3 ideas
| 18801 | Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett] |
| Full Idea: Explanations of classical negation assume that knowing what it is for the truth-condition of some statement to obtain, independently of recognising it to obtain, we thereby know what it is for it NOT to obtain; but this presupposes classical negation. | |
| From: Michael Dummett (The Logical Basis of Metaphysics [1991], p.299), quoted by Ian Rumfitt - The Boundary Stones of Thought 1.1 | |
| A reaction: [compressed wording] This is Dummett explaining why he prefers intuitionistic logic, with its doubts about double negation. |
| 17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
| Full Idea: In 1846 De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated 'universe of discourse'. It replaced Boole's original - and metaphysically a bit suspect - universe of 'all things'. | |
| From: report of Augustus De Morgan (works [1846]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 | |
| A reaction: This not only brings formal logic under control, but also reflects normal talk, because there is always an explicit or implicit domain of discourse when we talk. Of virtually any conversation, you can say what it is 'about'. |
| 1422 | God's existence is either necessary or impossible, and no one has shown that the concept of God is contradictory [Malcolm] |
| Full Idea: God's existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists. | |
| From: Norman Malcolm (Anselm's Argument [1959], §2) | |
| A reaction: The concept of God suggests paradoxes of omniscience, omnipotence and free will, so self-contradiction seems possible. How should we respond if the argument suggests God is necessary, but evidence suggests God is highly unlikely? |