Friday, May 28, 2010

Material Logic: Quia Demonstrations vs. Propter Quid Demonstrations


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From St. Thomas' Summa theologiae I.2.2c:

I answer that it must be said that demonstration is twofold: One which is through the cause, and is called demonstration "propter quid" [lit., 'on account of which'] and this is [to argue] from what is prior simply speaking (simpliciter). The other is through the effect, and is called a demonstration "quia" [lit., 'that']; this is [to argue] from what is prior relatively only to us (quoad nos). When an effect is better known to us than its cause, from the effect we proceed to the knowledge of the cause. And from every effect the existence of its proper cause can be demonstrated, so long as its effects are better known to us (quoad nos); because since every effect depends upon its cause, if the effect exists, the cause must pre-exist.

From Aristotle's Posterior Analytics I.13:

"Knowledge of the fact (quia demonstration) differs from knowledge of the reasoned fact (propter quid demonstrations). [...] You might prove as follows that the planets are near because they do not twinkle: let C be the planets, B not twinkling, A proximity. Then B is predicable of C; for the planets do not twinkle. But A is also predicable of B, since that which does not twinkle is near--we must take this truth as having been reached by induction or sense-perception. Therefore A is a necessary predicate of C; so that we have demonstrated that the planets are near. This syllogism, then, proves not the reasoned fact (propter quid) but only the fact (quia); since they are not near because they do not twinkle, but, because they are near, do not twinkle...."

A (major term) = close heavenly body
B (middle term) = non-twinkling heavenly body
C (minor term) = planet

Major Premise: B is A
Minor Premise: C is B
Conclusion: C is A

=

Major Premise: Non-Twinkling heavenly bodies are close heavenly bodies.
Minor Premise: Planets are non-twinkling heavenly bodies (effect).
Conclusion: Planets are close heavenly bodies (cause).


From Aristotle's Posterior Analytics I.13 (cont'd):

"The major and middle of the proof, however, may be reversed, and then the demonstration will be of the reasoned fact (propter quid). Thus: let C be the planets, B proximity, A not twinkling. Then B is an attribute of C, and A-not twinkling-of B. Consequently A is predicable of C, and the syllogism proves the reasoned fact (propter quid), since its middle term is the proximate cause...."

A (major term) = non-twinkling heavenly body
B (middle term) = close heavenly body
C (minor term) = planet

Major Premise: B is A
Minor Premise: C is B
Conclusion: C is A

=

Major Premise: Close heavenly bodies are non-twinkling heavenly bodies.
Minor Premise: Planets are close heavenly bodies (cause).
Conclusion: Planets are non-twinkling heavenly bodies (effect).


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