38 ideas
3600 | Slow and accurate thought makes the greatest progress [Descartes] |
Full Idea: Those who go forward only very slowly can progress much further if they always keep to the right path, than those who run and wander off it. | |
From: René Descartes (A Discourse on Method [1637], §1.2) | |
A reaction: Like Descartes' 'Method'. This seems to place a low value on 'nous' or intuition. |
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. |
3601 | Most things in human life seem vain and useless [Descartes] |
Full Idea: Looking at the various activities and enterprises of mankind with the eye of a philosopher, there is hardly one which does not seem to me vain and useless. | |
From: René Descartes (A Discourse on Method [1637], §1.3) | |
A reaction: Well, yes. The obvious retort is that everything is vain and useless; or if not, then certainly metaphysics is. Useful for what? Is ornamental gardening useless, or sport? Art? What is the use of cosmology? He's right, of course. |
3602 | Almost every daft idea has been expressed by some philosopher [Descartes] |
Full Idea: There is nothing one can imagine so strange or so unbelievable that has not been said by one or other of the philosophers. | |
From: René Descartes (A Discourse on Method [1637], §2.16) | |
A reaction: Actually I think that extensive areas of logical possibilities for existence remain totally unexplored. On the other hand, most of the metaphysical beliefs of most of the human race, including the majority of philosophers, strike me as being false. |
3603 | Methodical thinking is cautious, analytical, systematic, and panoramic [Descartes, by PG] |
Full Idea: Descartes' four principles for his method of thinking are: be cautious, analyse the problem, be systematic from simple to complex, and keep an overview of the problem | |
From: report of René Descartes (A Discourse on Method [1637], §2.18) by PG - Db (ideas) |
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) |
3612 | Clear and distinct conceptions are true because a perfect God exists [Descartes] |
Full Idea: That the things we grasp very clearly and very distinctly are all true, is assured only because God is or exists, and because he is a perfect Being. | |
From: René Descartes (A Discourse on Method [1637], §4.38) |
3610 | Truth is clear and distinct conception - of which it is hard to be sure [Descartes] |
Full Idea: I take it as a general rule that the things we conceive very clearly and very distinctly are all true, but that there is merely some difficulty in properly discerning which are those which we distinctly conceive. | |
From: René Descartes (A Discourse on Method [1637], §4.33) |
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. |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
Full Idea: Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order. | |
From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165) | |
A reaction: Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology. |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
Full Idea: Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard. | |
From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166) | |
A reaction: This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it. |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
Full Idea: If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers. | |
From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164) | |
A reaction: It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412. |
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? |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
Full Idea: No account of an individual number is adequate unless it relates that number to the series of which it is a member. | |
From: Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.169) | |
A reaction: Thus it is not totally implausible to say that 2 is several different numbers or concepts, depending on whether you see it as a natural number, an integer, a rational, or a real. This idea is the beginning of modern structuralism. |
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) |
3605 | We can believe a thing without knowing we believe it [Descartes] |
Full Idea: The action of thought by which one believes a thing, being different from that by which one knows that one believes it, they often exist the one without the other. | |
From: René Descartes (A Discourse on Method [1637], §3.23) |
1583 | In morals Descartes accepts the conventional, but rejects it in epistemology [Roochnik on Descartes] |
Full Idea: Descartes' procedure for treating values (accepting normal conventions when faced with uncertainty) is the exact antithesis of that used to attain knowledge. | |
From: comment on René Descartes (A Discourse on Method [1637], §3.23) by David Roochnik - The Tragedy of Reason p.73 |
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. |
3607 | In thinking everything else false, my own existence remains totally certain [Descartes] |
Full Idea: While I decided to think that everything was false, it followed necessarily that I who thought thus must be something; the truth 'I think therefore I am' was so certain that the most extravagant scepticism could never shake it. | |
From: René Descartes (A Discourse on Method [1637], §4.32) |
3617 | I aim to find the principles and causes of everything, using the seeds within my mind [Descartes] |
Full Idea: I have tried to find in general the principles or first causes of everything which is or which may be in the world, ..without taking them from any other source than from certain seeds of truth which are naturally in our minds. | |
From: René Descartes (A Discourse on Method [1637], §6.64) |
3611 | Understanding, rather than imagination or senses, gives knowledge [Descartes] |
Full Idea: Neither our imagination nor our senses could ever assure us of anything, if our understanding did not intervene. | |
From: René Descartes (A Discourse on Method [1637], §4.37) |
3606 | I was searching for reliable rock under the shifting sand [Descartes] |
Full Idea: My whole plan had for its aim simply to give me assurance, and the rejection of shifting ground and sand in order to find rock or clay. | |
From: René Descartes (A Discourse on Method [1637], §3.29) | |
A reaction: I take this to be characteristic of an age when religion is being quietly rocked by the revival of ancient scepticism. If he'd settled for fallibilism, our civilization would have gone differently. |
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) |
3604 | When rebuilding a house, one needs alternative lodgings [Descartes] |
Full Idea: Before beginning to rebuild the house in which one lives…. one must also provide oneself with some other accommodation in which to be lodge conveniently while the work is going on. | |
From: René Descartes (A Discourse on Method [1637], §3.22) |
3618 | Only experiments can settle disagreements between rival explanations [Descartes] |
Full Idea: I observe almost no individual effect without immediately knowing that it can be deduced in many different ways, ..and I know of no way to resolve this but by experiments such that the results are different according to different explanations. | |
From: René Descartes (A Discourse on Method [1637], §6.65) |
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. |
3615 | Little reason is needed to speak, so animals have no reason at all [Descartes] |
Full Idea: Animals not only have less reason than men, but they have none at all; for we see that very little of it is required in order to be able to speak. | |
From: René Descartes (A Discourse on Method [1637], §5.58) |
3609 | I am a thinking substance, which doesn't need a place or material support [Descartes] |
Full Idea: I concluded that I was a substance, of which the whole essence or nature consists in thinking, and which, in order to exist, needs no place and depends on no material thing. | |
From: René Descartes (A Discourse on Method [1637], §4.33) | |
A reaction: To me that sounds like "I concluded that I wasn't a human being", which highlights the bizarre wishful thinking that seems to have gripped the human race for the first few thousand years of its serious thinking. |
3608 | I can deny my body and the world, but not my own existence [Descartes] |
Full Idea: I could pretend that I had no body, and that there was no world or place that I was in, but I could not, for all that, pretend that I did not exist. | |
From: René Descartes (A Discourse on Method [1637], §4.32) | |
A reaction: He makes the (in my opinion) appalling blunder of thinking that because he can pretend that he has no body, that therefore he might not have one. I can pretend that gold is an unusual form of cheese. However, "I don't exist" certainly sounds wrong. |
3613 | Reason is universal in its responses, but a physical machine is constrained by its organs [Descartes] |
Full Idea: Whereas reason is a universal instrument which can serve on any kind of occasion, the organs of a machine need a disposition for each action; so it is impossible to have enough different organs in a machine to respond to all the occurrences of life. | |
From: René Descartes (A Discourse on Method [1637], §5.57) | |
A reaction: How can Descartes know that reason is 'universal' rather than just 'very extensive'? Is there any information which cannot be encoded in a computer? It doesn't feel as if there any intrinsic restrictions to reason, but note Idea 4688. |
3616 | The soul must unite with the body to have appetites and sensations [Descartes] |
Full Idea: It is not sufficient that the reasonable soul should be lodged in the body like a pilot in a ship, unless perhaps to move its limbs, but it needs to be united more closely with the body in order to have sensations and appetites, and so be a true man. | |
From: René Descartes (A Discourse on Method [1637], §5.59) | |
A reaction: The idea that the pineal gland is the link suggests that Descartes has the 'pilot' view, but this idea shows that he believes in very close and complex interaction between mind and body. But how can a mind 'have' appetites if it has no physical needs? |
3614 | A machine could speak in response to physical stimulus, but not hold a conversation [Descartes] |
Full Idea: One may conceive of a machine made so as to emit words, and even emit them in response to a change in its bodily organs, such as being touched, but not to reply to the sense of everything said in its presence, as the most unintelligent men can. | |
From: René Descartes (A Discourse on Method [1637], §5.56) | |
A reaction: A critique of the Turing Test, written in 1637! You have to admire. Because of the advent of the microprocessor, we can 'conceive' more sophisticated, multi-level machines than Descartes could come up with. |
1581 | Greeks elevate virtues enormously, but never explain them [Descartes] |
Full Idea: The ancient pagans place virtues on a high plateau and make them appear the most valuable thing in the world, but they do not sufficiently instruct us about how to know them. | |
From: René Descartes (A Discourse on Method [1637], §1.8) |
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) |
16686 | God has established laws throughout nature, and implanted ideas of them within us [Descartes] |
Full Idea: I have noticed certain laws that God has so established in nature, and of which he has implanted such notions in our souls, that …we cannot doubt that they are exactly observed in everything that exists or occurs in the world. | |
From: René Descartes (A Discourse on Method [1637], pt 5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.5 | |
A reaction: This is the view of laws which still seems to be with us (and needs extirpating) - that some outside agency imposes them on nature. I suspect that even Richard Feynman thought of laws like that, because he despised philosophy, and was thus naïve. |