23 ideas
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] |
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
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] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
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] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
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] |
23304 | The ancient Memorists said virtually all types of thinking could be done simply by memory [Sorabji] |
23303 | Stoics say true memory needs reflection and assent, but animals only have perceptual recognition [Sorabji] |
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] |