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Semantic Holism

Nuel D. Belnap Jr. and Gerald J. Massey
Studia Logica: An International Journal for Symbolic Logic
Vol. 49, No. 1 (Mar., 1990), pp. 67-82
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015479
Page Count: 16
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Semantic Holism
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Abstract

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 'v' 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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