Willard Van Orman Quine

Quine on Modality 205
so that, by (SUBST),
(2) (∃ x)(x CEvening Star .∼ ⊓(x CMorning Star)).
Since the open sentences quantified in (1) and (2) are mutual contraries,
Quine concludes that there are at least two objects congruent
to the Evening Star. Similarly, if the term ‘Venus’ is introduced, a
third such object can be inferred.
Parallel arguments may be used to show that the contemplated
version of quantified modal logic is committed to an ontology repudiating
classes and admitting only attributes, Quine adds. But the
argument concerning individuals just stated is, of course, more disturbing
for modal logicians.
Later the same year, in his review of Ruth Barcan’s “The Identity of
Individuals in a Strict Functional Calculus of Second Order,” Quine
remarks that Barcan’s system is “best understood by reconstructing
the so-called individuals as ‘individual concepts’” (RRB 96).
difficulties that do not depened
on singular terms
The article “Reference and Modality” in Quine’s From a Logical
Point of View (1953) is a fusion of “Notes on Existence and Necessity”
with “The Problem of Interpreting Modal Logic.” But new
arguments are added, notably arguments to the effect that we cannot
properly quantify into a modal context.
First, lest the reader feel that the arguments against quantification
into modal contexts always turn on an interplay between singular
terms like ‘Tully’ and ‘Cicero’, ‘9’ and ‘the number of planets’,
‘Evening Star’ and Morning Star’, Quine reargues the meaninglessness
of quantification into modal contexts without reverting to singular
terms. He points out that one and the same number x is
uniquely determined by these conditions:
(3) x = √ x + √ x + √ x �= √ x
and
(4) There are exactly x planets.
Nevertheless (3) has ‘x > 7’ as a necessary consequence, while (4) has
not. “Necessary greaterness than 7 makes no sense as applied to a
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