Philosophy of Logic

Essays in Philosophy

by Hilary Putnam

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.

Genres: Philosophy, Logic, Nonfiction

90 pages, Hardcover

First published January 1, 1971

About the author

Hilary Whitehall Putnam was an American philosopher, mathematician, and computer scientist who was a central figure in analytic philosophy from the 1960s until his death, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. He was known for his willingness to apply an equal degree of scrutiny to his own philosophical positions as to those of others, subjecting each position to rigorous analysis until he exposed its flaws. As a result, he acquired a reputation for frequently changing his own position. Putnam was Cogan University Professor Emeritus at Harvard University.

Reviews

[Jonah Marcus · Rating 4 out of 5]

Haven't read analytic philosophy in a while so lowkey I was not picking up what he was putting down 🦹‍♂️🐮

This was mostly concerned with the ontological questions in logic, namely nominalism vs realism. It is an extended argument against nominalism on indispensability grounds.

Essentially: quantification over abstract entities is essential for mathematics and sciences and since these theories are successful we should accept these entities. (pg 73)

The discussion of why logic is an interesting philosophical problem is interesting (ch1) was cool. We know what we believe is logical (all men are mortal, Socrates is..., p, p->q, so q) but it is unclear how to interpret these statements. Are they about sentences? entities? forms of thought? - "the interpretation of an unchanging truth has changed considerably"

I think the main argument against nominalism is that no matter how mathematics is formalized we need concepts like truth, infinity, formula, to talk about the formalization. Essentially we MUST talk about some abstract entity to do mathematics.

It is incredibly unclear to me what it means for an entity to exist actually means. What does it mean to talk about sets existing. They seem like a stable concept to talk about but the "king of France" is also something I can talk about but that does not exist.

I am convinced that nominalism is wrong or at least unhelpful but I don't exactly know what it means to be a realist. Don't we already talk about abstract entities as if they are real? If the purpose of mathematics is to be able to talk about these entities aren't they real enough?

The discussion of predicative and impredicative conceptions of set was cool. (Ch-VI)

[David Scarratt · Rating 4 out of 5]

If this is the book I think it is -- and I think it is -- then I think it's essentially an extended argument against nominalism, of the Nelson Goodman kind. But I read it a long time ago when I was even more of a novice in philosophy than I am now, so I may be misremembering a poor understanding.

[Steven H · Rating 5 out of 5]

THE ANALYTIC PHILOSOPHER ARGUES AGAINST NOMINALISM, ETC.

Hilary Whitehall Putnam (born 1926) is an American analytic philosopher, mathematician, and computer scientist who taught at Harvard for many years. He wrote many other books, such as 'Realism with a Human Face,' 'Pragmatism: An Open Question,' 'Reason, Truth and History,' etc.

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)

This book, though more than 50 years old, will still appeal to students of contemporary logic.