September 17, 2012

An Infinite Regress of Nominalistic Paraphrases

Filed under: Philosophy — camcintosh @ 9:29 pm

In “A Theory of Properties,” Peter van Inwagen suggests that an adequate nominalist paraphrase of a sentence S that seems to be ontologically committing to some property p is a sentence that

(i) could be used in place of S
(ii) does not even seem to have the existence of p as a logical consequence

Regardless of whether these are good criteria, a metaontological issue surfaces: what prevents the Platonist from saying, “why shouldn’t I regard your paraphrase sentence as adequate iff it has the property of satisfying (i) and (ii)?” So where p designates the property of satisfying (i) and (ii), an adequate nominalist paraphrase will be a sentence S that has p. So:

S has p

But then we’d need an adequate nominalist paraphrase of that sentence; so

S has p’ has p

But then also…

‘‘S has p’ has p’ has p
‘‘‘S has p’ has p’ has p’ has p

Clearly, the task of offering an adequate nominalist paraphrasing sentence entails an infinite regress: we must offer paraphrases of paraphrases, and paraphrases of paraphrases of paraphrases, and so on. But what kind of regress is this? More importantly, is it vicious? If it is not vicious, does this pose a different sort of problem for the nominalist? And would any attempt to offer criteria for a successful nominalist paraphrase face this issue?



  1. When you fill in the schema ‘S has P,’ where ‘S’ is a sentence and ‘P’ is a predicate (it must be a predicate, predicates are linguistic items that are alleged to name properties), you will not immediately yield a sentence that quantifies over an abstract object. Suppose S is a sentence that is a nominalistic paraphrase of another sentence, and P is being an adequate nominalistic paraphrase. We now have filled in our schema, but we are not committed to any properties, only sentences (and the nominalist will insist we speak of sentence-tokens). The reason why is because once we quantify into the sentence our quantifier will only range over the sentence and not the property. Take ‘there is a sentence such that it is an adequate nominalistic paraphrase.’ This will be translated into: ∃(x) Px. Remember that we look to our bound variables to see what we are committed to.

    Mere predication does not commit one to properties. You need sentences that appear to quantify over properties, that’s why van Inwagen discusses sentences like ‘there are distinct species that share anatomical features.’

    To get a regress your going to need to look for sentences, that the nominalist will want to affirm, that look like they quantify over features of sentences.

    Comment by CGibbs — September 19, 2012 @ 10:31 am | Reply

    • That seems quite right, Cameron. I suspected something must be awry somewhere, and what you say seems right to me (as far as I can tell). Thanks!

      Comment by camcintosh — September 19, 2012 @ 11:37 am | Reply

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