Monday, October 25, 2010

Demonstration of the reason why

This month I am struggling with Aristotle's Posterior Analytics. It gives Aristotle's account of demonstration, especially scientific demonstration. There is a nice illustration in Book I chapter 13 of the difference between what the scholastics called propter quid and quia demonstration. Demonstration propter quid (which Muir translates as 'demonstration of the reasoned fact' is when syllogistic reasoning shows us the reason why something happens. For example (ignoring Aristotle's actual science* for sake of argument).

Propter quid
Near things do not twinkle
Planets are near
Planets do not twinkle

The reasoning is from cause (nearness) to effect (not twinkling). With demonstration quia, on the other and, we reason from effect to cause, as follows.

Things that do not twinkle are near
Planets do not twinkle
Planets are near

Here, you have demonstrated a fact by reasoning from effect to cause. Of course pretty much all demonstration in the natural sciences is of this sort. The medieval Aristotelians were perfectly aware of this.

Sometimes that which is more known in reference to us is not more known
absolutely, as happens in natural sciences where the essences and powers of
things are hidden, because they are in matter, but are disclosed to us through
the things which appear outwardly. Hence in these sciences the demonstrations
are for the most part made through effects which are better known in reference
to us but not absolutely. (Lectures on the Posterior Analytics, Book I lecture

* On the actual science, I found this helpful. If this is correct, the propter quid syllogism should be as follows:

Objects sufficiently large that they have non-zero apparent diameter when viewed from the Earth do not twinkle
Planets [or nebulas] have non-zero apparent diameter when viewed from the Earth
Planets [or nebulas] do not twinkle

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