7 ideas
| 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. |
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
| A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
| 8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
| Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
| A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
| 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. |