20 ideas
9254 | In philosophy the truth can only be reached via the ruins of the false [Prichard] |
Full Idea: In philosophy the truth can only be reached via the ruins of the false. | |
From: H.A. Prichard (What is the Basis of Moral Obligation? [1925]) | |
A reaction: A lovely remark! In a flash you suddenly see why philosophers expend such vast energy on such unpromising views of reality (e.g. idealism, panpsychism). This might be the best definition of philosophy I have yet discovered. |
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) |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
From: Ian Rumfitt ("Yes" and "No" [2000]) | |
A reaction: This is the standard view which Rumfitt sets out to challenge. |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
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. |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
9256 | I see the need to pay a debt in a particular instance, and any instance will do [Prichard] |
Full Idea: How can I be brought to see the truth of the principle of paying a debt except in connection with a particular instance? For this purpose any instance will do. If I cannot see that I ought to pay this debt, I shall not see that I ought to a debt. | |
From: H.A. Prichard (What is the Basis of Moral Obligation? [1925]) | |
A reaction: This isn't quite particularism, which would (I think) say that the degree of obligation will never be quite the same in any two situations, and so one instance will not suffice to understand the duty. |
9257 | The complexities of life make it almost impossible to assess morality from a universal viewpoint [Prichard] |
Full Idea: Owing to the complication of human relations, the problem of what one ought to do from the point of view of life as a whole is one of intense difficulty. | |
From: H.A. Prichard (What is the Basis of Moral Obligation? [1925]) | |
A reaction: I suspect that the difficulty is not the problems engendered by complexity, but that there is no answer available from the most objective point of view. Morality simply is a matter of how daily life is conducted, with medium-term goals only. |
9255 | Seeing the goodness of an effect creates the duty to produce it, not the desire [Prichard] |
Full Idea: The appreciation of the goodness of the effect is different from desire for the effect, and will originate not the desire but the sense of obligation to produce it. | |
From: H.A. Prichard (What is the Basis of Moral Obligation? [1925]) | |
A reaction: A wonderful rebuttal of Hume, and a much better account of duty than Kant's idea that it arises from reason. Perception of value is what generates duty. And (with Frankfurt) we may say that love is what generates value. |
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) |