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- Barbara Abbott, Conditionals in English and FOPL.In the 1960’s, both Montague (e.g. 1970, 222) and Grice (1975, 24) famously declared that natural languages were not so different from the formal languages of logic as people had thought. Montague sought to comprehend the grammars of both within a single theory, and Grice sought to explain away apparent divergences as due to the fact that the former, but not the latter, were used for conversation. But, if we confine our concept of logic to first order predicate logic (or FOPL) with identity (that is, omitting everything which is not required for the pursuit of mathematical truth), then there are of course many other aspects, in addition to its use in conversation, which distinguish natural language from logic. Conventional implicature, information structure (including presupposition), tense and time reference, and the expression of causation and inference are several of these, which combine as well with syntactic complexities which are unnecessary in first order predicate logic. In this paper I will argue that such distinguishing aspects should be more fully exploited to explain the differences between the material conditional of logic and the indicative conditional of one natural language (English).In my reading list | Discuss this article | Edit | Categorize |My bibliography
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This collection introduces the reader to some of the most interesting current work on conditionals. Particular attention is paid to possible world semantics for conditionals, the role of conditional probability in helping us to understand conditionals, implicature and the material conditional, and subjunctive versus indicative conditionals. Contributors include V.H. Dudman, Dorothy Edgington, Nelson Goodman, H.P. Grice, David Lewis, and Robert Stalnaker.
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| | Other links: blackwell-synergy.com | Scholar | More.. In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field''s probabilistic semantics. Along the way I will show how Field''s semantics differs from a substitutional interpretation (...)
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