Bruno Whittle (Yale University)

6 Nov, 2pm, LH 302.

The talk will be about a question that is generally taken to be settled: are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results (which I of course do not dispute) answer the question given an almost universally accepted principle relating size to the existence of functions. The principle is: for any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the talk, however, is to argue that the question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in a position to know this principle. I will do this by looking at what seem to be the strongest reasons for thinking that we are in a position to know the principle, and arguing against them.

Teresa Kouri (Ohio State University)

13 Nov, 2pm, LH 302.

There are several options for logical pluralism on the table. Rudolf Carnap puts forward a position in which the logical connectives never mean the same thing in distinct logics, and JC Beall & Greg Restall put forward a position in which they always do. However, neither of them are capable of accounting for all of our intuitions. In particular, neither Carnap nor Beall & Restall can make sense of the fact that it seems there are some contexts in which distinct logics seem to have the same logical terminology, and some context in which distinct logics have distinct logical terminology. In this paper, I will present a view (in line with that of Stewart Shapiro’s) which can account for both of these intuitions.

Christopher Porter (University of Florida)

18 Sep, 2pm, LH 302.

In this talk, I will frame a number of definitions of algorithmic randomness as instances of what I refer to as the logical approach to randomness. In order to better understand this logical approach, I will contrast it with one of the standard approaches to defining randomness in classical mathematics, which I call the valuative approach to randomness. I will focus specifically on two potential problems faced by the logical approach that threaten to trivialize this approach to defining randomness. I will address these two potential problems, arguing that the logical approach fills an important role, namely, that of supplementing the valuative approach by yielding additional information about classically random objects, which is unearthed when we bring the tools of mathematical logic to bear on the study of randomness.

Cleo Condoravdi

1 May, 2pm-3:30pm, LH 306

Detachment via Modus Ponens (factual detachment) faces well-known problems for conditionals with deontic modals. One class of conditionals where the validity of factual detachment has been contested are those conditioning on an agent’s preferences, known in the linguistic literature as anankastic conditionals and in the philosophical literature as hypothetical imperatives. This talk presents a semantics for such conditionals which validates detachment and then examines why detachment appears to fail when it does.

We claim that an endorsement component enters the interpretation of the modal in the conclusion, but, crucially, not that of the conditional premise. In the problematic cases, this endorsement component is at odds with what can be reasonably assumed about normal speakers, hence the unease assenting to the conclusion even when assenting to both premises. We argue that the source of the endorsement component is pragmatic, and that, therefore, these cases do not provide a reason to adopt a semantics for this type of conditional that invalidates Modus Ponens.

Kai Wehmeier

10 Apr, 2pm-3:30pm, LH 306

Orthodox approaches to formal semantics for modal operator languages, following Kripke and Kaplan, supplement the familiar compositional semantics embodied in the recursive definition of truth-at-a-world by a “postsemantics” that consists in identifying truth simpliciter with truth at the actual world. I will propose an alternative, Tarski-inspired approach that makes do without any appeal to a postsemantics. This Tarskian approach, I will argue, is superior to the orthodoxy on both empirical and methodological grounds, and has some remarkable philosophical consequences.

Ezra Cook

27 Mar, 4-5:30pm, LH 306

Any semantics for modals and conditionals must prove its worth by resolving some standard problem cases. I start with a solution to Frank-Zvolensky conditionals. Consider the following:

(1) If John speeds, he should speed.
(2) If the Dalai Lama is mad, then he should be mad.

These conditionals should not be predicted as theorems of any natural language semantics for conditional constructions. A solution to this problem extends the Kratzerian restrictor analysis with a consistent modal base expansion and contraction operation. Following this, some past-shifted conditional constructions will be considered. Past-shifted conditionals, such as the Morgenbesser conditional:

(3) If you had bet heads, you would have won.

Are shown to be resolvable by connecting the modal base, in a Kratzerian framework, and the Stalnakerian common ground. This connection is shown to generate truth conditional differences exactly where they should be predicted. Along the way, the standard Kratzerian ordering source will be generalized to accommodate an arbitrary number of independent ordering sources, factoring in the possibility of inconsistencies.

Andrew Parisi

13 Feb, 2-3:30pm, LH 306

Various forms of inferentialism require a proof-theoretic account of modality. Many modal logics can be adequately captured with the sequent calculus. But there is no account yet discovered that can capture the full range of modal logics that might be of interest to inferentialists. In particular, no straightforward cut-free account of S5 has been discovered, and no account of logics much weaker than S4 can uniquely characterize the necessitation operator, i.e. a second necessitation operator with the same introduction rules is not everywhere intersubstitutible with the first necessitation operator. An alternative to sequents, hypersequents, is offered as a solution to some of these problems. Hypersequent accounts of various modal logics have been discovered that meet the above two criteria for an inferentialist account of the modal connectives. The various systems are obtained only by restrictions of the external structural rules of the hypersequent calculus.

Francesca Boccuni

6 Feb, 2-3:30pm, LH 306

An abstraction principle has the form §F = §G RE(F, G), where § is an abstraction operator mapping Fregean concepts into objects, and RE is an equivalence relation holding between concepts. Abstraction principles trace back to Frege. Well-known examples are Hume’s Principle and Basic Law V. These principles provide identity conditions for the individuation of abstracta, since they provide a means to identify the entities the identity statement of the left-hand side involves, by appealing to the identity criterion embodied by the equivalence relation on the right-hand side. By individuation, they also provide a way to attach referents to the abstract-terms on the left-hand side. Famously, though, abstraction principles fail to provide sufficient conditions for such an individuation, and thus, it may be argued, they fail to provide a way to fix the reference of the abstract-terms they govern. This is known as the Julius Caesar problem. By the notion of parametric reference in logico-mathematical reasoning, I propose to detach individuation of abstracta from the fixing of reference of abstract-terms. I argue for this view and I provide an appropriate semantics for parametric reference. Furthermore, I investigate a possible argument against this view, according to which the philosophical advantages of the (neo-)Fregean interpretation of abstraction principles as unveiling the nature of Fregean abstracta are lost by the approach via parametric reference, and make this latter approach philosophically unsubstantial. As a reply, I claim that, by using parametric reference, philosophical advantages other than those the (neo-)Fregeans envisage may be obtained. In this respect, I investigate the relation between parametric reference and the notion of invariance under permutations, recently put forward by Aldo Antonelli, in order to retrieve the logicality of abstraction principles on different grounds than the (neo-)Fregeans’.

Katalin Bimbo

20 Feb, 2-3:30pm, LH 306

The use of a binary accessibility relation in the semantics for normal modal logics that was invented by Kripke in the late 1950s is well motivated not only philosophically, but also mathematically. A similar semantics for relevance logics that was introduced by Routley and Meyer in the early 1970s uses a ternary accessibility relation. Gaggle theory that was invented by Dunn in the early 1990s generalizes both Kripke’s as well as Routley and Meyer’s semantics. Gaggle theory predicts that a standard relational semantics for the major relevance logics such as T, E and R should have a ternary accessibility relation.

In this talk, I explore how the Routley-Meyer semantics for T and R fare, respectively, for the implicational fragments of these logics (or for slight extensions thereof).