13 ideas
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 23551 | It is necessary for a belief that it be held for a length of time [Fricker,M] |
| Full Idea: A mental state cannot count as a belief unless it has a reasonable life expectancy. It must be the sort of thing that one is disposed to assert not only now but in the future too. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 2.3) | |
| A reaction: There are obvious counterexamples, where a firm belief is strongly formed, only to be dashed by a counterexample (such as a new witness in court) soon afterwards. That said, this idea is obviously correct. |
| 23558 | Offering knowledge needs accuracy and sincerity; receiving it needs testimonial justice [Fricker,M] |
| Full Idea: Accuracy and Sincerity sustain trust as regards contributing knowledge to the pool; Testimonial Justice helps sustain trust as regards acquiring knowledge from the pool. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 5.1) | |
| A reaction: Fricker's contribution is to show that acquiring knowledge has its own virtues, alongside discovering and communicating it. I take the underlying virtue to be absolute respect for all possible contributors. |
| 23550 | Burge says we are normally a priori entitled to believe testimony [Fricker,M] |
| Full Idea: In Tyler Burge's view we have an a priori entitlement for believing what others tell us, other things being equal. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 1.3 n11) | |
| A reaction: [Burge 'Content Preservation' 1992] Close to Davidson's Charity (that without a default assumption of truth-speaking language won't work at all). Davidson is right about casual conversation, but for important testimony Burge should be more cautious. |
| 23552 | We assess testimonial probabilities by the speaker, the listener, the facts, and the circumstances [Fricker,M] |
| Full Idea: A person should receive the word of his interlocutor in the light of the probability that someone like that would (be able and willing to) to tell someone like him the truth about something like this in circumstances like these. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 3.2) | |
| A reaction: That's a pretty good summary of the rational response to testimony. I can't think of any other factors. |
| 23553 | Testimonial judgement is not logical, but produces reasons and motivations [Fricker,M] |
| Full Idea: Moral/testimonial judgement is non-inferential, uncodifiable, intrinsically motivating, intrinsically reason-giving, and typically has an emotional aspect. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 3.3) | |
| A reaction: Fricker's compressed summary of her findings about testimony. The first words indicate her belief that assessment of testimony is a moral affair. |
| 23555 | Assessing credibility involves the impact of both the speaker's and the listener's social identity [Fricker,M] |
| Full Idea: For a hearer to identify the impact of identity power in their credibility judgements they must be alert to the impact not only of the speaker's social identity, but also the impact of the own social identity on their credibility judgements. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 4.1) | |
| A reaction: [why are all sentences in academic writing twice as long as they need to be? - that question is deeper than it looks!] This is a salutary warning. Not just 'what are my prejudices?', but also 'what is this person willing to tell a person like me?'. |
| 23554 | Judgements can be unreflective and non-inferential, yet rational, by being sensitive to experience [Fricker,M] |
| Full Idea: Our idea of testimonial sensibility is a spontaneous critical sensitivity permanently in training and adapting to experience. …This gives us a picture of how judgements can be rational yet unreflective, critical yet non-inferential. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 3.4) | |
| A reaction: Love this. I want to connect human reasoning to good judgement by animals, and I offer the word 'sensible' to bridge the gap. Dogs and scientists can be sensible. Fricker spells out more fully what I have in mind, with reference to testimony. |
| 23557 | To judge agents in remote times and cultures we need a moral resentment weaker than blame [Fricker,M] |
| Full Idea: I think that identifying forms of moral resentment that fall short of blame but which are agent-directed is the key to achieving appropriate moral response across historical and cultural distance. | |
| From: Miranda Fricker (Epistemic Injustice [2007], 4.2) | |
| A reaction: Very good. Simple blame for horrible actions performed in remote rather horrible societies is pointless. But switching off moral sensibilities when reading history and anthropology looks like a slippery slope, so 'moral resentment' is nice. |