48 ideas
| 2557 | Analytical philosophy seems to have little interest in how to tell a good analysis from a bad one [Rorty] |
| 2556 | Rational certainty may be victory in argument rather than knowledge of facts [Rorty] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 4726 | Rorty seems to view truth as simply being able to hold one's view against all comers [Rorty, by O'Grady] |
| 2549 | For James truth is "what it is better for us to believe" rather than a correct picture of reality [Rorty] |
| 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] |
| 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] |
| 15312 | We get the idea of power by abstracting from ropes, magnets and electric shocks [Priestley] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 2548 | If knowledge is merely justified belief, justification is social [Rorty] |
| 6599 | Knowing has no definable essence, but is a social right, found in the context of conversations [Rorty] |
| 2566 | You can't debate about whether to have higher standards for the application of words [Rorty] |
| 2553 | The mind is a property, or it is baffling [Rorty] |
| 2550 | Pain lacks intentionality; beliefs lack qualia [Rorty] |
| 2554 | Is intentionality a special sort of function? [Rorty] |
| 2565 | Nature has no preferred way of being represented [Rorty] |
| 2560 | Can meanings remain the same when beliefs change? [Rorty] |
| 2562 | A theory of reference seems needed to pick out objects without ghostly inner states [Rorty] |
| 2559 | Davidson's theory of meaning focuses not on terms, but on relations between sentences [Rorty] |
| 2558 | Since Hegel we have tended to see a human as merely animal if it is outside a society [Rorty] |
| 15311 | Attraction or repulsion are not imparted to matter, but actually constitute it [Priestley] |