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All the ideas for 'Logical Pluralism', 'The World as Will and Idea' and 'Philosophy of Mathematics'

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74 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?
3. Truth / A. Truth Problems / 1. Truth
Some truths have true negations [Beall/Restall]
     Full Idea: Dialetheism is the view that some truths have true negations.
     From: JC Beall / G Restall (Logical Pluralism [2006], 7.4)
     A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'.
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
A truthmaker is an object which entails a sentence [Beall/Restall]
     Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3)
     A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall]
     Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not.
     From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2)
     A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative?
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
Excluded middle must be true for some situation, not for all situations [Beall/Restall]
     Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
     A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation.
It's 'relevantly' valid if all those situations make it true [Beall/Restall]
     Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
     A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here.
Relevant logic does not abandon classical logic [Beall/Restall]
     Full Idea: We have not abandoned classical logic in our acceptance of relevant logic.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.4)
     A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable.
Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall]
     Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3)
     A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems.
A doesn't imply A - that would be circular [Beall/Restall]
     Full Idea: We could reject the inference from A to itself (on grounds of circularity).
     From: JC Beall / G Restall (Logical Pluralism [2006], 8)
     A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal.
Relevant logic may reject transitivity [Beall/Restall]
     Full Idea: Some relevant logics reject transitivity, but we defend the classical view.
     From: JC Beall / G Restall (Logical Pluralism [2006], 8)
     A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion.
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall]
     Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain.
     From: JC Beall / G Restall (Logical Pluralism [2006], 7.1)
     A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
     Full Idea: Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical.
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.2)
     A reaction: The second principle is a standard axiom of ZFC. The first principle causes the trouble.
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
     Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
     A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic.
Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
     Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.5)
     A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence!
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
     Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
     A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all.
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]
     Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.1)
     A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view.
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
The model theory of classical predicate logic is mathematics [Beall/Restall]
     Full Idea: The model theory of classical predicate logic is mathematics if anything is.
     From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1)
     A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics.
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
There are several different consequence relations [Beall/Restall]
     Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence.
     From: JC Beall / G Restall (Logical Pluralism [2006], 8)
     A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it.
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
A sentence follows from others if they always model it [Beall/Restall]
     Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X.
     From: JC Beall / G Restall (Logical Pluralism [2006], 3.2)
     A reaction: This why the symbol |= is often referred to as 'models'.
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
     Full Idea: In classical semantics the function of singular terms is to refer, and that of quantifiers, to range over appropriate domains of entities.
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 7.1)
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]
     Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.2)
     A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
     Full Idea: Considered in isolation, the axioms of group theory are not assertions but comprise an implicit definition of some abstract structure,
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.5)
     A reaction: The traditional Euclidean approach is that axioms are plausible assertions with which to start. The present idea sums up the modern approach. In the modern version you can work backwards from a structure to a set of axioms.
To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
     Full Idea: Mathematics investigates the deductive consequences of axiomatic theories, but it also needs its own foundational axioms in order to provide models for its various axiomatic theories.
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.1)
     A reaction: This is a problem which faces the deductivist (if-then) approach. The deductive process needs its own grounds.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall]
     Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.4)
     A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one?
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
     Full Idea: If the 2nd Incompleteness Theorem undermines Hilbert's attempt to use a weak theory to prove the consistency of a strong one, it is still possible to prove the consistency of one theory, assuming the consistency of another theory.
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.6)
     A reaction: Note that this concerns consistency, not completeness.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
     Full Idea: Philosophical structuralism holds that mathematics is the study of abstract structures, or 'patterns'. If mathematics is the study of all possible patterns, then it is inevitable that the world is described by mathematics.
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 11.1)
     A reaction: [He cites the physicist John Barrow (2010) for this] For me this is a major idea, because the concept of a pattern gives a link between the natural physical world and the abstract world of mathematics. No platonism is needed.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
     Full Idea: Modern logic requires that logical truths be true in all models, including ones devoid of any mathematical objects. It follows immediately that the existence of mathematical objects can never be a matter of logic alone.
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 2)
     A reaction: Hm. Could there not be a complete set of models for a theory which all included mathematical objects? (I can't answer that).
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
     Full Idea: Game Formalism seeks to banish all semantics from mathematics, and Term Formalism seeks to reduce any such notions to purely syntactic ones.
     From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.3)
     A reaction: This approach was stimulated by the need to justify the existence of the imaginary number i. Just say it is a letter!
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?
10. Modality / A. Necessity / 3. Types of Necessity
Relevant necessity is always true for some situation (not all situations) [Beall/Restall]
     Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.2)
     A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences.
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.
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
Judgement is always predicating a property of a subject [Beall/Restall]
     Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.5)
     A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates?
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall]
     Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'.
     From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4)
     A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality.
19. Language / D. Propositions / 1. Propositions
Propositions commit to content, and not to any way of spelling it out [Beall/Restall]
     Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out.
     From: JC Beall / G Restall (Logical Pluralism [2006], 2.1)
     A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I.
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.