Types and Tokens: On Abstract Objects by Linda Wetzel

Author:Linda Wetzel [Wetzel, Linda]
Language: eng
Format: epub, pdf
Tags: Language Arts & Disciplines, Linguistics, General, Philosophy, Epistemology
ISBN: 9780262013017
Google: qmBcmwEACAAJ
Publisher: MIT Press
Published: 2009-07-15T00:35:38.374013+00:00

4 Quantification

I have been writing as though the main impediment to the nominalist program is its apparent inability to paraphrase away singular references to types, either in a systematic or even a piecemeal fashion. This has been a ruse, for which I beg the reader’s pardon. It was a necessary ruse in that nominalists often offer paraphrases of apparent singular references to types as though such singular references are the main problem for their program, so hope that this could be done had to be laid to rest before we could proceed. But it was not strictly philosophically necessary. The coup de grâce for (5) (or anything like it) is the virtual impossibility of doing away with apparent quantifications over types. We saw many examples in chapter 1, including this one, but note especially the sheer volume in a typical paragraph from Mayr:

Classifying species as monotypic or polytypic is a first step in a quantitative analysis of phenotypic variation. Another way is to analyze the subdivisions of polytypic species: What is the average number of subspecies per species in various groups of animals and what is their average geographic range? There are believed to be about 28,500 subspecies of birds in a total of 8,600 species, an average of 3.3 subspecies per species. It is unlikely that this average will be raised materially (let us say above 3.7) even after further splitting. The average differs from family to family: 79 species of swallows (Hirundinidae) have an average of 2.6 subspecies, while 70 species of cuckoo shrikes (Campephagidae) average 4.6 subspecies. . . .

To appreciate the monumental challenge of analyzing away all quantifications over species in the preceding paragraph into talk merely of concrete individuals, consider Goodman and Quine’s (1947, p. 180) nominalistic translation of the far simpler ‘there are more cats than dogs’:

Every individual [in Goodman’s mereological sense3] that contains a part of each cat, where the part is just as big as the smallest animal among all cats and dogs, is bigger than some individual that contains a part of each dog, where the part is just as big as the smallest animal among all cats and dogs.4

It is certain that there is no actual nominalist paraphrase token of the Mayr passage yet in existence, and a good bet that none will ever exist. I, for one, have no idea how to even begin to come up with a paraphrase that quantifies over only concrete individuals. In the absence of such a paraphrase we remain committed to species. The same remark applies, mutatis mutandis, to genes, proteins, traits, receptors, germline mutations, words, syllables, sound-segments, vowels, accents, phonemes, phonological representations, alternations, parts of the speech organs, languages, language trees, computers, chess games, openings, gambits, piano concerti, notes, opening measures, octave leaps, atoms, spectral lines, forces, fields, subatomic particles, and all the other types that we saw quantified over in chapter 1. As Quine (1961a, (p. 13, my italics) remarked:

when we say that some zoölogical species are cross-fertile we are committing ourselves to recognizing as entities the several species themselves, abstract though they are.

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