Customer Reviews

A Preface to Logic

5 star:		(2)
4 star:		(0)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

PtL is a rigorous and thoughtful introduction to a fascinating subject: logic. It is a series of essays (best read together, in my view) on the various uses (and abuses) of logic in the sciences and philosophy. Though addressed, by and large, to a readership at least somewhat familiar with major trends in modern philosophy, PtL is more than accessible to an interested (and persistent) novice. It is an expository gem, a model of lucid argumentation and writing. I recommend PtL highly.

Although Cohen was unrivaled in contemporary American philosophy for the diversity of the subjects with which he occupied himself, it is from logic that he draws the basic principles that enable him to survey so wide a domain with such a unity of view. Early in life, through the study of Russell's Principles of Mathematics, he became convinced of the reality of abstract or mathematical relations. That pure mathematics asserts only logical implications and that such logical implications or relations cannot be identified with either psychological or physical events, but are involved as determinants of both, seemed to him to offer a well-grounded and fruitful starting point for philosophy. It at once ruled out for him the empiricism of Mill, since relations if they exist in the mind only cannot connect things external to the mind; it also ruled out for him the Hegelian effort to locate relations in an absolute totality that is beyond human understanding and therefore of no explanatory value. On the positive side the doctrine, since it constitutes a ground for the procedures of scientific method generally, permitted him to take full advantage of the remarkable developments of modern scientific thought. It led him also to return to what constituted the concern of classical philosophy before it became preoccupied with the problem of knowledge--mathematics, physics, biology, psychology, ethics, law, art, and religion. In philosophy proper it enabled him in the course of his extensive writings to raise almost every metaphysical question of importance and it re sulted in the composition of his book Reason and Nature, one of the few inexhaustible philosophical volumes written in America.

When the second edition of Russell's Principles of Mathematics appeared in 1938 Russell pointed out that the Pythagorean numerology

". . . has misled mathematicians and the Board of Education down to the present day. Consequently, to say that numbers are sym bols which mean nothing appears as a horrible form of atheism. At the time when I wrote the Principles, I shared with Frege a belief in the Platonic reality of numbers, which, in my imagina tion, peopled the timeless realm of Being. It was a comforting faith, which I later abandoned with regret."

Many of the disciples, however, refused to give up the faith and have busily defended the doctrines of the first edition against those of the second. Cohen long before the appearance of the second edition had detected this shift in Russell's thought. He remarked that with the publication of the Principles Russell became his Allah, and that Mohammed has kept the faith even though Allah himself has perhaps somewhat departed from it. Perhaps no more bitter controversy has been engendered in the mathematico-logical field than the dispute touched upon briefly by Russell in the passage quoted above. "What is all this frog-and-mouse battle among the mathematicians about?" even Einstein paused to ask. Its ramifications were extensive, and the militancy of contemporary logical positivism is current evidence that the questions still evoke strong partisanship.

Cohen in the present volume pays his respects once again to this and numerous other controversial matters, related more to the metaphysical foundations of logic than to the traditional technical themes. Logic, for him the most general of all the sciences, attempts to isolate the elements or operations common to all of them. From this it follows that the laws of logic have no contraries which possess meaning or are applicable to any possible determinate object, a condition which is not true of the special sciences, the systems of which have contraries which are abstractly possible. Cohen's view is that the distinctive subject matter of logic is formal truth, that such truth is concerned with the implication, consistency or necessary connection between objects asserted in propositions, the relations generally expressed by if--then necessarily. This conception of the subject matter of logic, although it is an accurate description of the basic content of the classical Aristotelian logic, has many assailants. In fact it is argued today, so unsettled is the whole matter, that there is no ground for asserting that logic has any subject matter.

Against such a delimitation of the subject matter of formal logic as that attempted by Cohen the objection is offered that it is a deduction from a particular philosophy, and that the field of logic should not be determined by such partial considerations. Cohen's position avowedly is an expression of his philosophy of logical realism. But since his conception of logic can be deduced from many philosophies, although not all the interpretations which Cohen puts upon the various logical doctrines can be so deduced, the validity of the conception should be judged by other considerations. If a true philosopher is one who has grounds for his belief, then Cohen assuredly, in the present case, qualifies for that distinction; however, since a true conclusion can follow from a false premise his understanding of logic is not undermined by a disproof of his philosophy. The argument that there is no ground in the present condition of logical knowledge to hold that logic has a distinctive subject matter, is an admonition of caution, and as such undoubtedly has merit. But in the absence of the construction of a non-Aristotelian logic, in which the contraries of the principles of contradiction and excluded middle are assumed to be true, and from which valid inferences can be drawn, we may assume that logical truths have been discovered, and that their study is the subject matter of logic.

Notwithstanding the fact that Cohen's emphasis is upon the abstract qualities of logic, he has always been careful to disassociate himself from logical positivism, which maintains that formal logic deals with linguistic expressions without any reference to sense or meaning. This attitude of the logical positivists is a development of Hubert's formalism, according to which mathematics is a game played according to simple, definite rules with meaningless marks on paper. Mathematics is held to be comparable to a game of chess. It is said that chess players do not ask what a particular game "means," although at some future day the game may acquire a meaning, if it should be interpreted in terms of law, economics or religion. However, the analogy is not strictly accurate, since today the result of a game of chess may mean that A is better than or equal to B in chess playing ability. In his application of Hubert's idea to logical inference Carnap uses the example of meaningless symbols: From "Pirots karulize elastically" and "A is a Pirot," we can infer that "A karulizes elatically," without knowing the meaning of the three words or the sense of the three sentences. Cohen denies that this is so. He points out that Carnap admits these are sentences only because we assume that "Pirots" is a substantive, "karulizes" is a verb (both of these terms being plural in the first sentence and singular in the others) and "elastically" is an adverb describing a way in which a process takes place.

"These expressions [Cohen writes] are therefore not entirely meaningless as would be undiluted gibberish. If instead of "Pirots" we put "the members of any class of objects" and instead of "karulize elastically" we put "are members of another class" we have as an inference that "a member of the first class is necessarily a member of the second class." And this I submit is the actual meaning which Professor Carnap's example suggests to anyone to whom the inference seems a valid one. This statement applies to all possible objects irrespective of any of their specific or differential traits but assuredly is not therefore entirely meaningless."

But is this Carnap's point? His position in fact is, that in order to determine whether or not one sentence is a consequence of another, no reference need be made to the meaning of the sentences; it is sufficient that the syntactical design of the sentences be given. Cohen seems to admit this when he grants that "A karulizes elastically" follows from the premises. Before he made that concession, surely it was not necessary for him to translate the nonsense words of Carnap's syllogism into his own meaningful sentences. Although Carnap's position is not answered by a demonstration that if a certain consequence is deducible from the manipulation of sentences possessing only a syntactical meaning, then a meaning otherwise than syntactical can be read into the sentences, it does point the way to the principal defect of the positivistic logic. All that Carnap says may be true, but we are still faced with the problem of giving language a material application. It is of the essence of language from the point of view of science that it communicate meaning with respect to matters which are true or false. If we start with, "If X, then Y," the problem is to arrive at, "If Socrates, then mortal," and not, "If Socrates, then immortal." If Carnap's conclusion that logic is nothing but syntax were true, logic would lose its scientific significance. Professor Carnap's effort to meet this problem through his method of ostensive definition reveals the real difficulties of his position.

Cohen's importance in contemporary thought is due as much to his application of the methods of science to problems of human existence as to his technical contributions to philosophy. Since Hegel he and Jordan were the only philosophers of standing who concerned themselves extensively with the problems of the legal ordering of society. Thus he rejects altogether the view that since science can deal only with the facts of existence, judgments of what ought to be are so arbitrary that no science of norms is possible. He insists that the essence of science consists of the formulation of hypotheses based upon the best available knowledge and anticipating new situations which can be experimentally tested so that greater determination can be achieved. He maintains that this procedure is open to ethics. An ethical system, he argues, can achieve the status of a scientific system if adequate hypotheses as to what is good or bad, or what is necessary in order to achieve certain ends, are developed. This position seems unassailable as far as it goes, but does it answer the real difficulty? It disposes of those who maintain that facts are the starting point of inquiry; but what of those who admit that facts are the ends to be achieved by inquiry, and who still deny the possibility of a science of ethics on the ground of the complexity of the subject matter or that of the ultimate irrelevance of ethical judgments to life on this earth? The hypothetico-deductive system has yielded extra ordinary knowledge of the physical world; but that process has been successful, in part at least, because of the ability of the physicist to simplify and deal only with ideal entities. Where the scientist has not been able to simplify he has failed, as in cancer research. We do not know if the method of simplification, i.e., the pursuit of the implications or effects of one single aspect or factor of a situation, is available in ethical inquiry in any significant sense, since the nature of human conduct may be such that it will not yield to that technique. Furthermore, since we see no ground for such action we do not today pass judgment on the goodness or badness of the universe, the evil ness of volcanic eruptions, or the practice of slavery among the ants. Whatever our preferences may be, Cohen's argument does not negative the possibility that ethical judgments of human conduct may be just as irrelevant as evaluations of the physical universe. This argument does not foreclose the possibility of a technology of ethics founded on unsystematized preferences and ends, in which normative judgments to that extent possess relevance. But a science of ethics demands as a prerequisite a determinate system, a condition which the complexities of conduct may make impossible.

Cohen's present volume is devoted, as can be seen from the foregoing, to an analysis of problems lying on the borderlines of logic, and not with the customary subject matter of the usual treatises. Since his writing is distinguished by an admirable clarity, his argument can be followed with ease by the intelligent reader. All the topics which he discusses are the subject of radical inquiry in philosophical circles. They embrace such matters as the nature of propositions, the theory of meaning and implication, the overlap of logical classes, fictions, the statistical view of nature, logic and the world order and a chapter on probability which is a valuable supplement to the discussion of the same topic in Reason and Nature. These topics may seem innocuous, but they harbor questions the analysis of which has led within recent years to actual assassination, and the framers of political programs have found it expedient to take official notice of them. As a whole the volume is one of the best existing statements in the field of logic of the point of view of that branch of American philosophy which deals with its subject matter through the methods of science.