Antonio Piccolomini d´Aragona: Objects, acts and traces: a comparison of Prawitz's and Sundholm's semantics

Organized by the Department of Logic

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Antonio Piccolomini d´Aragona (Institute of Philosophy, CAS):
Objects, acts and traces: a comparison of Prawitz's and Sundholm's semantics

Abstract

In a seminal paper from 1998, Göran Sundholm has tried to convince Dag Prawitz that a semantic theory of deduction had better employ three notions of proof: proof-object, proof-act and proof-trace. Proof-objects are abstract truth-makers for propositions; as such, they are devoid of epistemic content. Proof-acts are demonstrations used to justify assertions; therefore, they are epistemic in nature. Proof-traces reify proof-acts, so they are objects too; in spite of this, however, they carry epistemic force, as one can use them as "recipes" for performing the proof-acts they describe. In the beginning, Prawitz was sceptical that Sundholm’s distinction was actually needed. In fact, in Prawitz’s earlier semantics of valid arguments, the three notions can be seen to collapse into each other. This collapse, however, results in a number of circularity and decidability problems. To solve these problems, Prawitz’s later theory of grounds introduces an objects-acts-traces distinction reminiscent of that put forward by Sundholm. This notwithstanding, Prawitz’s ground-theoretic picture retains many significant peculiarities. These mainly concern the way objects, acts and traces relate to each other, and the epistemic status assigned to proof-objects. In my talk, I aim to provide an overview and comparison of Prawitz’s and Sundholm’s semantics, and I argue that the divergences between the two stem from a difference in how Prawitz and Sundholm respectively conceive of the notion of assertion.