David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 49 (1):67-82 (1990)
A bivalent valuation is snt iff sound (standard PC inference rules take truths only into truths) and non-trivial (not all wffs are assigned the same truth value). Such a valuation is normal iff classically correct for each connective. Carnap knew that there were non-normal snt valuations of PC, and that the gap they revealed between syntax and semantics could be jumped as follows. Let VAL snt be the set of snt valuations, and VAL nrm be the set of normal ones. The bottom row in the table for the wedge is not semantically determined by VAL snt, but if one deletes from VAL snt all those valuations that are not classically correct at the aforementioned row, one jumps straights to VAL nrm and thus to classical semantics. The conjecture we call semantic holism claims that the same thing happens for any semantic indeterminacy in any row in the table of any connective of PC, i.e., to remove it is to jump straight to classical semantics. We show (i) why semantic holism is plausible and (ii) why it is nevertheless false. And (iii) we pose a series of questions concerning the number of possible steps or jumps between the indeterminate semantics given by VAL snt and classical semantics given by VAL nrm
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References found in this work BETA
Gerald J. Massey (1981). The Pedagogy of Logic. Teaching Philosophy 4 (3/4):303-336.
Citations of this work BETA
Panu Raatikainen (2008). On Rules of Inference and the Meanings of Logical Constants. Analysis 68 (300):282-287.
James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.
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