Combining Texts

All the ideas for 'fragments/reports', 'Our Knowledge of the External World' and 'An Axiomatization of Set Theory'

unexpand these ideas     |    start again     |     specify just one area for these texts


45 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
A sense of timelessness is essential to wisdom [Russell]
     Full Idea: Both in thought and in feeling, to realize the unimportance of time is the gate of wisdom.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 6)
     A reaction: A very rationalist and un-Heraclitean view of wisdom. This picture may give wisdom a bad name, if wise people are (at a minimum) at least expected to give good advice about real life.
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophical disputes are mostly hopeless, because philosophers don't understand each other [Russell]
     Full Idea: Explicit controversy is almost always fruitless in philosophy, owing to the fact that no two philosophers ever understand one another.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 1)
     A reaction: Contemporaries don't even seem to read one another very much, especially these days, when there are thousands of professional philosophers. (If you are a professional, have you read all the works written by your colleagues and friends?)
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Philosophical systems are interesting, but we now need a more objective scientific philosophy [Russell]
     Full Idea: The great systems of the past serve a very useful purpose, and are abundantly worthy of study. But something different is required if philosophy is to become a science, and to aim at results independent of the tastes of the philosophers who advocate them.
     From: Bertrand Russell (Our Knowledge of the External World [1914], Pref)
     A reaction: An interesting product of this move in philosophy is (about sixty years later) the work of David Lewis, who set out to be precise and scientific, and ended up creating a very personal system. Why not a collaborative system?
Hegel's confusions over 'is' show how vast systems can be built on simple errors [Russell]
     Full Idea: Hegel's confusion of the 'is' of predication with the 'is' of identity ...is an example of how, for want of care at the start, vast and imposing systems of philosophy are built upon stupid and trivial confusions.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 2 n1)
     A reaction: [He explains the confusion in more detail in the note] Russell cites an English translation, and I am wondering how this occurs in the German. Plato has been accused of similar elementary blunders about properties. Russell treats Berkeley similarly.
Philosophers sometimes neglect truth and distort facts to attain a nice system [Russell]
     Full Idea: The desire for unadulterated truth is often obscured, in professional philosophers, by love of system: the one little fact which will not come inside the philosophical edifice has to be pushed and tortured until it seems to consent.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 8)
     A reaction: Bit of hypocrisy here. Russell was continually trying to find a system, grounded in physics and logic. Presumably his shifting views are indications of integrity, because he changes the system rather than the facts.
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Physicists accept particles, points and instants, while pretending they don't do metaphysics [Russell]
     Full Idea: Physicists, ignorant and contemptuous of philosophy, have been content to assume their particles, points and instants in practice, while contending, with ironical politeness, that their concepts laid no claim to metaphysical validity.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 4)
     A reaction: Presumably physicists are allowed to wave their hands and utter the word 'instrumentalism', and then get on with the job. They just have to ensure they never speculate about what is being measured.
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
When problems are analysed properly, they are either logical, or not philosophical at all [Russell]
     Full Idea: Every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 2)
     A reaction: [All Lecture 2 discusses 'logical'] I think Bertie was getting carried away here. In his life's corpus he barely acknowledges the existence of ethics, or political philosophy, or aesthetics. He never even engages with 'objects' the way Aristotle does.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
     Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong.
     From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives the method of research in philosophy [Russell]
     Full Idea: Logic gives the method of research in philosophy, just as mathematics gives the method in physics.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 8)
     A reaction: I'm struck by how rarely philosophers actually prove anything. Mostly they just use the language of logic as a tool for disambiguation. Only a tiny handful of philosophers can actually create sustained and novel proofs.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The logical connectives are not objects, but are formal, and need a context [Russell]
     Full Idea: Such words as 'or' and 'not' are not names of definite objects, but are words that require a context in order to have a meaning. All of them are formal.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 7)
     A reaction: [He cites Wittgenstein's 1922 Tractatus in a footnote - presumably in a later edition than 1914] This is the most famous idea which Russell acquired from Wittgenstein. It was yet another step in his scaling down of ontology.
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell]
     Full Idea: The idea that an infinite number of instants make up an infinitely long time is not true, and therefore the conclusion that Achilles will never overtake the tortoise does not follow.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 6)
     A reaction: Aristotle spotted this, but didn't express it as clearly as Russell.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
All the axioms for mathematics presuppose set theory [Neumann]
     Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory.
     From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2
     A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this.
7. Existence / A. Nature of Existence / 5. Reason for Existence
Nothing could come out of nothing, and existence could never completely cease [Empedocles]
     Full Idea: From what in no wise exists, it is impossible for anything to come into being; for Being to perish completely is incapable of fulfilment and unthinkable.
     From: Empedocles (fragments/reports [c.453 BCE], B012), quoted by Anon (Lyc) - On Melissus 975b1-4
7. Existence / B. Change in Existence / 1. Nature of Change
Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle]
     Full Idea: Empedocles claims that things are alternately changing and at rest - that they are changing whenever love is creating a unity out of plurality, or hatred is creating plurality out of unity, and they are at rest in the times in between.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Physics 250b26
     A reaction: I suppose one must say that this an example of Ruskin's 'pathetic fallacy' - reading human emotions into the cosmos. Being constructive little creatures, we think goodness leads to construction. I'm afraid Empedocles is just wrong.
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Atomic facts may be inferrable from others, but never from non-atomic facts [Russell]
     Full Idea: Perhaps one atomic fact may sometimes be capable of being inferred from another, though I do not believe this to be the case; but in any case it cannot be inferred from premises no one of which is an atomic fact.
     From: Bertrand Russell (Our Knowledge of the External World [1914], p.48)
     A reaction: I prefer Russell's caution to Wittgenstein's dogmatism. I presume utterly simple facts give you nothing to work with. Hegel thought that you could infer new concepts from given concepts.
7. Existence / D. Theories of Reality / 8. Facts / d. Negative facts
A positive and negative fact have the same constituents; their difference is primitive [Russell]
     Full Idea: It must not be supposed that a negative fact contains a constituent corresponding to the word 'not'. It contains no more constituents than a positive fact of the correlative positive form. The differenece between the two forms is ultimate and irreducible.
     From: Bertrand Russell (Our Knowledge of the External World [1914], VIII.279), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 41 'Neg'
     A reaction: ['Harvard Lectures'] The audience disliked this. How does one fact exclude the other fact? Potter asks whether absence is a fact, and whether an absence can be a truthmaker.
8. Modes of Existence / A. Relations / 1. Nature of Relations
With asymmetrical relations (before/after) the reduction to properties is impossible [Russell]
     Full Idea: When we come to asymmetrical relations, such as before and after, greater and less etc., the attempt to reduce them to properties becomes obviously impossible.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 2)
     A reaction: The traditional Aristotelian reduction to properties is attributed by Russell to logic based on subject-predicate. As an example he cites being greater than as depending on more than the mere magnitudes of the entities. Direction of the relation.
8. Modes of Existence / B. Properties / 11. Properties as Sets
When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell]
     Full Idea: When a group of objects have the similarity we are inclined to attribute to possession of a common quality, the membership of the group will serve all the purposes of the supposed common quality ...which need not be assumed to exist.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 2)
     A reaction: This is the earliest account I have found of properties being treated as sets of objects. It more or less coincides with the invention of set theory. I am reminded of Idea 9208. What is the bazzing property? It's what those three things have in common.
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle]
     Full Idea: Empedocles says there is no coming-to-be of anything, but only a mingling and a divorce of what has been mingled.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314b08
     A reaction: Aristotle comments that this prevents Empedocleans from distinguishing between superficial alteration and fundamental change of identity. Presumably, though, that wouldn't bother them.
9. Objects / E. Objects over Time / 10. Beginning of an Object
Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles]
     Full Idea: There is no creation of substance in any one of mortal existence, nor any end in execrable death, but only mixing and exchange of what has been mixed.
     From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Plutarch - 74: Reply to Colotes 1111f
     A reaction: also Aristotle 314b08
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / c. Representative realism
Science condemns sense-data and accepts matter, but a logical construction must link them [Russell]
     Full Idea: Men of science condemn immediate data as 'merely subjective', while maintaining the truths of physics from those data. ...The only justification possible for this must be one which exhibits matter as a logical construction from sense-data.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 4)
     A reaction: Since we blatantly aren't doing logic when we stare out of the window, this aspires to finding something like the 'logical form' of perception.
12. Knowledge Sources / B. Perception / 4. Sense Data / c. Unperceived sense-data
When sense-data change, there must be indistinguishable sense-data in the process [Russell]
     Full Idea: In all cases of sense-data capable of gradual change, we may find one sense-datum indistinguishable from another, and that indistinguishable from a third, while yet the first and third are quite easily distinguishable.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 5)
     A reaction: This point is key to the sense-data theory, because it gives them independent existence, standing between reality and subjective experience. It is also the reason why they look increasingly implausible, if they may not be experienced.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Empirical truths are particular, so general truths need an a priori input of generality [Russell]
     Full Idea: All empirical evidence is of particular truths. Hence, if there is any knowledge of general truths at all, there must be some knowledge of general truths which is independent of empirical evidence.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 2)
     A reaction: Humean empiricists respond by being a sceptical of general truths. At this stage of his career Russell looks like a thoroughgoing rationalist, and he believes in the reality of universals, relations and propositions. He became more empirical later.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
Objects are treated as real when they connect with other experiences in a normal way [Russell]
     Full Idea: Objects of sense are called 'real' when they have the kind of connection with other objects of sense which experience has led us to regard as normal; when they fail this, they are called 'illusions'.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 3)
     A reaction: This rests rather too much on the concept of 'normal', but offers an attractive coherence account of perception. Direct perceptions are often invoked by anti-coherentists, but I think coherence is just as much needed in that realm.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate [Russell]
     Full Idea: Universal scepticism, though logically irrefutable, is practically barren; it can only, therefore, give a certain flavour of hesitancy to our beliefs, and cannot be used to substitute other beliefs for them.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 3)
     A reaction: Spot on. There is no positive evidence for scepticism, so must just register it as the faintest of possibilities, like the existence of secretive fairies.
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
One vision is produced by both eyes [Empedocles]
     Full Idea: One vision is produced by both eyes
     From: Empedocles (fragments/reports [c.453 BCE], B088), quoted by Strabo - works 8.364.3
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
Other minds seem to exist, because their testimony supports realism about the world [Russell, by Grayling]
     Full Idea: Russell gives an argument that other minds exist, because if one is entitled to believe this, then one can rely on the testimony of others, which, jointly with one's own experience, will give powerful support to the view that there a real spatial world.
     From: report of Bertrand Russell (Our Knowledge of the External World [1914], 3) by A.C. Grayling - Russell Ch.2
     A reaction: I rather like this argument. It is quite close to Wittgenstein's Private Language Argument, which also seems to refute scepticism about other minds. I think Russell's line, using testimony, knowledge and realism, may be better than Wittgenstein's.
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Wisdom and thought are shared by all things [Empedocles]
     Full Idea: Wisdom and power of thought, know thou, are shared in by all things.
     From: Empedocles (fragments/reports [c.453 BCE]), quoted by Sextus Empiricus - Against the Logicians (two books) II.286
     A reaction: Sextus quotes this, saying that it is 'still more paradoxical', and that it explicitly includes plants. This may mean that Empedocles was not including inanimate matter.
18. Thought / A. Modes of Thought / 1. Thought
For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus]
     Full Idea: Empedocles assumes that thinking is either identical to or very similar to sense-perception.
     From: report of Empedocles (fragments/reports [c.453 BCE], A86) by Theophrastus - On the Senses 9
     A reaction: Not to be sniffed at. We can, of course, control our thinking (though we can't control the controller) and we contemplate abstractions, but that might be seen as a sort of perception. Vision is not as visual as we think.
22. Metaethics / B. Value / 2. Values / j. Evil
Empedocles said good and evil were the basic principles [Empedocles, by Aristotle]
     Full Idea: Empedocles was the first to give evil and good as principles.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Metaphysics 985a
     A reaction: Once you start to think that good and evil will only matter if they have causal powers, it is an easy step to the idea of a benevolent god, and a satanic anti-god. Otherwise the 'principles' could be ignored.
26. Natural Theory / A. Speculations on Nature / 1. Nature
'Nature' is just a word invented by people [Empedocles]
     Full Idea: Nature is but a word of human framing.
     From: Empedocles (fragments/reports [c.453 BCE], B008), quoted by Aristotle - Metaphysics 1015a
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus]
     Full Idea: In Empedocles we have a dividing principle, 'Strife', set against 'Friendship' - which is the One and is to him bodiless, while the elements represent matter.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Plotinus - The Enneads 5.1.09
     A reaction: The first time I've seen the principle of Love in Empedocles identified with the One of Parmenides. Plotinus is a trustworthy reporter, I think, because he was well read, and had access to lost texts.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle]
     Full Idea: Empedocles holds that the corporeal elements are four, but that all the elements, including those which create motion, are six in number.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a16
Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood]
     Full Idea: Empedocles used numerical ratios to explain different kinds of matter; for example, bone is two parts water, four parts fire, two parts earth; and blood is an equal blend of all four elements.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Brad Inwood - Empedocles
     A reaction: Why isn't the ration 1:2:1? This presumably shows the influence of Pythagoras (who had also been based in Italy, like Empedocles), as well as that of the earlier naturalistic philosophers. It was a very good theory, though wrong.
Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle]
     Full Idea: Empedocles says that Fire, Water, Air and Earth are four elements, and are thus 'simple' rather than flesh, bone and bodies which, like these, are 'homoeomeries'.
     From: report of Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a26
     A reaction: The translation is not quite clear. I take it that flesh and bone may look simple, because they are homoeomerous, but they are not really - but what is his evidence for that? Compare Idea 13208.
All change is unity through love or division through hate [Empedocles]
     Full Idea: These elements never cease their continuous exchange, sometimes uniting under the influence of Love, so that all become One, at other times again moving apart through the hostile force of Hate.
     From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1-
The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles]
     Full Idea: Empedocles says it is evident that all the other bodies down to the 'elements' have their coming-to-be and their passing-away: but it is not clear how the 'elements' themselves, severally in their aggregated masses, come-to-be and pass-away.
     From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 325b20
     A reaction: Presumably the elements are like axioms - and are just given. How do electrons and quarks come-to-be?
Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles]
     Full Idea: It is not an adequate explanation to say that 'Love and Strife set things moving', unless the very nature of Love is a movement of this kind and the very nature of Strife a movement of that kind.
     From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 333b23
     A reaction: I take this to be of interest for showing Aristotle's quest for explanations, and his unwillingness to be fobbed off with anything superficial. I take a task of philosophy to be to push explanations further than others wish to go.
If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles]
     Full Idea: Besides these elements, nothing else comes into being, nor does anything cease. For if they had been perishing continuously, they would Be no more; and what could increase the Whole? And whence could it have come?
     From: Empedocles (fragments/reports [c.453 BCE], B017), quoted by Simplicius - On Aristotle's 'Physics' 158.1-
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
We never experience times, but only succession of events [Russell]
     Full Idea: There is no reason in experience to suppose that there are times as opposed to events: the events, ordered by the relations of simultaneity and succession, are all that experience provides.
     From: Bertrand Russell (Our Knowledge of the External World [1914], 4)
     A reaction: We experience events, but also have quite an accurate sense of how much time has passed during the occurrence of events. If asked how much time has lapsed, why don't we say '32 events'? How do we distinguish long events from short ones?
27. Natural Reality / G. Biology / 3. Evolution
Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle]
     Full Idea: Is it just an accident that teeth and other parts of the body seem to have some purpose, and creatures survive because they happen to be put together in a useful way? Everything else has been destroyed, as Empedocles says of his 'cow with human head'.
     From: report of Empedocles (fragments/reports [c.453 BCE], 61) by Aristotle - Physics 198b29
     A reaction: Good grief! Has no one ever noticed that Empedocles proposed the theory of evolution? It isn't quite natural selection, because we aren't told what does the 'destroying', but it is a little flash of genius that was quietly forgotten.
28. God / A. Divine Nature / 2. Divine Nature
God is a pure, solitary, and eternal sphere [Empedocles]
     Full Idea: God is equal in all directions to himself and altogether eternal, a rounded Sphere enjoying a circular solitude.
     From: Empedocles (fragments/reports [c.453 BCE], B028), quoted by John Stobaeus - Anthology 1.15.2
God is pure mind permeating the universe [Empedocles]
     Full Idea: God is mind, holy and ineffable, and only mind, which darts through the whole cosmos with its swift thought.
     From: Empedocles (fragments/reports [c.453 BCE], B134), quoted by Ammonius - On 'De Interpretatione' 4.5.249.6
28. God / A. Divine Nature / 4. Divine Contradictions
In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles]
     Full Idea: It is a consequence of Empedocles' view that God is the most unintelligent thing, for he alone is ignorant of one of the elements, namely strife, whereas mortal creatures are familiar with them all.
     From: comment on Empedocles (fragments/reports [c.453 BCE]) by Aristotle - De Anima 410b08
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
It is wretched not to want to think clearly about the gods [Empedocles]
     Full Idea: Wretched is he who cares not for clear thinking about the gods.
     From: Empedocles (fragments/reports [c.453 BCE], B132), quoted by Clement - Miscellanies 5.140.5.1