65 ideas
| 18877 | Moral realism doesn't seem to entail the existence of any things [Cameron] |
| 18868 | Surely if some propositions are grounded in existence, they all are? [Cameron] |
| 18928 | If maximalism is necessary, then that nothing exists has a truthmaker, which it can't have [Cameron] |
| 18867 | Orthodox Truthmaker applies to all propositions, and necessitates their truth [Cameron] |
| 18873 | God fixes all the truths of the world by fixing what exists [Cameron] |
| 15395 | Give up objects necessitating truths, and say their natures cause the truths? [Cameron] |
| 18931 | Determinate truths don't need extra truthmakers, just truthmakers that are themselves determinate [Cameron] |
| 18879 | What the proposition says may not be its truthmaker [Cameron] |
| 18880 | Rather than what exists, some claim that the truthmakers are ways of existence, dispositions, modalities etc [Cameron] |
| 18874 | Truthmaking doesn't require realism, because we can be anti-realist about truthmakers [Cameron] |
| 18932 | The facts about the existence of truthmakers can't have a further explanation [Cameron] |
| 15394 | Truthmaker requires a commitment to tropes or states of affairs, for contingent truths [Cameron] |
| 18869 | Without truthmakers, negative truths must be ungrounded [Cameron] |
| 18923 | The present property 'having been F' says nothing about a thing's intrinsic nature [Cameron] |
| 18926 | One temporal distibution property grounds our present and past truths [Cameron] |
| 18929 | We don't want present truthmakers for the past, if they are about to cease to exist! [Cameron] |
| 18871 | I support the correspondence theory because I believe in truthmakers [Cameron] |
| 18870 | Maybe truthmaking and correspondence stand together, and are interdefinable [Cameron] |
| 15102 | S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 18875 | Realism says a discourse is true or false, and some of it is true [Cameron] |
| 18878 | Realism says truths rest on mind-independent reality; truthmaking theories are about which features [Cameron] |
| 18881 | For realists it is analytic that truths are grounded in the world [Cameron] |
| 18924 | Being polka-dotted is a 'spatial distribution' property [Cameron] |
| 15401 | Essentialists say intrinsic properties arise from what the thing is, irrespective of surroundings [Cameron] |
| 15393 | An object's intrinsic properties are had in virtue of how it is, independently [Cameron] |
| 15396 | Most criteria for identity over time seem to leave two later objects identical to the earlier one [Cameron] |
| 18930 | Change is instantiation of a non-uniform distributional property, like 'being red-then-orange' [Cameron] |
| 15103 | Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron] |
| 18872 | We should reject distinct but indiscernible worlds [Cameron] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| 15104 | The 'moving spotlight' theory makes one time privileged, while all times are on a par ontologically [Cameron] |
| 18927 | Surely if things extend over time, then time itself must be extended? [Cameron] |