Re: Quine -- On the Limits of Decision

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OLOD.  Note 3

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| On the Limits of Decision (cont.)
|
| The answer obviously is that this criterion is too
| severe, because the component quantifications are
| not always independent of one another.  A formula
| of quantification theory might be valid in spite
| of failing this truth-table test.  It might fail
| the test by turning out false for some assignment
| of truth values to its component quantifications,
| but that assignment might be undeserving of notice
| because incompatible with certain interdependences
| of the component quantifications.
|
| If, on the other hand, we can put a formula of quantification
| theory into the form of a truth function of quantifications
| which are independent of one another, then the truth table
| will indeed serve as a validity test.  And this is just
| what we can do for monadic formulas of quantification
| theory.  Herbrand showed this in 1930.
|
| Quine, "Limits of Decision", p. 157.
|
| W.V. Quine, "On the Limits of Decision", pp. 156-163 in
|'Theories and Things, Harvard University Press, Cambridge,
| MA, 1981.  A shorter version of this paper appeared in the
|'Akten des XIV. internationalen Kongresses für Philosophie',
| vol. 3, 1969.

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