| 21696 | Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine] |
| Full Idea: 'Nominalism' is distinct from 'extensionalism'. The main point of the latter doctrine is rejection of properties or attributes in favour of classes. But class are universals equally with attributes, and nominalism in the defined sense rejects both. | |
| From: Willard Quine (Lecture on Nominalism [1946], §3) | |
| A reaction: Hence Quine soon settled on labelling himself as an 'extensionalist', leaving proper nominalism to Nelson Goodman. It is commonly observed that science massively refers to attributes, so they can't just be eliminated. |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| Full Idea: Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9) |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| Full Idea: The style of nominalism which aims to reduce statements about numbers to statements about their applications does not work for the natural numbers, because they have many applications, and it is arbitrary to choose just one of them. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.iii) |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| Full Idea: The most popular approach of nominalistically inclined philosophers is to try to reinterpret mathematics, so that its terms and quantifiers only make reference to, say, physical objects, or linguistic expressions, or mental constructions. | |
| From: Hartry Field (Science without Numbers [1980], Prelim) | |
| A reaction: I am keen on naturalism and empiricism, but only referring to physical objects is a non-starter. I think I favour constructions, derived from the experience of patterns, and abstracted, idealised and generalised. Field says application is the problem. |
| 19002 | A nominalist can assert statements about mathematical objects, as being partly true [Yablo] |
| Full Idea: If I am a nominalist non-Platonist, I think it is false that 'there are primes over 10', but I want to be able to say it like everyone else. I argue that this because the statement has a part that I do believe, a part that remains interestingly true. | |
| From: Stephen Yablo (Aboutness [2014], 05.8) | |
| A reaction: This is obviously a key motivation for Yablo's book, as it reinforces his fictional view of abstract objects, but aims to capture the phenomena, by investigating what such sentences are 'about'. Admirable. |