Month: January 2015

Reference and Invariance in Abstraction Principles

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’.

Relational semantics for logics with thin sets of connectives

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).

Backtracking counterfactuals, revisited.

Justin Khoo

23 Jan, 4pm-5:30pm, LH 306

I discuss three observations about backtracking counterfactuals not predicted by existing theories of counterfactuals, and then motivate a theory of counterfactuals that does predict them. On my theory, counterfactuals quantify over a suitably restricted set of historical possibilities from some contextually relevant past time. I motivate each feature of the theory relevant to predicting our three observations about backtracking counterfactuals.