20 ideas
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 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'. |
| 8970 | Our notion of identical sets involves identical members, which needs absolute identity [Hawthorne] |
| Full Idea: Our conceptual grip on the notion of a set is founded on the axiom of extensionality: a set x is the same as a set y iff x and y have the same members. But this axiom deploys the notion of absolute identity ('same members'). | |
| From: John Hawthorne (Identity [2003], 3.1) | |
| A reaction: Identity seems to be a primitive, useful and crucial concept, so don't ask what it is. I suspect that numbers can't get off the ground without it (especially, in view of the above, if you define numbers in terms of sets). |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 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 |