61 ideas
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
1564 | True and false statements can use exactly the same words [Anon (Diss)] |
10455 | Free logic at least allows empty names, but struggles to express non-existence [Bach] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
17803 | Limitation of size is part of the very conception of a set [Mayberry] |
17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
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] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
1561 | Anything can be acceptable in some circumstances and unacceptable in others [Anon (Diss)] |
1560 | Lydians prostitute their daughters to raise a dowery, but no Greek would marry such a girl [Anon (Diss)] |
1559 | Thracians think tattooing adds to a girl's beauty, but elsewhere it is a punishment [Anon (Diss)] |
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] |
1567 | How could someone who knows everything fail to act correctly? [Anon (Diss)] |
1563 | Every apparent crime can be right in certain circumstances [Anon (Diss), by PG] |
1562 | It is right to lie to someone, to get them to take medicine they are reluctant to take [Anon (Diss)] |
1566 | The first priority in elections is to vote for people who support democracy [Anon (Diss)] |
1565 | We learn language, and we don't know who teaches us it [Anon (Diss)] |