3.7: Footnotes
- Page ID
- 374963
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- Even amputees. Being a biped is belonging to a species that naturally has two legs. ↵
- Note that denying that S is even partially included in P is the same as affirming that S and P are exclusive. ↵
- Since ‘Universal affirmative’—along with the names of the other three types of categorical proposition—is a bit of a mouthful, we will follow custom and assign the four categoricals (shorthand for ‘categorical propositions’) single-letter nicknames. The universal affirmative is the A proposition. ↵
- I’ve been using Trump in this example for a decade; I’m not going to stop just because he got elected president. Moreover, I take it that even Trump’s supporters would acknowledge that he’s a jerk. He tells it like it is and doesn’t care whose feelings get hurt—or something like that, right? ↵
- Just play along here. ↵
- The justification for this choice requires an argument, which I will not make here. The basic idea is that the ‘some aren’t’ bit that’s often communicated is not part of the core meaning of ‘some’; it’s an implicature, which is something that’s (often, but not always) communicated over and above the core meaning. ↵
- Aristotelian Logic is blind to tense: present, past, future, past perfect, future perfect, etc. are all the same. Sometimes the validity of an inference depends on tense. Aristotelian Logic cannot make such judgments. This is one of the consequences of limiting ourselves to a simpler, more precise portion of natural language. There are more advanced logics that take verb tense into consideration (they’re unsurprisingly called “tense logics”), but that’s a topic for a different book. ↵
- And the universal propositions are called superalterns. ↵
- I doubt it’s true; there’s gotta be at least one surfing priest, no? Then again…. Point is, the O doesn’t tell us whether it’s true or not. ↵
- As always, I’m using ‘priests’ to refer to Catholic priests, all of whom are men. ↵
- If you need proof, watch his final speech, given the night before he was shot, in Memphis. The stirring finish: “So I’m happy tonight. I’m not worried about anything. I’m not fearing any man. Mine eyes have seen the glory of the coming of the Lord!” Just watch it; trust me. Amazing. ↵
- We’re getting a little sloppy here. Technically, it’s propositions, not sentences, that are true or false. Further complication: we’re not even talking about actual sentences here, but generic sentence-patterns, with placeholder letters ‘S’ and ‘P’ standing in for actual class terms. Can those sorts of things be true or false? Ugh. Let’s just agree not to be fussy and not to worry about it. We all understand what’s going on. ↵
- It is not clear, however, that it is correct to attribute this view to Aristotle. While he clearly did believe that universal affirmative (A) propositions had existential import, it’s not clear that he thought the same about universal negatives. His rendering of the particular negative (O) was ‘Not all S are P’, which could be (trivially, vacuously) true when S is empty. In that case, O’s being the subaltern of E does not force us to attribute Existential Import to the latter. For discussion, see Parsons, Terence, "The Traditional Square of Opposition", The Stanford Encyclopedia of Philosophy (Summer 2015 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/s...ntries/square/>. ↵
- Sad but true: the invalid syllogistic forms do not have mnemonic nicknames. ↵