51 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. |
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) |
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) |
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
Full Idea: The best known axiomatization of PL is Whitehead/Russell. There are four axioms: (p∨p)→p, q→(p∨q), (p→q)→(q∨p), and (q→r)→((p∨q)→(p∨r)), plus Substitution and Modus Ponens rules. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by GE Hughes/M Cresswell - An Introduction to Modal Logic Ch.1 |
21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
Full Idea: The axiom of Reducibility ...is crucial in the reduction of classes to logic, ...and seems to be a quite legitimate logical notion for Russell. | |
From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 6.4 | |
A reaction: This is an unusual defence of the axiom, which is usually presumed to have been kicked into the long grass by Quine. If one could reduce classes to logic, that would destroy the opposition to logicism in a single neat coup. |
10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
Full Idea: Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements). | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459 | |
A reaction: Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table? |
18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
Full Idea: Classes, so far as we introduce them, are merely symbolic or linguistic conveniences, not genuine objects. | |
From: B Russell/AN Whitehead (Principia Mathematica [1913], p.72), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication. | |
From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177 | |
A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'. |
9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual. | |
From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366 | |
A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning. |
21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic. |
10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
Full Idea: In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 | |
A reaction: I presume this is accounting for relations in terms of ordered sets. |
18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 |
18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
Full Idea: Although Russell takes numbers to be certain classes, his 'no-class' theory then eliminates all mention of classes in favour of the 'propositional functions' that define them; and in the case of the numbers these just are the numerical quantifiers. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by David Bostock - Philosophy of Mathematics 9.B.4 |
10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
Full Idea: Russell and Whitehead took arithmetic to be higher-order logic, ..and came close to identifying numbers with numerical quantifiers. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.148 | |
A reaction: The point here is 'higher-order'. |
8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
Full Idea: Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.1 | |
A reaction: If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything. |
10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
Full Idea: What is missing, above all, in 'Principia', is a precise statement of the syntax of the formalism. | |
From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 |
10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
Full Idea: Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3 | |
A reaction: I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables. |
8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
Full Idea: The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'. | |
From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.6 | |
A reaction: To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths. |
10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
Full Idea: In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates. | |
From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267 | |
A reaction: This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic. |
8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
Full Idea: Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.1 | |
A reaction: This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts. |
8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
Full Idea: Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 | |
A reaction: Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to. |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
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 |
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) |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
Full Idea: By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452 | |
A reaction: The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept. |
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. |
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) |
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? |
21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
Full Idea: The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief. | |
From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
A reaction: This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities. |
23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
Full Idea: When a judgement occurs, there is a certain complex entity, composed of the mind and the various objects of the judgement. | |
From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44) | |
A reaction: This is Russell's multiple-relation theory of judgement, which replaced his earlier belief in unified propositions (now 'false abstractions'). He seems to have accepted Locke's view, that the act of judgement produces the unity. |
23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging. | |
From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus | |
A reaction: Morris says this is Russell's multiple-relations theory of judgement. The theory accompanies the rejection of the concept of the unified proposition. When I hear 'Socrates had a mole on his shoulder' I get the meaning without judging. |
23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
Full Idea: When Russell moved to his multiple relation theory of judgement …he then faced difficulties making sense of the unity of sentences. | |
From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.44) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3A | |
A reaction: Roughly, he seems committed to saying that there is only unity if you think there is unity; there is no unity in a sentence prior to the act of judgement. |
18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging, and we no longer have an incomplete symbol. | |
From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap | |
A reaction: Personally I would have thought that you needed to know the meaning properly before you could make the judgement, but then he is Bertrand Russell and I'm not. |
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. |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
Full Idea: A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one. | |
From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E | |
A reaction: This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs? |
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) |
4787 | Causation interaction is an exchange of conserved quantities, such as mass, energy or charge [Dowe, by Psillos] |
Full Idea: Dowe argues that a 'causal process' is a world line of an object with a conserved quantity (such as mass, energy, momentum, charge), and a 'causal interaction' is an exchange between two such objects. | |
From: report of Phil Dowe (Physical Causation [2000]) by Stathis Psillos - Causation and Explanation §4.4 | |
A reaction: This looks very promising. Nice distinction between causal process and causal interaction. 'Conserved quantities' is better physics than just 'energy'. We can hand causation over to the scientist? |
14586 | Physical causation consists in transference of conserved quantities [Dowe, by Mumford/Anjum] |
Full Idea: For Dowe physical causation consists in transference of conserved quantities. | |
From: report of Phil Dowe (Physical Causation [2000]) by S.Mumford/R.Lill Anjum - Getting Causes from Powers 10.2 | |
A reaction: [see Psillos 2002 on this] This is evidently a modification of the idea of physical causation as energy-transfer, but narrowing it down to exclude trivial cases. I guess. Need better physics. |
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. |
4788 | Dowe commends the Conserved Quantity theory as it avoids mention of counterfactuals [Dowe, by Psillos] |
Full Idea: Dowe commends the Conserved Quantity theory because it avoids any mention of counterfactuals. | |
From: report of Phil Dowe (Physical Causation [2000]) by Stathis Psillos - Causation and Explanation §4.4 | |
A reaction: Clearly the truth of a counterfactual is quite a problem for an empiricist/scientist, but one needs to distinguish between reality and our grasp of it. We commit ourselves to counterfactuals, even if causation is transfer of conserved quantities. |