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ARE INTENSIONS NECESSARY?
Almerindo Ojeda
University of California-Davis
Friday, April 29, 3:30PM MJH Rm 126
Sponsored by the Stanford Humanities Center/Mellon Foundation
Graduate Research Program
Possible-worlds semantics (PWS) reaches a well-known impasse as it attempts to interpret expressions that have the same
intension yet differ in meaning. To overcome this impasse, PWS is routinely supplemented with structural theories of meaning.
According to these theories, the meaning of an expression e is not just its intension e', but rather a structure of
intensions--say, a tree--that reflects the way in which e' was built, compositionally, from simpler intensions.
It is generally agreed that structural theories of meaning are strong enough to carry PWS over the wall of nonsynonymous
cointensionals. It thus comes as a surprise that considerations of simplicity did not lead us to ask whether structural
theories of meaning were not strong enough to carry all of the weight PWS lifted--or whether structural theories of meaning
could not supplant rather than supplement PWS. This is the question I will address in this talk.
To do so I develop a purely extensional structural theory (PEST) of meaning. According to this PEST, the meaning of an
expression e is not just its extension e', but rather a structure of extensions (say, a tree) that reflects the way in which
e' was built, compositionally, from simpler extensions. I then show that, coupled with independently-motivated proof-theoretic
interpretations of modality and counterfactuals, PESTs can afford satisfying solutions to the problems that drove extensional
semantics into the ground--and can do so, of course, without appealing to the vast intractable ontology of possible worlds.
The talk closes with replies to plausible objections that might be levelled against PESTs. For, morphosyntactic structure
underdetermines meaning. And overdetermines it as well. Even more fundamentally, like all structural theories of meaning,
PESTs clash with the set-theoretic Axiom of Well-Foundedness.
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