81 ideas
| 15010 | Your metaphysics is 'cheating' if your ontology won't support the beliefs you accept [Sider] |
| 14977 | Metaphysics is not about what exists or is true or essential; it is about the structure of reality [Sider] |
| 14994 | Extreme doubts about metaphysics also threaten to undermine the science of unobservables [Sider] |
| 15003 | It seems unlikely that the way we speak will give insights into the universe [Sider] |
| 14986 | Conceptual analysts trust particular intuitions much more than general ones [Sider] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 15015 | It seems possible for a correct definition to be factually incorrect, as in defining 'contact' [Sider] |
| 14981 | Philosophical concepts are rarely defined, and are not understood by means of definitions [Sider] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 14992 | We don't care about plain truth, but truth in joint-carving terms [Sider] |
| 15012 | Orthodox truthmaker theories make entities fundamental, but that is poor for explanation [Sider] |
| 15023 | The Barcan schema implies if X might have fathered something, there is something X might have fathered [Sider] |
| 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] |
| 15004 | 'Gunk' is an object in which proper parts all endlessly have further proper parts [Sider] |
| 14984 | Which should be primitive in mereology - part, or overlap? [Sider] |
| 14980 | There is a real issue over what is the 'correct' logic [Sider] |
| 15000 | 'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p' [Sider] |
| 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] |
| 15020 | Classical logic is good for mathematics and science, but less good for natural language [Sider] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 15029 | Modal accounts of logical consequence are simple necessity, or essential use of logical words [Sider] |
| 15019 | Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral [Sider] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 15001 | 'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted [Sider] |
| 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] |
| 17914 | He made a molten sea, which was ten cubits across, and thirty cubits round the edge [Anon (Kings)] |
| 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] |
| 15017 | Supervenience is a modal connection [Sider] |
| 15008 | Is fundamentality in whole propositions (and holistic), or in concepts (and atomic)? [Sider] |
| 15013 | Tables and chairs have fundamental existence, but not fundamental natures [Sider] |
| 15014 | Unlike things, stuff obeys unrestricted composition and mereological essentialism [Sider] |
| 15009 | We must distinguish 'concrete' from 'abstract' and necessary states of affairs. [Sider] |
| 14983 | Accept the ontology of your best theory - and also that it carves nature at the joints [Sider] |
| 14978 | A property is intrinsic if an object alone in the world can instantiate it [Sider] |
| 14995 | Predicates can be 'sparse' if there is a universal, or if there is a natural property or relation [Sider] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 15026 | Essence (even if nonmodal) is not fundamental in metaphysics [Sider] |
| 15030 | Humeans say that we decide what is necessary [Sider] |
| 15031 | Modal terms in English are entirely contextual, with no modality outside the language [Sider] |
| 15027 | If truths are necessary 'by convention', that seems to make them contingent [Sider] |
| 15028 | Conventionalism doesn't seem to apply to examples of the necessary a posteriori [Sider] |
| 15033 | Humeans says mathematics and logic are necessary because that is how our concept of necessity works [Sider] |
| 15025 | The world does not contain necessity and possibility - merely how things are [Sider] |
| 14988 | A theory which doesn't fit nature is unexplanatory, even if it is true [Sider] |
| 14982 | If I used Ramsey sentences to eliminate fundamentality from my theory, that would be a real loss [Sider] |
| 14989 | Problem predicates in induction don't reflect the structure of nature [Sider] |
| 14997 | Two applications of 'grue' do not guarantee a similarity between two things [Sider] |
| 14990 | Bayes produces weird results if the prior probabilities are bizarre [Sider] |
| 15005 | Explanations must cite generalisations [Sider] |
| 15011 | If the ultimate explanation is a list of entities, no laws, patterns or mechanisms can be cited [Sider] |
| 15018 | Intentionality is too superficial to appear in the catalogue of ultimate physics [Sider] |
| 14999 | Prior to conventions, not all green things were green? [Sider] |
| 14998 | Conventions are contingent and analytic truths are necessary, so that isn't their explanation [Sider] |
| 15016 | Analyticity has lost its traditional role, which relied on truth by convention [Sider] |
| 14985 | The notion of law doesn't seem to enhance physical theories [Sider] |
| 14987 | Many of the key theories of modern physics do not appear to be 'laws' [Sider] |
| 14991 | Space has real betweenness and congruence structure (though it is not the Euclidean concepts) [Sider] |
| 15021 | The central question in the philosophy of time is: How alike are time and space? [Sider] |
| 15024 | The spotlight theorists accepts eternal time, but with a spotlight of the present moving across it [Sider] |