Cases of Knowing a Rule and Concepts

This weekend, avoiding some other things I probably should have been doing, I re-read part I of the Philosophical Investigations. Some weeks previously I read the Tractatus, and the same thing struck me both times: just how little Wittgenstein is a soup-to-nuts metaphysician, and how unsuitable his work is for generalizing beyond the very specific problems he sets himself in the philosophy of logic and philosophy of mind. That being said, I’m going to try with a feature of Wittgenstein’s discussion of rule-following in the Investigations which is little-remarked-upon. As is well-known, in the middle of part I Wittgenstein rejects what seems to be an intuitive understanding of how human beings follow rules in, e.g., continuing numerical series; he holds that following a rule is to engage in a practice, rather than have an infinitely extensible prototype of the rule’s applications.

What commentators pay relatively little attention to is one of the options Wittgenstein rejects: that to be able to continue a mathematical series is to have an idea of its algebraic equation. He argues that a would-be calculator may have an idea of the equation for a series and yet be unable to produce the series, while someone who has an intuitive grasp of the rule can produce the series without having an explicit understanding of the equation that “produces” it. This point about the adequacy of a rough-and-ready understanding dovetails nicely with another neglected point at the beginning of the book. In dismissing the project of discerning “logical form” so central to the Tractatus, Russell, and Frege, Wittgenstein argues that one of the failings of understanding language by assimilating words to the tractable form of the proper name is that this falsifies, not only the practice of using the word grammatically, but also the thought which is actually associated with it. Since the majority of the Investigations is very hard on the use of mental states to conceptualize understanding, this early attention to language and thought has gone unnoticed.

These two facets of Wittgenstein’s work, taken together, suggest a program for the philosophy of mind which is moderately “anti-logocentric”: if it is wrong to understand the use of concepts by appeal to logic, because this falsifies the actual habits of mind, we not only need to ensure that mental processes are instantiable either in familiar domains or in only never-never-land. Additionally, the surveying of human beings’ grasp of the world in understanding (Wittgenstein later uses “grammar” in a more positive sense to describe this) must form an unprejudiced basis for thinking of the capacities we attribute to the human mind and the “mechanisms” by which they operate. For example, consider the concept. Today it is no longer the function from extensions to truth-values that Frege described: we attribute concepts to the “realm of sense”, and attempt to describe their enabling of general thought in terms compatible with what we learn from the most trustworthy cognitive science.

But according to Wittgenstein, balance is not enough: if we prejudice the operations of concepts by understanding them as “intensional”, we would be leaving the sober analysis of mind for an unfortunately “metaphysical” consideration of the forms by which we represent thought. It seems to me that Wittgenstein is provocatively saying that this, which many today understand as the primary task of the “philosophy of thought”, is not enough if we want to truly understand the mind and language.