Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Second Commentary on 'Isagoge'' and 'Parerga and Paralipomena'

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


31 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Metaphysics studies the inexplicable ends of explanation [Schopenhauer]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
7. Existence / D. Theories of Reality / 2. Realism
For me the objective thing-in-itself is the will [Schopenhauer]
8. Modes of Existence / D. Universals / 5. Universals as Concepts
If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
Knowledge is not power! Ignorant people possess supreme authority [Schopenhauer]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
A priori propositions are those we could never be seriously motivated to challenge [Schopenhauer]
14. Science / D. Explanation / 1. Explanation / a. Explanation
All knowledge and explanation rests on the inexplicable [Schopenhauer]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
Half our thinking is unconscious, and we reach conclusions while unaware of premises [Schopenhauer]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
We don't control our own thinking [Schopenhauer]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
All of our concepts are borrowed from perceptual knowledge [Schopenhauer]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
Aesthetics concerns how we can take pleasure in an object, with no reference to the will [Schopenhauer]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
The beautiful is a perception of Plato's Forms, which eliminates the will [Schopenhauer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Man is essentially a dreadful wild animal [Schopenhauer]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Pleasure is weaker, and pain stronger, than we expect [Schopenhauer]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
A man's character can be learned from a single characteristic action [Schopenhauer]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The five Chinese virtues: pity, justice, politeness, wisdom, honesty [Schopenhauer]
Buddhists wisely start with the cardinal vices [Schopenhauer]
23. Ethics / F. Existentialism / 4. Boredom
Boredom is only felt by those clever enough to need activity [Schopenhauer]
Human life is a mistake, shown by boredom, which is direct awareness of the fact [Schopenhauer]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The state only exists to defend citizens, from exterior threats, and from one another [Schopenhauer]
25. Social Practice / A. Freedoms / 1. Slavery
Poverty and slavery are virtually two words for the same thing [Schopenhauer]
25. Social Practice / A. Freedoms / 3. Free speech
The freedom of the press to sell poison outweighs its usefulness [Schopenhauer]
25. Social Practice / F. Life Issues / 4. Suicide
If suicide was quick and easy, most people would have done it by now [Schopenhauer]
25. Social Practice / F. Life Issues / 5. Sexual Morality
Would humanity still exist if sex wasn't both desired and pleasurable? [Schopenhauer]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Only religion introduces serious issues to uneducated people [Schopenhauer]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
The Creator created the possibilities for worlds, so should have made a better one than this possible [Schopenhauer]