11 ideas
| 18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
| Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
| From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
| 18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
| Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
| From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
| 19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
| Full Idea: The proposition that understanding does not involve knowledge is widespread (for example, in discussions of what philosophy aims at), but hardly withstands scrutiny. If you do not know how a jet engine works, you do not understand how it works. | |
| From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.24) | |
| A reaction: This seems a bit disingenuous. As in 'Theaetetus', knowing the million parts of a jet engine is not to understand it. More strongly - how could knowledge of an infinity of separate propositional truths amount to understanding on their own? |
| 19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
| Full Idea: An essential prerequisite for useful discussion of the relation between knowledge and understanding is systematic explicitness about what is to be known or understood. | |
| From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.25) | |
| A reaction: This is better. I say what needs to be known for understanding is the essence of the item under discussion (my PhD thesis!). Obviously understanding needs some knowledge, but I take it that epistemology should be understanding-first. That is the main aim. |
| 19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
| Full Idea: If we say our cognitive aim is to get knowledge, the opposing views are the naturalistic view that what matters is just true belief (or just 'getting by'), or that there are rival epistemic goods such as understanding and wisdom. | |
| From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.17) | |
| A reaction: [compressed summary] I'm a fan of understanding. The accumulation of propositional knowledge would relish knowing the mass of every grain of sand on a beach. If you say the propositions should be 'important', other values are invoked. |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| Full Idea: Much theorizing about justification conflates issues of justified belief with issues of justified/blameless believers. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.12) | |
| A reaction: [They cite Kent Bach 1985] Presumably the only thing that really justifies a belief is the truth, or the actual facts. You could then say 'p is a justified belief, though no one actually believes it'. E.g. the number of stars is odd. |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| Full Idea: If knowledge is indeed unanalyzable, that could be seen as a liberation of justification to assume importance in its own right. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.11) | |
| A reaction: [They cite Kvanvig 2003:192 and Greco 2010:9-] See Scruton's Idea 3897. I suspect that we should just give up discussing 'knowledge', which is a woolly and uninformative term, and focus on where the real epistemological action is. |
| 7522 | A full neural account of qualia will give new epistemic access to them, beyond private experience [Churchlands] |
| Full Idea: When the hidden neurophysiological structure of qualia (if there is any) gets revealed by unfolding research, then we will automatically gain a new epistemic access to qualia, beyond each person's native and exclusive capacity for internal discrimination. | |
| From: Churchland / Churchland (Recent Work on Consciousness [1997]) | |
| A reaction: Carefully phrased and hard to deny, but something is impenetrable. What experience does an insect have when it encounters ultra-violet light? Nothing remotely interesting about their qualia is likely to emerge from the study of insect brains. |
| 7521 | It is question-begging to assume that qualia are totally simple, hence irreducible [Churchlands] |
| Full Idea: One of the crucial premises of the antireductionists - concerning the intrinsic, nonrelational, metaphysical simplicity of our sensory qualia - is a question-begging and unsupported assumption. | |
| From: Churchland / Churchland (Recent Work on Consciousness [1997]) | |
| A reaction: This is a key point for reductionists, with emphasis on the sheer numbers of connections involved in a simple quale (I estimate a billion involved in one small patch of red). |
| 7523 | The qualia Hard Problem is easy, in comparison with the co-ordination of mental states [Churchlands] |
| Full Idea: The so-called Hard Problem (of qualia) appears to be one of the easiest, in comparison with the problems of short-term memory, fluid and directable attention, the awake state vs sleep, and the unity of consciousness. | |
| From: Churchland / Churchland (Recent Work on Consciousness [1997]) | |
| A reaction: Most of their version of the Hard Problems centre on personal identity, and the centralised co-ordination of mental events. I am inclined to agree with them. Worriers about qualia should think more about the complexity of systems of neurons. |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
| Full Idea: Entailment is modelled in formal semantics as set inclusion. 'Cat' entails 'mammal' because the cats are a subset of the mammals. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.10) | |
| A reaction: I would have thought that this was only one type of entailment. 'Travelling to Iceland entails flying'. Travelling includes flying, the reverse of cats/mammals, to a very complex set-theoretic account is needed. Interesting. |