display all the ideas for this combination of texts
2 ideas
| 3746 | Logic seems to work for unasserted sentences [O'Connor] |
| Full Idea: If sentences can have truth-values only when they occur as asserted, it would be impossible to have a truth-functional basis to logic. | |
| From: D.J. O'Connor (The Correspondence Theory of Truth [1975], Ch.6) |
| 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! |