Willard Van Orman Quine

Quine on Reference and Ontology 147
to speculate on the nature of reification and its utility for scientific
theory” (PTb 8, emphasis added).
8. See WO 93. In a striking image, Quine there compares such acquisition
to a climbers ascent of a “chimney,” or narrow space between two
rock faces: “The contextual learning of these various particles goes on
simultaneously, we may suppose, so that they are gradually adjusted to
one another and a coherent pattern of usage is evolved matching that
of society. The child scrambles up an intellectual chimney, supporting
himself against each side by pressure against the others.”
9. Ludwig Wittgenstein, Philosophical Investigations, trans. G. E. M.
Anscombe (New York: Macmillan, 1953), §257.
10. Very roughly, first-order quantification theory is a logic that enables us
to generalize over all objects – and hence to speak of all objects being
thus-and-so, or no objects, or at least one object. Quine generally takes
logic to include the notion of identity and rules governing its use (see
PL, chap. 6). By contrast with first-order logic, second-order logic would
add the capacity to generalize about properties or qualities of objects.
Quine does not favor second-order logic, both because its truths cannot
be captured by any precisely formulated system of axioms or rules and
because he finds the idea of a property or quality to be unclear. He
holds that it is both philosophically less misleading and technically
more advantageous to use instead a combination of first-order logic and
set theory.
11. Thus Quine speaks of the “triviality” of the connection between ontology
and quantification, saying that the connection “is trivially assured
by the very explanation of referential quantification” (see RFK 174–5).
By “referential quantification,” Quine here means the sort of qualification
just explained, which he, along with most logicians, generally takes
as standard. It is opposed to “substitutional quantification,” in which
we think not of open sentences being true of this or that object but
rather as yielding truths when a given name replaces the variable. The
difference shows up if we admit objects not all of which have names;
in the case of real numbers, we cannot avoid doing so, since there are
more of them than there can be names.
12. Quine is perhaps influenced here by his early work in set theory, where
the question of the entities in the range of the quantifiers of a given theory
is a very natural measure of the strength of that theory and where the
strength of the theory is in turn crucial to its vulnerability to paradox.
I am indebted here to Stephen Menn.
13. The theory is first set forth in Russell’s “On Denoting” (Mind 14 [1905]:
479–93; very widely reprinted) but is perhaps to be seen more clearly in
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