63 ideas
| 17275 | Realist metaphysics concerns what is real; naive metaphysics concerns natures of things [Fine,K] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 17282 | Truths need not always have their source in what exists [Fine,K] |
| 17283 | If the truth-making relation is modal, then modal truths will be grounded in anything [Fine,K] |
| 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] |
| 17286 | Logical consequence is verification by a possible world within a truth-set [Fine,K] |
| 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] |
| 22121 | The concept of being has only one meaning, whether talking of universals or of God [Duns Scotus, by Dumont] |
| 22122 | Being (not sensation or God) is the primary object of the intellect [Duns Scotus, by Dumont] |
| 17272 | 2+2=4 is necessary if it is snowing, but not true in virtue of the fact that it is snowing [Fine,K] |
| 17276 | If you say one thing causes another, that leaves open that the 'other' has its own distinct reality [Fine,K] |
| 17284 | An immediate ground is the next lower level, which gives the concept of a hierarchy [Fine,K] |
| 17285 | 'Strict' ground moves down the explanations, but 'weak' ground can move sideways [Fine,K] |
| 17288 | We learn grounding from what is grounded, not what does the grounding [Fine,K] |
| 17281 | If grounding is a relation it must be between entities of the same type, preferably between facts [Fine,K] |
| 17280 | Ground is best understood as a sentence operator, rather than a relation between predicates [Fine,K] |
| 17290 | Only metaphysical grounding must be explained by essence [Fine,K] |
| 17274 | Philosophical explanation is largely by ground (just as cause is used in science) [Fine,K] |
| 17278 | We can only explain how a reduction is possible if we accept the concept of ground [Fine,K] |
| 17287 | Facts, such as redness and roundness of a ball, can be 'fused' into one fact [Fine,K] |
| 22125 | Duns Scotus was a realist about universals [Duns Scotus, by Dumont] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 22127 | Scotus said a substantial principle of individuation [haecceitas] was needed for an essence [Duns Scotus, by Dumont] |
| 22126 | Avicenna and Duns Scotus say essences have independent and prior existence [Duns Scotus, by Dumont] |
| 17279 | Even a three-dimensionalist might identify temporal parts, in their thinking [Fine,K] |
| 17273 | Each basic modality has its 'own' explanatory relation [Fine,K] |
| 17289 | Every necessary truth is grounded in the nature of something [Fine,K] |
| 22129 | Certainty comes from the self-evident, from induction, and from self-awareness [Duns Scotus, by Dumont] |
| 22130 | Scotus defended direct 'intuitive cognition', against the abstractive view [Duns Scotus, by Dumont] |
| 22128 | Augustine's 'illumination' theory of knowledge leads to nothing but scepticism [Duns Scotus, by Dumont] |
| 17291 | We explain by identity (what it is), or by truth (how things are) [Fine,K] |
| 17271 | Is there metaphysical explanation (as well as causal), involving a constitutive form of determination? [Fine,K] |
| 22131 | The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont] |
| 17277 | If mind supervenes on the physical, it may also explain the physical (and not vice versa) [Fine,K] |
| 22123 | The concept of God is the unique first efficient cause, final cause, and most eminent being [Duns Scotus, by Dumont] |
| 22124 | We can't infer the infinity of God from creation ex nihilo [Duns Scotus, by Dumont] |