45 ideas
| 14721 | Metaphysical enquiry can survive if its conclusions are tentative [Sider] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 14760 | Four-dimensionalism sees things and processes as belonging in the same category [Sider] |
| 14194 | Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider] |
| 14745 | If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider] |
| 14740 | If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider] |
| 14752 | Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider] |
| 14743 | The stage view of objects is best for dealing with coincident entities [Sider] |
| 16614 | Matter and form give true unity; subject and accident is just unity 'per accidens' [Duns Scotus] |
| 14747 | 'Composition as identity' says that an object just is the objects which compose it [Sider] |
| 14757 | Mereological essentialism says an object's parts are necessary for its existence [Sider] |
| 14727 | Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider] |
| 14738 | Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider] |
| 14726 | Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider] |
| 14728 | 4D says intrinsic change is difference between successive parts [Sider] |
| 14729 | 4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider] |
| 14730 | Temporal parts exist, but are not prior building blocks for objects [Sider] |
| 14762 | Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider] |
| 14731 | Temporal parts are instantaneous [Sider] |
| 14758 | How can an instantaneous stage believe anything, if beliefs take time? [Sider] |
| 14741 | The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider] |
| 14754 | If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider] |
| 14763 | Counterparts rest on similarity, so there are many such relations in different contexts [Sider] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 14725 | Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider] |
| 14735 | Space is 3D and lacks a direction; time seems connected to causation [Sider] |
| 14722 | Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider] |
| 14756 | For Presentists there must always be a temporal vantage point for any description [Sider] |
| 14724 | Presentists must deny truths about multiple times [Sider] |
| 14723 | Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider] |
| 14734 | The B-series involves eternalism, and the reduction of tense [Sider] |
| 14736 | The B-theory is adequate, except that it omits to say which time is present [Sider] |