16 ideas
| 9944 | We understand some statements about all sets [Putnam] |
| 9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
| 9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
| 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] |
| 9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
| 9941 | Science requires more than consistency of mathematics [Putnam] |
| 9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
| 17402 | Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri] |
| 17399 | Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev] |
| 17400 | Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri] |
| 17401 | Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev] |