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All the ideas for 'Causes and Counterfactuals', 'The World as Will and Idea' and 'Philosophy of Mathematics'

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97 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy considers only the universal, in nature as everywhere else [Schopenhauer]
Everyone is conscious of all philosophical truths, but philosophers bring them to conceptual awareness [Schopenhauer]
1. Philosophy / D. Nature of Philosophy / 8. Humour
Absurdity is incongruity between correct and false points of view [Schopenhauer]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics must understand the world thoroughly, as a principal source of knowledge [Schopenhauer]
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative definitions are wrong, because they change the set that is being defined? [Bostock]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
There is no single agreed structure for set theory [Bostock]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
A 'proper class' cannot be a member of anything [Bostock]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
We could add axioms to make sets either as small or as large as possible [Bostock]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Replacement enforces a 'limitation of size' test for the existence of sets [Bostock]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
The completeness of first-order logic implies its compactness [Bostock]
First-order logic is not decidable: there is no test of whether any formula is valid [Bostock]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Substitutional quantification is just standard if all objects in the domain have a name [Bostock]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
The Deduction Theorem is what licenses a system of natural deduction [Bostock]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock]
Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
A cardinal is the earliest ordinal that has that number of predecessors [Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock]
The number of reals is the number of subsets of the natural numbers [Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Modern axioms of geometry do not need the real numbers [Bostock]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
The Peano Axioms describe a unique structure [Bostock]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
There are many criteria for the identity of numbers [Bostock]
Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock]
Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Numbers can't be positions, if nothing decides what position a given number has [Bostock]
Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
Nominalism about mathematics is either reductionist, or fictionalist [Bostock]
Nominalism as based on application of numbers is no good, because there are too many applications [Bostock]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Actual measurement could never require the precision of the real numbers [Bostock]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock]
Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock]
Many crucial logicist definitions are in fact impredicative [Bostock]
If Hume's Principle is the whole story, that implies structuralism [Bostock]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Higher cardinalities in sets are just fairy stories [Bostock]
A fairy tale may give predictions, but only a true theory can give explanations [Bostock]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
The best version of conceptualism is predicativism [Bostock]
Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
The usual definitions of identity and of natural numbers are impredicative [Bostock]
If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock]
Predicativism makes theories of huge cardinals impossible [Bostock]
If mathematics rests on science, predicativism may be the best approach [Bostock]
If we can only think of what we can describe, predicativism may be implied [Bostock]
The predicativity restriction makes a difference with the real numbers [Bostock]
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]
7. Existence / D. Theories of Reality / 3. Reality
Schopenhauer, unlike other idealists, says reality is irrational [Schopenhauer, by Lewis,PB]
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]
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]
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]
The world only exists in relation to something else, as an idea of the one who conceives it [Schopenhauer]
We know reality because we know our own bodies and actions [Schopenhauer]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Kant rightly separates appearance and thing-in-itself [Schopenhauer]
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]
12. Knowledge Sources / B. Perception / 5. Interpretation
All perception is intellectual [Schopenhauer]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
A consciousness without an object is no consciousness [Schopenhauer]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
We have hidden and unadmitted desires and fears, suppressed because of vanity [Schopenhauer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
I know both aspects of my body, as representation, and as will [Schopenhauer]
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]
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]
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]
19. Language / F. Communication / 2. Assertion
In logic a proposition means the same when it is and when it is not asserted [Bostock]
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]
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]
Only the will is thing-in-itself, seen both in blind nature and in human action [Schopenhauer]
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]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Schopenhauer is a chief proponent of aesthetic experience as 'disinterested' [Schopenhauer, by Janaway]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
A principal pleasure of the beautiful is that it momentarily silences the will [Schopenhauer]
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]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
Schopenhauer emphasises Ideas in art, unlike most romantics [Schopenhauer, by Lewis,PB]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
The will-less contemplation of art brings a liberation from selfhood [Schopenhauer, by Gardner]
Man is more beautiful than anything else, and the loftiest purpose of art is to reveal his nature [Schopenhauer]
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]
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]
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]
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]
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]
22. Metaethics / B. Value / 2. Values / f. Altruism
Altruistic people make less distinction than usual between themselves and others [Schopenhauer]
22. Metaethics / B. Value / 2. Values / i. Self-interest
Only self-love can motivate morality, but that also makes it worthless [Schopenhauer]
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]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
We can never attain happiness while our will is pursuing desires [Schopenhauer]
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]
26. Natural Theory / A. Speculations on Nature / 1. Nature
The essence of nature is the will to life itself [Schopenhauer]
26. Natural Theory / C. Causation / 1. Causation
Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Many counterfactuals have nothing to do with causation [Kim, by Tooley]
Counterfactuals can express four other relations between events, apart from causation [Kim]
Causation is not the only dependency relation expressed by counterfactuals [Kim]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Christianity is a pessimistic religion, in which the world is equated with evil [Schopenhauer]
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]