17 ideas
| 14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
| Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
| A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
| From: George Boolos (On Second-Order Logic [1975], p.45) | |
| A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
| 10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
| Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
| From: George Boolos (On Second-Order Logic [1975], p.44) | |
| A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
| From: George Boolos (On Second-Order Logic [1975], p.46) | |
| A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
| 10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
| Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
| From: George Boolos (On Second-Order Logic [1975], p.52) | |
| A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
| 13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
| Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
| From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
| 10833 | Many concepts can only be expressed by second-order logic [Boolos] |
| Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
| From: George Boolos (On Second-Order Logic [1975], p.48) |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |