Combining Texts

All the ideas for 'Set Theory', 'Structure of Scientific Revolutions (2nd ed)' and 'Quaestiones Disputatae de Malo'

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34 ideas

2. Reason / A. Nature of Reason / 1. On Reason
We are coerced into assent to a truth by reason's violence [Aquinas]
2. Reason / A. Nature of Reason / 4. Aims of Reason
The mind is compelled by necessary truths, but not by contingent truths [Aquinas]
3. Truth / A. Truth Problems / 3. Value of Truth
For the mind Good is one truth among many, and Truth is one good among many [Aquinas]
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]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas]
14. Science / A. Basis of Science / 6. Falsification
Most theories are continually falsified [Kuhn, by Kitcher]
Kuhn's scientists don't aim to falsifying their paradigm, because that is what they rely on [Kuhn, by Gorham]
14. Science / B. Scientific Theories / 4. Paradigm
Switching scientific paradigms is a conversion experience [Kuhn]
14. Science / B. Scientific Theories / 5. Commensurability
Kuhn has a description theory of reference, so the reference of 'electron' changes with the descriptions [Rowlands on Kuhn]
Incommensurability assumes concepts get their meaning from within the theory [Kuhn, by Okasha]
Galileo's notions can't be 'incommensurable' if we can fully describe them [Putnam on Kuhn]
16. Persons / F. Free Will / 3. Constraints on the will
If we saw something as totally and utterly good, we would be compelled to will it [Aquinas]
16. Persons / F. Free Will / 4. For Free Will
Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas]
However habituated you are, given time to ponder you can go against a habit [Aquinas]
Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas]
The will is not compelled to move, even if pleasant things are set before it [Aquinas]
Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas]
16. Persons / F. Free Will / 5. Against Free Will
We must admit that when the will is not willing something, the first movement to will must come from outside the will [Aquinas]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
The will must aim at happiness, but can choose the means [Aquinas]
We don't have to will even perfect good, because we can choose not to think of it [Aquinas]
The will can only want what it thinks is good [Aquinas]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Without free will not only is ethical action meaningless, but also planning, commanding, praising and blaming [Aquinas]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Good applies to goals, just as truth applies to ideas in the mind [Aquinas]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas]