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Full Idea
Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth.
Gist of Idea
Intuitionists rely on assertability instead of truth, but assertability relies on truth
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.143
A Reaction
I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed.
Related Idea
Idea 18073 Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
| 18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
| 18073 | Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| 13715 | You can employ intuitionist logic without intuitionism about mathematics [Sider] |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| 8708 | Double negation elimination is not valid in intuitionist logic [Friend] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
| 18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |