ONT Quine -- On the Limits of Decision
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OLOD. Note 1
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| On the Limits of Decision
|
| Because these congresses occur at intervals of five years, they make
| for retrospection. I find myself thinking back over a century of logic.
| A hundred years ago George Boole's algebra of classes was at hand. Like
| so many inventions, it had been needlessly clumsy when it first appeared;
| but meanwhile, in 1864, W.S. Jevons had taken the kinks out of it. It was
| only in that same year, 1864, that DeMorgan published his crude algebra of
| relations. Then, around a century ago, C.S. Peirce published three papers
| refining and extending these two algebras -- Boole's of classes and DeMorgan's
| of relations. These papers of Peirce's appeared in 1867 and 1870. Even our
| conception of truth-function logic in terms of truth tables, which is so clear
| and obvious as to seem inevitable today, was not yet explicit in the writings
| of that time. As for the logic of quantification, it remained unknown until
| 1879, when Frege published his 'Begriffsschrift'; and it was around three
| years later still that Peirce began to become aware of this idea, through
| independent efforts. And even down to litle more than a half century ago
| we were weak on decision procedures. It was only in 1915 that Löwenheim
| published a decision procedure for the Boolean algebra of classes, or,
| what is equivalent, monadic quantification theory. It was a clumsy
| procedure, and obscure in the presentation -- the way, again, with
| new inventions. And it was less than a third of a century ago that
| we were at last forced, by results of Gödel, Turing, and Church, to
| despair of a decision procedure for the rest of quantification theory.
|
| Quine, "Limits of Decision", pp. 156-157.
|
| W.V. Quine, "On the Limits of Decision",
| pp. 156-163 in 'Theories and Things,
| Harvard University Press, Cambridge, MA.
| A shorter version of this paper appeared
| in the 'Akten des XIV. internationalen
| Kongresses für Philosophie', vol. 3, 1969.
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