22 ideas
13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
9586 | In a number-statement, something is predicated of a concept [Frege] |
9580 | Our concepts recognise existing relations, they don't change them [Frege] |
9589 | Numbers are not real like the sea, but (crucially) they are still objective [Frege] |
9577 | The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
9581 | Many people have the same thought, which is the component, not the private presentation [Frege] |
9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
9588 | Number-abstraction somehow makes things identical without changing them! [Frege] |
9583 | Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege] |
9584 | Identity baffles psychologists, since A and B must be presented differently to identify them [Frege] |
13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |