more on this theme | more from this text
Full Idea
We can get a less ontologically perilous presentation of the semantics of the predicate calculus by using sets instead of concepts.
Gist of Idea
An ontologically secure semantics for predicate calculus relies on sets
Source
Vann McGee (Logical Consequence [2014], 4)
Book Ref
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.36
A Reaction
The perilous versions rely on Fregean concepts, and notably Russell's 'concept that does not fall under itself'. The sets, of course, have to be ontologically secure, and so will involve the iterative conception, rather than naive set theory.
Related Idea
Idea 18752 'The concept "horse"' denotes a concept, yet seems also to denote an object [Frege, by McGee]
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |