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Published online by Cambridge University Press: 18 December 2009
The ladder leads next to deductive logic, the branch of logic treating of logical implication and other logical relationships among propositions. This chapter sketches a theory of deductive logic that builds on the subjective probability theory arising from the theorems of the previous chapter. The theory is laid out in such a way as to make the deductive relationships traceable back through the probability considerations to their evolutionary roots.
The connections between probability theory and deductive logic have been variously characterized. The account of their relationship to be presented here is not necessarily the only one possible, but lends itself to a reductive approach. Much of the material is standard except for a reorganization designed to reveal the reductive architecture. Many of the underlying concepts are due originally to Rudolf Carnap (1942; 1943; 1950) Carnap and Jeffrey (1971) and Alfred Tarski (1956). However, these luminaries should not on that account be suspected of harboring any ideas about biological reducibility.
SYNTAX, SEMANTICS, AND PRAGMATICS
A logical system can be presented on any of three different levels of detail, traditionally called the pragmatic, semantic, and syntactic levels. Carnap, following Morris, characterized them as follows (1942, 9):
… If in an investigation explicit reference is made to the speaker, or, to put it in more general terms, to the user of the language, then we assign it to the field of pragmatics. … If we abstract from the user of the language and analyze only the expressions and their designata, we are in the field of semantics. And if, finally, we abstract from the designata also and analyze only the relation between the expressions, we are in (logical) syntax.
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