display all the ideas for this combination of texts
5 ideas
18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
Full Idea: Double Negation Elimination is a rule of inference which the classicist accepts without restriction, but which the intuitionist accepts only for decidable propositions. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) | |
A reaction: This cures me of my simplistic understanding that intuitionists just reject the rules about double negation. |
18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
Full Idea: Although intuitionistic propositional and first-order logics are sub-systems of the corresponding classical systems, intuitionistic second-order logic affirms the negations of some classical theorems. | |
From: Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1) |
19663 | We can allow contradictions in thought, but not inconsistency [Meillassoux] |
Full Idea: For contemporary logicians, it is not non-contradiction that provides the criterion for what is thinkable, but rather inconsistency. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) | |
A reaction: The point is that para-consistent logic might permit isolated contradictions (as true) within a system, but it is only contradiction across the system (inconsistencies) which make the system untenable. |
19664 | Paraconsistent logics are to prevent computers crashing when data conflicts [Meillassoux] |
Full Idea: Paraconsistent logics were only developed in order to prevent computers, such as expert medical systems, from deducing anything whatsoever from contradictory data, because of the principle of 'ex falso quodlibet'. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) |
19665 | Paraconsistent logic is about statements, not about contradictions in reality [Meillassoux] |
Full Idea: Paraconsistent logics are only ever dealing with contradictions inherent in statements about the world, never with the real contradictions in the world. | |
From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 3) | |
A reaction: Thank goodness for that! I can accept that someone in a doorway is both in the room and not in the room, but not that they are existing in a real state of contradiction. I fear that a few daft people embrace the logic as confirming contradictory reality. |