De Morgan, Augustus. by G. L. FarreReview by: Alonzo ChurchThe Journal of Symbolic Logic, Vol. 40, No. 4 (Dec., 1975), p. 596Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2271798 .

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596 REVIEWS

J. A. LADRItRE. Axiomatic system. Ibid., pp. 1140-1141. This is an account of the ideas of Curry (e.g. in XVI 56, XXXVIII 149) about the axiomatic

method and the nature of mathematical and scientific theories. The statement of Godel's incompleteness theorem at the end of the article fits better here than elsewhere in the encyclo- pedia, since it comes after an explanation of the notions of a formalized deductive theory and of its "epitheory" (i.e., metatheory). ALONZO CHURCH

T. A K. KLOYDA. Bolzano, Bernhard. Ibid., vol. 2, p. 653. This is an excellent brief biographical article but is defective in omitting even to mention

Bolzano's Wissenschaftslehre (A171). ALONZO CHURCH

G. L. FARRE. Boole, George. Ibid., p. 701. This very brief article is in error in saying that Boole's logic "was a development and a

systematization of work begun by A. De Morgan"; on the contrary Boole's 191 and De Morgan's 201A were published in the same year and even (it is said) on the very same day. Also dubious is the statement in the article that "two major defects" of Boole's system are "the definition of disjunction as exclusive rather than inclusive and the absence of any well-defined concept of inclusion." As to the first of the two asserted defects, the author seems to be repeating an error which has recurred too often in the literature and appears once more in the article by Thomas reviewed below (XL 596). ALONZO CHURCH

G. L. FARRE. De Morgan, Augustus. Ibid., vol. 4, p. 760. In another very brief article there is an error in attributing to De Morgan laws which are

written as "ENKpqANpNq and ENApqKNpNq." Indeed De Morgan's name was later trans- ferred to these laws of propositional calculus, but De Morgan himself never considers propo- sitional calculus and his discovery is rather of the analogous laws of class calculus. It is also true that Ockham's introduction of these laws of propositional calculus (of course verbally stated) had been forgotten during the period of decline of logic, but the account in the article oversimplifies the relationship between the work of the two men. ALONZO CHURCH

G. L. FARRE. Frege, Gottlob. Ibid., vol. 6, p. 141. The article is in some ways good. But the content of Frege's Grundgesetze (4910,16) is seriously

misrepresented by failing to say that its main purpose is to carry out in rigorous detail the deti- vation of arithmetic from logic by the methods which had been discussed and described in the Grundlagen (495). (In 4916 there is further an unfinished treatment of real numbers on the same basis.)

Farre's article has also a terminological error in calling Russell's antinomy semantical, and what may be a historical error in wording which at least suggests that Russell first obtained the antinomy by studying 4910. As in Kiely's article reviewed below (XL 597), an " arithmetiza- tion of analysis" is attributed to Frege; the reviewer knows of no justification for this beyond the material just mentioned in the second volume of Grundgesetze. ALONZO CHURCH

H. A. NIELSEN. Linguistic analysis. Ibid., vol. 8, pp. 773-775. To a large extent this is a duplication of the article Analytical philosophy reviewed above,

but it adds some account of Peirce, Ogden and Richards, and Korzybski. ALONZO CHURCH

I. THOMAS. Logic, history of. Ibid., pp. 958-962. This is an excellent short historical article, valuable especially for its account of the ancient,

medieval, and post-Renaissance periods. There are nevertheless some errors, which demand correction all the more strongly because of the value of the article as a whole.

In the reviewer's opinion there is an unfortunate underestimate of Junge (or Jungius as his name appears on the title page of lII, XXXIII 139) when it is said of him, only that he "showed a deductive interest in the syllogism and some appreciation of Aristotle's logic of relations." Indeed one may not speak of "Aristotle's logic of relations" in the same sense as of (e.g.)

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