Author: Marcus Rossberg

Vague Identity: A Uniform Approach

Xinhe Wu

There are numerous apparent examples of vague identity, i.e., examples where two objects appear to be neither determinately identical nor determinately distinct. Philosophers disagree on whether the source of vagueness in identity is semantic or ontic/metaphysical. In this talk, I explore the use of Boolean-valued models as a many-valued semantic framework for identity. I argue that this semantics works well with both a semantic and ontic conception of vague identity. I also discuss, in the context of Boolean-valued logic, responses to the Evans’ argument under the two conceptions.

Modal QUARC and Barcan

Jonas Raab

I develop a modal extension of the Quantified Argument Calculus (QUARC)—a novel logical system introduced by Hanoch Ben-Yami. QUARC is meant to better capture the logic of natural language. The purpose of this paper is to develop a variable domain semantics for modal QUARC (M-QUARC), and to show that even if the usual restrictions are imposed on models with variable domains, M-QUARC-analogues of the Barcan and Converse Barcan formulas still are not validated. I introduce new restrictions—restrictions on the extension of the predicates—and show that with these in place, the Barcan and Converse Barcan formulas are valid. The upshot is that M-QUARC sheds light on the in-/validity of such formulas.

Relevant Logics as Topical Logics

Andrew Tedder

There is a simple way of reading a structure of topics into the matrix models of a given logic, namely by taking the topics of a given matrix model to be represented by subalgebras of the algebra reduct of the matrix, and then considering assignments of subalgebras to formulas. The resulting topic-enriched matrix models bear suggestive similarities to the two-component frame models developed by Berto et. al. in Topics of Thought. In this talk I’ll show how this reading of topics can be applied to the relevant logic R, and its algebraic characterisation in terms of De Morgan monoids, and indicate how we can, using this machinery and the fact that R satisfies the variable sharing property, read R as a topic-sensitive logic. I’ll then suggest how this approach to modeling topics can be applied to a broader range of logics/classes of matrices, and gesture at some avenues of research.

Towards a Structuralist Metasemantics for Number Words

Eric Snyder

According to non-eliminative structuralism, the referents of numerical singular terms, such as the numeral ‘two’ or ‘the number two’, are numbers, construed as positions within the natural number structure. However, a potential problem comes in the form of sentences like ‘{∅, {∅}} is the number two among the von Neumann ordinals’. If this is an identity statement, then its truth would seemingly require identifying the second position of the natural number structure with a particular set, thus giving rise to a version of Benacerraf’s famous Identification Problem. In response, Stewart Shapiro (1997) draws an analogy to expressions like ‘the Vice President’, which are ambiguous between denoting an office-holder (e.g. Kamala Harris) or an office (the office of the Vice Presidency). Similarly, Shapiro suggests that in ordinary arithmetic contexts, such as ‘Two is less than three’, we view positions as analogous to office-holders, while in other contexts, we view them instead as analogous to offices occupied by entities playing the role of numbers, e.g. {∅, {∅}}. However, this suggestion faces two serious challenges. First, what exactly is the nature of this purported ambiguity, and what empirical evidence, if any, is there for it? Second, even if we grant the ambiguity, we appear to get a revenge version of the Identification Problem anyway: just permute the positions within the natural number structure. The purpose of this talk is to defend Shapiro’s ambiguity thesis, by supplying the empirical support required, and explaining how, when appropriately understood, the semantics assumed does not give rise to a revenge form of the Identification Problem.

Is Functionalism Inconsistent?

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.

Logic, Natural Language and Semantic Paradoxes

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.

Detachability and LP: An Alternative Perspective

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.

A Tale of Two Logics: Did Priest Get Lost in India?

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.

On VDV (Variable Designated Value) Logics

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).