Cesare Cozzo

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.

The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. In sections 5 and 6 I discuss some problems arising with regard to Prawitz’s views.

What is the role of a notion of truth in our form of life? What is it to possess a notion of truth? How different would we be, if we did not possess a notion of truth? Gulliver’s description of three peoples encountered during his fifth travel will help me to answer. One might say that the basic anti-realist tenet is that we should explain the notion of truth by connecting it with our practice of assertion. In this sense the outcome of my commentary of the fifth part of Gulliver’s Travels will amount to a non-reductive anti-realist conception of truth. It can be called a dialectical conception of truth because it focuses on a particular way of resolving disagreements: an epistemically virtuous practice of verbal exchange that cares for truth. The main thesis is that an implicit awareness of the epistemically virtuous practice is a necessary condition for being in full possession of the notion of truth. The commentary will also involve an argument against deflationism and a critique of some claims made by Huw Price.