21 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) |
| 1635 | Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine] |
| Full Idea: Mathematics reduces only to set theory, and not to logic proper… but set theory cannot claim the same firmness and obviousness as logic. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.69-70) |
| 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) |
| 7627 | You can't reduce epistemology to psychology, because that presupposes epistemology [Maund on Quine] |
| Full Idea: There is something seriously misguided about Quine's project of reducing epistemology to psychology, since psychology, like any of the natural sciences, presupposes an epistemology. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Barry Maund - Perception Ch.1 | |
| A reaction: I wonder if epistemology presupposes psychology? Belief, for example, is a category of folk psychology, which could be challenged. There is a quiet battle going on between philosophy and science. |
| 8871 | We should abandon a search for justification or foundations, and focus on how knowledge is acquired [Quine, by Davidson] |
| Full Idea: Quine is suggesting that philosophy should abandon the attempt to provide a foundation for knowledge, or otherwise justify it, and should instead give an account of how knowledge is acquired. | |
| From: report of Willard Quine (Epistemology Naturalized [1968]) by Donald Davidson - Epistemology Externalized p.193 | |
| A reaction: If you are going to explain how 'knowledge' is acquired, you'd better know what knowledge is. My suspicion is that Quine would be quite happy (in the pragmatist tradition) to just focus on belief, and forget about knowledge entirely. |
| 8826 | If we abandon justification and normativity in epistemology, we must also abandon knowledge [Kim on Quine] |
| Full Idea: Quine asks us to set aside the entire framework of justification-centered epistemology, ..and repudiate normativity. ..But then knowledge itself drops out of epistemology, for our concept of knowledge is inseparably tied to that of justification. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Jaegwon Kim - What is 'naturalized epistemology'? p.305 | |
| A reaction: Presumably this would not bother Quine, who wants to hand so-called 'epistemology' over to the psychologists. A psychological account of belief seems plausible. Presumably false beliefs could only be pragmatically characterised. |
| 8827 | Without normativity, naturalized epistemology isn't even about beliefs [Kim on Quine] |
| Full Idea: If normativity is wholly excluded from naturalized epistemology it cannot even be thought of as being about beliefs. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Jaegwon Kim - What is 'naturalized epistemology'? p.306 | |
| A reaction: And if it doesn't refer to beliefs, it certainly doesn't refer to knowledge. One might try to subsume normativity under evolutionary pragmatic 'drives', or something. Quine's project would then become wildly speculative, and hence boring. |
| 8899 | Epistemology is a part of psychology, studying how our theories relate to our evidence [Quine] |
| Full Idea: Epistemology falls into place as a chapter of psychology, and hence of natural science. ..We study meagre input and torrential output, to see how evidence relates to theory, and in what ways one's theory of nature transcends any available evidence. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.83) | |
| A reaction: It depends what you are interested in. If you just want to know what makes humans tick, then Quine is your man, but if you want to know things in general, and want to know how to get it right, then the normative side of epistemology is unavoidable. |
| 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. |
| 8898 | Inculcations of meanings of words rests ultimately on sensory evidence [Quine] |
| Full Idea: All inculcation of meanings of words must rest ultimately on sensory evidence. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.75) | |
| A reaction: This betrays Quine's behaviourist tendencies, and rules out introspection, definitions and inferences. Quine's conclusion is fairly total scepticism about meaning, but that is not surprising, given his external and meaningless starting point. |
| 8900 | In observation sentences, we could substitute community acceptance for analyticity [Quine] |
| Full Idea: Perhaps the controversial notion of analyticity can be dispensed with, in our definition of observation sentences, in favour of the straightforward attitude of community-wide acceptance. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.86) | |
| A reaction: That might be a reasonable account of 'bachelors'. If the whole community accepts 'God exists', does that make it analytic? If a whole (small!) community claims to actually observe a ghost or a flying saucer, is that then analytic? |
| 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) |