[73] Cours, I, 128-9. [74] Cours, III. 642. [75] Pol. pos. II. 427. [76] Pol. pos. 431. [77] Cours, VI. 690. [78] Pol. pos. I. 588. [79] Pol. pos. II. 30. [80] Cours, XI., 740-46; Pol. pos., I, 494-5. [81] Pol. pos., IV., 173-80. [82] Pol. pos., II. 33. CHAPTER VI SCIENCE (CONTINUED)--POSITIVE LOGIC Logic, says Comte, almost in the terms of Descartes, is the sole portion of ancient philosophy which is capable of still presenting some appearance of utility.[83] And does even this appearance correspond to a very solid reality? If we distinguish, according to custom, formal logic from applied logic, Comte in his system will find no place for the former, which establishes _a priori_ the principles and the mechanism of reasoning. As to the principles, which are the laws of the understanding, positive philosophy has shown that the only way to discover them is to study the products of the human intellect, that is to say, the development of the sciences. And it is again from these sciences that, through observation, the theory of reasoning must be drawn. Formal logic, as metaphysicians have constructed it, especially develops the dialectical faculty, that is to say, an aptitude more harmful than useful, for proving without finding.[84] Descartes said the same, in speaking of the syllogism, that it serves more for explaining to others the things which we know, than to discover those which we ignore. All the utility which we can attribute to the study of logic properly so-called is found again more extended, more varied, more complete, more luminous, in mathematical studies. The mechanism of reasoning is everywhere the same. Whatever may be the phenomena which are the objects of a science the nature of deduction and induction never changes in them. Thus in practising these forms of reasoning in the most simple and the most general phenomena, those whose science is most advanced, we learn to know them with the most entire evidence, and in all the generality of which they are capable. Nowhere is reasoning so exact, so rigorous as in mathematics. They accustom the mind not to feed upon false reasons, and it is in that school that men ought to learn the theory and the practice of reasoning. But, if the old pure logic is thus replaced by mathematics, must we not at least preserve the general study of the processes used in the various sciences, which is called methodology? Has not Comte himself insisted upon the irreducibleness of the several orders of laws to one another, and in particular to the mathematical laws? Is not the legitimate object of logic to define the processes of investigation and of proof particular to each of the fundamental sciences?