Prior to reading this treatise by Aristotle, I thought that the man’s *other* treatises were complex.
The Prior Analytics is a study of the art of developing a syllogism. That concept, from the realm of deductive reasoning, will be familiar to anyone who has taken a logic class, and indeed is something that you may have been exposed to in a freshman English class at your college or university. The concept of the syllogism, as it is usually taught in contemporary times, generally involves three things:
• A major premise - a broad, all-encompassing statement that is held to be always true;
• A minor premise - a more specific statement, all of the elements of which are contained within the major premise; and
• A conclusion that should follow logically from the premises.
A well-known example of the syllogism, one that you may have heard back at university, is
• "All human beings are mortal." (major premise)
• "Socrates is a human being." (minor premise)
• "Therefore, Socrates is mortal." (conclusion)
All of which seems pretty straightforward – until one finds that in the Prior Analytics, Aristotle is interested in discussing syllogisms with a lot more moving parts than that.
Throughout the Prior Analytics, Aristotle is interested in seeing how the elements of a potential syllogism can or cannot be logically related to one another, as when he writes that “if it is not possible that A should belong to any B, but B may belong to some of the C’s, it is necessary that A should not belong to some of the C’s. For if A belongs to all C, but cannot belong to any B, neither can B belong to any A.”
You get the idea. It can help to take notes, and to try out applications of these principles.
I found that I got more out of the Prior Analytics when Aristotle offered specific examples in support of his principles – something that I have often found when reading the philosopher’s work, as when he states that “A term which is repeated in the premises ought to be joined to the first extreme, not to the middle”, and then offers this example:
I mean for example that if a syllogism should be made proving that there is knowledge of justice, that it is good, the expression “that it is good”…should be joined to the first term. Let A stand for “knowledge that it is good,” B for good, C for justice. It is true to predicate A of B. For of the good, there is knowledge that it is good. It is also true to predicate C of B. For justice is identical with a good….But if the expression “that it is good” were added to B, the conclusion will not follow: for A will be true of B, but B will not be true of C.
Where Aristotle does not provide specifics of that kind, the relations that he sets forth between and among various premises are more difficult to understand.
It can also take some time getting used to the terms that Aristotle likes to use to set forth his ideas, as when he writes that “Demonstration per impossibile differs from ostensive proof in that it posits what it wishes to refute by reduction to a statement admitted to be false; whereas ostensive proof starts from admitted positions.” The term “demonstration per impossibile can be related to the concept of reductio ad absurdum - showing, by tracing out the logical consequences of a premise, that said premise would inevitably lead to an absurd or self-contradictory conclusion - and “ostensive proof” is simply proving by showing examples. It was a similar sort of learning experience, for me, when Aristotle wrote earlier in the Prior Analytics about what happens “whenever the major premise is universal, but assertoric, not problematic”. The term “assertoric,” it turns out, simply means that one is asserting that something is true – e.g., “Baltimore is larger than Gaithersburg” – whereas “problematic” refers to setting forth the problem of whether something could be true, so that an attempt can be made to solve the problem– e.g., “Gaithersburg could have a more fully functional infrastructure than Baltimore.”
A first reading of any Aristotlelian treatise generally leaves me feeling as though I just went 15 rounds with a boxing champion; I usually feel pretty beat-up afterward. But I appreciate the chance to struggle with the ideas being set forth by one of the greatest minds in all of human history. And I know that I will want to return to the Prior Analytics someday – before I go on to its no-doubt-just-as-challenging sequel, the Posterior Analytics.