17 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) |
| 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. |
| 22049 | Transcendental idealism aims to explain objectivity through subjectivity [Bowie] |
| Full Idea: The aim of transcendental idealism is to give a basis for objectivity in terms of subjectivity. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 1) | |
| A reaction: Hume used subjectivity to undermine the findings of objectivity. There was then no return to naive objectivity. Kant's aim then was to thwart global scepticism. Post-Kantians feared that he had failed. |
| 22055 | The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie] |
| Full Idea: The Idealist saw in Kant that knowledge, which depends on the spontaneity of judgement, and self-determined spontaneous action, can be seen as sharing the same source, which is not accessible to scientific investigation. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010]) | |
| A reaction: This is the 'spontaneity' of judgements and choices which was seen as the main idea in Kant. It inspired romantic individualism. The judgements are the rule-based application of concepts. |
| 22054 | German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie] |
| Full Idea: A central aim of German Idealism is to overcome Kant's oppositions between appearances and thing in themselves, and between receptivity and spontaneity. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 2) | |
| A reaction: I have the impression that there were two strategies: break down the opposition within the self (Fichte), or break down the opposition in the world (Spinozism). |
| 22056 | Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie] |
| Full Idea: A crucial idea for German Idealism (from Hamann) is that apparently passive receptivity and active spontaneity are in fact different degrees of the same 'activity, and the gap between subject and world can be closed. | |
| From: Andrew Bowie (German Philosophy: a very short introduction [2010], 3) | |
| A reaction: The 'passive' bit seems to be Hume's 'impressions', which are Kant's 'intuitions', which need 'spontaneous' interpretation to become experiences. Critics of Kant said this implied a dualism. |
| 9379 | A sentence is obvious if it is true, and any speaker of the language will instantly agree to it [Quine] |
| Full Idea: A sentence is obvious if (a) it is true and (b) any speaker of the language is prepared, for any reason or none, to assent to it without hesitation, unless put off by being asked so obvious a question. | |
| From: Willard Quine (Reply to Hellman [1975], p.206), quoted by Paul Boghossian - Analyticity Reconsidered §III | |
| A reaction: This comes from someone who is keen to deny a priori knowledge, but what are we to make of the expostulations "It's obvious, you idiot!", and "Now I see it, it's obvious!", and "It seemed obvious, but I was wrong!"? |
| 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. |
| 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) |