Nominalists need some account of correctness for sentences committed to the existence of abstract objects. This paper proposes a new statement of such conditions specifically for properties. The account builds on an earlier proposal of mine, but avoids the counter-examples against the latter pointed out by Thomas Schindler, particularly, the sentence ‘There are inexpressible properties’. I argue that the new proposal is independently motivated and more faithful to the spirit of the kind of error-theoretic nominalism that the original proposal was (...) part of. Along the way, I also propose novel treatments of Arthur Pap’s and W.V.O. Quine’s notoriously hard-to-paraphrase sentences about abstracta. (shrink)

Although Benjamin Schnieder’s theory of the “ordinary conception” of properties successfully handles paradoxical properties—particularly, the property of non-self-instantiation—it fails to account for ordinary, non-pathological cases. The theory allows the inference of ‘a has the property of being F’ only given F(a) and the prior assertibility of ‘the property of being F can exist’. While this allows us to block an inference to a contradiction, it also blocks all of the non-pathological instances of the inference from ‘a is F’ to ‘a (...) has the property of being F’. It thereby fails both as a theory of the ordinary conception and as a replacement of the ordinary notion, assuming the latter is defective. (shrink)

Naturalism, as I understand it, includes cosmological naturalism, ontological naturalism and methodological naturalism. After clarifying these three theses I argue that the combination of ontological with methodological naturalism is untenable. I do so by providing a pro tanto case against ontological naturalism and show that it can be resisted, but only by abandoning methodological naturalism. The pro tanto case is that ontological naturalism requires a version of what I call Redundancy Nominalism, but methodological naturalists should either reject it or at (...) very least treat it, and hence ontological naturalism, as a speculation. (shrink)