i.e., the position according to which logical laws do not have any epistemologically or metaphysically privileged status. Hopefully, the analysis will shed some lights on whether anti-exceptionalism might be able to face its biggest threat, namely circularity objections.
Stewart Shapiro (OSU)
Open Texture and Mathematics (joint work with Craige Roberts)
The purpose of this paper is to explore the extent to which the notion of open texture, as characterized by Friedrich Waismann, applies to the languages of mathematics. Open texture, we argue, is a design feature of natural languages, allowing the flexibility needed to adapt to new situations and new cases and new discoveries. We show that the informal or pre-formal languages of mathematics are indeed subject to open texture, but the ideal of rigor demands that it be eliminated.
Gila Sher (UCSD)
The Metaphysical Commitments of Logic
In this talk I will sort out the metaphysical commitments and non-commitments of logic on several levels, with special emphasis on invariance, veridicality, and existence.
Sebastian Speitel (UCSD)
Minimizing Metaphysical Commitment and Fixing a Logical Term
Logical terms play a crucial role in the definition of logical consequence: by determining the logical form of sentences they establish which features are to be considered relevant when assessing the dimension along which truth is preserved in an inference. This important function is reflected in their privileged status in logical systems - their meaning is held “fixed” throughout. However, it is not fully clear (i) what precisely it means for a logical term’s meaning to be held fixed; (ii) why this is a feature that should solely be reserved for logical terms; and (iii) what metaphysical and semantic assumptions and implications go along with this. The goal of the talk is to assess some aspects pertaining to this interrelated cluster of questions.