Ton Deuteron Ploun

I found this to be a nearly incomprehensible chapter. The notes below barely make sense, Barnes’ commentary, while helpful, was also baffling (although I doubt Barnes is at fault here). This is something I need to go back to at a future date when I might have a better idea of what is going on.

PA, Alpha, Chapter 4

Because it is impossible for understanding simpliciter to be otherwise, demonstrative understanding will be necessary.

A demonstration is a deduction which proceeds from necessities. SO we must see what kind of items demonstrations proceed from..

We must define three things:
1) ‘of every case’
2) ‘in itself’
3) ‘universally’

Something holds of every case if it does not hold in some cases and not in others, nor at some times and not at others.
* for example, if ‘animal’ holds of every man then if this is true to call this a man, it is true to call him an animal, and if he is now he also was previously.

Something holds in itself if it holds in it what it is.
* for example, the line of triangles or points of lines. (The essence of a triangle comes from the lines.)
If what it holds in itself inheres in the account which shows what it is, there is an account which specifies the specific thing it is.
* for example, ’straight’ and ‘curves’ both hold of lines; ‘even’ and ‘odd’ both hold of numbers.

Aristotle gives four ways A can hold of B ‘in itself’. The first two:
1) A holds of B in itself = df ‘A holds of B and A inheres in the definition of B’
ex: animal holds of man in itself
2) A holds of B in itself = df ‘A holds of B and B inheres in the definition of A’
ex: mortal holds of animal (good example?)

Barnes then talks of I-predication. A proposition is an I-predication if
a) it is of the form ‘Every B is an A’ and
b) it is true in virtue of the fact that A holds of B in itself.
The proposition is an I1 proposition if ‘in itself’ is taken in sense 1 (above) and a proposition is an I2 proposition if ‘in itself’ is taken in sense 2 (above).

Certain items are not said of some other underlying subject. Things that aren’t said of an underlying subject are called things in themselves.

A. distinguishes things that exist in themselves (independently) with things that exist incidentally.

A distinction between natural and unnatural predications. If ‘x is y’ is a natural predication, then
1) ‘x is y’ doesn’t entail something else is Y and happens to be X
2) X is not ontologically dependent on anything else, and
3) x is an independently identifiable subject of change

Another way to describe that something holds ‘in itself’ is to say that what holds of something because of itself holds of it in itself.
* for example, if something died while being sacrificed, it died in the sacrifice since it died because of being sacrificed and it was not incidental that it died while being sacrificed.

This involves a connection between events

When something is understandable simpliciter and is said to hold of things in themselves either by
1) inhering in what is predicated or
2) being inhered in
then it holds of them because of themselves and from necessity. This is because it is not possible for them not to hold
1) either simpliciter or
2) as regards the opposites.

A. is referring to I1 and I2 predications. When A. says that “A holds of B simpliciter” he is talking of I2 predication, and when he refers to “as regards the opposites” he refers to I2 predications.

‘Universal’ is defined as what holds of every case in itself and as such.

Something holds universally when it is proves of an arbitrary and primitive case.

The definition of ‘universal ‘has three components:
1) ‘of every case’
2) ‘in itself’, and
3) ‘as such’ (qua)

A holds B as such iff there is no term C which explains why A holds of B; iff AaB is immediate.

Being an I-predication and holding as such are logically equivalent.

reread Barnes’ summary of the chapter on pp 120-2. Are there any articles that might make this a bit more clear?