School’s back, but I’m not!
However, since I have to keep the ol’ noggin running, since this blog can’t just be about res ludorum but also studiorum, I’ve decided to use it to help me crack open some philosophy. These aren’t meant to be brilliant pieces of scholarship or an actual introduction to whatever it is I’m reading (I’m, well, just not good enough for that yet). Just me posting my notes online. I’m not going to make much of If this stuff is interesting/helpful to anyone else aside from me, then great. If not, just ignore these posts. This time around: Aristotle’s Prior Analytics.
Logic is one of my minor regrets in university; I took enough of it to whet my appetite, but chickened out of it afterward, only finding myself in another logic class during my last semester. As a way to ease my way back into it and score some more Ancient philosophy cred, I thought I’d go way back to the beginning.
(I’m using the Robin Smith translation, published by Hackett. Smith sets out a formal model of Aristotle’s theory of deduction in the introduction; I just want to go through the text and break down what Aristotle is saying, giving my own thoughts as they come up, skipping over whatever I don’t find interesting. I want to avoid just regurgitating Smith’s interpretation, though, this being logic, there’s bound to be overlap)
Aristotle begins by stating that his inquiry “is about demonstration and its object is demonstrative science” (24a10), and laying out some terminology:
Premise: A sentence which predicates something of a subject, whether in affirmation or negation (“Socrates is human”; “Socrates is not human”)
Premises can take three forms:
– Universal: “All humans are Socrates”. “No humans are Socrates”
– Particular: “Some human is Socrates”. “Not every human is Socrates.”
– Indeterminate: “Pleasure is not a good” (Aristotle’s example)
The first two are pretty straightforward and map onto the universal and existential quantifiers of modern logic (I need to figure out how to get them working on wordpress), as is the last: it just lacks any quantification.
[From the ‘determinate’ premises, we can get four different types of premises (I’ll follow after Smith and use the classical aeio notation here):
– Universal affirmative (a)
– Universal negative (e)
– Particular affirmative (i)
– Particular negative (o)]
Term: The units which connect together to form a premise. Subject and predicate.
Deduction: When a new statement (conclusion) arises as a result of certain premises that are supposed and nothing else.
Complete Deduction: When the necessity of the deduction is made manifestly apparent by the premises themselves.
Incomplete Deduction: This seems to be the case of an enthymeme where one or more of the necessary premises is missing, or is only implied by another premise and itself requires a deduction.
Aristotle introduces the notion of modal “prefixes”, (possibility, necessity) but then immediately gives conversion rules for nonmodal premises.
– AeB (no A is B) converts to BeA (no B is A)
– AaB (All As are B) converts to BiA (Some B is A)
– AiB (Some A is B) converts to BiA (Some B is A)