Ton Deuteron Ploun

PA Book 1 chapter 6

The central claim of this chapter is that P is demonstrated through necessary principles.

1. If demonstrative understanding proceeds from necessary principles; and
2) if whatever holds of an object in itself is necessary, then
3) demonstrative deduction will proceed from certain items of this sort (ie necessary items)…because everything holds either incidentally or in this way (presumably through demonstrative deduction)

We must argue like this or posit as a principle that demonstration is necessary. “for from truths you can deduce without demonstrating, but from necessities you cannot deduce without demonstrating.”

There is evidence for this idea that demonstration proceeds from necessity because we say that the premises aren’t necessary if we think it possible for them to be otherwise.

A further argument in favor of the idea that demonstration must proceed from necessities is as follows:
1) if in a case of demonstration, someone who doesn’t possess an account of the reason why doesn’t have understanding; and
2) if it might be A holds of C by necessity but B (the middle term through which this is demonstrated) do not hold from necessity, then
3) he doesn’t know the reason why.

If I ‘demonstrate’ the necessary proposition AaC from non-necessary premises, then I don’t know why AaC and thus do not understand AaC

If premises are contingent, then AaC can’t hold because of them.

This seems to indicate that the way to come to understand the reason why comes via demonstration with necessary truths. Hopefully later he’ll give an account of how demonstrations act as a proper way to come to know the reason why. Or why the results of demonstration are considered accounts of the reason why.

It’s also interesting to note the idea that understanding does not come about without having an account of the reason why.

If someone does not know something now
1) although he has an account,
2) the account is preserved (ie the person is alive)
3) the object is preserved (the truth; p is true at t1 and at t2)
4) he has not forgotten
Then he didn’t know it earlier.

A presupposition apparent in (3) is that a proposition (P) might change its truth value between t1 and t2.

Would this be for things that happen for the most part? Necessary truths can’t change their truth value, surely.

But the middle term might perish (be false) if it isn’t necessary.

But because the person is preserved, and the object is preserved, he will possess an account, and yet he doesn’t have knowledge, and therefore he didn’t have knowledge earlier.
* even if this hasn’t occurred, it can (because the middle term might perish) and so one can’t have knowledge in these conditions.

Even if a conclusion holds of necessity, the middle term need not because you can deduce a necessary truth from non-necessary truths (in the same way you can deduce a truth from non-truths).
*BUT when the middle term holds from necessity, the conclusion also holds from necessity (like a conclusion from true propositions is always true).

Since understanding from demonstration must hold from necessity, your demonstration must proceed from a middle term which is necessary. Otherwise you will understand neither the reason why nor that it is necessary for it to be the case.

Of incidentals which do not hold of things in themselves, there isn’t demonstrative understanding because you can’t prove the conclusion from necessity (because it is possible for the incidental to be otherwise).

One might wonder why one would even ask about incidentals if it isn’t necessary for the conclusion to hold.

For any argument of the form P so necessarily Q will be good since NO argument of that form will be good, where Q is not necessary.

We should ask these questions NOT because the conclusion will be necessary because of the points proposed in the question but rather because it is necessary for anyone who accepts the proposals to state the conclusion (truly).

Since whatever holds of something in itself and as such holds of it by necessity, it is clear that demonstrations must proceed from such items (in itself & by necessity). This is true because what is incidental doesn’t hold necessarily and so you don’t know necessarily that the conclusion holds (even if it is always the case)…because you will not understand in itself
1) that it holds in itself, nor
2) why it holds