14 ideas
4187 | 'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer] |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
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] |
7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
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] |
3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
4189 | Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer] |