The semantics of predicate logic

Workshop organizers: Marcus Kracht and Udo Klein

{marcus.kracht, udo.klein}@uni-bielefeld.de

2. September 2010
Bielefeld University, HS10

Workshop description

In recent years it has become evident that the semantics of predicate logic needs thorough revision. Two concepts have been identified as highly problematic: variables and relations. Work by Albert Visser and Kit Fine on the notion of variables has shown that the standard Tarskian semantics is deficient. One problem is that it is not compositional. Also, Kit Fine has criticised the standard concept of a relation employed in the semantics of predicate logic as metaphysically inadequate because it assumes fixed positions for its arguments. Though a lot of progress has been made, it is far from clear what alternatives we should be looking for. The workshop brings together key researchers in this area in the hope of paving the way for alternative semantics that do not suffer from the abovementioned problems.

Workshop program

09:30 - 10:30	Albert Visser (Utrecht University):
	The rex around the corner: a reflection on the nature of the variable
10:30 - 11:00	discussion and coffee
11:00 - 12:00	Joop Leo (Utrecht University):
	Indiscernibility in relations
12:00 - 12:30	discussion and coffee
12:30 - 13:30	lunch
13:30 - 14:30	Jim Pryor (New York University):
	Hyper-Evaluativity
14:30 - 15:00	discussion and coffee
15:00 - 16:00	Marcus Kracht (Bielefeld University):
	Alphabetic innocence and compositionality
16:00 - 16:30	discussion and coffee
16:30 - 17:30	Kit Fine (New York University):
	Variables and variable objects
17:30 - 18:00	discussion and coffee
19:30 -	dinner

Abstracts

1. Albert Visser: The rex around the corner: a reflection on the nature of the variable
   
   We pursue an analogy between the computer game of Nanosaur and the treatment of variables in predicate logic. We will address both syntactical and semantical issues, to be specific:
   1. Expressions: abstract versus concrete
   2. Left-to-right text construction versus the inductive definition
   3. Text in this world and its semantical other-worldly counterpart
   We hope the metaphor will blow away more smoke than it creates. Tempore volente, we will say a bit about Kit Fine's approach to the variable.

2. Joop Leo: Indiscernibility in relations
   
   I will consider some indiscernibility issues of different view on relations. According to the positionalist view, relations come with argument-places. A problem with this view is that a state like a's being adjacent to b has two corresponding complexes, but there is (metaphysically) nothing to distinguish them. If we conceive of argument-places as structureless places, then the argument-places of the adjacency relation are indiscernible, but switching arguments still gives another complex. On the antipositionalist view, a given relation may also have states with more than one corresponding complex, but in this case the complexes are always genuinely distinct. However, a complex may have indiscernible occurrences of objects, as in the complex a's resembling a. For antipositionalism, substitution is a primitive operation, but the question is, how can we substitute different objects for indiscernible occurrences?

3. Jim Pryor: Hyper-Evaluativity
   
   Predicates are "hyper-evaluative" when they depend on more than just the semantic values (be they intensional or more fine-grained) of their individual arguments, but also on the way those arguments are "coordinated" or "wired." I examine motivations and semantic implementations for such predicates, drawing from linguistics and computer science.

4. Marcus Kracht: Alphabetic innocence and compositionality
   
   Alphabetic innocence is the principle that the meaning of a formula does not depend on the names of the occurring variables. I shall show that as soon as such a principle is adopted there no longer is a compositional context free grammar for predicate logic. Only when we restrict to a finite variable fragment can we get it back.

5. Kit Fine: Variables and variable objects
   
   I discuss some difficulties that remain in providing a variable object semantics for variables even after one adopts a relational form of semantics.