58 ideas
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 18986 | Truth is just a name for verification-processes [James] |
| 18983 | In many cases there is no obvious way in which ideas can agree with their object [James] |
| 18972 | Ideas are true in so far as they co-ordinate our experiences [James] |
| 18973 | New opinions count as 'true' if they are assimilated to an individual's current beliefs [James] |
| 18984 | True ideas are those we can assimilate, validate, corroborate and verify (and false otherwise) [James] |
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| 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] |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| 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] |
| 18987 | A 'thing' is simply carved out of reality for human purposes [James] |
| 18981 | 'Substance' is just a word for groupings and structures in experience [James] |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| 18974 | Truth is a species of good, being whatever proves itself good in the way of belief [James] |
| 18989 | Pragmatism accepts any hypothesis which has useful consequences [James] |
| 18971 | Theories are practical tools for progress, not answers to enigmas [James] |
| 18985 | True thoughts are just valuable instruments of action [James] |
| 18982 | Pragmatism says all theories are instrumental - that is, mental modes of adaptation to reality [James] |
| 18975 | We return to experience with concepts, where they show us differences [James] |
| 18980 | If there is a 'greatest knower', it doesn't follow that they know absolutely everything [James] |
| 18978 | It is hard to grasp a cosmic mind which produces such a mixture of goods and evils [James] |
| 18991 | If the God hypothesis works well, then it is true [James] |
| 18977 | The wonderful design of a woodpecker looks diabolical to its victims [James] |
| 18979 | Things with parts always have some structure, so they always appear to be designed [James] |
| 18976 | Private experience is the main evidence for God [James] |
| 18990 | Nirvana means safety from sense experience, and hindus and buddhists are just afraid of life [James] |