Combining Texts

All the ideas for 'Defending the Axioms', 'Truth-makers' and 'The Art of the Infinite'

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19 ideas

3. Truth / B. Truthmakers / 2. Truthmaker Relation
10911 Part-whole is the key relation among truth-makers [Mulligan/Simons/Smith]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
10909 Truth-makers cannot be the designata of the sentences they make true [Mulligan/Simons/Smith]
10906 Moments (objects which cannot exist alone) may serve as truth-makers [Mulligan/Simons/Smith]
10907 The truth-maker for a sentence may not be unique, or may be a combination, or several separate items [Mulligan/Simons/Smith]
10912 Despite negative propositions, truthmakers are not logical complexes, but ordinary experiences [Mulligan/Simons/Smith]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
10908 Correspondence has to invoke facts or states of affairs, just to serve as truth-makers [Mulligan/Simons/Smith]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
15717 Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
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 / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]