7 ideas
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| Full Idea: In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom. |
| 14365 | Scientific understanding is always the grasping of a correct explanation [Strevens] |
| Full Idea: I defend what I call the 'simple view', that scientific understanding is that state produced, and only produced, by grasping a correct explanation. | |
| From: Michael Strevens (No Understanding without Explanation [2011], Intro) | |
| A reaction: I like this because it clearly states what I take to be the view of Aristotle, and the key to understanding the whole of that philosopher's system. I take the view to be correct. |
| 14368 | We may 'understand that' the cat is on the mat, but not at all 'understand why' it is there [Strevens] |
| Full Idea: 'Understanding why' is quite separate from 'understanding that': you might be exquisitely, incandescently aware of the cat's being on the mat without having the slightest clue how it got there. My topic is understanding why. | |
| From: Michael Strevens (No Understanding without Explanation [2011], 2) | |
| A reaction: Can't we separate 'understand how' from 'understand why'? I may know that someone dropped a cat through my letterbox, but more understanding would still be required. (He later adds understanding 'with' a theory). |
| 14369 | Understanding is a precondition, comes in degrees, is active, and holistic - unlike explanation [Strevens] |
| Full Idea: Objectors to the idea that understanding requires explanation say that understanding is a precondition for explanation, that understanding comes in degrees, that understanding is active, and that it is holistic - all unlike explanations. | |
| From: Michael Strevens (No Understanding without Explanation [2011], 4) | |
| A reaction: He works through these four objections and replies to them, in defence of the thesis in Idea 14365. I agree with Strevens on this. |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
| Full Idea: Two propositions might contradict each other despite appearing self-evident when considered separately. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: Russell's proposal (Idea 5416) is important here, that self-evidence comes in degrees. If self-evidence was all-or-nothing, Grayling's point would be a major problem, but it isn't. Bonjour explores the idea more fully (e.g. Idea 3704) |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| Full Idea: Intentional theory is vacuous as psychology because it presupposes and does not explain rationality or intelligence. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.15?) | |
| A reaction: Virtually every philosophical theory seems to founder because it presupposes something like the thing it is meant to explain. I agree that 'intentionality' is a slightly airy concept that would probably reduce to something better. |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| Full Idea: Intentional systems don't really have beliefs and desires, but one can explain and predict their behaviour by ascribing beliefs and desires to them. This strategy is pragmatic, not right or wrong. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.7?) | |
| A reaction: If the ascription of beliefs and desires explains behaviour, then that is good grounds for thinking they might be real features of the brain, and even if that is not so, they are real enough as abstractions from brain events, like the 'economic climate'. |