Grades of Essentialism in Quantified Modal Logic
Parsons (Terence)
Source: Noûs, Vol. 1, No. 2 (May, 1967), pp. 181-191
Paper - Abstract

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Author’s Introduction1

  1. W. V. Quine distinguishes three grades of modal involvement2.
    1. The first grade occurs when predicates like "is analytic" are appended to names of sentences.
    2. The second occurs when a word like "necessarily" is used within sentences as an operator.
    3. And the third occurs as soon as this necessity operator is allowed to precede open sentences containing variables which are bound by quantifiers which precede the operator.
    This third grade of modal involvement, Quine says, commits one to Aristotelian essentialism – a philosophically suspect doctrine.
  2. From this ground, Quine launches an attack on the meaningfulness of a quantified modal logic which permits modal operators to intermingle with quantifiers. The structure of his attack is this:
    1. quantified modal logic permits quantifiers outside of a modal operator to bind variables within the scope of that operator (i.e., we have the third grade of modal involvement);
    2. therefore quantified modal logic is committed to Aristotelian essentialism;
    3. but there are insuperable difficulties in making sense of Aristotelian essentialism; so
    4. there are insuperable difficulties in making sense of quantified modal logic3.
  3. I shall claim that this reasoning is fallacious because of a crucial equivocation on "Aristotelian essentialism." To show this, I will define four different grades or levels of "Aristotelian essentialism." (This is a subclassification of Quine's third grade of involvement). It is only the first of these grades of essentialism which Quine has shown to be required by quantified modal logic. But it is only the fourth that he has argued to be paradoxical. Thus, steps (ii) and (iii) are plausible only if he is referring to the first grade of essentialism in step (ii), but the fourth grade in step (iii). But then the inference to step (iv) is invalid.

In-Page Footnotes

Footnote 1: Parsons thanks Ruth Barcan Marcus for “helpful comments”.

Footnote 2: See "Quine (W.V.) - Three Grades of Modal Involvement".

Footnote 3: We’re referred additionally to "Quine (W.V.) - Reference and Modality".

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2018
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)

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