Combining Texts

All the ideas for 'Defending the Axioms', 'Lecture on Applicability of Mathematics' and 'Beauty: a very short introduction'

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19 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason
18543 Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton]
3. Truth / A. Truth Problems / 2. Defining Truth
18542 Defining truth presupposes that there can be a true definition [Scruton]
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]
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 / 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 / b. Indispensability of mathematics
8732 It is spooky the way mathematics anticipates physics [Weinberg]
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]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
18546 The pleasure taken in beauty also aims at understanding and valuing [Scruton]
18550 Art gives us imaginary worlds which we can view impartially [Scruton]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
18544 Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton]
18553 Beauty shows us what we should want in order to achieve human fulfilment [Scruton]
18556 Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
18548 Natural beauty reassures us that the world is where we belong [Scruton]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
18551 Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18541 Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton]
25. Social Practice / F. Life Issues / 5. Sexual Morality
18554 Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton]