Combining Texts

All the ideas for 'Two Problems of Epistemology', 'Cardinality, Counting and Equinumerosity' and 'Beauty: a very short introduction'

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23 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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
17453 The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17450 Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17459 Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17454 Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17449 We can understand cardinality without the idea of one-one correspondence [Heck]
17458 Equinumerosity is not the same concept as one-one correspondence [Heck]
14. Science / A. Basis of Science / 6. Falsification
18284 Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
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]