20 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) |
| 9169 | A statement can be metaphysically necessary and epistemologically contingent [Putnam] |
| Full Idea: A statement can be (metaphysically) necessary and epistemologically contingent. Human intuition has no privileged access to metaphysical necessity. | |
| From: Hilary Putnam (Meaning and Reference [1973], p.160) | |
| A reaction: The terminology here is dangerously confusing. 'Contingent' is a term which (as Kripke insists) refers to reality, not to our epistemological abilities. The locution of adding the phrase "for all I know" seems to handle the problem better. |
| 5819 | Conceivability is no proof of possibility [Putnam] |
| Full Idea: Conceivability is no proof of possibility. | |
| From: Hilary Putnam (Meaning and Reference [1973], p.159) | |
| A reaction: This strikes me as a really basic truth which all novice philosophers should digest. It led many philosophers, especially rationalists, into all sorts of ill-founded claims about what is possible or necessary. Zombies, for instance… |
| 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. |
| 9168 | I can't distinguish elm trees, but I mean by 'elm' the same set of trees as everybody else [Putnam] |
| Full Idea: My concept of an elm tree is exactly the same as my concept of a beech tree (I blush to confess). ..We still say that the extension of 'elm' in my idiolect is the same as the extension of 'elm' in anyone else's, viz. the set of all elm trees. | |
| From: Hilary Putnam (Meaning and Reference [1973], p.154) | |
| A reaction: This example is clearer and less open to hair-splitting than his water/XYZ example. You could, with Putnam, say that his meaning of 'elm' is outside his head, but you could also say that he doesn't understand the word very well. |
| 5820 | 'Water' has an unnoticed indexical component, referring to stuff around here [Putnam] |
| Full Idea: Our theory can be summarized as saying that words like 'water' have an unnoticed indexical component: "water" is stuff that bears a certain similarity relation to the water around here. | |
| From: Hilary Putnam (Meaning and Reference [1973], p.160) | |
| A reaction: This is the causal theory of reference, which leads to externalism about concepts, which leads to an externalist view of thought, which undermines internal accounts of the mind like functionalism, and leaves little room for scepticism… Etc. |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. | |
| From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1 | |
| A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are. |
| 9170 | We need to recognise the contribution of society and of the world in determining reference [Putnam] |
| Full Idea: Traditional semantic theory leaves out two contributions to the determination of reference - the contribution of society and the contribution of the real world; a better semantic theory must encompass both. | |
| From: Hilary Putnam (Meaning and Reference [1973], p.161) | |
| A reaction: I strongly agree that there is a social aspect to reference-fixing, but I am much more dubious about the world 'determining' anything. The whole of his Twin Earth point could be mopped up by a social account, with 'experts' as the key idea. |
| 5817 | Language is more like a cooperative steamship than an individual hammer [Putnam] |
| Full Idea: There are tools like a hammer used by one person, and there are tools like a steamship which require cooperative activity; words have been thought of too much on the model of the first sort of tool. | |
| From: Hilary Putnam (Meaning and Reference [1973], p.156) | |
| A reaction: This clear thought strikes me as the most fruitful and sensible consequence of Wittgenstein's later ideas (as opposed to the relativistic 'language game' ideas). I am unconvinced that a private language is logically impossible, but it would be feeble. |
| 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) |
| 5818 | If water is H2O in the actual world, there is no possible world where it isn't H2O [Putnam] |
| Full Idea: Once we have discovered that water (in the actual world) is H2O, nothing counts as a possible world in which water isn't H2O. | |
| From: Hilary Putnam (Meaning and Reference [1973], p.159) | |
| A reaction: Presumably there could be a possible world in which water is a bit cloudy, so the fact that it is H2O is being judged as essential. Presumably the scientists in the possible world might discover that we are wrong about the chemistry of water? |