Combining Texts

All the ideas for 'Two Problems of Epistemology', 'Set Theory' and 'The Sentiment of Rationality'

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30 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
22659 It is wisdom to believe what you desire, because belief is needed to achieve it [James]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
22657 All good philosophers start from a dumb conviction about which truths can be revealed [James]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
22647 A complete system is just a classification of the whole world's ingredients [James]
2. Reason / A. Nature of Reason / 5. Objectivity
22648 A single explanation must have a single point of view [James]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
22644 Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
7. Existence / E. Categories / 2. Categorisation
22649 Classification can only ever be for a particular purpose [James]
14. Science / A. Basis of Science / 1. Observation
22655 Scientific genius extracts more than other people from the same evidence [James]
14. Science / A. Basis of Science / 6. Falsification
22658 Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James]
18284 Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
14. Science / C. Induction / 3. Limits of Induction
22654 We can't know if the laws of nature are stable, but we must postulate it or assume it [James]
14. Science / C. Induction / 6. Bayes's Theorem
22656 Trying to assess probabilities by mere calculation is absurd and impossible [James]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
22646 We have a passion for knowing the parts of something, rather than the whole [James]
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
22652 The mind has evolved entirely for practical interests, seen in our reflex actions [James]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
22651 Dogs' curiosity only concerns what will happen next [James]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
22650 How can the ground of rationality be itself rational? [James]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
22643 It seems that we feel rational when we detect no irrationality [James]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
22660 Evolution suggests prevailing or survival as a new criterion of right and wrong [James]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
22645 Understanding by means of causes is useless if they are not reduced to a minimum number [James]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
22653 Early Christianity says God recognises the neglected weak and tender impulses [James]