Monday, June 07, 2010

Thought is quick

"Enthymeme" is a form of argument where one or more of the assumptions is so obvious that it need not be stated. Suppose at a party my wife says "It's past eleven". I know what she means, which can be expressed by the following syllogism.

(Major) If it is past eleven and we are out, then leave now!
(Minor) It is past eleven and we are out
(Conclusion) Leave now!

She does not need to state the major premiss, nor even the conclusion, but I catch her drift. Note both the major and the conclusion contain an imperative. Arthur Prior investigated the logic of arguments containing imperatives in his paper "On Some Proofs of the Existence of God" , published in Papers in Logic and Ethics, Duckworth 1976.

Note also that the minor premiss is an assertion, and must be understood as such for the argument to be valid. If by contrast it meant something like "Would you like another large gin and tonic?" her conclusion would not follow. The point being, "linguistic meaning" is king. If it were not for the meaning we assign to expression types, we would not be able to express ourselves in ways like this, that superficially suggest that meaning constantly fluctuates, and that some expressions have no linguistic meaning.

Thomas Hobbes gives an entertaining example in Leviathan Chapter III (my emphasis).

"For in a discourse of our present civil war, what could seem more impertinent than to ask, as one did, what was the value of a Roman penny. Yet the coherence to me was manifest enough. For the thought of the war introduced the thought of the delivering up the king to his enemies; the thought of that brought in the thought of the delivering up of Christ; and that again the thought of the thirty pence, which was the price of that treason; and thence easily followed that malicious question; and all this in a moment of time—for thought is quick."

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