46 ideas
15130 | If a property is possible, there is something which can have it [Williamson] |
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] |
22919 | A thing which makes no difference seems unlikely to exist [Le Poidevin] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
22926 | In addition to causal explanations, they can also be inferential, or definitional, or purposive [Le Poidevin] |
22932 | We don't just describe a time as 'now' from a private viewpoint, but as a fact about the world [Le Poidevin] |
22927 | The logical properties of causation are asymmetry, transitivity and irreflexivity [Le Poidevin] |
22922 | We can identify unoccupied points in space, so they must exist [Le Poidevin] |
22924 | If spatial points exist, then they must be stationary, by definition [Le Poidevin] |
22923 | Absolute space explains actual and potential positions, and geometrical truths [Le Poidevin] |
22928 | For relationists moving an object beyond the edge of space creates new space [Le Poidevin] |
22931 | We distinguish time from space, because it passes, and it has a unique present moment [Le Poidevin] |
22917 | Since nothing occurs in a temporal vacuum, there is no way to measure its length [Le Poidevin] |
22921 | Temporal vacuums would be unexperienced, unmeasured, and unending [Le Poidevin] |
22934 | Time can't speed up or slow down, so it doesn't seem to be a 'process' [Le Poidevin] |
22938 | To say that the past causes the present needs them both to be equally real [Le Poidevin] |
22939 | The B-series doesn't seem to allow change [Le Poidevin] |
22940 | If the B-universe is eternal, why am I trapped in a changing moment of it? [Le Poidevin] |
22947 | An ordered series can be undirected, but time favours moving from earlier to later [Le Poidevin] |
22952 | If time's arrow is causal, how can there be non-simultaneous events that are causally unconnected? [Le Poidevin] |
22951 | If time's arrow is psychological then different minds can impose different orders on events [Le Poidevin] |
22948 | There are Thermodynamic, Psychological and Causal arrows of time [Le Poidevin] |
22949 | Presumably if time's arrow is thermodynamic then time ends when entropy is complete [Le Poidevin] |
22950 | If time is thermodynamic then entropy is necessary - but the theory says it is probable [Le Poidevin] |
22953 | Time's arrow is not causal if there is no temporal gap between cause and effect [Le Poidevin] |
22943 | Instantaneous motion is an intrinsic disposition to be elsewhere [Le Poidevin] |
22945 | The dynamic view of motion says it is primitive, and not reducible to objects, properties and times [Le Poidevin] |
22937 | If the present could have diverse pasts, then past truths can't have present truthmakers [Le Poidevin] |
22925 | The present is the past/future boundary, so the first moment of time was not present [Le Poidevin] |
22944 | The primitive parts of time are intervals, not instants [Le Poidevin] |
22942 | If time is infinitely divisible, then the present must be infinitely short [Le Poidevin] |
22946 | The multiverse is distinct time-series, as well as spaces [Le Poidevin] |
22941 | How could a timeless God know what time it is? So could God be both timeless and omniscient? [Le Poidevin] |