34 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. |
6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
Full Idea: Metaphysical systems have not usually rested upon any observed facts, or not in any great degree. They are chiefly adopted because their fundamental propositions seem 'agreeable to reason', which means that which we find ourselves inclined to believe. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.15) | |
A reaction: This leads to Peirce's key claim - that we should allow our beliefs to be formed by something outside of ourselves. I don't share Peirce's contempt for metaphysics, which I take to be about the most abstract presuppositions of our ordinary beliefs. |
6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
Full Idea: The object of reasoning is to find out, from the consideration of what we already know, something else which we do not know. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 7) | |
A reaction: I defy anyone to come up with a better definition of reasoning than that. The emphasis is on knowledge rather than truth, which you would expect from a pragmatist. …Actually the definition doesn't cover conditional reasoning terribly well. |
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) |
21492 | Realism is basic to the scientific method [Peirce] |
Full Idea: The fundamental hypothesis of the method of science is this: There are real things, whose characters are entirely independent of our opinion of them. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877]), quoted by Albert Atkin - Peirce 3 'method' | |
A reaction: He admits later that this is only a commitment and not a fact. It seems to me that when you combine this idea with the huge success of science, the denial of realism is crazy. Philosophy has a lot to answer for. |
6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
Full Idea: Nobody can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.19) | |
A reaction: This rests on Peirce's view that all that really matters is a sense of genuine dissatisfaction, rather than a theoretical idea. So even at the end of Meditation One, Descartes isn't actually worried about whether his furniture exists. |
11976 | Aristotelian essentialism says essences are not relative to specification [Lewis] |
Full Idea: So-called 'Aristotelian essentialism' is the doctrine of essences not relative to specifications. | |
From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], III) | |
A reaction: In other words, they are so-called 'real essences', understood as de re. Quine says essences are all de dicto, and relative to some specification. I vote for Aristotle. |
11978 | Causal necessities hold in all worlds compatible with the laws of nature [Lewis] |
Full Idea: Just as a sentence is necessary if it holds in all worlds, so it is causally necessary if it holds in all worlds compatible with the laws of nature. | |
From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], V) | |
A reaction: I don't believe in the so-called 'laws of nature', so I'm not buying that. Is there no distinction in Lewis's view between those sentences which must hold, and those which happen to hold universally? |
11979 | It doesn't take the whole of a possible Humphrey to win the election [Lewis] |
Full Idea: Even if Humphrey is a modal continuant, it doesn't take the whole of him to do such things as winning. | |
From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], Post B) | |
A reaction: This responds to Kripke's famous example, that people only care about what happens to themselves, and not to some 'counterpart' of themselves. |
16994 | Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis] |
Full Idea: Probably Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. Thus Lewis's view seems even more bizarre that the usual transworld identification it replaces. | |
From: comment on David Lewis (Counterpart theory and Quant. Modal Logic [1968]) by Saul A. Kripke - Naming and Necessity notes and addenda note 13 | |
A reaction: I begin to see this as a devastating reply to a theory I previously found quite congenial. |
11974 | Counterparts are not the original thing, but resemble it more than other things do [Lewis] |
Full Idea: Your counterparts resemble you closely in content and context in important respects. They resemble you more closely than do the other things in their worlds. But they are not really you. | |
From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], I) | |
A reaction: It is a dilemma. If my counterpart were exactly me, I couldn't contemplate possibly losing a leg, or my sanity. But if my counterpart isn't exactly me, then I don't have much interest in its fate. Only essences can save us here. Cf. me tomorrow. |
11975 | If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis] |
Full Idea: If whatever thing in world w6 it is that resembles you more closely than anything else in w6 is nevertheless quite unlike you; nothing in w6 resembles you at all closely. If so, you have no counterpart in w6. | |
From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], I) | |
A reaction: This is the nub, because the whole theory rests on deciding whether two things resemble sufficiently 'closely'. But then we need a criterion of closeness, so we must start talking about which properties matter. Essences loom. |
11977 | Essential attributes are those shared with all the counterparts [Lewis] |
Full Idea: An essential attribute of something is an attribute it shares with all its counterparts. | |
From: David Lewis (Counterpart theory and Quant. Modal Logic [1968], III) | |
A reaction: I don't like this. It ties essence entirely to identity, but I think essence precedes identity. Essence is a nexus of causal and explanatory powers which bestows an identity on each thing. But essence might be unstable, and identity with it. |
6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
Full Idea: The feeling of believing is a more or less sure indication of there being established in our nature some habit which will determine our actions. Doubt never has such an effect. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.10) | |
A reaction: It is one thing to assert this fairly accurate observation, and another to assert that this is the essence or definition of a belief. Perhaps it is the purpose of belief, without being the phenomenological essence of it. We act in states of uncertainty. |
6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
Full Idea: The mere putting of a proposition into the interrogative form does not stimulate the mind to any struggle after belief; there must be a real and living doubt. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
A reaction: This the attractive aspect of Peirce's pragmatism, that he is always focusing on real life rather than abstract theory or pure logic. |
6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
Full Idea: As soon as a firm belief is reached we are entirely satisfied, whether the belief be true or false. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.10) | |
A reaction: This does not deny that the truth or falsehood of a belief is independent of whether we are satisfied with it. It is making a fair point, though, about why we believe things, and it can't be because of truth, because we don't know how to ensure that. |
6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
Full Idea: We seek for a belief that we shall think to be true; but we think each one of our beliefs to be true, and, indeed, it is mere tautology to say so. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
A reaction: If, as I do, you like to define belief as 'commitment to truth', Peirce makes a rather startling observation. You are rendered unable to ask whether your beliefs are true, because you have defined them as true. Nice point… |
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. |
6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
Full Idea: It is necessary that a method should be found by which our beliefs be determined by nothing human, but by some external permanency - by something upon which our thinking has no effect. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877]), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5 | |
A reaction: This very sensible and interesting remark hovers somewhere between empiricism and pragmatism. Fogelin very persuasively builds his account of knowledge on it. The key point is that we hardly ever choose what to believe. See Idea 2454. |
6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
Full Idea: It is a common idea that demonstration must rest on indubitable propositions, either first principles of a general nature, or first sensations; but actual demonstration is completely satisfactory if it starts from propositions free from all actual doubt. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
A reaction: Another nice example of Peirce focusing on the practical business of thinking, rather than abstract theory. I agree with this approach, that explanation and proof do not aim at perfection and indubitability, but at what satisfies a critical mind. |
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) |
6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
Full Idea: To satisfy our doubts it is necessary that a method should be found by which our beliefs may be determined by nothing human, but by some external permanency - by something upon which our thinking has no effect. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.18) | |
A reaction: This may be the single most important idea in pragmatism and in the philosophy of science. See Fodor on experiments (Idea 2455). Put the question to nature. The essential aim is to be passive in our beliefs - just let reality form them. |
6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
Full Idea: Some people seem to love to argue a point after all the world is fully convinced of it. But no further advance can be made. When doubt ceases, mental action on the subject comes to an end; and, if it did go on, it would be without purpose. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
A reaction: This is the way Peirce's pragmatism, which deals with how real thinking actually works (rather than abstract logic), deals with scepticism. However, there is a borderline where almost everyone is satisfied, but the very wise person remains sceptical. |
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. |
6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
Full Idea: The guiding principle is that what is true of one piece of copper is true of another; such a guiding principle with regard to copper would be much safer than with regard to many other substances - brass, for example. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 8) | |
A reaction: Peirce is so beautifully simple and sensible. This gives the essential notion of a natural kind, and is a key notion in our whole understanding of physical reality. |
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) |
6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
Full Idea: It is probably of more advantage to an animal to have his mind filled with pleasing and encouraging visions, independently of their truth; and thus, upon unpractical subjects, natural selection might occasion a fallacious tendency of thought. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 8) | |
A reaction: Note that this is a pragmatist saying that a set of beliefs might work fine but be untrue. So Peirce does not have the highly relativistic notion of truth of some later pragmatists. Good for him. Note the early date to be thinking about Darwin. |
6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |
Full Idea: If death is annihilation, then the man who believes that he will certainly go straight to heaven when he dies, provided he have fulfilled certain simple observances in this life, has a cheap pleasure which will not be followed by the least disappointment. | |
From: Charles Sanders Peirce (The Fixation of Belief [1877], p.12) | |
A reaction: This is a nicely wicked summary of one side of Pascal's options. All the problems of the argument are built into Peirce's word "cheap". Peirce goes on to talk about ostriches burying their heads. |