16 ideas
| 9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
| Full Idea: It is not out of the question to hold that without circular justifications there is no reasonableness at all. That is the view of a certain kind of coherence theorist. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 2) | |
| A reaction: This nicely captures a gut feeling I have had for a long time. Being now thoroughly converted to coherentism, I am drawn to the idea - like a moth to a flame. But how do we distinguish cuddly circularity from its cruel and vicious cousin? |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| Full Idea: A natural principle is the same kind of paradox will have the same kind of solution. Standardly Ramsey's first group are solved by denying the existence of some totality, and the second group are less clear. But denial of the groups sink both. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §5) | |
| A reaction: [compressed] This sums up the argument of Priest's paper, which is that it is Ramsey's division into two kinds (see Idea 13334) which is preventing us from getting to grips with the paradoxes. Priest, notoriously, just lives with them. |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| Full Idea: König: there are indefinable ordinals, and the least indefinable ordinal has just been defined in that very phrase. (Recall that something is definable iff there is a (non-indexical) noun-phrase that refers to it). | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: Priest makes great subsequent use of this one, but it feels like a card trick. 'Everything indefinable has now been defined' (by the subject of this sentence)? König, of course, does manage to pick out one particular object. |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| Full Idea: Berry: if we take 'x is a natural number definable in less than 19 words', we can generate a number which is and is not one of these numbers. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [not enough space to spell this one out in full] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| Full Idea: Richard: φ(x) is 'x is a definable real number between 0 and 1' and ψ(x) is 'x is definable'. We can define a real by diagonalization so that it is not in x. It is and isn't in the set of reals. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [this isn't fully clear here because it is compressed] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| Full Idea: Burali-Forti: φ(x) is 'x is an ordinal', and so w is the set of all ordinals, On; δ(x) is the least ordinal greater than every member of x (abbreviation: log(x)). The contradiction is that log(On)∈On and log(On)∉On. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| Full Idea: Mirimanoff: φ(x) is 'x is well founded', so that w is the cumulative hierarchy of sets, V; &delta(x) is just the power set of x, P(x). If x⊆V, then V∈V and V∉V, since δ(V) is just V itself. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| Full Idea: In the family of the Liar is the Knower Paradox, where φ(x) is 'x is known to be true', and there is a set of known things, Kn. By knowing a sentence is not in the known sentences, you know its truth. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [mostly my wording] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| Full Idea: There are liar chains which fit the pattern of Transcendence and Closure, as can be seen with the simplest case of the Liar Pair. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [Priest gives full details] Priest's idea is that Closure is when a set is announced as complete, and Transcendence is when the set is forced to expand. He claims that the two keep coming into conflict. |
| 9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
| Full Idea: Propositions such as 'People usually tell the truth' seem to count as default reasonable, but it is odd to count them as a priori. Empirical indefeasibility seems the obvious way to distinguish those default reasonable propositions that are a priori. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 1) | |
| A reaction: Sounds reasonable, but it would mean that all the uniformities of nature would then count as a priori. 'Every physical object exerts gravity' probably has no counterexamples, but doesn't seem a priori (even if it is necessary). See Idea 9164. |
| 9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
| Full Idea: I argue not that our most basic rules are a priori or empirically indefeasible, but that we treat them as empirically defeasible and indeed a priori; we don't regard anything as evidence against them. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 4) | |
| A reaction: This is the fictionalist view of a priori knowledge (and of most other things, such as mathematics). I can't agree. Most people treat heaps of a posteriori truths (like the sun rising) as a priori. 'Mass involves energy' is indefeasible a posteriori. |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| Full Idea: I call 'entitlement' (as opposed to justification) the epistemic rights or warrants that need not be understood by or even be accessible to the subject. | |
| From: Tyler Burge (Content Preservation [1993]), quoted by Paul Boghossian - Analyticity Reconsidered §III | |
| A reaction: I espouse a coherentism that has both internal and external components, and is mediated socially. In Burge's sense, animals will sometimes have 'entitlement'. I prefer, though, not to call this 'knowledge'. 'Entitled true belief' is good. |
| 9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
| Full Idea: Reliability is not a 'factual property'; in calling a rule reasonable we are evaluating it, and all that makes sense to ask about is what we value. We place a high value on the reliability of our inductive and perceptual rules that lead to truth. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 5) | |
| A reaction: This doesn't seem to be a contradiction of reliabilism, since truth is a pretty widespread epistemological value. If you do value truth, then eyes are pretty reliable organs for attaining it. Reliabilism is still wrong, but not for this reason. |
| 9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
| Full Idea: Reliability is not all we want in an inductive rule. Completely reliable methods are available, such as believing nothing, or only believing logical truths. But we don't value them, but value less reliable methods with other characteristics. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 3) | |
| A reaction: I would take this excellent point to be an advertisement for inference to the best explanation, which requires not only reliable inputs of information, but also a presiding rational judge to assess the mass of evidence. |
| 9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
| Full Idea: We should concede that different people have slightly different basic epistemological standards. ..I doubt that any clear sense could be given to the notion of 'correctness' here. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 5) | |
| A reaction: I think this is dead right. There is a real relativism about knowledge, which exists at the level of justification, rather than of truth. The scientific revolution just consisted of making the standards tougher, and that seems to have been a good idea. |
| 9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |
| Full Idea: If some inductive rule is basic for us, in the sense that we never assess it using any rules other than itself, then it must be one that we treat as empirically indefeasible (hence as fully a priori, given that it will surely have default status). | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 4) | |
| A reaction: This follows on from Field's account of a priori knowledge. See Ideas 9160 and 9164. I think of induction as simply learning from experience, but if experience goes mad I will cease to trust it. (A rationalist view). |