24 ideas
9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
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] |
10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
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] |
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] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |