[Alta-Logic] LOGIC TALK TODAY! Aldo Antonelli (Davis)

[Richard Zach]

Aldo Antonelli - "Home on the Range: Where Semantics and Ontology Play"

Thursday October 4, 4-6 pm
Social Sciences Building, Room 1253

About the Talk:

In his 1950 dissertation, Leon Henkin showed how to provide higher-order 
quantifiers with non-standard, or "general" interpretations, in which, 
for instance, second-order quantifiers are taken to range over 
collections of subsets of the domain that may fall short of the full 
power-set.  In contrast, first-order quantifiers are usually regarded as 
immune to this sort of non-standard interpretation, at least in the 
sense that the semantics for first-order quantifiers is ordinarily taken 
to be determined once a first-order domain of objects is fixed.  After 
introducing the notion of a general interpretation for arbitrary 
first-order quantifiers, this talk explores some of the properties of 
quantifiers so construed, emphasizing the effects of imposing further 
constraints that the interpretation is to satisfy.  The possibility of 
general interpretations for first-order quantifier bears directly on the 
viability of the Quinean criterion for ontological commitment, according 
to which "to be is to be the value of a bound variable".  But on the 
general interpretation, first-order quantifiers are just sa radically 
semantically indeterminate as their second-order counterparts.  It 
follows that the Quinean criterion ascribing existence to those objects 
that fall within the range of the quantifiers is neither necessary nor 
(in an importantly different sense) sufficient for ontological commitment.

Aldo Antonelli is Professor of Philosophy at the University of 
California, Davis.  His primary areas of specialization are Logic and 
Applications, Defeasable Reasoning and Knowledge Representation, 
Philosophy of Mathematics, Philosophy of Logic, Philosophy of Language, 
and Early Analytic Philosophy.