Workshop Practice-based Philosophy of Logic and Mathematics

Workshop Practice-based Philosophy of Logic and Mathematics: Theme

Why a practice-based approach?



Traditionally, the philosophy of logic pays little attention to the actual practices of logicians. This is somewhat surprising: the works of Kuhn (1962), Latour (1999) and others have shown the relevancy of attending to actual scientific practices within the philosophy of the empirical sciences; this focus allows for an account of certain aspects of the empirical sciences that traditional approaches have difficulties dealing with, such as the actual patterns of scientific change, the tendentiousness of experiments etc. Moreover, in the philosophy of mathematics there is a growing tendency (albeit still less influential than more traditional approaches) to take mathematical practices into account in attempts to make sense of mathematics in all its aspects (for example, those working in the tradition of I. Lakatos).

But there is no hint of a similar pragmatic turn in the philosophy of logic. In fact, the logic that philosophers of logic talk about is all too often the logic of several decades ago, when (mathematical) logic was almost exclusively concerned with the foundations of mathematics, and first-order logic was seen as the quintessential (if not the only) logical system. In recent developments, however, logic is no longer only concerned with mathematics, but treats of a wide variety of topics at the interface with numerous other areas (computer science, game theory, decision theory, linguistics, cognitive science etc.); furthermore, several logical systems besides first-order logic are regularly used and studied. But these recent developments are not sufficiently taken into account within mainstream philosophy of logic.

It seems thus that it is high time to introduce a new possible line of research within the philosophy of logic, namely one that takes the actual practices of logic as a discipline as its starting point. The approach must not necessarily replace more traditional approaches; rather, it may offer yet another vantage point into what is after all an essentially human and social activity, the practice of logic. What do logicians do? How do they conduct their researches, individually and within the scientific community? How do they communicate with each other? Answers to these questions may offer new insights into the most fundamental issues that the philosophy of logic must address, such as: What is logic? What is logic about? Is there a common ground to the different activities that receive the label ‘logic’ at different times and places, or is it a mere case of equivocation? To address the matter of what logic is about, for example, the observation of what logicians actually talk about and deal with in their practices seems a more promising strategy than aprioristic definitions of what logic ought to be about.

A promising theoretical background for this approach is the oeuvre of L. Wittgenstein (see (Bloor 1983) for a general application of this framework). His investigations are fundamentally marked by an emphasis on (social) practices and activities, on observations of what people do and how they move about in the world (most notably but not exclusively in his Philosophical Investigations). Wittgenstein wrote extensively on logic and mathematics, and even though his (later) writings are often read as a forceful critique of logic as a general enterprise and as a defense of a conventionalist and skeptical view of (logical) knowledge, this interpretation seems to disregard the possibility that Wittgenstein may have been essentially trying to understand what the whole enterprise is about by looking at what is actually done under the heading of logic, and thus questioning the purported inexorability of such practices but not their intrinsic value. Now, this is precisely the core of the pragmatic, phenomenological approach to logic (i.e. based on the observation of actual practices) proposed here. Wittgenstein’s remarks on mathematics (in particular in his Remarks on the Foundations of Mathematics) may be particularly helpful to set up a similar approach to logic, given the strong connection between these two disciplines.

The workshop ‘Practice-based approaches to logic and mathematics’ is intended to enable philosophers, logicians and mathematicians (possibly sociologists as well) to discuss the fruitfulness and viability of this approach. The focus will not be exclusively on Wittgenstein’s philosophy of logic and mathematics as such (even though it remains an important source of inspiration), but rather on a general approach that emphasizes actual practices and activities within logic and mathematics. Within the philosophy of mathematics this approach already has a certain standing, so the practice-based approach to mathematics can serve as a starting point for the development of a practice-based approach to logic. It is to be hoped that the talks and discussions at the workshop will clarify what such an approach would consist of, what it can accomplish, its underlying methodology etc., and thus that the workshop may set the agenda for a new line of research.