6 ideas
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
Full Idea: If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence. | |
From: David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind' | |
A reaction: If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later. |
14263 | Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K] |
Full Idea: Under strong Kleene tables, a disjunction will be true if one of the disjuncts is true, regardless of whether or not the other disjunct has a truth-value; under the weak table it is required that the other disjunct also have a value. So for other cases. | |
From: Kit Fine (Some Puzzles of Ground [2010], n7) | |
A reaction: [see also p.111 of Fine's article] The Kleene tables seem to be the established form of modern three-valued logic, with the third value being indeterminate. |
14262 | Formal grounding needs transitivity of grounding, no self-grounding, and the existence of both parties [Fine,K] |
Full Idea: The general formal principles of grounding are Transitivity (A«B, B«C/A«C: if A helps ground B and B helps C, then A helps C), Irreflexivity (A«A/absurd: A can't ground itself) and Factivity (A«B/A; A«/B: for grounding both A and B must be the case). | |
From: Kit Fine (Some Puzzles of Ground [2010], 4) |
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. |