"Syllogisms which produce understanding"


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.


Posted 2019-02-03T11:42:54.640

Reputation: 199

For introduction to A's syllogism.

– Mauro ALLEGRANZA – 2019-02-03T12:33:36.630

See also John Corcoran, Aristotle's Demonstrative Logic, HPL (2009) and John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, HPL (2003).

– Mauro ALLEGRANZA – 2019-02-03T12:35:05.410

But syllogism in the "technical" sense is not all of formal logic. There are many more valid argument forms than syllogism (and Aristtotle was aware of this) and very few demonstartions of Euclid's Elements can be formalized with syllogism. – Mauro ALLEGRANZA – 2019-02-03T12:43:24.983

Aristotle does say that "demonstration is syllogism that can show the cause", and his meaning of "cause" is close to what we would call "explanation" or "reason why", see The Four Causes. See also a nice summary of demonstration as explanation in Cohen's Lectures on Posterior Analytics.

– Conifold – 2019-02-03T13:14:44.607

Are you asking: "How do we know when a syllogism is the efficient cause of understanding?" or "What makes a syllogism be the efficient cause of understanding?" – Geremia – 2019-02-05T18:52:16.883

@Geremia: Yes, that is exactly what I am saying. Thank you for clarifying. – user27928 – 2019-02-06T10:11:13.287



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).


Posted 2019-02-03T11:42:54.640

Reputation: 33 575


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 71a24:

  1. 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).


Posted 2019-02-03T11:42:54.640

Reputation: 6 907

This is perfect, thank you very much. Is there a particular book that explains the issues surrounding these matters (other than Aristotle's Prior/Posterior analytics which I found hard to understand). Note that I am simply trying to learn logic for the purposes of improving my ability to learn and understand things. Thus, if all that is needed is what you have said in your answer, then I am happy not to learn any further logic. Please clarify. – user27928 – 2019-02-06T10:17:48.333

(In particular, I am not interested in the different types of syllogisms and how they are made etc, because I have found that my mathematical education in proof writing has been more than sufficient for this.) – user27928 – 2019-02-06T10:18:51.847

@user27928 Perhaps The Material Logic of John of St. Thomas: Basic Treatises (which comes from his larger work, Ars Logica).

– Geremia – 2019-02-06T17:38:51.240

Dear Geremia, I am still very interested in this issue of how the four causes apply to knowledge/understanding. You quoted a passage which says "Now the principles in demonstrative matters are to the conclusion as efficient causes in natural things are to their effects". Does Aristotle also go into how the four causes in general can be applied to understanding? This links in very closely to some recent questions I posted: cont... – user27928 – 2019-04-29T16:16:52.123

This in general stems from my curiosity for understanding how exactly knowledge parallels the physical world. In the passage you quoted itself Aristotle makes this comparison. I am simply interested in how this comparison is amplified by a complete treatment of the four causes as applied to knowledge and understanding. al-Farabi seems to touch on this in question 1 I linked above. Anything which goes into this in more detail would be an excellent starting point for me. – user27928 – 2019-04-29T16:18:33.563

@user27928 Did you read Physics II [l. 5], cited above, esp. #183-198 on Aristotle saying (195ᵃ15) "All the causes now mentioned fall into four familiar divisions. …"?

– Geremia – 2019-04-29T17:45:59.123

I have read it, yes. However I was wondering if there was a more general treatment, maybe in one of Aristotle's logical works or his metaphysics. Or was this kind of knowledge learnt from his Physics? Is it not covered elsewhere in his works in as much detail? – user27928 – 2019-04-29T19:17:45.293

@user27928 Since semiotics is related to logic, you should read John of St. Thomas's Tractatus de Signis, esp. ch. 2 "The Definition and Divisions of Signs" (pp. 25-27), where he discusses the "fourfold cause of knowledge".

– Geremia – 2019-04-29T20:17:57.890

@user27928 (cf. also Deely's Basics of Semiotics or Four Ages of Understanding)

– Geremia – 2019-04-30T15:34:32.197

@user27928 Have you read "The Definition and Divisions of Signs" (pp. 25-27) yet? It's only 3 pages; it comes from John of St. Thomas (John Poinsot)'s Summulæ (beginners') books (Summulæ = "little summary treatises").

– Geremia – 2019-05-03T19:31:14.047

Dear Geremia, I have skimmed the chapter, however it doesn't quite seem to be what I am looking for. What makes this hard is not knowing what the subject is even called. If this was simply algebra for example I could simply ask someone to recommend me a good algebra book to start learning it. In this case however, I am searching for a science/art which I do not even know the name of. All I know is that it seems to be hinted at by Thomas Aquinas, al Farabi and Ibn Sina in various parts of their works, and seems to be an art by which one can know whether they have understood something or not. – user27928 – 2019-05-05T07:39:34.180

I should probably mention that Thomas Aquinas's foreward to his explanation of Aristotle's Posterior Analytics was very promising. Thus, I believe that the art I am looking for is simply what Aristotle explains in the Posterior Analytics. I have thus decided to start reading his Logical works. – user27928 – 2019-05-05T07:41:05.283

@user27928 "If this was simply algebra for example I could simply ask someone to recommend me a good algebra book to start learning it." Math pedagogy is quite diverse (there are Bourbaki, Russian, inductive, deductive, etc., styles); cf. #1 & #2 of Crowe's famous "Ten misconceptions about mathematics and its history."

– Geremia – 2019-05-05T20:57:03.600

@user27928 "I am searching for a science/art which I do not even know the name of." It's called logic, which is both a speculative science and an art ("this art is logic, i.e., the science [scientia = knowledge] of reason"). I, too, have struggled with logic; it is quite deep; see my question: "What is the philosophical study of classification called?"

– Geremia – 2019-05-05T21:01:09.737

Dear Geremia, thank you for the link. The reason I want to study this art is because during my studies of other subjects such (eg physics) I have found myself basically re-discovering the science of logic and spending a lot of my time meditating on logical questions rather than the subject I am studying itself. This is why I started searching for this science, which I don't even know the name of. I eventually stumbled across the Dialectic of Peter Ramus, and in the end I decided that this is what I was looking for. However, the problem is that Ramus does not seem to explain understanding... – user27928 – 2019-05-07T10:34:06.313

...theoretically. Instead, he focuses on structure and classification. His work certainly shows how one can structure and classify a science, but not how understanding works. In the end, I think I am now simply going to ignore the question of understanding and simply focus on understanding what I study in a natural way rather than trying to find a science for this. The problem with finding a science for this becomes apparent when one realizes that one has to understand the science itself without yet having studied the science of understanding. I feel it is better to leave understanding to... – user27928 – 2019-05-07T10:35:36.897

...nature and classification to logic. So classification is really the only problem in my opinion. Also, the problem with classification itself is classifying as you study a subject. Classifying after you are done is much easier. So at least for me, the problem reduces to "classifying while learning a new subject". Without getting into too much detail, the way I have found most useful for this is to skim the chapter/book you are reading before taking any notes, and note down the "sections" and "classifications" you find. For example, in a typical chapter of "work and energy" in physics, one... – user27928 – 2019-05-07T10:38:07.170

...will quickly find that there are two types of energy: kinetic and potential. Also, he will find that potential energy is described differently depending on whether the force is conservative or nonconservative. It is very Ramean. One could also simply note down the main topics they find by experimentation. just note down every new classification you come across, and collect them together and make that your classification. For example, when reading an experimental chemistry book, one will notice three main divisions: equipment, the actual experiment, the piece of theory needed to... – user27928 – 2019-05-07T10:41:49.277

...understand the experiment. These will form one's main divisions. Then one can read the chapter will classifying each proposition, definition, argument and application (applications are applications of propositions) into one of the categories. In fact, the classification could be an entirely mental thing, which I believe is best. Then one repeats this for other chapters, until one completes the book, always categorizing as they go along. By the time one finishes, one's classification should be detailed and complex. It is a mental tool rather than something that should necessarily be put... – user27928 – 2019-05-07T10:43:45.883

...into words. I like to keep in mind when studying that understanding is what I am looking for, not memorization or classification or any other superficial aspect of the subject. It is only understanding. Thus, I aim at understanding and meditation on what I am learning, while treating the other aspects as secondary tools. However, I have found classification to be the most useful for understanding, which is what Ramus seems to have believed too. Why this is the case eludes me. It would be nice to understand why it is the case, but for now I am happy to keep studying and understanding... – user27928 – 2019-05-07T10:45:32.923

...more important things. – user27928 – 2019-05-07T10:45:38.623

This is really the crux of the matter then: why is classification so bound up to understanding? This is what I believe Aquinas, al Farabi, Ibn Sina, Aristotle and others knew well using their science of logic (or metaphysics, or whatever science it was). A small clue I have gathered from my own studies is that classification does not lead to understanding if one does not understand the logical connection between the branches. One must understand why this branch is first, why this division has only two rather than three sub divisions, etc. So one must understand the "why" behind the tree. – user27928 – 2019-05-07T10:51:33.350

It is this "why" which I think leads to true understanding. Knowing the tree itself does not really help much when it comes to understanding. But going down the Ramean tree and asking "why". Why is this topic first? Why does this divide into two? Why does this subject start from here? What principles is this subject based on? I think that if this process is carried out backwards, then one can take off from the first principles of the subject to the subject preceding it, until one reaches metaphysics. I think this is what Aquinas and al Farabi were saying. Plato also discusses backwards.... – user27928 – 2019-05-07T10:54:21.177

...motion in his Republic. He says that mathematics doesn't deal with first principles, but only secondary ones. Mathematicians remain within these bounds as they do mahematics. Only the Dialectician, he says, is able to question the axioms of mathematics themselves and realize that they are not ultimate first principles. He can then travel backwards towards reality itself. So this science may be called "Dialectic" (as Plato and Plotinus called it), or Logic (as I believe al Farabi and Ibn Sina called it), or perhaps even metaphysics. It is the same science: the backwards ascent towards God. – user27928 – 2019-05-07T10:56:14.520

Let us continue this discussion in chat.

– Geremia – 2019-05-07T18:09:45.180