Owain Griffin (OSU)

Starting with Bealer (1978), some authors have claimed that Beth-style definability results show functionalism about the mind to be inconsistent. If these arguments go through, then the Beth result provides a way of collapsing functionalism into reductionism – exactly what functionalists purport to deny. While this has received discussion in the literature (See Hellman & Thompson (1975), Block (1980), Tennant (1985)) it has recently been resuscitated and refined by Halvorson (2019). In this paper, we question the argument’s accuracy, and propose a new objection to it. We claim that in order to derive its conclusion, the argument relies fundamentally on equivocations concerning the notion of definability.

Amit Pinsker

How should we respond to semantic paradoxes? I argue that the answer to this question depends on what we take the relation between logic and natural language to be. Focusing on the Liar paradox as a study case, I distinguish two approaches solving it: one approach (henceforth ‘NL’) takes logic to be a model of Natural Language, while the other (henceforth ‘CC’) suggests that a solution should be guided by Conceptual Considerations pertaining to truth. As it turns out, different solutions can be understood as taking one approach or the other. Furthermore, even solutions within the same ‘family’ take different approaches, and are motivated by NL and CC to different extents, which suggests that the distinction is not a binary one – NL and CC are two extremes of a spectrum.

Acknowledging this has two significant upshots. First, some allegedly competing solutions are in fact not competing, since they apply logic for different purposes. Thus, various objections and evaluations of solutions in the literature are in fact misplaced: they object to NL-solutions based on considerations that are relevant only to CC or vice versa. Second, the plausible explanation of this discrepancy is that NL and CC are two ways of cashing out what Priest calls “the canonical application of logic”: deductive ordinary reasoning. These two ways are based on two different assumptions about the fundamental relation between logic and natural language. The overall conclusion is thus that a better understanding of the relation between logic and natural language could give us a better understanding of what a good solution to semantic paradoxes should look like.

Thomas M Ferguson

In this talk, I aim to connect two strands of work related to strict-tolerant consequence and the logic of paradox (LP). First is work (“Monstrous Content and the Bounds of Discourse”, JPL) that argues that considerations of topic-theoretic conversational boundaries are captured by the strict-tolerant interpretation of weak Kleene matrices. Second is work (“Deep ST”, JPL) arguing that all the metainferential properties of inference rules in the strict-tolerant hierarchy are already encoded in standard LP. Synthesizing these two strands is particularly useful when asking about settings accommodating both topic-theoretic and veridical semantic defects. Importantly, this synthesis yields a novel defense of LP as a particularly compelling logic and allows a reevaluation of the failure of detachability for the LP conditional.

Chris Rahlwes

With his extensive work on the Buddhist tetralemma (catuṣkoṭi) and the Jaina sevenfold sentences (saptabhaṅgī), Graham Priest has presented Indian logic as dialetheic, in which there are true contradictions. While Priest is not the only logician to present Indian logic as non-classical or paraconsistent, his dialetheic reading has gained widespread attraction among contemporary logicians. This attraction has led many logicians to posit that Priest is (historically) correct in his reading. However, those who study Buddhism and Jainism often do not share these convictions. The backlash from such specialists often simplifies Priest’s account and ignores the challenge that the dialetheic reading brings regarding the nature of negation. Following Priest’s claim that Aristotelian logic is incompatible with classical logic, I argue that Priest uses the wrong logical framework – the non-classical heir of classical logic – to understand Indian logic. In so doing, I present a neo-Pāṇinian or neo-Aristotelian account of Buddhist and Jaina logic emphasizing negation, denial, and (to a lesser degree) contradiction.

Graham Priest

In this talk I will isolate a class of logics which I shall call Variable Designated Values (VDV) Logics, and consider some of their properties. VDV logics are many-valued logics in which different sets of designated values are used for the premises and conclusions. The idea goes back, as far as I know, to Malinowski (1990) and (1994), though much use of the idea has been made by logicians recently in the form of the logics ST and TS (S= Strict; T = Tolerant).

Andrew Tedder

This talk investigates the odd fact that one may add connexive theses to relevant logics, giving rise to contraclassical systems, and obtain logics which are not trivial, still obey many of the desired relevance properties, and yet allow one to prove every negated implication. I’ll show why this is the case, and investigate alternative connexive relevant logics in the area that don’t have this undesirable property.

Eugenio Orlandelli

We present a general approach to quantified modal logics (QML) that can simulate most other approaches. The language is based on operators indexed by terms which allow to express de re modalities and to control the interaction of modalities with the first-order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between n-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many or no object in an accessible world. Moreover by taking as primitive a relation between n-tuples we avoid the shortcomings of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete QML.

Walter Dean

The goal of this talk is to use the sorites paradox to illustrate the methodology of “reverse philosophy”—i.e. the application of methods from reverse mathematics to study the mathematical involvement of recognized arguments in analytic philosophy. After briefly motivating such a program, I will focus on the following: 1) the role of measurement and representation theorems in the linguistic formulation of various forms of the sorites; 2) the role of a weak form of Hölder’s Theorem in the formulation of the conditional sorites for predicates such as “tall”; 3) the role of a stronger form of Hölder’s Theorem in the formulation of the so-called continuous sorites for predicates such as “red” of Weber & Colyvan 2010/Weber 2021. Contrasts will be drawn between the constructivity of the weaker form (as observed by Krantz 1968 and formalized in RCA_0 by Solomon 1998) and the non-constructivity of the latter form (due to its apparent dependence on Arithmetical Comprehension).

Lionel Shapiro

I’ll propose an application to logic of the “neopragmatist” program. Neopragmatists argue that inquiry into the nature of what we think and talk about can be fruitfully replaced by inquiry into the functions of concepts and expressions. Logical vocabulary can serve as a particular target for neopragmatist theorizing, but it has also been taken to pose obstacles to neopragmatist accounts more generally. I’ll argue that a neopragmatist approach to logical relations (such as logical consequence), as well as to ascriptions of content, undermines two constraints on neopragmatist accounts of logical connectives (such as “and”, “or”, and “not”). Freed from these constraints, I’ll sketch a simple version of such an account, on which logical connectives express dialectical attitudes. The resulting approach is deflationary in two ways: it’s based on deflationism about logical relations and it aims to deflate some of neopragmatists’ usual theoretical ambitions.