[FOM] Realism as a Conservative Extension of Nominalism

[Dean Buckner]

Digging around in the FOM archives and elsewhere I found the following
passage by Steve Simpson (1998 posting)

>If we show that T' is conservative over T for S-sentences, then that
>result can be interpreted as saying that the primitives and/or axioms
>that are present in T' but not in T can be "eliminated" or, viewing it
>the other way round, these primitives and/or axioms can be "harmlessly
>introduced" on top of T, i.e. they can be viewed as mere instruments
>which we introduce artificially in order to make it easier or more
>convenient for us to prove S-sentences, without increasing our
>ontological commitments beyond what is already in T.

This neatly illustrates the dilemma of nominalism, brilliantly handled in
"Nominalism Reconsidered" by Rosen and Burgess.  Either

(i) nominalists concede that their philosophical position is at odds with
established mathematical and scientific opinion.  So they are at odds with
existence theorems "often published in journals with the most stringent peer
review procedures, and the vast majority of these published theorems survive
subsequent scrutiny on the part of competent practitioners"

(ii) or nominalists hold that the objectionable statements can be translated
into some form of words that is more acceptable.  But then, if the realist
utters the sentence s, which "really" means that p, and the nominalist
agrees that p, then how is he (or she) really disagreeing with the realist?
If "Numbers exist" really means "numerals exist/could exist" or something
like that, then "Numbers exist" is perfectly true.  To concede to the
translated sentences "is to concede all the antinominalist maintains [Alston
1958]"

More to come on this.  Some references to papers by Stephen Yablo attached.
Stephen is an occasional contributor to this group.

The papers by Burgess, some of which discuss Harvey's work, are at

http://www.princeton.edu/~jburgess

Harvey writes

"Burgess continues to emphasize plural quantification. I haven't yet
taken a view as to how much is gained, philosophically, by this, and
want to look into it further."  He should, though I'm dubious of Burgess'
treatment of PQ.


Dean


Alston, W. [1958] "Ontological Commitments", Philosophical Studies 9: 8-17.
(quoted in Burgess).
Yablo, S. [1998] "Does Ontology Rest on a Mistake?" Proceedings of the
Aristotelian Society, Supp. Volume 72: 229-261.

Yablo, S. [2000a]  "A Paradox of Existence," in T. Hofweber, ed. Empty
Names, Fiction and the Puzzle of Existence , CSLI.

Yablo S. [2000b] Apriority & Existence," in P. Boghossian and C. Peacocke,
ed. New Essays on the A Priori, Oxford University Press.

Yablo, S. [forthcoming a]  "The Myth of the Seven", in M. Kalderon, ed.
Fictionalist Approaches to Metaphysics, Oxford University Press.

Yablo, S. [forthcoming b] "Go Figure: A Path through Fictionalism",  Midwest
Studies in Philosophy.






Dean Buckner
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ENGLAND

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