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      Review of Jevons’s Pure Logic

      Pure Logic, and Other Minor Works. By W. Stanley Jevons. Edited by Robert Adamson and Harriet A. Jevons. Macmillan & Co. 1890.

      Though called Minor, these are scientifically Jevons’s most important writings. As when they first appeared, they impress us by their clearness of thought, but not with any great power. The first piece, “Pure Logic,” followed by four years De Morgan’s Syllabus of Logic, a dynamically luminous and perfect presentation of an idea. In comparison with that, Jevons’s work seemed, and still seems, feeble enough. Its leading idea amounts to saying that existence can be asserted indirectly by denying the existence of something else. But among errors thick as autumn leaves in Vallambrosa, the tract contains a valuable suggestion, a certain modification of Boole’s use of the symbol + in logic. This idea, directly suggested by De Morgan’s work, soon presented itself independently to half-a-dozen writers. But Jevons was first in the field, and the idea has come to stay. Mr. Venn is alone in his dissent.

      The substance of the second piece in this volume, “The Substitution of Similars,” is in its title. Cicero had a wart on his nose; so Burke would be expected to have something like it. This is Mill’s inference from particulars to particulars. As a matter of psychology, it is true the one statement suggests the other, but logical connection between them is wholly wanting. The substitution of similars might well be taken as the grand formula of bad reasoning.

      Both these tracts warmly advocate the quantification of the predicate—that it is preferable in formal logic to take A = B as the fundamental form of proposition rather than “If A, then B,” or “A belongs among the Bs.” The question is not so important as Jevons thought it to be; but we give his three arguments with refutations. First, he says the copula of identity is logically simpler than the copula of inclusion. Not so, for the statement that “man = rational animal” is equivalent to a compound of two propositions with the copula of inclusion, namely, “If anything is a man, it is a rational animal,” and “If anything is a rational animal, it is a man.” True, Jevons replies that these propositions can be written with a copula of identity, A = AB. But A and B are not symmetrically situated here. They are not simply joined by a sign of equality. Second, Jevons says that logic takes a more unitary development with the proposition of identity than with that of inclusion. He thinks his doctrines of not quantified logic and the substitution of similars call for this copula, but this is quite an error. And then an inference supposes that if the premises are true, the conclusion is true. The relation of premises to conclusion is thus just that of the terms of the proposition of inclusion. Thus the illative “ergo” is really a copula of inclusion. Why have any other? Third, Jevons holds the proposition of identity to be the more natural. But, psychologically, propositions spring from association. The subject suggests the predicate. Now the difficulty of saying the words of any familiar thing backwards shows that the suggesting and suggested cannot immediately change places.

      The third piece in the volume describes Jevons’s logical machine, in every respect inferior to that of Prof. Allan Marquand, and adequate only to inferences of childish simplicity. The higher kinds of reasoning concerning relative terms cannot (as far as we can yet see) be performed mechanically.

      The fourth paper advocates the treatment of logic by means of arithmetic—without previous logical analysis of the conception of number, which would call for the logic of relatives. To exhibit the power of his method, Jevons shows that it draws at once such a difficult conclusion as this: “For every man in the house, there is a person who is aged; some of the men are not aged. It follows, that some of the persons in the house are not men.” Unfortunately, this is an exhibition not of the power of the method, but of its imbecility, since the reasoning is not good. For if we substitute for “person,” even number, for “man,” whole number, for “aged,” double of an integer, we get this wonderful reasoning: “Every whole number has its double; some whole numbers are not doubles of integers. Hence, some even numbers are not whole numbers.”

      The remainder of the book is taken up with Jevons’s articles against Mill, which were interrupted by his death. The first relates to Mill’s theory of mathematical reasoning, which in its main features is correct. The only defect which Jevons brings out is, that no satisfactory mode of proving the approximate truth of the geometrical axioms is indicated. But this

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