Combining Texts

All the ideas for 'Set Theory', 'Being and Nothingness' and 'The Sentiment of Rationality'

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40 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
It is wisdom to believe what you desire, because belief is needed to achieve it [James]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
All good philosophers start from a dumb conviction about which truths can be revealed [James]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
A complete system is just a classification of the whole world's ingredients [James]
2. Reason / A. Nature of Reason / 5. Objectivity
A single explanation must have a single point of view [James]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
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
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
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
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
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
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
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
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
Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
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
Constructibility: V = L (all sets are constructible) [Kunen]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
For Sartre there is only being for-itself, or being in-itself (which is beyond experience) [Sartre, by Daigle]
7. Existence / E. Categories / 2. Categorisation
Classification can only ever be for a particular purpose [James]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Appearances do not hide the essence; appearances are the essence [Sartre]
14. Science / A. Basis of Science / 1. Observation
Scientific genius extracts more than other people from the same evidence [James]
14. Science / A. Basis of Science / 6. Falsification
Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James]
14. Science / C. Induction / 3. Limits of Induction
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
Trying to assess probabilities by mere calculation is absurd and impossible [James]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
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
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
Dogs' curiosity only concerns what will happen next [James]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Sartre says consciousness is just directedness towards external objects [Sartre, by Rowlands]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
How can the ground of rationality be itself rational? [James]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
It seems that we feel rational when we detect no irrationality [James]
18. Thought / C. Content / 1. Content
Sartre rejects mental content, and the idea that the mind has hidden inner features [Sartre, by Rowlands]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
Evolution suggests prevailing or survival as a new criterion of right and wrong [James]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Man is a useless passion [Sartre]
Man is the desire to be God [Sartre]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
Sartre's freedom is not for whimsical action, but taking responsibility for our own values [Sartre, by Daigle]
22. Metaethics / B. Value / 2. Values / g. Love
Love is the demand to be loved [Sartre]
23. Ethics / F. Existentialism / 3. Angst
Fear concerns the world, but 'anguish' comes from confronting my self [Sartre]
23. Ethics / F. Existentialism / 6. Authentic Self
Sincerity is not authenticity, because it only commits to one particular identity [Sartre, by Aho]
We flee from the anguish of freedom by seeing ourselves objectively, as determined [Sartre]
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
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
Early Christianity says God recognises the neglected weak and tender impulses [James]