Laurence Goldstein

(1947 - 2014)

Upon discovering that the place he is now calling 'London' and deprecating as unlovely is the same town as the one that he had previously been calling 'Londres' and extolling as 'jolie', what would Pierre do? If he is wise, he would castigate himself for rashly jumping to premature conclusions on the basis of insufficient evidence. But his evidence is as strong as that of his Parisian friends who also judged Londres jolie, and of his new London neighbors who rate their town not beautiful. All this shows is that they too (and we too) should be more circumspect when forming beliefs. It reflects poorly on the human race that we generally don't.

I published in Philosophy a play re-creating Wittgenstein's viva. Although the play is based on the historical 1929 viva, in this recreation, Wittgenstein receives a proper grilling from his examiners, Bertrand Russell and G.E.Moore, and they end up failing him for insufficient defence of the main theses of the work and for lack of originality. The play came in for some foolish and dishonest criticism by Michael Cohen and, in this paper, I respond to that but, more importantly, illustrate the originality of Wittgenstein's later work by contrasting that with the Tractatus, much of which was derivative.

Logicism is one of the great reductionist projects. Numbers and the relationships in which they stand may seem to possess suspect ontological credentials - to be entia non grata - and, further, to be beyond the reach of knowledge. In seeking to reduce mathematics to a small set of principles that form the logical basis of all reasoning, logicism holds out the prospect of ontological economy and epistemological security. This paper attempts to show that a fundamental logicist project, that of defining the number one in terms drawn only from logic and set theory, is a doomed enterprise. The starting point is Russell's Theory of Descriptions, which purports to supply a quantificational analysis of definite descriptions by adjoining a uniqueness clause' to the formal rendering of indefinite descriptions. That theory fails on at least two counts. First, the senses of statements containing indefinite descriptions are typically not preserved under the Russellian translation. Second (and independently), the uniqueness clause' fails to trim 'some' to 'one'. The Russell-Whitehead account in Principia Mathematica fares no better. Other attempts to define 'one' are covertly circular. An ontologically non-embarrassing alternative account of the number words is briefly sketched.

Although he toyed with the idea that contradictions in mathematics are harmless, Wittgenstein did not subscribe to the claim that they are true. He took the highly distinctive line that contradictions are neither true nor false, a view he defended early and late. He argued that contradictions are not statements and hence are not in the true/false game; this appears to be Aristotle's view too. This chapter considers a variety of paradoxes, including the Barber, Russell's paradox, Catch-22, the lawyer paradox involving Protagoras and Euathlus, the paradox of the stone, the Liar and Yablo's paradox. What the examination of these paradoxes reveals is that a satisfyingly unified treatment of them can be had if we have in place a principled denial of the assumption that contradictions and biconditionals of the form _p_, if and only if not-_p_ are necessarily false. It is the latter that Wittgenstein supplies.

Logicism is one of the great reductionist projects. Numbers and the relationships in which they stand may seem to possess suspect ontological credentials – to be entia non grata – and, further, to be beyond the reach of knowledge. In seeking to reduce mathematics to a small set of principles that form the logical basis of all reasoning, logicism holds out the prospect of ontological economy and epistemological security. This paper attempts to show that a fundamental logicist project, that of defining the number one in terms drawn only from logic and set theory, is a doomed enterprise. The starting point is Russell's Theory of Descriptions, which purports to supply a quantificational analysis of definite descriptions by adjoining a 'uniqueness clause' to the formal rendering of indefinite descriptions. That theory fails on at least two counts. First, the senses of statements containing indefinite descriptions are typically not preserved under the Russellian translation. Second (and independently), the 'uniqueness clause' fails to trim 'some' to 'one'. The Russell–Whitehead account in Principia Mathematica fares no better. Other attempts to define 'one' are covertly circular. An ontologically non-embarrassing alternative account of the number words is briefly sketched.