"Syllogisms which produce understanding"

Question

I remember reading somewhere that the aim of Aristotle's Prior and Posterior analytics was to show which kinds of syllogisms produce understanding. I do not remember where I read this but I think it was in a translation of one of al Farabi's works. in any case, this notion is very interesting to me because it means that Aristotle was not merely trying to investigate syllogisms in general, but was instead trying to discover which ones lead to understanding. I feel that knowing this would help me a lot practically in my studies because whenever I study a subject, I often have difficulties identifying whether or not I really understand something. Too often, I feel like I understand something, and then some years down the line a counter example comes up which shows that I didn't really understand the thing at a fundamental level.

More recently, I am starting to come to the conclusion that the kinds of syllogisms which produce understanding are ones which show how I think originates from first principles. In other words, it is no good learning how to use something practically (for example), or the relations it bears to other things within the same subject, as this will not lead to fundamental understanding. The only kind of explanation that will lead to fundamental understanding is one that shows how the thing originates from the first principles of the subject, just like Euclid's Elements.

So my question is this: Was this really the aim of Aristotle's two books on analytics, and if so, is there a short modern explanation of Aristotle's conclusions on "syllogisms which produce understanding"?

Note: I am not a philosopher and have never taken philosophy, so I apologize in advance for any errors in my post.

Answer 1

See Pr.An, Bk.I :

It is first requisite to say what is the subject, concerning which, and why, the present treatise is undertaken, namely, that it is concerning demonstration, and for the sake of demonstrative science; we must afterwards define, what is a proposition, what a term, and what a syllogism, also what kind of syllogism is perfect, and what imperfect.

In a nutshell, demostration for Aristotle is to deduce a sentence from first principles (already known to be true) by way of valid arguments (that preserve truth).

Thus, demonstration will ensure that the sentence deduced will be true :

Wherefore a syllogistic proposition will be simply an affirmation or negation of something concerning something, it is however demonstrative if it be true, and assumed through hypotheses from the beginning.

Lastly, a syllogism is a sentence in which certain things being laid down, something else different from the premises necessarily results, in consequence of their existence. I say that, "in consequence of their existence," something results through them, but though something happens through them, there is no need of any external term in order to the existence of the necessary (consequence).

See Jonathan Lear, Aristotle and Logical Theory, Cambridge UP (1986).

More generally, see : Jonathan Lear. Aristotle: The Desire to Understand, Cambridge UP (1986).

Answer 2

Not all syllogisms produce understanding.

For example, the syllogism

1. All A is B.
2. All B is C.
3. ∴, all A is C

doesn't tell us anything beyond rules of logic (formal logic); unless we know what A, B, and C signify (in which case the study of this syllogism would pertain to material logic).

Premises of a syllogism are the efficient cause of its conclusion.

The Material Logic of John of St. Thomas, O.P. (João Poinsot) "VI. On Demonstration and Science", question 24 "On Conditions Anterior to Demonstration and on Premises", treats of the question (article 2) of "Whether the influence of the premises upon the conclusion belongs to the genus of efficient causality or to some other genus of cause" (pp. 446-453). In answering this question, he follows St. Thomas Aquinas's interpretation of Aristotle's Posterior Analytics 71^a24:

24. Before he was led on to recognition or before he actually drew a conclusion, we should perhaps say that in a manner he knew, in a manner not. If he did not in an unqualified sense of the term know the existence of this triangle, how could he know without qualification that its angles were equal to two right angles? No: clearly he knows not without qualification but only in the sense that he knows universally.

which says (Expositio Posteriorum lib. 1 l. 3 "Pre-existent Knowledge of the Conclusion" n. 1):

First (71a24), he establishes the truth of the fact (veritatem), saying that before an induction or syllogism is formed to beget knowledge of a conclusion, that conclusion is somehow known and somehow not known: for, absolutely speaking (simpliciter), it is not known; but in a qualified sense (secundum quid), it is known. Thus, if the conclusion that a triangle has three angles equal to two right angles has to be proved, the one who obtains science [scientiam, knowledge] of this fact through demonstration already knew it in some way (quodammodo) before it was demonstrated; although absolutely speaking (simpliciter), he did not know it. Hence in one sense he already knew it, but in the full sense he did not. And the reason is that, as has been pointed out, the principles of the conclusion must be known beforehand. Now the principles in demonstrative matters are to the conclusion as efficient causes in natural things are to their effects; hence in Physics II [l. 5] the propositions of a syllogism are set in the genus of efficient cause. But an effect, before it is actually produced, pre-exists virtually (virtute) in its efficient causes but not actually (actu), which is to exist absolutely (simpliciter). In like manner, before it is drawn out of its demonstrative principles, the conclusion is pre-known virtually (virtute), although not actually (actu), in its self-evident principles. For that is the way it pre-exists in them. And so it is clear that it is not pre-known in the full sense (simpliciter), but in some sense (secundum quid).

In this way Aristotle solves the problem of the Meno, in which Plato insinuates "that either a man learns nothing or he learns what he already knew" (ibid. n. 2).