The Logic and Metaphysics Workshop will meet on May 3rd from 4:15-6:15 (NY time) via Zoom for a talk by Graziana Ciola (Radboud Nijmegen).

Title: Marsilius of Inghen, John Buridan and the Semantics of Impossibility

Abstract: In the 14th-century, imaginable yet in some sense impossible non-entities start playing a crucial role in logic, natural philosophy and metaphysics. Throughout the later middle ages and well into early modernity, Marsilius of Inghen’s name comes to be unavoidably associated with the semantics of imaginable impossibilities in most logical and metaphysical discussions. In this paper I analyse Marsilius of Inghen’s semantic treatment of impossible referents, through a comparison with John Buridan’s. While in many ways Marsilius is profoundly influenced by Buridan’s philosophy, his semantic analysis of impossibilia is radically different from Buridan’s. Overall, Buridan tends to analyse away impossible referents in terms of complex concepts by combining possible simple individual parts. Marsilius, on the one hand, treats impossibilia as imaginable referents that are properly unitary; on the other hand, he extends the scope of his modal semantics beyond the inclusion of merely relative impossibilities, allowing for a full semantic treatment of absolute impossibilities as well. Here, I will explore the extent of these differences between Buridan’s and Marsilius of Inghen’s semantics, their presuppositions, and their respective conceptual impact on early modern philosophy of logic and mathematics.

The Logic and Metaphysics Workshop will meet on May 10th from 4:15-6:15 (NY time) via Zoom for a talk by Filippo Casati (Lehigh).

Title: Heidegger on the Limits and Possibilities of Human Thinking

Abstract: In my talk, I will address what Heidegger calls ‘the basic problem’ of his philosophy, that is, the alleged incompatibility between the notion of Being, our thinking, and logic. First of all, I will discuss some of the ways in which Heideggerians have dealt with this incompatibility by distinguishing what I call the irrationalist and rationalist interpretation. Secondly, I will argue that these two interpretations face both exegetical and philosophical problems. To conclude, I will defend an alternative way to address the incompatibility between the notion of Being, our thinking, and logic. I will argue that, in some of his late works, Heidegger seems to suggest that the real problem lies in the philosophical illusion that we can actually assess the limits of our thinking and, therewith, our logic. Heidegger’s philosophy, I deem, wants to free us from such a philosophical illusion by delivering an experience which reminds us that our thinking is something we can never ‘look at from above’ in order to either grasp its limits or realize that it has no limits whatsoever.

The Logic and Metaphysics Workshop will meet on April 26th from 4:15-6:15 (NY time) via Zoom for a talk by Rohan French (UC Davis).

Title: Non-Classical Metatheory

Abstract: A common line of thinking has it that proponents of non-classical logics who claim that their preferred logic L gives the correct account of validity, while at the same time giving proofs of theorems about L using classical logic, are in some sense being insincere in their claim that L is the correct logic. This line of thought quite naturally motivates a correctness requirement on a non-classical logic L: that it be able to provide internally acceptable proofs of its main metatheorems. Of central importance amongst such metatheorems will typically be soundness and completeness results, such results being apt to play important roles in arguments showing that a given logic gives the correct account of validity. On the face of it this sounds like a reasonable requirement, but determining its precise content requires us to settle two important conceptual questions: what counts as a completeness proof for a logic, and what does it mean for a result to be internally acceptable? To get clearer on this issue we will look at three different results which have some claim to being internally acceptable soundness and completeness proofs, focusing for ease of comparison on the case of intuitionistic propositional logic, examining the extent to which they can be said to provide internally acceptable soundness and completeness results.

The Logic and Metaphysics Workshop will meet on April 19th from 4:15-6:15 (NY time) via Zoom for a talk by V. Alexis Peluce (CUNY).

Title: Brouwer’s First Act of Intuitionism

Abstract: L.E.J. Brouwer famously argued that mathematics was completely separated from formal language. His explanation for why this is so leaves room for interpretation. Indeed, one might ask: what sort of philosophical background is required to make sense of the strong anti-linguistic views of Brouwer? In this talk, we outline some possible answers to the above. We then present an interpretation that we argue best makes sense of Brouwer’s first act.

The Logic and Metaphysics Workshop will meet on April 12th from 4:15-6:15 (NY time) via Zoom for a talk by William Nava (NYU).

Title: Logical deducibility and substitution in Bolzano (and beyond)

Abstract: Bolzano is famously responsible for an influential substitutional account of logical consequence (or, as he calls it, logical deducibility): a proposition, 𝜑, is logically deducible from a set of propositions, Γ, iff every uniform substitution of non-logical ideas in Γ∪{𝜑} that makes every proposition in Γ true also makes 𝜑 true. There are two problems with making sense of Bolzano’s proposal, however. One is that Bolzano argues that every proposition is of the form a has B—in other words, is a monadic atomic predication. So, for Bolzano, logically complex propositions like ‘𝜑 and 𝜓’ cannot have the semantic structure they appear to. This can be addressed, roughly, by taking complex propositions to predicate logical ideas of collections of propositions. But this introduces the second problem: for Bolzano, familiar logical ideas like ‘and’, ‘or’, and ‘not’ are complex ideas with compositional structure. I’ll show that, as a result of this structure, we cannot use the simple and familiar notion of uniform substitution in order to understand logical deducibility. We must instead use what I’ll call form-sensitive substitution. I will end by drawing some general lessons about substitutional definitions of logical consequence in languages with the resources to generate complex predicates of propositions.

The Logic and Metaphysics Workshop will meet on April 5th from 4:15-6:15 (NY time) via Zoom for a talk by Federico Pailos and Eduardo Barrio (Buenos Aires).

Title: A Metainferential Solution to the Adoption Problem

Abstract: In ‘The Question of Logic’ (Kripke 2020) and “The Adoption Problem and the Epistemology of Logic” (Padró 2020), Kripke and Padró argue against the possibility of adopting an alternative logic. Without having already endorsed a logic, it is not possible to derive the consequences of an alternative system. In particular, without Modus Ponens in the metatheory, one could not adopt any inferential rule at all. This seems to cause trouble for logics like LP, that does not validate this rule. Modus Ponens is a self-governing rule that cannot be adopted and could not be rejected. This is connected with the problem of the tortoise reasoner (Scambler 2019) and the problem of the tortoise Logic (Priest 2021). In this talk, we offer a new solution. With the metainferential logic TS/LP it is possible to model metalogical Modus Ponens-like reasoning while still rejecting Modus Ponens.