Volume 2: Elements of Logic. Book 1: General and Historical Survey of Logic Chapter 1: Critical Analysis of Logical Theories †1 §1. Logic's PromisesP 1. Begin, if you will, by calling logic the theory of the conditions which determine reasonings to be secure. A conception at once more exact and more extended may be looked for in the sequel. †2 Meantime, this description will serve for our preparatory studies of the yet unvisited country into which we propose to push our explorations. Logic, then, is a theory. The end of any theory is to furnish a rational account of its object. A theory directly aims at nothing but knowing. Maybe, if it be sound, it is likely, some day, to prove useful. Still, fairness forbids our making utility the criterion of the excellence of the theory. One must acknowledge that such a way of thinking would not abase logic, as it does the generality of the sciences. To judge of logic by its applications would only be to judge of it by how far it does, or does not, in a certain manner, help us to understand things. Clearly, it is the proper aim of any theory to do that. Looking at the matter on the other side, this very consideration tends to show that the touchstone of utility is superfluous and impertinent for logic. Suppose the science supports the test; what then? That would merely show that it aids the understanding. Grant that it is a sound theory, and it must have been prepared to do that, application or no application. 2. From this point of view, we can see that logic may be useful, apart from any direct application, by supplying us with modes of conception which are useful. There are few theories, if any, of which this is equally true. 3. For the most part, theories do little or nothing for everyday business. Nobody fit to be at large would recommend a carpenter who had to put up a pigsty or an ordinary cottage to make an engineer's statical diagram of the structure. In particular, applications of theories would be worse than useless where they would interfere with the operation of trained instincts. Who could play billiards by analytic mechanics? We all have a natural instinct for right reasoning, which, within the special business of each of us, has received a severe training by its conclusions being constantly brought into comparison with experiential results. Nay, we not only have a reasoning instinct, but as I shall early show, †1 we have an instinctive theory of reasoning, which gets corrected in the course of our experience. So, it would be most unreasonable to demand that the study of logic should supply an artificial method of doing the thinking that his regular business requires every man daily to do. 4. Still, I repeat it, it is not in questions closely concerning a man's business that he can with any semblance of fairness look to finding the theory of reasoning helpful. †2 Such help is rather to be expected in extraordinary and unusual problems—especially in those of a speculative character, where conclusions are not readily checked by experience, and where our instinctive reasoning power begins to lose its self-confidence; as when we question what we ought to think about psychical research, †3 about the Gospels, about difficult questions of political economy, †4 about the constitution of matter; †5 or when we inquire by what methods we can most speedily advance our knowledge of such matters. †6 5. But, as I said before, were direct applications of logic, such as these, never useful, instead of being frequently so, as they are, yet its indirect utility, through the useful conceptions with which it supplies us, would be immense. 6. Meantime, its highest and greatest value is that it affords us an understanding of the processes of reasoning. That the Platos are thoroughly right in that estimate will be more and more impressed upon our convictions as our acquaintance with the science grows. 7. On the other hand, we shall find reason to maintain, with Auguste Comte, that a theory cannot be sound unless it be susceptible of applications, immediate or remote, whether it be good economy so to apply it or not. †1 This is perhaps no more true of logic than of other theories; simply because it is perfectly true of all. Yet there is a special reason why it is more important to bear this point in mind in logic. Namely, logic is the theory of right reasoning, of what reasoning ought to be, not of what it is. On that account, it used to be called a directive science, but of late years Überweg's adjective normative †P1 has been generally substituted. It might be that a normative science, in view of the economies of the case, should be quite useless for any practical application. Still, whatever fact had no bearing upon a conceivable application to practice would be entirely impertinent to such a science. It would be easy enough—much too easy—to marshal a goodly squadron of treatises on logic, each of them swelled out with matter foreign to any conceivable applicability until, like a corpulent man, it can no longer see on what it is standing, and the reader loses all clear view of the true problems of the science. But since the relation of the theory of logic to conceivable applications of it will, by and by, come up for closer examination, we need not now consider it further. §2. Of Minute AccuracyP 8. How shall the theory of right reasoning be investigated? The nature of the subject must be an important factor in determining the method. Before touching that, however, suppose we ask how, in the roughest sense, any theory ought to be investigated. Am I wrong in thinking I catch a whisper from good sense, that, for one item of the reply, a theory should be investigated carefully and minutely? Yet, strange to say, such a recommendation would be in flat contradiction to prevailing opinion. A month does not pass, scarce a fortnight will pass, without my attention being drawn to some new discussion by a man of strength relating to some broad, far-reaching question of science or philosophy. Every such dissertation will be sure to refer to principles of reasoning which are more or less contested. Upon the correctness of these the whole question hinges. How, then, do I find these logical principles are sought to be established? By the same severe and minute examination which the same author would approve in regard to a question of physics? Never: I am very sure he would condemn such piddling minuteness as inappropriate to so broad a question. He proceeds slap-dash, depicting the logical situation as in a blackboard diagram rather than as in a critically accurate anatomical plate. For the most part, he has but the vaguest notion of how he has come by his principles. He has gathered them casually, after the custom of amateurs. It might seem to behoove every man who has occasion to lay down principles of reasoning in a grave scientific discussion to be more than an amateur in logic. Voluminous writers, however, on logic there are who deliberately adopt vague substitutes for any definite method of establishing principles of reasoning. 9. When I was beginning my philosophical reading, my father, Benjamin Peirce, †1 forced me to recognize the extremely loose reasoning common to the philosophers. It was a matter open to the remark of every mathematician even before Weierstrass, when mathematical reasoning was far less strict than it has since become. The more recent philosophers certainly show an improvement in this respect. The metaphysics of our best contemporaries lacks but little of the rank of a science; but logical criticism has also grown more searching, and you may search the whole library of modern metaphysics from Descartes to the most accurate metaphysical reasoners †1 of today and hardly find a vital argument of an elaborate and apodictic kind that does not leave room to drive a coach and four through it. †1 10. The effect upon the minds of those who have been nourished on such food mainly, becomes deplorably patent to everybody who finds himself in contact with them. Their natural sense of logic is enfeebled and diseased. I am confident I detect something of this even in the majority of those young men who become known to me as only having paid particular attention to philosophy in the universities; although there are some whose logical instincts have been too robust to be so easily debilitated. 11. The Greek philosophers could not be persuaded that minute analysis was proper in physical science. Born Hegelian sensualists, they could not divest themselves of their belief that no worse way of getting at any comprehension of a flower could be devised than beginning by picking it to pieces, and so spoiling the flower. What was the result? Manifold have been the theories that have been successively offered, considered, and rejected, to account for the non-success of the Greeks in physics. That the vast intellect of an Aristotle, so great in zoölogy, in the science of politics, in rhetoric, in the history of philosophy; so gigantic in ethics, logic, metaphysics, and psychology, should, in physics, have sunk into abject inferiority to the cranks of modern times, the refuters of Newton, the proposers of perpetual motions, has hitherto not been adequately explained. What better account of the matter could one desire than that in physics the Hellenic element of Aristotle's nature—that Greek estheticism which forbade analysis and required that the phenomenon should be contemplated in its concreteness—here governed him? That this was the cause is shown by the fact that all the other Greeks who shared the same prejudice were equally unsuccessful; while the few who did not share it, Hipparchus, Eratosthenes, Posidonius, Ptolemy, Archimedes, were eminently successful in the physical sciences.