Nominalism and the Substitutional Quantifier
Marcus (Ruth Barcan)
Source: The Monist, Vol. 61, No. 3, Nominalism: Past and Present (July, 1978), pp. 351-362
Paper - Abstract

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Author’s Introduction

  1. It has been suggested that a substitutional semantics for quantification theory lends itself to nominalistic aims. I should like in this paper to explore that claim.
  2. Debates about nominalism and realism can be seen in relief against background theories about the relation of a language to the objects which the language purports to be about. Confining ourselves to those parts of a language which are vehicles for truth claims, complete sentences, or statements if you like, the supposition of nominalists and realists alike is that there are, in any meaningful statement, links between some or all of the words in the statement, taken singly or in concatenation, and objects which the statements are about. Statements contrive somehow to mention or refer, directly or obliquely, to objects. Plato, in arguing against the Sophists' claim that erroneous beliefs are not about anything, says, "Whenever there is a statement it must be about something," and that, he claimed, holds for true statements as well as false ones.
  3. Statements, true or false, speak of objects. In this, nominalists and realists are generally in agreement. The disagreement on the metaphysical side is about which objects; what exactly is being mentioned, directly or in directly by a statement. The disagreement on the linguistic side is about which words are doing the mentioning.

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