Rivista di Filosofia 95 (1):63-92 (2004)

Cesare Cozzo
Università degli Studi di Roma La Sapienza
In spite of some objections voiced by Cora Diamond, the author agrees with Michael Dummett, who detects in Wittgenstein’s Remarks on the Foundations of Mathematics a denial of the objectivity of proof: Wittgenstein identifies being-a-proof with being-treated-as-a-proof. The denial of the objectivity of proof is implausible. But it seems to be a consequence of the rule-following considerations. After examining interpretations of the rule-following considerations advanced by Saul Kripke, Crispin Wright and John McDowell, an argument is exhibited, which starts from Wright’s interpretation and leads to the denial of the objectivity of proof. It is shown, however, that the argument contains at least two problematic steps and should be rejected. The result is that one can consistently adopt the view that meaning is «plastic» or «open» which stems from the rule-following considerations) without renouncing the objectivity of proof.
Keywords mathematical proof  objectivity  rule-following  meaning
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DOI 10.1413/12818
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