79 ideas
| 12667 | Metaphysics aims at the simplest explanation, without regard to testability [Ellis] |
| 14480 | Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson] |
| 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] |
| 12666 | We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 14471 | Analytical entailments arise from combinations of meanings and inference rules [Thomasson] |
| 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] |
| 12688 | Mathematics is the formal study of the categorical dimensions of things [Ellis] |
| 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] |
| 14493 | Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson] |
| 12683 | Objects and substances are a subcategory of the natural kinds of processes [Ellis] |
| 12670 | A physical event is any change of distribution of energy [Ellis] |
| 14491 | Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson] |
| 14489 | Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson] |
| 12673 | Physical properties are those relevant to how a physical system might act [Ellis] |
| 12665 | I support categorical properties, although most people only want causal powers [Ellis] |
| 12682 | Essentialism needs categorical properties (spatiotemporal and numerical relations) and dispositions [Ellis] |
| 12684 | Spatial, temporal and numerical relations have causal roles, without being causal [Ellis] |
| 12672 | Properties and relations are discovered, so they can't be mere sets of individuals [Ellis] |
| 12676 | Causal powers can't rest on things which lack causal power [Ellis] |
| 23781 | Categoricals exist to influence powers. Such as structures, orientations and magnitudes [Ellis, by Williams,NE] |
| 12686 | Causal powers are a proper subset of the dispositional properties [Ellis] |
| 14487 | The simple existence conditions for objects are established by our practices, and are met [Thomasson] |
| 14485 | Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson] |
| 21651 | It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber] |
| 14486 | Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson] |
| 14467 | Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson] |
| 14479 | To individuate people we need conventions, but conventions are made up by people [Thomasson] |
| 14481 | Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson] |
| 14482 | If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson] |
| 14483 | Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson] |
| 12685 | Categorical properties depend only on the structures they represent [Ellis] |
| 12679 | A real essence is a kind's distinctive properties [Ellis] |
| 14476 | Identity claims between objects are only well-formed if the categories are specified [Thomasson] |
| 14477 | Identical entities must be of the same category, and meet the criteria for the category [Thomasson] |
| 12668 | Metaphysical necessity holds between things in the world and things they make true [Ellis] |
| 12687 | Metaphysical necessities are those depending on the essential nature of things [Ellis] |
| 14478 | Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson] |
| 14466 | A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson] |
| 12669 | Science aims to explain things, not just describe them [Ellis] |
| 14475 | How can causal theories of reference handle nonexistence claims? [Thomasson] |
| 14474 | Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson] |
| 14488 | Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson] |
| 12681 | There are natural kinds of processes [Ellis] |
| 12680 | Natural kind structures go right down to the bottom level [Ellis] |
| 12675 | Laws of nature are just descriptions of how things are disposed to behave [Ellis] |
| 12671 | I deny forces as entities that intervene in causation, but are not themselves causal [Ellis] |
| 12674 | Energy is the key multi-valued property, vital to scientific realism [Ellis] |
| 12689 | Simultaneity can be temporal equidistance from the Big Bang [Ellis] |
| 12690 | The present is the collapse of the light wavefront from the Big Bang [Ellis] |