display all the ideas for this combination of texts
6 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. |
| 10429 | It is best to say that a name designates iff there is something for it to designate [Sainsbury] |
| Full Idea: It is better to say that 'For all x ("Hesperus" stands for x iff x = Hesperus)', than to say '"Hesperus" stands for Hesperus', since then the expression can be a name with no bearer (e.g. "Vulcan"). | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: In cases where it is unclear whether the name actually designates something, it seems desirable that the name is at least allowed to function semantically. |
| 10425 | Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury] |
| Full Idea: Almost everyone agrees that intelligible definite descriptions may lack a referent; this has historically been a reason for not counting them among referring expressions. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.2) | |
| A reaction: One might compare indexicals such as 'I', which may be incapable of failing to refer when spoken. However 'look at that!' frequently fails to communicate reference. |
| 10438 | Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury] |
| Full Idea: Definite descriptions used with referential intentions (usually in subject position) are normally rigid, ..but in predicate position they are normally not rigid, because there is no referential intention. | |
| From: Mark Sainsbury (The Essence of Reference [2006], 18.5) | |
| A reaction: 'The man in the blue suit is the President' seems to fit, but 'The President is the head of state' doesn't. Seems roughly right, but language is always too complex for philosophers. |
| 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. |