Laurence Goldstein

(1947 - 2014)

The Russell class does not exist because the conditions purporting to specify that class are contradictory, and hence fail to specify any class. Equally, the conditions purporting to specify the Liar statement are contradictory and hence, although the Liar sentence is grammatically in order, it fails to yield a statement. Thus the common source of these and related paradoxes is contradictory (or tautologous) specifying conditions-for such conditions fail to specify. This is the diagnosis. The cure consists of seeking and destroying the deep-seated preconceptions that make almost irresistible our belief in the existence of items which provably do not exist

The general aim of this project is to fundamentally re-think the design of teaching materials in view of what is now known about cognitive deficits and about what Howard Gardner has termed ‘multiple intelligences’. The applicant has implemented this strategy in two distinct areas, the first involving the writing of an English language programme for Chinese speakers, the second involving the construction of specialized equipment for teaching elementary logic to blind students. The next phase is to test the effectiveness of the logic device, because in theory – the one to be tested – materials the design of which is informed by the above rationale will provide a richer learning experience for non-impaired users.

The views on contradiction and consistency that Wittgenstein expressed in his later writings have met with misunderstanding and almost uniform hositility. In this paper, I trace the roots of these views by attempting to show that, in his early writings, Wittgenstein accorded a ?unique status? to tautologies and contradictions, marking them off logically from genuine propositions. This is integral both to his Tractatus project of furnishing a theory of inference, and to the enterprise of explaining the nature of the Satz (statement, proposition). Wittgenstein mantained that contradictions are not false. In his early writings this surprising thesis is a consequence of his view that contradictions are not statements. In his late writings he continues to advocate the thesis, but for quite different reasons. In these late writings, I contend, Wittgenstein succeeds in making the surprising thesis plausible

In a well-known story constructed by Saul Kripke , Pierre, a rational but monolingual Frenchman who has never visited England, acquires, on the evidence of many magazine pictures of London, the belief that London is beautiful. He is happy to declare ‘Londres est jolie’. Pierre eventually moves to England and settles in one of the seedier areas of London, travelling only to comparably shabby neighbourhoods. He learns English by immersion, though he does not realize that ‘London’ and ‘Londres’ are co-referential. Naturally enough, given his current circumstances, he acquires a belief that he is only too willing to express by uttering ‘It is not the case that London is beautiful’. So apparently he now holds contradictory beliefs. But rational people do not hold contradictory beliefs ….One popular response to Kripke's puzzle is that people …

It is uncontroversial that, on any run through a Sorites series, a subject, at some point, switches from an ‘F’ verdict on one exhibit to a non-‘F’ verdict on the next. (Where this ‘cut-off’ point occurs tend to differ from trial to trial.) It is a fallacy to infer that there must be a cut-off point simpliciter between F items and non-F items. The transition is from firm ground to swamp. In the Sorites reasoning, some conditionals of the form ‘If Item n is F, then Item n + 1 is F’ are not false but nonsensical. This solution respects boundarylessness