display all the ideas for this combination of philosophers
3 ideas
| 5395 | Demonstration always relies on the rule that anything implied by a truth is true [Russell] |
| Full Idea: All demonstrations involve the principle that 'anything implied by a true proposition is true', or 'whatever follows from a true proposition is true'. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: This is modus ponens, a broad principle of rationality, rather than of strict logicality, because it covers practical inferences and vague propositions. Presumably truth is a prior concept to implication, and therefore more metaphysically basic. |
| 14106 | Implication cannot be defined [Russell] |
| Full Idea: A definition of implication is quite impossible. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §016) |
| 14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
| Full Idea: It would be a vicious circle to define material implication as meaning that if one proposition is true, then another is true, for 'if' and 'then' already involve implication. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §037) | |
| A reaction: Hence the preference for defining it by the truth table, or as 'not-p or q'. |