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All the ideas for 'fragments/reports', 'Principia Mathematica' and 'The World as Will and Idea'

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71 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy considers only the universal, in nature as everywhere else [Schopenhauer]
     Full Idea: Philosophy considers only the universal, in nature as everywhere else.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], II 027)
     A reaction: I think what draws people to philosophy is an interest in whatever is timeless. Contingent reality is so frustrating and exhausting. Hence I agree.
Everyone is conscious of all philosophical truths, but philosophers bring them to conceptual awareness [Schopenhauer]
     Full Idea: Every person is conscious of all philosophical truths, but to bring them to conceptual awareness, to reflection, is the business of the philosopher.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.68)
     A reaction: I like this. All human beings are philosophical. It seems unlikely, though, that we are all pre-conceptually conscious of the higher levels of philosophical logic.
1. Philosophy / D. Nature of Philosophy / 8. Humour
Absurdity is incongruity between correct and false points of view [Schopenhauer]
     Full Idea: The more correct the subsumption of objects from one point of view, and the greater and more glaring the incongruity from another point of view, the greater is the ludicrous effect which is produced by this contrast.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 013), quoted by Roger Scruton - Laughter §5
     A reaction: This accounts for ludicrous humour, but there seem to be plenty of other types. Exceptional stupidity is usually amusing without necessarily being incongruous. Though it is a departure from the sensible norm.
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics must understand the world thoroughly, as a principal source of knowledge [Schopenhauer]
     Full Idea: The task of metaphysics is not to pass over experience in which the world exists, but to understand it thoroughly, since inner and outer experience are certainly the principal source of all knowledge.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 428), quoted by Christopher Janaway - Schopenhauer 3 'Will'
     A reaction: I wonder to what extent he meant ordinary experience, and to what extent he was advocating the study if science?
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
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.
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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?
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
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
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'.
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.
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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.
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
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
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
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
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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'.
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 Michčle 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.
'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
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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.
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 Michčle 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.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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 Michčle 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.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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.
7. Existence / A. Nature of Existence / 2. Types of Existence
Matter and intellect are inseparable correlatives which only exist relatively, and for each other [Schopenhauer]
     Full Idea: In my system matter and intellect are inseparable correlatives which exist only for each other, and so exist only relatively.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I.Supp)
     A reaction: A plausible picture, but built from dualist presuppositions. Personally I think intellect is built out of matter, so I am not going down Schopenhauer's road.
7. Existence / D. Theories of Reality / 3. Reality
Schopenhauer, unlike other idealists, says reality is irrational [Schopenhauer, by Lewis,PB]
     Full Idea: Schopenhauer radically departs from his fellow idealists in his assertion of the irrational character of reality.
     From: report of Arthur Schopenhauer (The World as Will and Idea [1819]) by Peter B. Lewis - Schopenhauer 4
     A reaction: This is the rejection of the original confidence about rationality of the stoics. And yet Schopenauer saw the principle of sufficient reason as axiomatic. Not sure how to reconcile those. Lewis identifies this idea as 'Romantic'.
7. Existence / D. Theories of Reality / 4. Anti-realism
The knowing subject and the crude matter of the world are both in themselves unknowable [Schopenhauer]
     Full Idea: The world has two poles - the knowing subject and crude matter, which are both completely unknowable, the former because it is the knower, the latter because without form and quality it cannot be perceived.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I Supp)
     A reaction: A nice concept, that all of reality comes from their relationship, but the two components are intrinsically unknowable. Does God the Knower know his own mind?
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
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.
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
Descartes found the true beginning of philosophy with the Cogito, in the consciousness of the individual [Schopenhauer]
     Full Idea: By taking Cogito Ergo Sum as the only certainty, and by his provisionally regarding the existence of the world as problematical, the essential starting point of all philosophy was found, and its true focus in the subjective, the individual consciousness.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I Supp)
     A reaction: Some people think this was a disaster, not a triumph. Descartes could have doubted himself and accepted the world as his starting point.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
Schopenhauer can't use force/energy instead of 'will', because he is not a materialist [Lewis,PB on Schopenhauer]
     Full Idea: Some say Schopenhauer would be less misunderstood if he had used 'force' or 'energy' rather than 'will' to characterise inner natures. But this would have steered his idealism towards materialism, of which he was an avowed opponent.
     From: comment on Arthur Schopenhauer (The World as Will and Idea [1819]) by Peter B. Lewis - Schopenhauer 4
     A reaction: I presume therefore that Nietzsche's will to power is a commitment to materialism, since it occurs in material objects as well as minds.
The world only exists in relation to something else, as an idea of the one who conceives it [Schopenhauer]
     Full Idea: The world which surrounds man exists only as idea - that is, only in relation to something else, the one who conceives the idea, which is himself. If any truth can be enunciated a priori, it is this.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 001)
     A reaction: Yes, but the idea we have is of a real world. It is definitely not part of the idea that it is an idea (unlike my idea for a Christmas present).
We know reality because we know our own bodies and actions [Schopenhauer]
     Full Idea: The double knowledge of the nature and action of our own body is the key to the inner being of every phenomenon in nature.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 105), quoted by Peter B. Lewis - Schopenhauer 4
     A reaction: Lewis calls this 'the heart of his philosophy'. Bodily awareness comes from acts of willing. So Lewis says 'the thing-in-itself is revealed to us in willing'. We experience Being and causation. Is he trying to combine idealism with the thing-in-itself?
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Kant rightly separates appearance and thing-in-itself [Schopenhauer]
     Full Idea: Kant's greatest merit is the distinction of the phenomenon from the thing-in-itself.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 417 App), quoted by Peter B. Lewis - Schopenhauer 3
     A reaction: This is Schopenhauer firmly opposing the Absolute Idealism of Kant's successors, who dismissed the 'thing-in-itsef'.
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Direct feeling of the senses are merely data; perception of the world comes with understanding causes [Schopenhauer]
     Full Idea: What the eye, the ear, or the hand feels, is not perception, it is merely data. Only when the understanding passes from the effect to the cause does the world lie before us as perception extended in space.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 004)
     A reaction: These certainly seems to be a sense-data theory. Philosophers are much more ready to separate the data from the understanding than neuroscientists are.
12. Knowledge Sources / B. Perception / 5. Interpretation
All perception is intellectual [Schopenhauer]
     Full Idea: All perception is intellectual.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 004)
     A reaction: Even in slugs? I suspect that this is a tautology. Schopenhauer will only allow my vision or hearing to become 'perception' when an intellectual element enters into it.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
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.
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
A consciousness without an object is no consciousness [Schopenhauer]
     Full Idea: A consciousness without an object is no consciousness.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I Supp)
     A reaction: This hints at Hume's observations about the self. Certainly totally vacant consciousness seems inconceivable, but is that a necessary or a contingent truth?
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
We have hidden and unadmitted desires and fears, suppressed because of vanity [Schopenhauer]
     Full Idea: We often do not know what we desire or fear. For years we can have a desire without admitting it to ourselves ....because the intellect is not to know anything about it, since the good opinion we have of ourselves would inevitably suffer thereby.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], II 210), quoted by Christopher Janaway - Schopenhauer 5 'Will'
     A reaction: The idea of unconscious thought crept up well before Freud. It is in La Rochefoucauld, and important in Nietzsche. Neuroscience seems to give it a strong priority over the conscious mind, which is a revolutionary idea.
16. Persons / C. Self-Awareness / 2. Knowing the Self
I know both aspects of my body, as representation, and as will [Schopenhauer]
     Full Idea: My body is the only object of which I know not merely the one side, that of the representation, but also the other, that is called 'will'.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 125), quoted by Christopher Janaway - Schopenhauer 3 'Will'
     A reaction: I'm not convinced that knowledge of the body through the will (and action, presumably) constitutes a different sort of knowledge. Philosophers are always trying to split the world in two (but not Nietzsche!).
16. Persons / E. Rejecting the Self / 4. Denial of the Self
It is as perverse to resent our individuality being replaced by others, as to resent the body renewing itself [Schopenhauer]
     Full Idea: It is as perverse to desire the continuity of one's individuality which is being replaced by other individuals, as to desire the permanence of the body's substance which is always being replaced by new substance.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.54)
     A reaction: If I let that go, what am I supposed to hang on to? Nothing? Non-existence is not an attractive condition to aspire to.
16. Persons / F. Free Will / 5. Against Free Will
We all regard ourselves a priori as free, but see from experience that character and motive compel us [Schopenhauer]
     Full Idea: Everyone regards himself a priori as free in his individual actions, and only a posteriori sees that necessarily his actions follow from the coincidence of character with motives.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.55)
     A reaction: I'm not sure what experience shows. Necessity seems more obvious when observing other people. Samuel Johnson said experience showed freedom, not necessity.
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Man's actions are not free, because they follow strictly from impact of motive on character [Schopenhauer]
     Full Idea: Man's action have been interpreted as free, which they are not, for every individual action follows with strict necessity from the impact of motive on character.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], II 023)
     A reaction: If 'character is fate' (Heraclitus) then presumably motive must also be fate to complete the determinist picture. I shall spend the next year redesigning my motivation.
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
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.
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.
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.
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.
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.
19. Language / D. Propositions / 3. Concrete Propositions
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?
20. Action / A. Definition of Action / 4. Action as Movement
Every true act of will is also at once and without exception a movement of the body [Schopenhauer]
     Full Idea: Every true act of will is also at once and without exception a movement of the body.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], II 018)
     A reaction: The word 'act' seems to beg the question (as does 'true'!). I am no longer sure that I know what an act of will is. Hobbes says there is no such thing.
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
Schopenhauer was caught in Christian ideals, because he didn't deify his 'will' [Nietzsche on Schopenhauer]
     Full Idea: Schopenhauer's interpretation of the in-itself as will was an essential step: but he didn't know how to deify the will, and remained caught in the moral, Christian ideal
     From: comment on Arthur Schopenhauer (The World as Will and Idea [1819]) by Friedrich Nietzsche - Writings from Late Notebooks 9[42]
     A reaction: Intriguingly, this seems to suggest that Nietzsche consciously sought to replace the absence of God with the human will, which strikes me as an odd, and very nineteenth century, idea. Loss of religion bothered them a lot.
Only the will is thing-in-itself, seen both in blind nature and in human action [Schopenhauer]
     Full Idea: Only the will is thing-in-itself. ...It appears in every blindly acting force of nature, and also in the deliberate conduct of man, and the great difference between the two concerns only the degree of the manifestation.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 110), quoted by Christopher Janaway - Schopenhauer 3 'Will'
     A reaction: If will acts 'blindly' in forces of nature, then these seems to be the same concept as Nietzsche's 'will to power'. This seems to be heading towards Heidegger's Dasein, as a central and distinctive mode of being.
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
If we were essentially intellect rather than will, our moral worth would depend on imagined motives [Schopenhauer]
     Full Idea: If, as all philosophers imagine, the intellect is our actual nature and the will is arrived at through knowledge, then only the motive from which we imagined we were acting would decide our moral worth. Imagined and true motive would be indistinguishable.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], II Supp)
     A reaction: A nice argument. If motive is morally decisive, it is certainly crucial to decide between real and imagined motive (especially since Freud). But uncontrollable motive seems morally irrelevant.
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Schopenhauer is a chief proponent of aesthetic experience as 'disinterested' [Schopenhauer, by Janaway]
     Full Idea: Schopenhauer belongs to a tradition which equates aesthetic experience with a 'disinterested' attitude towards its object, and is often cited as one of the chief proponents of such a view.
     From: report of Arthur Schopenhauer (The World as Will and Idea [1819]) by Christopher Janaway - Schopenhauer 6 'Aesthetic'
     A reaction: 'Disinterested' is quite a nice word for one's attitude to art, though you then have to capture why you are also involved in it.
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
A principal pleasure of the beautiful is that it momentarily silences the will [Schopenhauer]
     Full Idea: The momentary silencing of all volition …is one of the principal elements in our pleasure in the beautiful.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.65)
     A reaction: Iris Murdoch sees moral value in beauty, because it overrides selfishness. The perception of beauty is certainly something deeper than just another nice feeling. There is a cognitive element to it.
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
The Sublime fights for will-less knowing, when faced with a beautiful threat to humanity [Schopenhauer, by Lewis,PB]
     Full Idea: Exaltation of the Sublime is the struggle to maintain will-less knowing in the face of a threat to the human will. The Sublime contains an awful beauty and a delightful terror because it includes a threat to human existence.
     From: report of Arthur Schopenhauer (The World as Will and Idea [1819], I 201-7) by Peter B. Lewis - Schopenhauer 5
     A reaction: Can you experience the Sublime when looking down a microscope? Can a mere theory in cosmology be sublime? Can a supposed perception of the Sublime ever be incorrect? We no longer worry about these questions, it seems.
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
Schopenhauer emphasises Ideas in art, unlike most romantics [Schopenhauer, by Lewis,PB]
     Full Idea: The emphasis on the presentation of Platonic Ideas distinguishes Schopenhauer's theory of art from standard Romantic theories, which emphasize the expression of emotion and feeling.
     From: report of Arthur Schopenhauer (The World as Will and Idea [1819], II) by Peter B. Lewis - Schopenhauer 5
     A reaction: Theories of art that neglect ideas, even if subliminally expressed, have gone badly wrong.
21. Aesthetics / C. Artistic Issues / 6. Value of Art
The will-less contemplation of art brings a liberation from selfhood [Schopenhauer, by Gardner]
     Full Idea: For Schopenhauer, the point of art lies in the metaphysical liberation from selfhood that will-less aesthetic contemplation induces.
     From: report of Arthur Schopenhauer (The World as Will and Idea [1819]) by Sebastian Gardner - Aesthetics 3.6.3
     A reaction: I've never understood why anyone (Buddhists included) would want 'liberation from selfhood'. Certainly art can make us forget ourselves in a more objective view of things, but science can do that too.
Man is more beautiful than anything else, and the loftiest purpose of art is to reveal his nature [Schopenhauer]
     Full Idea: Man is more beautiful than anything else, and the loftiest purpose of art is to reveal his nature.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], III 41)
     A reaction: A bit of a shock, because it implies human vanity, but it fits the best works of art rather well. What else reveals humanity's beauty? Beautiful deeds must be recorded.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
The only aim of our existence is to grasp that non-existence would be better [Schopenhauer]
     Full Idea: Nothing else can be stated as the aim of our existence except the knowledge that it would be better for us not to exist.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], II 605), quoted by Christopher Janaway - Schopenhauer 8 'Denial'
     A reaction: Nonsense on stilts. Nietzsche rebelled against this. If there is such 'knowledge' then it obviously has nothing to do with the aim of our existence. It is just a rejection of aims. The aim is making the best of existence, not spurning it.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
We should no more expect ethical theory to produce good people than aesthetics to produce artists [Schopenhauer]
     Full Idea: We should be just as foolish to expect that our moral systems and ethics would create virtuous, noble and hold men, as that our aesthetics would produce poets, painterd and musicians.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 271), quoted by Christopher Janaway - Schopenhauer 7 'Against'
     A reaction: Presumably the aim of ethical theory is to understand the truths about ethics. That can't do any harm, can it? In every other area of life we think that understanding leads to improvement. Unless, of course, there are no truths of ethics....
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
Every good is essentially relative, for it has its essential nature only in its relation to a desiring will [Schopenhauer]
     Full Idea: Every good is essentially relative, for it has its essential nature only in its relation to a desiring will.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.65)
     A reaction: A nice way of stating the core of moral relativism. To me, though, it just seems a rejection of morality. Conflicting wills bring moral paralysis. Might is right.
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Will casts aside each of its temporary fulfilments, so human life has no ultimate aim [Schopenhauer, by Scruton]
     Full Idea: Since for Schopenhauer will has no intrinsic end, but breaks through all its temporary fulfilments and casts them aside as irrelevant once attained, it becomes impossible to assert that there is any ultimate aim to human activity.
     From: report of Arthur Schopenhauer (The World as Will and Idea [1819]) by Roger Scruton - Short History of Modern Philosophy Ch.13
     A reaction: This sums up part of the modern anti-teleological view of life, with its notion of purposes which can only arise out of consciousnesses. Such a view leaves untouched the key question, which is "What should I will?"
22. Metaethics / B. Value / 2. Values / e. Death
Most people would probably choose non-existence at the end of their life, rather than relive the whole thing [Schopenhauer]
     Full Idea: Perhaps no one at the end of his life, if he gives the matter sober consideration and is, at the same time, frank, ever wishes to live it over again; he more readily chooses non-existence.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.59)
     A reaction: Hence Nietzsche's doctrine of 'eternal return' (Gay Science §341, idea 2936). From Schopenhauer it is just bleak pessimism, but from Nietzsche it is a wonderful challenge to live, perhaps the best ever.
22. Metaethics / B. Value / 2. Values / f. Altruism
Altruistic people make less distinction than usual between themselves and others [Schopenhauer]
     Full Idea: If we observe an altruistic action the simplest explanation and the essential character of the person's conduct is that they make less distinction than is usually made between themselves and others.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.66)
     A reaction: Obvious, really, but Schopenhauer is talking about the will. Is the effacement of the Self desirable, apart from the benefit it might bring to other people. I don't find it appealing.
22. Metaethics / B. Value / 2. Values / i. Self-interest
Only self-love can motivate morality, but that also makes it worthless [Schopenhauer]
     Full Idea: A theory of morals which motivates can only do so by working on self-love, but what springs from this latter has no moral worth.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.66)
     A reaction: I just don't believe this pessimism. Schopenhauer was an incipient social darwinist who needed a course in modern game theory. Or he just needed to be a nicer man.
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Happiness is the swift movement from desire to satisfaction, and then again on to desire [Schopenhauer]
     Full Idea: We are fortunate if we keep up the game whereby desire passes into satisfaction, and satisfaction into new desire - if the pace of this is swift, it is called happiness, and if it is slow, sorrow.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], II 029)
     A reaction: This seems to be the dream of the addict, as Socrates points out with his example of the leaky jar in 'Gorgias'. Should we want more desires?
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
We can never attain happiness while our will is pursuing desires [Schopenhauer]
     Full Idea: So long as our consciousness is filled by our will, so long as we are given up to the throng of desires with its constant hopes and fears, so long as we are the subject of willing, we never attain lasting happiness or peace.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], I 196), quoted by Christopher Janaway - Schopenhauer 6 'Aesthetic'
     A reaction: I hate this idea. It obviously leads to his Buddhism, and the eastern idea that life is generally a bad idea and to be avoided. I think Nietzsche rebelled strongly against this attitude of Schopenhauer's.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Virtue must spring from an intuitive recognition that other people are essentially like us [Schopenhauer]
     Full Idea: Virtue must spring from that intuitive knowledge which recognises in the individuality of others the same essence as in our own.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.66)
     A reaction: After all his pessimism, he arrives at a view similar to Hume's, that morality is built on natural empathy. But why built a moral theory on one base. Everything points us towards morality! Moral actions are more beautiful.
26. Natural Theory / A. Speculations on Nature / 1. Nature
The essence of nature is the will to life itself [Schopenhauer]
     Full Idea: The essence of nature is the will to life itself.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.60)
     A reaction: How would he have responded to Darwin? The will to life is the product, there, of a different and more remote force, such as the 'energy' of the physicist (whatever that is!).
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Christianity is a pessimistic religion, in which the world is equated with evil [Schopenhauer]
     Full Idea: Let no one think that Christianity is conducive to optimism; on the contrary, in the Gospels 'world' and 'evil' are used almost synonymously.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.59)
     A reaction: The source of Nietzsche's 'Beyond Good and Evil'. Do any religions throw you vigorously back into the middle of life, with its conflict and creativity?
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion is the mythical clothing of the truth which is inaccessible to the crude human intellect [Schopenhauer]
     Full Idea: All systems of religion are the mythical clothing of the truth which is inaccessible to the crude human intellect.
     From: Arthur Schopenhauer (The World as Will and Idea [1819], IV.63)
     A reaction: Is this a compliment? It seems to be, because at least the mysteries are identified and given an outward form. A nice thought.