display all the ideas for this combination of texts
4 ideas
19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
Full Idea: Contrary to what Quine supposes, it is neither necessary nor desirable to interpret bound higher-order variables as ranging over sets. Sets are a species of object. They should range over entities of a completely different type: properties and relations. | |
From: Bob Hale (Necessary Beings [2013], 08.2) | |
A reaction: This helpfully clarifies something which was confusing me. If sets are objects, then 'second-order' logic just seems to be the same as first-order logic (rather than being 'set theory in disguise'). I quantify over properties, but deny their existence! |
19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
Full Idea: An old objection to conventionalism claims that it confuses sentences with propositions, confusing what makes sentences mean what they do with what makes them (as propositions) true. | |
From: Bob Hale (Necessary Beings [2013], 05.2) | |
A reaction: The conventions would presumably apply to the sentences, but not to the propositions. Since I think that focusing on propositions solves a lot of misunderstandings in modern philosophy, I like the sound of this. |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality. | |
From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4 | |
A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional. |
19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
Full Idea: In contrast with axiomatic systems, in natural deductions systems of logic neither the premises nor the conclusions of steps in a derivation need themselves be logical truths or theorems of logic. | |
From: Bob Hale (Necessary Beings [2013], 09.2 n7) | |
A reaction: Not sure I get that. It can't be that everything in an axiomatic proof has to be a logical truth. How would you prove anything about the world that way? I'm obviously missing something. |