16 ideas
17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
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] |
17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
5040 | Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz] |
13159 | Only God sees contingent truths a priori [Leibniz] |
5039 | If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz] |
22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |
5041 | God does everything in a perfect way, and never acts contrary to reason [Leibniz] |