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

If nowadays categories seems to cover a multitude of different enquiries, we can see some continuity and coherence among them, and we can get some sense of what the subject is, by going back to the first treatise to receive the name, the Categories of Aristotle. The scheme of categories worked out by Aristotle in that book was used by him in subsequent works to solve a variety of problems. On one plausible hypothesis, Aristotle’s scheme was partly shaped by ontological considerations. However, one can construct categorial schemes that are free of ontological assumptions, and I call such schemes and the principles on which they are constructed “pure.” A purified Aristotelian scheme is one of a multiplicity of categorial schemes that can be generated by a sufficiently general pure categorial principle. In the penultimate section of this paper I consider a useful scheme, generated in this way, that categorizes the elements of our discourse about discourse. This links up with J. L. Austin’s discussion of the nature of illocutionary acts and throws light on the interconnections between such problematic notions as sentence, meaning, and proposition.

Our interpretation of the "parmenides" 132a1 - 132b2 has the following features. (i) it stresses that the third man argument is an infinite regress and (ii) notes its epistemological thrust. (iii) a faithful translation of the last line of the argument reads "and no longer will each of the forms be for you one but each is infinite in multitude." parmenides' point is that each form, which socrates believed to be complete (one), turns out to be an unbounded, incompletable series of subforms useless for comprehending the unity of many particulars. (iv) related problems are seen to occupy plato in the "philebus" and in the "sophist"

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).

The author recommends an involved study of logical fallacies in order to provide a database of testable hypotheses for error reasoning. The purpose of the study is to make the study of logical fallacies accessible to a wider audience. Following a recent study conducted by Ludwig Schlecht, the author presents a diagnostic method to illustrate how an argument can be fallacious from the breach of particular rational principles. The diagnosis method also serves as investigation into other forms of argumentative fallacies and the author suggests it could later be the basis for training programs for undergraduate students in logic courses.