As previously reported, I will be in St. Andrews at the beginning of April to attend a workshop on paradox and logical revision, and to deliver a talk at Arché in the context of the Foundations of Logical Consequence project. The title of my talk there is the same as the title of this post, 'The myth of the pre-theoretical notion of logical consequence', and is very much related to some of the things I was talking about in my post on proofs and dialogues this week. I've just written a tentative abstract for the talk, and I thought it might be interesting to share it with people here and see what you all think. So, as usual, comments are much appreciated!
The myth of the pre-theoretical notion of logical consequence
Catarina Dutilh Novaes
The concept of a pre-theoretical or intuitive notion of logical consequence has played a crucial role in discussions on logical consequence, in particular in Tarski’s seminal 1936 paper and Etchemendy’s (1990, 2008) criticism of the Tarskian account of logical consequence. Tarski attempted to capture the main features of what he refers to as the ‘everyday’ notion of logical consequence (in the 2002 translation) in his condition of material adequacy (F). Etchemendy famously claimed that the Tarskian account failed to capture the ‘intuitive notion’ of logical consequence, but he was not sufficiently clear on what this intuitive notion would be (as noted by (Shapiro 1998)). Shapiro (2005) and Prawitz (2005) then went on to dig deeper in what appear to be the main features of the so-called pre-theoretical notion of logical consequence (henceforth, SCPTLC), and came up with a cluster of different, sometimes conflicting aspects. But they still seemed to take for granted the epistemic status of these notions as pre-theoretical.
In this talk, I argue that there is no such thing as a pre-theoretical notion of logical consequence, strictly speaking. Not only is the presupposition of uniqueness contentious, but more importantly, the notions in question are inherently couched in robust theoretical frameworks: that of inferential practices and theories within mathematics and logic (P. Smith (2010) and T. Smiley (1988) make similar points). To argue for the non-existence of SCPTLC, or in any case for the claim that what we usually take to be the pre-theoretical notion of logical consequence is not in any way pre-theoretical, I look into two obvious potential sources for this notion on a pre-theoretical level: the linguistic and the inferential practices of ordinary, untrained people. I argue that, in both cases, whether there is a sufficiently stable core is an inherently empirical question, not to be settled by philosophers from their armchair, and that some results emerging from empirical work in the psychology of reasoning (as reported in (Evans 2002)) strongly suggest that people’s linguistic and inferential practices differ significantly from the core features of SCPTLC. In particular, there is significant divergence among different speakers, suggesting that there is no such thing as a core class of arguments in natural language that we all agree to be ‘intuitively valid’. Moreover, the (untrained) inferential patterns that do emerge from these results point in the direction of a high level of non-monotonicity, while SCPTLC has necessary truth-preservation and monotonicity as some of its main components. (For these two claims, I rely essentially on (Stenning 2002) and (Stenning & van Lambalgen 2008).)
Thus, the question remains as to the actual sources for the emergence of SCPTLC. In the final part of the talk, I argue that the answer is to be found in the history of mathematics, logic and philosophy. To illustrate my claim, I propose an account of the development of the notion of necessary truth preservation against the background of the emergence of the deductive method in Ancient Greece (as reported in (Netz 1999)), and of the development of the notions of formality and invariance as core features of SCPTLC in terms of the history of applications of hylomorphism to logic (Dutilh Novaes forthcoming). In both cases, the frameworks in question are entirely theoretical, which leads me to conclude that it is a fundamental mistake to think of SCPTLC as a pre-theoretical notion. It may still be described as ‘intuitive’, if one wishes to do so, as long as it is clear that the intuitions in question are those of theorists, not of untrained people ‘on the street’.