42 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] |
10455 | Free logic at least allows empty names, but struggles to express non-existence [Bach] |
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] |
10454 | In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach] |
10453 | In logic constants play the role of proper names [Bach] |
10452 | Proper names can be non-referential - even predicate as well as attributive uses [Bach] |
10456 | Millian names struggle with existence, empty names, identities and attitude ascription [Bach] |
10440 | An object can be described without being referred to [Bach] |
10444 | Definite descriptions can be used to refer, but are not semantically referential [Bach] |
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 naďve 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] |
10446 | Fictional reference is different inside and outside the fiction [Bach] |
10447 | We can refer to fictional entities if they are abstract objects [Bach] |
10443 | You 'allude to', not 'refer to', an individual if you keep their identity vague [Bach] |
10439 | What refers: indefinite or definite or demonstrative descriptions, names, indexicals, demonstratives? [Bach] |
10441 | If we can refer to things which change, we can't be obliged to single out their properties [Bach] |
10442 | We can think of an individual without have a uniquely characterizing description [Bach] |
10445 | It can't be real reference if it could refer to some other thing that satisfies the description [Bach] |
10457 | Since most expressions can be used non-referentially, none of them are inherently referential [Bach] |
10463 | Just alluding to or describing an object is not the same as referring to it [Bach] |
10459 | Context does not create reference; it is just something speakers can exploit [Bach] |
10460 | 'That duck' may not refer to the most obvious one in the group [Bach] |
10461 | What a pronoun like 'he' refers back to is usually a matter of speaker's intentions [Bach] |
10462 | Information comes from knowing who is speaking, not just from interpretation of the utterance [Bach] |
10458 | People slide from contextual variability all the way to contextual determination [Bach] |