ONT Re: Quine -- On the Limits of Decision
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OLOD. Note 2
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| On the Limits of Decision (cont.)
|
| It is hard now to imagine not seeing truth-function logic
| as a trivial matter of truth tables, and it is becoming hard
| even to imagine the decidability of monadic quantification theory
| as other than obvious. For monadic quantification theory in a modern
| perspective is essentially just an elaboration of truth-function logic.
| I want now to spend a few minutes developing this connection.
|
| What makes truth-function logic decidable by truth tables
| is that the truth value of a truth function can be computed
| from the truth values of the arguments. But is a formula of
| quantification theory not a truth-function of quantifications?
| Its truth vaue can be computed from whatever truth values may be
| assigned to its component quantifications. Why does this not make
| quantification theory decidable by truth tables? Why not test a
| formula of quantification theory for validity by assigning all
| combinations of truth values to its component quantifications
| and seeing whether the whole comes out true every time?
|
| 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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