Combining Texts

All the ideas for 'Quaestiones Disputatae de Malo', 'Lecture on Applicability of Mathematics' and 'The Art of the Infinite'

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24 ideas

2. Reason / A. Nature of Reason / 1. On Reason
1848 We are coerced into assent to a truth by reason's violence [Aquinas]
2. Reason / A. Nature of Reason / 4. Aims of Reason
1858 The mind is compelled by necessary truths, but not by contingent truths [Aquinas]
3. Truth / A. Truth Problems / 3. Value of Truth
1852 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 / j. Axiom of Choice IX
15717 Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
15712 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
15711 The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
15714 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
15715 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
8732 It is spooky the way mathematics anticipates physics [Weinberg]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
1860 Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
16. Persons / F. Free Will / 3. Constraints on the will
1855 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
1856 Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas]
1862 However habituated you are, given time to ponder you can go against a habit [Aquinas]
1849 Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas]
1861 The will is not compelled to move, even if pleasant things are set before it [Aquinas]
1853 Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas]
16. Persons / F. Free Will / 5. Against Free Will
1854 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
1847 The will must aim at happiness, but can choose the means [Aquinas]
1857 We don't have to will even perfect good, because we can choose not to think of it [Aquinas]
1846 The will can only want what it thinks is good [Aquinas]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
1850 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
1851 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
1859 Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas]