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I'm sure I recall Quine saying in various places that one distinction between logic and set theory is that logic should have no ontological presuppositions (or, at most should presuppose some thing exists). He followed a line that Russell also took, from 1903 through Principia Mathematica, that existence claims such as the axiom of infinity are not logical truths. And I find on the Stanford Encyclopedia that one reason Quine gave to calling second order logic set theory, as opposed to first order logic which he considered properly logic, is "that first-order logic has no ontological presuppositions of its own." But no citation is given.

Where does Quine say things like this?

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    See WVO Quine, Philosophy of Logic (2nd Edition), Ch.5 : The Scope of Logic. – Mauro ALLEGRANZA Oct 12 '14 at 19:36
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    But Quine's view dates back to 1941, with Whitehead and the Rise of Modern Logic, reprinted into Willard Van Orman Quine, Selected Logic Papers (enlarged ed - 1995), page 3-on. – Mauro ALLEGRANZA Oct 13 '14 at 6:11
  • @MauroALLEGRANZA Terrific, the Whitehead article makes a textual link to Principia Mathematica. – Colin McLarty Oct 13 '14 at 6:32
  • Why your astonishment ? See Wiki : he has Ph.D. in philosophy from Harvard University in 1932. His thesis supervisor was Alfred North Whitehead. During the academic year 1932–33, he travelled in Europe thanks to a Sheldon fellowship, meeting Polish logicians (including Alfred Tarski) and members of the Vienna Circle (including Rudolf Carnap). – Mauro ALLEGRANZA Oct 13 '14 at 6:40
  • @MauroALLEGRANZA I am not astonished. My question notes he continued ideas of Russell. I am just happy to have a good text to cite for it. – Colin McLarty Oct 13 '14 at 14:01
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Quine's Philosophy of Logic, chapter 5 "The Scope of Logic" distinguishes logic from set theory in that logic gives no ontology and set theory gives one. He even says logic can "simulate" ontology by using schematic variables which look as if they took classes as values, but they actually do not. In contrast "When we take on set theory forthrightly and without simulation, we take on both vocabulary and ontology." That is page 72 but the thought recurs in slight variants throughout the chapter.

The essay on Whitehead discusses the logical issues at length, but so far as I can see it does not specify that the difference between logic and set theory is that set theory has an ontology. Albeit numerous web sites claim Quine in this essay calls second order logic "set theory in disguise," the essay does not seem to discuss second order logic at all and does not seem to contain the word "disguise." I suspect that a reasonable interpretation of what Quine is saying, somehow morphed over time into a factitious quote.

The logical issues are discussed again in Quine's book Set Theory and its Logic but I do not find concise quotable expression of the philosophic claim that this is difference between logic and set theory .

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Quine says similar things in many of his works (See Quine (1948) Quine (1951a) Quine (1951b) and Quine (1953b) Here is Quine's 'On What There Is (1948)', in which he says the following:

The use of alleged names is no criterion, for we can repudiate their namehood at the drop of a hat unless the assumption of a corresponding entity can be spotted in the things we affirm in terms of bound variables.

And,

We can very easily involve ourselves in ontological commitments by saying, for example, that there is something (bound variable) which red houses and sunsets have in common; or that there is something which is a prime number larger than a million. But, this is, essentially, the only way we can involve ourselves in ontological commitments: by our use of bound variables.

And,

The variables of quantification, „something‟, „nothing‟, „everything‟, range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.

  • Thanks, but I am not just looking for anything about ontology. I am looking for claims that logic per se does (or should) make no ontological commitment. – Colin McLarty Oct 12 '14 at 20:37

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