9 ideas
| 13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
| Full Idea: Weak Limitation of Size: If there are no more Fs than Gs and the Gs form a collection, then Fs form a collection. Strong Limitation of Size: A property F fails to be collectivising iff there are as many Fs as there are objects. | |
| From: report of George Boolos (Iteration Again [1989]) by Michael Potter - Set Theory and Its Philosophy 13.5 |
| 13768 | Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington] |
| Full Idea: If your interest in logic is confined to applications to mathematics or other a priori matters, it is fine for validity to preserve certainty, ..but if you use conditionals when arguing about contingent matters, then great caution will be required. | |
| From: Dorothy Edgington (Conditionals [2001], 17.2.1) |
| 13770 | There are many different conditional mental states, and different conditional speech acts [Edgington] |
| Full Idea: As well as conditional beliefs, there are conditional desires, hopes, fears etc. As well as conditional statements, there are conditional commands, questions, offers, promises, bets etc. | |
| From: Dorothy Edgington (Conditionals [2001], 17.3.4) |
| 13764 | Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington] |
| Full Idea: Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? Are they non-truth-functional, like 'because' or 'before'? Do the values of A and B, in some cases, leave open the value of 'If A,B'? | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: I would say they are not truth-functional, because the 'if' asserts some further dependency relation that goes beyond the truth or falsity of A and B. Logical ifs, causal ifs, psychological ifs... The material conditional ⊃ is truth-functional. |
| 13765 | 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington] |
| Full Idea: If it were possible to have A true, B false, and If A,B true, it would be unsafe to infer B from A and If A,B: modus ponens would thus be invalid. Hence 'If A,B' must entail ¬(A & ¬B). | |
| From: Dorothy Edgington (Conditionals [2001], 17.1) | |
| A reaction: This is a firm defence of part of the truth-functional view of conditionals, and seems unassailable. The other parts of the truth table are open to question, though, if A is false, or they are both true. |
| 22480 | Possessing the virtue of justice disposes a person to good practical rationality [Foot] |
| Full Idea: If justice is a virtue it must make action good by disposing its possessor to goodness in practical rationality; the latter consisting of the right recognition of reasons, and corresponding action. | |
| From: Philippa Foot (Rationality and Virtue [1994], p.174) | |
| A reaction: This somewhat inverts Aristotle, who says the possessing of good practical reason is the key to acquiring the virtues. Foot suggests that possessing the virtue promotes the practical rationality. Someone can be sensible without being virtuous. |
| 22477 | Calling a knife or farmer or speech or root good does not involve attitudes or feelings [Foot] |
| Full Idea: No one thinks that calling a knife a good knife, a farmer a good farmer, a speech a good speech, a root a good root, necessarily expresses or even involves an attitude or feeling towards it. | |
| From: Philippa Foot (Rationality and Virtue [1994], p.163) | |
| A reaction: This is the Aristotelian idea (which I favour) that good derives from function. In such a case it seems obvious that it has nothing to do with expressing emotions. |
| 22478 | The essential thing is the 'needs' of plants and animals, and their operative parts [Foot] |
| Full Idea: The key notion is the concept of need, …as when we say what a plant or animal of a certain species needs to have, …and what its operative features, such roots, leaves, hearts and lungs, need to do. | |
| From: Philippa Foot (Rationality and Virtue [1994], p.164) | |
| A reaction: Good. That takes it away from the idea of a function, which could be possessed by an inanimate machine (even though that still entails success and failure). Strictly, we need oxygen, but the goodness resides in the lungs. |
| 22479 | Observing justice is necessary to humans, like hunting to wolves or dancing to bees [Foot] |
| Full Idea: The teaching and observing of the rules of justice is as necessary a part of the life of human beings as hunting together in packs with a leader is a necessary part of the lives of wolves, or dancing part of the life of the dancing bee. | |
| From: Philippa Foot (Rationality and Virtue [1994], p.168) | |
| A reaction: So why are some men unjust? All wolves hunt, and all appropriate bees dance. A few men even thrive on injustice. |