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.

According to some commentators, Wittgenstein’s Tractatus is all one big joke: we plough through the text trying to extract the sense out of each spare and heroic proposition, only to be told at the end, that anyone who understands the author will realize that all of his propositions are nonsensical and so are not even propositions. The whole work is a kind of hoax; the readers are ridiculed, but, with luck, will eventually have to laugh when they come to recognize that what they had taken for deep philosophy was all so much gibberish. As a result of this revelation, they will be cured for ever of the urge to philosophize.

Letting is a common practice in mathematics. For example, we let x be the sum of the first n integers and, after a short proof, conclude that x = n(n+1)/2; we let J be the point where the bisectors of two of the angles of a triangle intersect and prove that this coincides with H, the point at which another pair of bisectors of the angles of that triangle intersect. Karl Weierstrass's colleagues, in an attempt to solve optimization problems, stipulated that the minimum area for a triangle with a given perimeter be a straight line segment conceived as a triangle with zero altitude. (Weierstrass complained that this obscured the insight that some problems have no solutions.) In mathematics applied to physics, we let x be the temperature in Fahrenheit corresponding to 30° Centigrade; we let v be the velocity of the Earth through the luminiferous ether. Before the error was spotted, the official rules for Little League Baseball made an inconsistent stipulation about the dimensions of home plate (Bradley 1996).

For familiar reasons, stereotyping is believed to be irresponsible and offensive. Yet the use of stereotypes in humor is widespread. Particularly offensive are thought to be sexual and racial stereotypes, yet it is just these that figure particularly prominently in jokes. In certain circumstances it is unquestionably wrong to make jokes that employ such stereotypes. Some writers have made the much stronger claim that in all circumstances it is wrong to find such jokes funny; in other words that people who laugh at such jokes betray sexist/racist attitudes. This conclusion seems false. There is, as I shall argue, a thin dividing line between being properly sensitive to the rights and feelings of women and of racial groups different from our own, and being excessively sensitive to oversensitivity. Oversensitivity is, in this context, a kind of intolerance, and there is no reason why we should pander to that. One can be opposed to the unchecked dissemination of certain kinds of racist or sexist humor without oneself being a racist or sexist for finding such humor funny. The use of various stereotypes in humor serves the linguistic purpose of facilitating brevity and punch, the cultural purpose of preserving, in a sanitized form traditional rivalries and antipathies, and the psychological purpose of discharging fears. Blanket moral condemnation is inappropriate, though there will, of course, be circumstances under which the promulgation of certain types of humor, or even its enjoyment, ought to be condemned