18 ideas
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| Full Idea: Any new discovery as to mathematical method and principles is likely to upset a great deal of otherwise plausible philosophising, as well as to suggest a new philosophy which will be solid in proportion as its foundations in mathematics are securely laid. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.283) | |
| A reaction: This is a manifesto for modern analytic philosophy. I'm not convinced, especially if a fictionalist view of maths is plausible. What Russell wants is rigour, but there are other ways of getting that. Currently I favour artificial intelligence. |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
| Full Idea: Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: Thagard picked this remark out, in support of his work on coherence. |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| Full Idea: The law of contradiction must have been originally discovered by generalising from instances, though, once discovered, it was found to be quite as indubitable as the instances. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) |
| 7332 | There is a huge range of sentences of which we do not know the logical form [Davidson] |
| Full Idea: We do not know the logical form of sentences about counterfactuals, probabilities, causal relations, belief, perception, intention, purposeful action, imperatives, optatives, or interrogatives, or the role of adverbs, adjectives or mass terms. | |
| From: Donald Davidson (Truth and Meaning [1967], p.35) | |
| A reaction: [compressed] This is the famous 'Davidson programme', where teams of philosophers work out the logical forms for this lot, thus unravelling the logic of the world. If they are beavering away, some sort of overview should have emerged by now... |
| 17629 | Which premises are ultimate varies with context [Russell] |
| Full Idea: Premises which are ultimate in one investigation may cease to be so in another. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
| Full Idea: In mathematics, except in the earliest parts, the propositions from which a given proposition is deduced generally give the reason why we believe the given proposition. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17640 | Finding the axioms may be the only route to some new results [Russell] |
| Full Idea: The premises [of a science] ...are pretty certain to lead to a number of new results which could not otherwise have been known. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.282) | |
| A reaction: I identify this as the 'fruitfulness' that results when the essence of something is discovered. |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| Full Idea: It is an apparent absurdity in proceeding ...through many rather recondite propositions of symbolic logic, to the 'proof' of such truisms as 2+2=4: for it is plain that the conclusion is more certain than the premises, and the supposed proof seems futile. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) | |
| A reaction: Famously, 'Principia Mathematica' proved this fact at enormous length. I wonder if this thought led Moore to his common sense view of his own hand - the conclusion being better than the sceptical arguments? |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| Full Idea: Even where there is the highest degree of obviousness, we cannot assume that we are infallible - a sufficient conflict with other obvious propositions may lead us to abandon our belief, as in the case of a hallucination afterwards recognised as such. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: This approach to fallibilism seems to arise from the paradox that undermined Frege's rather obvious looking axioms. After Peirce and Russell, fallibilism has become a secure norm of modern thought. |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| Full Idea: Although intrinsic obviousness is the basis of every science, it is never, in a fairly advanced science, the whole of our reason for believing any one proposition of the science. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) |
| 17631 | Induction is inferring premises from consequences [Russell] |
| Full Idea: The inferring of premises from consequences is the essence of induction. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) | |
| A reaction: So induction is just deduction in reverse? Induction is transcendental deduction? Do I deduce the premises from observing a lot of white swans? Hm. |
| 7772 | Compositionality explains how long sentences work, and truth conditions are the main compositional feature [Davidson, by Lycan] |
| Full Idea: Davidson's main argument in favour of his truth conditions theory of meaning is that compositionality is needed to account for our understanding of long, novel sentences, and a sentence's truth condition is its most obviously compositional feature. | |
| From: report of Donald Davidson (Truth and Meaning [1967]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: This seems to me exactly right. As we hear a new long sentence unfold, we piece together the meaning. At the end we may spot that the meaning is silly, or an unverifiable speculation, or not what the speaker intended - but it is too late! It means. |
| 7327 | Davidson thinks Frege lacks an account of how words create sentence-meaning [Davidson, by Miller,A] |
| Full Idea: Davidson thinks that Frege's model for a theory of semantic value (and thereby for a systematic theory of sense) is unsatisfactory, because it provides no useful or explanatory account of how sentence-meaning can be a function of word-meaning. | |
| From: report of Donald Davidson (Truth and Meaning [1967]) by Alexander Miller - Philosophy of Language 8.1 | |
| A reaction: Put like that, it is not clear to me how you could even start to explain how word-meaning contributes to sentence meaning. Try speaking any sentence slowly, and observe how the sentence meaning builds up. Truth is, of course, relevant. |
| 7769 | You can state truth-conditions for "I am sick now" by relativising it to a speaker at a time [Davidson, by Lycan] |
| Full Idea: Davidson's response to the problem of how you would state truth conditions for "I am sick now" ...is to relativize its truth to a particular speaker and a time. | |
| From: report of Donald Davidson (Truth and Meaning [1967]) by William Lycan - Philosophy of Language Ch.9 | |
| A reaction: Lycan is not happy with this, but it seems a reasonable way to treat the truth of any statement containing indexicals. Never mind the 'truth conditions theory of meaning' - just ask whether "I am sick now" is true. |
| 6179 | Should we assume translation to define truth, or the other way around? [Blackburn on Davidson] |
| Full Idea: The concern of some philosophers has been expressed by saying that whereas Tarski took translation for granted, and sought to understand truth, Davidson takes truth for granted, and seeks to understand translation. | |
| From: comment on Donald Davidson (Truth and Meaning [1967]) by Simon Blackburn - Oxford Dictionary of Philosophy p.82 | |
| A reaction: We can just say that the two concepts are interdependent, but my personal intuitions side with Davidson. If you are going to take something as fundamental and axiomatic, truth looks a better bet than translation. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| Full Idea: The law of gravitation leads to many consequences which could not be discovered merely from the apparent motions of the heavenly bodies. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.275) |