Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

324 jeremy avigadto be had by exploring the relationships between such fundamental judgments,and unraveling problems that arise from confused or misguided applications ofthe terms.From the perspective of the Investigations, language is a community practice.It determines what can meaningfully be said, while the meaning of a wordor sentence is, reciprocally, determined by the way that word or sentencefunctions in the practice. On that view, meaning is closely linked with thepossibilities for use. Philosophical difficulties arise, however, when we try toexplain the relationship between the two.When someone says the word ‘cube’ to me, for example, I know what it means.But can the whole use of the word come before my mind, when I understand itin this way?Well, but on the other hand isn’t the meaning of the word also determinedby this use? And can these ways of determining meaning conflict? Can whatwe grasp in a flash accordwithause,fitorfailtofitit?Andhowcanwhatispresent to us in an instant, what comes before our mind in an instant, fit a use?(Wittgenstein, 1953, §139)The problem is that understanding is only made manifest in an infinite arrayof uses. The common philosophical tendency is therefore to distinguish thetwo, and take understanding to be ‘possession’ of a meaning that somehow‘determines’ the appropriate usage.Perhaps you will say here: to have got the system (or again, to understand it) can’tconsist in continuing the series up to this or that number: that is only applyingone’s understanding. The understanding itself is a state which is the source ofcorrect use. (§146)But Wittgenstein urges us against this way of thinking.If one says that knowing the ABC is a state of the mind, one is thinking of astate of a mental apparatus (perhaps of the brain) by means of which we explainthe manifestations of that knowledge. Such a state is called a disposition. But thereare objections to speaking of a state of mind here, inasmuch as there ought tobe two different criteria for such a state: a knowledge of the construction of theapparatus, quite apart from what it does ... (§149)The discussion in the Investigations aims to convince us that this last way offraming matters is problematic. For example, we may attribute someone’sability to continue a sequence of numbers correctly to the fact that he hasgrasped the right pattern. But substituting the phrase ‘grasping the correctpattern’ for ‘understanding’ is little more than word play, unless we say moreabout what has been ‘grasped’. The appropriate pattern may, perhaps, bedescribed by an algebraic formula, and so, at least in some cases, we may