13 ideas
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| Full Idea: Most accounts of the concept of mathematical truth can be identified with serving one or another of either semantic theory (matching it to ordinary language), or with epistemology (meshing with a reasonable view) - always at the expense of the other. | |
| From: Paul Benacerraf (Mathematical Truth [1973], Intro) | |
| A reaction: The gist is that language pulls you towards platonism, and epistemology pulls you towards empiricism. He argues that the semantics must give ground. He's right. |
| 17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
| Full Idea: Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and anti-realists have a good epistemology but an unorthodox semantics. | |
| From: report of Paul Benacerraf (Mathematical Truth [1973]) by Mark Colyvan - Introduction to the Philosophy of Mathematics 1.2 |
| 9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
| Full Idea: The principle defect of the standard (platonist) account of mathematical truth is that it appears to violate the requirement that our account be susceptible to integration into our over-all account of knowledge. | |
| From: Paul Benacerraf (Mathematical Truth [1973], III) | |
| A reaction: Unfortunately he goes on to defend a causal theory of justification (fashionable at that time, but implausible now). Nevertheless, his general point is well made. Your theory of what mathematics is had better make it knowable. |
| 7566 | The Identity of Indiscernibles is really the same as the verification principle [Jolley] |
| Full Idea: Various writers have noted that the Identity of Indiscernibles is really tantamount to the verification principle. | |
| From: Nicholas Jolley (Leibniz [2005], Ch.3) | |
| A reaction: Both principles are false, because they are the classic confusion of epistemology and ontology. The fact that you cannot 'discern' a difference between two things doesn't mean that there is no difference. Things beyond verification can still be discussed. |
| 23438 | Full rationality must include morality [Foot] |
| Full Idea: You haven't got a full idea of rationality until you've got morality within it. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.35) | |
| A reaction: Does this mean that mathematical proofs are not rational, or that they are moral? |
| 23437 | Practical reason is goodness in choosing actions [Foot] |
| Full Idea: Practical rationality is goodness in respect of reason for actions, just as rationality of thinking is goodness in respect of beliefs. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.35) | |
| A reaction: It is very Greek to think that rationality involves goodness. There seems to be a purely instrumental form of practical reason that just gets from A to B, as when giving accurate street directions to someone. |
| 23436 | It is an odd Humean view to think a reason to act must always involve caring [Foot] |
| Full Idea: One would need a very special, very Humean, view about reasons for actions to think a man doesn't have a reason unless he cares. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.34-5) | |
| A reaction: She says she used to believe this, but was wrong. It is hard to imagine acting for reasons if they don't care about anything at all (even that it's their job). But then people just do care about things. |
| 23431 | Human defects are just like plant or animal defects [Foot] |
| Full Idea: We describe defects in human beings in the same way as we do defects in plants and animals. …You cannot talk about a river as being defective. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.33) | |
| A reaction: This is a much clearer commitment to naturalistic ethics than I have found in her more academic writings. My opinion of Foot (which was already high) went up when I read this interview. …She says vice is a defect of the will. |
| 23432 | Concepts such as function, welfare, flourishing and interests only apply to living things [Foot] |
| Full Idea: There are concepts which apply only to living things, considered in their own right, which would include function, welfare, flourishing, interests and the good of something. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.33) | |
| A reaction: This is a very Aristotelian view, with which I entirely agree. The central concept is function. |
| 23433 | Humans need courage like a plant needs roots [Foot] |
| Full Idea: A plant needs strong roots in the same way human beings need courage. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.33) | |
| A reaction: I'm not quite convince by the analogy, but I strongly agree with her basic approach. |
| 23434 | There is no fact-value gap in 'owls should see in the dark' [Foot] |
| Full Idea: If you say 'an owl should be able to see in the dark' …you're not going to think that there's a gap between facts and evaluation. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.33) | |
| A reaction: I take this to be a major and fundamental idea, which pinpoints the failure of Humeans to understand the world correctly. There is always total nihilism, of course, but that is a sort of blindness to how things are. Demanding 'proof' of values is crazy. |
| 23439 | Principles are not ultimate, but arise from the necessities of human life [Foot] |
| Full Idea: I don't believe in ultimate principles that must be simply affirmed or denied, but rather in an appeal to the necessities of human life. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], p.37) | |
| A reaction: I agree. Humans have a strong tendency to elevate anything which they consider important into an absolute (such as the value of life, or freedom). |
| 23435 | If you demonstrate the reason to act, there is no further question of 'why should I?' [Foot] |
| Full Idea: You lose the sense of 'should' if you go on saying 'why should I?' when you've finished the argument about what is rational to do, what you've got reason to do. | |
| From: Philippa Foot (Interview with Philippa Foot [2003], P.34) | |
| A reaction: Some people reify the concept of duty, so that they do what is required without caring about the reason. I suppose that would wither if they were shown that no reason exists. |