13 ideas
10190 | From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki] |
Full Idea: From the axiomatic point of view, mathematics appears as a storehouse of abstract forms - the mathematical structures. | |
From: Nicholas Bourbaki (The Architecture of Mathematics [1950], 221-32), quoted by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.79 | |
A reaction: This seems to be the culmination of the structuralist view that developed from Dedekind and Hilbert, and was further developed by philosophers in the 1990s. |
15200 | How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin] |
Full Idea: McTaggart objects, to Russell 1903, that change cannot consist of a conjunction of changeless facts. | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927]) by Robin Le Poidevin - Past, Present and Future of Debate about Tense 1 (b) | |
A reaction: I agree with McTaggart. Logicians like to model processes with domains of timeless entities, but it just won't do. |
14761 | Change is not just having two different qualities at different points in some series [McTaggart] |
Full Idea: The fact that it is hot at one point in a series and cold at other points cannot give change, if neither of these facts change. If two points on a line have different properties, this doesn't give change. | |
From: J.M.E. McTaggart (The Nature of Existence vol.2 [1927], 33.315-6), quoted by Theodore Sider - Four Dimensionalism 6.2 | |
A reaction: [The second half compresses an example about the Meridian] This objection is aimed at Russell's view, that change is just different properties at different times. I (unlike Sider) am wholly with McTaggart on this one. Change is 'dynamic'. |
22628 | Substance has to exist, with no intrinsic qualities or relations [McTaggart] |
Full Idea: Something must exist, then, and have qualities, without being itself either a quality or a relation. And this is Substance. | |
From: J.M.E. McTaggart (The Nature of Existence vol.1 [1921], §67), quoted by R.D. Ingthorsson - A Powerful Particulars View of Causation 7.2 | |
A reaction: Ingthorsson quotes this as 'the most extreme analytic view', which is a long way from the Aristotelian view. This is the implausible bare substrate. |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |
2608 | For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer] |
Full Idea: McTaggart says we can speak of events in time in two ways, as past, present or future, or as being before or after or simultaneous with one another. The first cannot be reduced to the second, as the second makes no provision for the passage of time. | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927], II.329-) by A.J. Ayer - The Central Questions of Philosophy 1.D |
22936 | A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin] |
Full Idea: McTaggart's proof of time's unreality: A-series positions (past, present and future) are mutually incompatible, so no event can exhibit more than one of them; but since A-series events change position, all events have all A-series posititions. Absurd! | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927]) by Robin Le Poidevin - Travels in Four Dimensions 08 'McTaggart's' | |
A reaction: I'm not convinced that this is any more contradictory than someone being married at one time and unmarried at another. No one is suggesting that an A-series event can be both past and future simultaneously. |
4231 | Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe] |
Full Idea: McTaggart argued that time involves change, only the A-series can explain change, the A-series involves contradictions (past, present and future), and hence time is unreal. | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927]) by E.J. Lowe - A Survey of Metaphysics p.313 | |
A reaction: I doubt whether it is a logical contradiction to say Waterloo has been past, present and future, though it is odd. |
8591 | There could be no time if nothing changed [McTaggart] |
Full Idea: It is universally admitted.... that there could be no time if nothing changed. | |
From: J.M.E. McTaggart (The Nature of Existence vol.2 [1927], II p.11), quoted by Sydney Shoemaker - Time Without Change p.49 | |
A reaction: This is set up alongside Aristotle (Idea 8590) to be attacked by Shoemaker. I think Shoemaker is right, and that the rejection of McTaggart's view is a key result in modern metaphysics. |
22935 | The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin] |
Full Idea: McTaggart says the A-series is more fundamental than the B-series. An objective being could not deduce the present moment of the A-series from the B-series, but the B-series can be deduced from the A-series. | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927]) by Robin Le Poidevin - Travels in Four Dimensions 08 'McTaggart's' | |
A reaction: [summarised] This has no ontological importance for McTaggart, since he thinks time is unreal either way. But giving the A-series priority because it reveals the present moment seems to nullify the B-series as incomplete. |
7802 | A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle] |
Full Idea: The A-series puts events into past, present and future. The B-series puts events into a series based on relationships of 'before' and 'after'. McTaggart said the A-series was contradictory, and the B-series failed to cope with essential features of time. | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927]) by Rod Girle - Modal Logics and Philosophy 8.10 | |
A reaction: The A-series is indexical. |
4230 | A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe] |
Full Idea: A-series expressions include words like 'today' and 'five weeks ago', and can be true at one time and false at another; B-series expressions are like 'simultaneously', and are always true, if true at all. | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927]) by E.J. Lowe - A Survey of Metaphysics p.308 | |
A reaction: A-series gives time separate existence, where B-series time is purely relational. Intuition favours the A-series, but how fast do events travel against this fixed background? |
15199 | The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin] |
Full Idea: McTaggart's argument is 1) B-series relations are temporal relations, 2) There cannot be temporal relations unless there is change, 3) There cannot be change unless there is real A-series ordering, so there can't be a B-series unless there is an A-series. | |
From: report of J.M.E. McTaggart (The Nature of Existence vol.2 [1927], vol.ii) by Robin Le Poidevin - Past, Present and Future of Debate about Tense 1 a |