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All the ideas for 'Through the Looking Glass', 'The World as Will and Idea' and 'The Nature of Mathematical Knowledge'

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76 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 / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
     Full Idea: Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
     Full Idea: Kitcher says maths is an 'idealising theory', like some in physics; maths idealises features of the world, and practical operations, such as segregating and matching (numbering), measuring, cutting, moving, assembling (geometry), and collecting (sets).
     From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984]) by Michael D. Resnik - Maths as a Science of Patterns One.4.2.2
     A reaction: This seems to be an interesting line, which is trying to be fairly empirical, and avoid basing mathematics on purely a priori understanding. Nevertheless, we do not learn idealisation from experience. Resnik labels Kitcher an anti-realist.
Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
     Full Idea: Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts).
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3)
     A reaction: Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means.
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
     Full Idea: What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3)
     A reaction: Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means.
The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
     Full Idea: Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4)
     A reaction: I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
     Full Idea: The real numbers stand to measurement as the natural numbers stand to counting.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.4)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
     Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
     A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A one-operation is the segregation of a single object [Kitcher]
     Full Idea: We perform a one-operation when we perform a segregative operation in which a single object is segregated.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.3)
     A reaction: This is part of Kitcher's empirical but constructive account of arithmetic, which I find very congenial. He avoids the word 'unit', and goes straight to the concept of 'one' (which he treats as more primitive than zero).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The old view is that mathematics is useful in the world because it describes the world [Kitcher]
     Full Idea: There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)
     A reaction: He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
     Full Idea: The method of infinitesimals is that you divide by the time, and then set the time to zero.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 10.2)
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Mathematical intuition is not the type platonism needs [Kitcher]
     Full Idea: The intuitions of which mathematicians speak are not those which Platonism requires.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.3)
     A reaction: The point is that it is not taken to be a 'special' ability, but rather a general insight arising from knowledge of mathematics. I take that to be a good account of intuition, which I define as 'inarticulate rationality'.
If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
     Full Idea: If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1)
     A reaction: This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it.
Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
     Full Idea: The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2)
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Mathematical knowledge arises from basic perception [Kitcher]
     Full Idea: Mathematical knowledge arises from rudimentary knowledge acquired by perception.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro)
     A reaction: This is an empiricist manifesto, which asserts his allegiance to Mill, and he gives a sophisticated account of how higher mathematics can be accounted for in this way. Well, he tries to.
My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
     Full Idea: The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro)
     A reaction: I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction.
We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
     Full Idea: I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2)
     A reaction: I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction.
The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
     Full Idea: Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
     A reaction: [A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
     Full Idea: Philosophers who hope to avoid commitment to abstract entities by claiming that mathematical statements are analytic must show how analyticity is, or provides a species of, truth not requiring reference.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.I)
     A reaction: [the last part is a quotation from W.D. Hart] Kitcher notes that Frege has a better account, because he provides objects to which reference can be made. I like this idea, which seems to raise a very large question, connected to truthmakers.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Arithmetic is an idealizing theory [Kitcher]
     Full Idea: I construe arithmetic as an idealizing theory.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: I find 'generalising' the most helpful word, because everyone seems to understand and accept the idea. 'Idealisation' invokes 'ideals', which lots of people dislike, and lots of philosophers seem to have trouble with 'abstraction'.
Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
     Full Idea: I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics.
We develop a language for correlations, and use it to perform higher level operations [Kitcher]
     Full Idea: The development of a language for describing our correlational activity itself enables us to perform higher level operations.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: This is because all language itself (apart from proper names) is inherently general, idealised and abstracted. He sees the correlations as the nested collections expressed by set theory.
Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
     Full Idea: The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
     Full Idea: Conceptualists claim that we have basic a priori knowledge of mathematical axioms in virtue of our possession of mathematical concepts.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.1)
     A reaction: I sympathise with this view. If concepts are reasonably clear, they will relate to one another in certain ways. How could they not? And how else would you work out those relations other than by thinking about them?
If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]
     Full Idea: Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6)
     A reaction: Nice question! He's a fan of getting at the explanatory in mathematics.
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 / A. Nature of Existence / 3. Being / e. Being and nothing
I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
     Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
     From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
     A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.
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 / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Abstract objects were a bad way of explaining the structure in mathematics [Kitcher]
     Full Idea: The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)
     A reaction: I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing.
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 / A. A Priori Knowledge / 1. Nature of the A Priori
A priori knowledge comes from available a priori warrants that produce truth [Kitcher]
     Full Idea: X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4)
     A reaction: [compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start.
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
In long mathematical proofs we can't remember the original a priori basis [Kitcher]
     Full Idea: When we follow long mathematical proofs we lose our a priori warrants for their beginnings.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2)
     A reaction: Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2.
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher]
     Full Idea: Knowledge is independent of experience if any experience which would enable us to acquire the concepts involved would enable us to have the knowledge.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.3)
     A reaction: This is the 'conceptualist' view of a priori knowledge, which Kitcher goes on to attack, preferring a 'constructivist' view. The formula here shows that we can't divorce experience entirely from a priori thought. I find conceptualism a congenial view.
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher]
     Full Idea: One can make a powerful case for supposing that some self-knowledge is a priori. At most, if not all, of our waking moments, each of us knows of herself that she exists.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.6)
     A reaction: This is a begrudging concession from a strong opponent to the whole notion of a priori knowledge. I suppose if you ask 'what can be known by thought alone?' then truths about thought ought to be fairly good initial candidates.
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.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher]
     Full Idea: A 'warrant' refers to those processes which produce belief 'in the right way': X knows that p iff p, and X believes that p, and X's belief that p was produced by a process which is a warrant for it.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.2)
     A reaction: That is, a 'warrant' is a justification which makes a belief acceptable as knowledge. Traditionally, warrants give you certainty (and are, consequently, rather hard to find). I would say, in the modern way, that warrants are agreed by social convention.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo]
     Full Idea: According to Kitcher, if experiential evidence can defeat someone's justification for a belief, then their justification depends on the absence of that experiential evidence.
     From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984], p.89) by Albert Casullo - A Priori Knowledge 2.3
     A reaction: Sounds implausible. There are trillions of possible defeaters for most beliefs, but to say they literally depend on trillions of absences seems a very odd way of seeing the situation
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.
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
     Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man.
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.
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!).
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.