7 ideas
| 11074 | 'It is true that this follows' means simply: this follows [Wittgenstein] |
| Full Idea: The proposition: "It is true that this follows from that" means simply: this follows from that. | |
| From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6 | |
| A reaction: Presumably this remark is simply expressing Wittgenstein's later agreement with the well-known view of Ramsey. Early Wittgenstein had endorsed a correspondence view of truth. |
| 11073 | Two and one making three has the necessity of logical inference [Wittgenstein] |
| Full Idea: "But doesn't it follow with logical necessity that you get two when you add one to one, and three when you add one to two? and isn't this inexorability the same as that of logical inference? - Yes! it is the same. | |
| From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6 | |
| A reaction: This need not be a full commitment to logicism - only to the fact that the inferential procedures in mathematics are the same as those of logic. Mathematics could still have further non-logical ingredients. Indeed, I think it probably does. |
| 19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
| Full Idea: If I utter 'I know I have a hand' then I can only be reckoned a cooperative conversant by my interlocutors on the assumption that there was a real question as to whether I have a hand. | |
| From: John Hawthorne (The Case for Closure [2005], 2) | |
| A reaction: This seems to point to the contextualist approach to global scepticism, which concerns whether we are setting the bar high or low for 'knowledge'. |
| 20769 | Sphaerus he was not assenting to the presence of pomegranates, but that it was 'reasonable' [Sphaerus, by Diog. Laertius] |
| Full Idea: When Sphaerus accepted pomegranates from the king, he was accused of assenting to a false presentation, to which Sphaerus replied that what he had assented to was not that they were pomegranates, but that it was reasonable that they were pomegranates. | |
| From: report of Sphaerus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.177 | |
| A reaction: He then cited the stoic distinction between a 'graspable' presentation and a 'reasonable' one. This seems a rather helpful response to Dretske's zebra problem. I like the word 'sensible' in epistemology, because animals can be sensible. |
| 19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
| Full Idea: Those who deny skepticism but accept closure will have to explain how we know the various 'heavyweight' skeptical hypotheses to be false. Do we then twist the concept of knowledge to fit the twin desiderata of closue and anti-skepticism? | |
| From: John Hawthorne (The Case for Closure [2005], Intro) | |
| A reaction: [He is giving Dretske's view; Dretske says we do twist knowledge] Thus if I remember yesterday, that has the heavyweight implication that the past is real. Hawthorne nicely summarises why closure produces a philosophical problem. |
| 19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
| Full Idea: Maybe one cannot know the logical consequences of the proposition that one knows, on account of the fact that small risks add up to big risks. | |
| From: John Hawthorne (The Case for Closure [2005], 1) | |
| A reaction: The idea of closure is that the new knowledge has the certainty of logic, and each step is accepted. An array of receding propositions can lose reliability, but that shouldn't apply to logic implications. Assuming monotonic logic, of course. |
| 19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
| Full Idea: How could we know that P and Q but not be in a position to know that P (as deniers of closure must say)? If my glass is full of wine, we know 'g is full of wine, and not full of non-wine'. How can we deny that we know it is not full of non-wine? | |
| From: John Hawthorne (The Case for Closure [2005], 2) | |
| A reaction: Hawthorne merely raises this doubt. Dretske is concerned with heavyweight implications, but how do you accept lightweight implications like this one, and then suddenly reject them when they become too heavy? [see p.49] |