Eric and list, EC
My initial inclination is to say that everything you pointed to does seem important, but doesn't seem obviously to hinge on anything I can easily understand as a difference between nominalists and realists
The simplest explanation I have ever read was by Alonzo Church -- in a lecture to Quine's logic group at Harvard: http://www.jfsowa.com/ontology/church.htm The Ontological Status of Women and Abstract Entities This excerpt from Church’s 1958 lecture was preserved by Tyler Burge. Cathy Legg posted it to her web site, from which I downloaded it. (I really wish we had a YouTube of that lecture and the debates between Church and Quine.) In my web page, I added URLs for a 1947 paper by Goodman and Quine and a response by Church in 1951. For anyone who wants to see an important *practical* difference between nominalism and realism, see the following excerpt from Church's book, _The Calculi of Lambda Conversion_: http://www.jfsowa.com/logic/alonzo.htm Nominalists like Quine deny the distinction between essence and accident in philosophy. In mathematics and computer science, they extend their ideology to deny the distinction between intensions and extensions. For a nominalist, a function or relation *is* a set of n-tuples. For a realist, the _intension_ of a function or relation is a rule, law, principle, or axiom. The _extension_ is the set of tuples determined by that rule, law, principle, or axiom. Peirce would add *habit* to that list. A habit is an informal law that could be made formal -- but only at the expense of losing its flexibility (AKA vagueness). Peirce said that vagueness is essential for mathematical discovery. George Polya did not cite Peirce in his books, but he made that point very clear. Carnap was a nominalist who denied the reality of all value judgments, including Truth. After talking with Tarski, he accepted the notion of truth because it could be defined in terms of sets. That led Carnap (1947) to define modal logic in terms of a set of undefined things called possible worlds. Other nominalists, such as Kripke and Montague adopted Carnap's method, but I believe that Michael Dunn's definition in terms of laws (related to methods by Aristotle, Peirce, and Hintikka) is more fundamental: http://www.jfsowa.com/pubs/5qelogic.pdf Quine & Co. also deny the existence of propositions. They insist on talking only about sentences. For a definition of proposition that was inspired by Peirce, but stated in a way that a nominalist could accept, see http://www.jfsowa.com/logic/proposit.pdf This article is a 5-page excerpt from a longer article that discusses the philosophical issues: http://www.jfsowa.com/pubs/worlds.pdf John
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