3 ideas
| 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
| Full Idea: Priest and Routley have developed paraconsistent relevant logic. 'Relevant' logics insist on there being some sort of connection between the premises and the conclusion of an argument. 'Paraconsistent' logics allow contradictions. | |
| From: report of Graham Priest (works [1998]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8 | |
| A reaction: Relevance blocks the move of saying that a falsehood implies everything, which sounds good. The offer of paraconsistency is very wicked indeed, and they are very naughty boys for even suggesting it. |
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties). | |
| From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1) | |
| A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it. |
| 6672 | Moore's Paradox: you can't assert 'I believe that p but p is false', but can assert 'You believe p but p is false' [Moore,GE, by Lowe] |
| Full Idea: Moore's Paradox says it makes no sense to assert 'I believe that p, but p is false', even though it makes perfectly good sense to assert 'I used to believe p, but p is false' or 'You believe p, but p is false'. | |
| From: report of G.E. Moore (works [1905]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.10 | |
| A reaction: I'm not sure if this really deserves the label of 'paradox'. I take it as drawing attention to the obvious fact that belief is commitment to truth. I think my assessment that p is true is correct, but your assessment is wrong. ('True' is not redundant!) |