Steps Beside a Constructive Nominalism: Token Supply, Agency, and the Record of a Correction

Goodman and Quine's Steps Toward a Constructive Nominalism (1947) raises, and then disposes of, a worry about whether there are enough concrete tokens to do the work abstract objects were doing. The disposal is an escape: inscriptions are appropriately shaped portions of matter, and a portion of matter is shaped whether or not anyone shaped it. This paper argues that the escape was a choice between two kinds of token supply rather than the recognition of one. A nominalist supply is either indexed — its extent depends on what some reasoner has actually done — or unmoored. Every reconstruction in the literature takes the unmoored horn: Goodman and Quine without remarking on it, Chihara deliberately and with the reason stated, Field and Hellman without the question arising. The reason is the mathematics, and it is a good one. What has not been done is to occupy the other horn and report what is there. Using a framework whose ontology does not move and whose register does, the paper shows that the indexed horn is habitable, that what it buys is a record in which a correction has happened and remains legible as having happened, and that what it costs is the whole of the syntactic apparatus the 1947 paper runs on, including Goodman's own calculus of individuals. The 1947 problem is not solved. It is shown to sit at a fork, with both bills now readable.