24 ideas
4187 | 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer] |
9331 | How do we determine which of the sentences containing a term comprise its definition? [Horwich] |
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] |
4192 | All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer] |
4190 | All understanding is an immediate apprehension of the causal relation [Schopenhauer] |
9333 | A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich] |
9342 | Understanding needs a priori commitment [Horwich] |
9332 | Meaning is generated by a priori commitment to truth, not the other way around [Horwich] |
9341 | Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich] |
9334 | If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich] |
9339 | A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich] |
4191 | What we know in ourselves is not a knower but a will [Schopenhauer] |
21368 | The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer] |
4189 | Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer] |