WITTGENSTEIN AND DEFINING CRITERIA

Let us introduce two antithetical terms in order to avoid certain elementary confusions: To the question “How do you know that so-and-so is the case?”, we sometimes answer by giving ‘criteria’ and sometimes by giving ‘symptoms. If medical science calls angina an inflammation caused by a particular bacillus, and we ask in a particular case “Why do you say this man has got angina?” then the answer “I have found the bacillus so-and-so in his blood” gives us the criterion, or what we may call the defining criterion of angina. If on the other hand the answer was, “His throat is inflamed”, this might give us a symptom of angina, I call “sympton” a phenomenon of which experience has taught us that it coincided, in some way or other, with the phenomenon which is our defining criterion, Then to say “A man has angina if this bacillus is found in him” is a tautology or it is a loose way of stating the definition of “angina”. But to say, “A man has angina whenever he has an inflamed throat” is to make a hypothesis. (BB, pp. 24–25)¹     

WITTGENSTEIN ON ACCORD*

Abstract: The paper deals with the interpretation of Wittgenstein's views on the power of occurrent mental states to sort objects or states of affairs as in accord or in conflict with them, as presented in the rule‐following passages of the Philosophical Investigations. I shall argue first that the readings advanced by Saul Kripke and John McDowell fail to provide a satisfactory construal of Wittgenstein's treatment of a platonist account of this phenomenon, according to which the sorting power of occurrent mental states is to be explained by reference to the mind's ability to grasp universals. I contend that the argument that Kripke extracts from Wittgenstein's discussion doesn’t succeed in undermining the platonist position. Then I argue that McDowell's reading exhibits a more serious shortcoming: the position that he ascribes to Wittgenstein is indistinguishable from the platonist account. Then I put forward a proposal as to how to articulate the relationship between Wittgenstein's views and the platonist position.     

WITTGENSTEIN AND STRONG MATHEMATICAL VERIFICATIONISM

Wittgenstein is accused by Dummett of radical conventionalism, the view that the necessity of any statement is a matter of express linguistic convention, i.e., a decision. This conventionalism is alleged to follow, in Wittgenstein's middle period, from his 'concept modification thesis', that a proof significantly changes the sense of the proposition it aims to prove. I argue for the assimilation of this thesis to Wittgenstein's 'no-conjecture thesis' concerning mathematical statements. Both flow from a strong verificationist view of mathematics held by Wittgenstein in his middle period, and this also explains his views on the law of excluded middle and consistency. Strong verificationism is central to making sense of Wittgenstein's middle-period philosophy of mathematics.