Philosophy of Logic (Anglais) Relié – 14 septembre 1972
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First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.--Ce texte fait référence à l'édition Relié.
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He wrote in the Preface to this 1971 book, “Many different philosophical issues arise in connection with logic… In the present essay I shall concern myself with the so-called ontological problem in the philosophy of logic and mathematics---that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. I shall also ask whether in logic itself… references to abstract entities is really indispensable, and I also shall take a look at the extent to which reference to such entities is necessary in physical science. My aim … will be not to present a survey of opinions on these problems, but to expound and defend one position in detail.”
He suggests, “There is no reason in stating logical principles to be more puristic, or more compulsive about avoiding references to ‘nonphysical entities,’ than in scientific discourse generally. References to classes of things, and not just to things, is a commonplace and useful mode of speech. If the nominalist wishes us to give it up, he must provide us with an alternative mode of speech which works just as well, not just in pure logic, but also in such empirical sciences as physics…” (Pg. 14)
He argues, “Another form of the second argument takes the form of an ‘appeal to ordinary language.’ Thus, it is contended that ‘(8) John made a true statement’ is perfectly correct ‘ordinary language.’ … [If] (8) does not imply [that statements exist as nonphysical entities], we may as well go on talking about ‘statements’ (and, for that matter, about ‘classes,’ ‘numbers,’ etc.), since it is agreed that such talk does not imply that statements … exist as nonphysical entities. Then nominalism is futile, since the linguistic forms it wants to get rid of are philosophically harmless. [If]… (8) is true and (8) implies the existence of nonphysical entities, it follows that these nonphysical entities do exist! So nominalism is false! Thus nominalism must be either futile or false.” (Pg. 19)
He contends, “I do not much care just where one draws the line between logic and mathematics, but this particular proposal of Quine’s seems to me hardly tenable… That ‘x is a crow’ is pretty well-defined predicate, ‘x is beautiful’ is pretty ill-defined, and ‘x is a snark’ is meaningless, is not LOGICAL knowledge, whatever kind of knowledge it may be… it is not important that the reader should agree with me here and not with Quine---all I insist on… is that the decision to call such statements … ‘principles of logic’ is not ill-motivated, either historically or conceptually.” (Pg. 28-30)
He concludes the third chapter with the statement, “if we are right, the natural understanding of logic is such that all logic, even quantification theory, involves reference to classes, that is, to just the sort of entity that the nominalist wishes to banish.” (Pg. 32)
He argues, "To refuse to make any a priori decisions as to which hypotheses are more or less plausible is just to commit oneself to never making any inductive extrapololation from past experience at all; for at any given time infinitely many mutually incompatible hypotheses are each compatible with any finite amount of data, so that if we ever declare that a hypothesis has been 'confirmed,' it is not because ALL other hypotheses have been ruled out, but because all the remaining hypotheses are rejected as too implausible even though they agree with and even predict the evidence---i.e., at some point hypotheses must be rejected on a priori grounds if any hypothesis is ever to be accepted at all." (Pg. 67-68)
This book, though nearly 45 years old, will still appeal to students of contemporary logic.