75 ideas
| 14721 | Metaphysical enquiry can survive if its conclusions are tentative [Sider] |
| Full Idea: Metaphysical enquiry can survive if we are willing to live with highly tentative conclusions. | |
| From: Theodore Sider (Four Dimensionalism [2001], Intro) | |
| A reaction: Nice. Nothing alienates the rather literal scientific sort of mind quicker that bold, dogmatic and even arrogant assertions about metaphysics. But to entirely close down metaphysical speculation for that reason is absurd. |
| 224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
| Full Idea: Doubtful questions should not be discussed in terms of visible objects or in relation to them, but only with reference to ideas conceived by the intellect. | |
| From: Plato (Parmenides [c.364 BCE], 135e) |
| 232 | Opposites are as unlike as possible [Plato] |
| Full Idea: Opposites are as unlike as possible. | |
| From: Plato (Parmenides [c.364 BCE], 159a) |
| 8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
| Full Idea: Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Georg W.F.Hegel - Phenomenology of Spirit Pref 71 | |
| A reaction: It is a long way from the analytic tradition of philosophy to be singling out a classic text for its 'artistic' achievement. Eventually we may even look back on, say, Kripke's 'Naming and Necessity' and see it in that light. |
| 13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
| Full Idea: Plato (in 'Parmenides') shows that the theory that 'Eide' are substances, and Kant that space and time are substances, and Bradley that relations are substances, all lead to aninomies. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Gilbert Ryle - Are there propositions? 'Objections' |
| 14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
| Full Idea: Plato's 'Parmenides' is perhaps the best collection of antinomies ever made. | |
| From: comment on Plato (Parmenides [c.364 BCE]) by Bertrand Russell - The Principles of Mathematics §337 |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
| From: David Hilbert (On the Infinite [1925], p.200) | |
| A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
| From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
| A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
| From: David Hilbert (On the Infinite [1925], p.195) | |
| A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| Full Idea: Operating with the infinite can be made certain only by the finitary. | |
| From: David Hilbert (On the Infinite [1925], p.201) | |
| A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
| From: David Hilbert (On the Infinite [1925], p.186) | |
| A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
| From: David Hilbert (On the Infinite [1925], p.192) | |
| A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
| From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
| 229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
| Full Idea: The one was and is and will be and was becoming and is becoming and will become. | |
| From: Plato (Parmenides [c.364 BCE], 155d) |
| 21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
| Full Idea: The Platonic Parmenides is more exact [than Parmenides himself]; the distinction is made between the Primal One, a strictly pure Unity, and a secondary One which is a One-Many, and a third which is a One-and-Many. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Plotinus - The Enneads 5.1.08 | |
| A reaction: Plotinus approves of this three-part theory. Parmenides has the problem that the highest Being contains no movement. By placing the One outside Being you can give it powers which an existent thing cannot have. Cf the concept of God. |
| 14760 | Four-dimensionalism sees things and processes as belonging in the same category [Sider] |
| Full Idea: Four-dimensionalism does not respect a deep difference between thing-talk and process-talk, because it tends to place events and things in the same ontological category. | |
| From: Theodore Sider (Four Dimensionalism [2001], 6.1) | |
| A reaction: He then quotes Broad, Idea 14759. This idea is the best reason yet for being sympathetic to the four-dimensionalist view, because I think processes really must have a central place in any decent ontology. |
| 221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
| Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us. | |
| From: Plato (Parmenides [c.364 BCE], 134c) |
| 14194 | Proper ontology should only use categorical (actual) properties, not hypothetical ones [Sider] |
| Full Idea: A proper ontology should invoke only categorical, or occurrent, properties and relations. Categorical properties involve what objects are actually like, whereas hypothetical properties 'point beyond' their instances. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.3) | |
| A reaction: This spectacularly leaves out powers and dispositions, which are actual properties which 'point beyond' their instances! This is the nub of the powers debate, and the most interesting topic in modern metaphysics. |
| 223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
| Full Idea: If a person denies that the idea of each thing is always the same, he will utterly destroy the power of carrying on discussion. | |
| From: Plato (Parmenides [c.364 BCE], 135c) |
| 227 | You must always mean the same thing when you utter the same name [Plato] |
| Full Idea: You must always mean the same thing when you utter the same name. | |
| From: Plato (Parmenides [c.364 BCE], 147d) |
| 210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
| Full Idea: Are there abstract ideas for such things as hair, mud and dirt, which are particularly vile and worthless? That would be quite absurd. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 220 | The concept of a master includes the concept of a slave [Plato] |
| Full Idea: Mastership in the abstract is mastership of slavery in the abstract. | |
| From: Plato (Parmenides [c.364 BCE], 133e) |
| 211 | If admirable things have Forms, maybe everything else does as well [Plato] |
| Full Idea: It is troubling that if admirable things have abstract ideas, then perhaps everything else must have ideas as well. | |
| From: Plato (Parmenides [c.364 BCE], 130d) |
| 219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
| Full Idea: None of the absolute ideas exists in us, because then it would no longer be absolute. | |
| From: Plato (Parmenides [c.364 BCE], 133c) |
| 228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
| Full Idea: These two ideas, greatness and smallness, exist, do they not? For if they did not exist, they could not be opposites of one another, and could not come into being in things. | |
| From: Plato (Parmenides [c.364 BCE], 149e) |
| 16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
| Full Idea: It seems to me that Plato in the later dialogues, beginning with the second half of 'Parmenides', wants to substitute a theory of genera and theory of principles that constitute these genera for the earlier theory of forms. | |
| From: report of Plato (Parmenides [c.364 BCE]) by Michael Frede - Title, Unity, Authenticity of the 'Categories' V | |
| A reaction: My theory is that the later Plato came under the influence of the brilliant young Aristotle, and this idea is a symptom of it. The theory of 'principles' sounds like hylomorphism to me. |
| 218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
| Full Idea: Participation is not by means of likeness, so we must seek some other method of participation. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
| Full Idea: Just as day is in many places at once, but not separated from itself, so each idea might be in all its participants at once. | |
| From: Plato (Parmenides [c.364 BCE], 131b) |
| 216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
| Full Idea: That by participation in which like things are made like, will be the absolute idea, will it not? | |
| From: Plato (Parmenides [c.364 BCE], 132e) |
| 215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
| Full Idea: If all things partake of ideas, must either everything be made of thoughts and everything thinks, or everything is thought, and so can't think? | |
| From: Plato (Parmenides [c.364 BCE], 132c) |
| 212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
| Full Idea: The whole idea of each form (of beauty, justice etc) must be found in each thing which participates in it. | |
| From: Plato (Parmenides [c.364 BCE], 131a) |
| 217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
| Full Idea: It is impossible for anything to be like an absolute idea, because a third idea will appear to make them alike, and if that is like anything, it will lead to another idea, and so on. | |
| From: Plato (Parmenides [c.364 BCE], 133a) |
| 214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
| Full Idea: If you regard the absolute great and the many great things in the same way, will not another appear beyond, by which all these must appear to be great? | |
| From: Plato (Parmenides [c.364 BCE], 132a) |
| 14745 | If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are [Sider] |
| Full Idea: Followers of the view that every entity is associated with some sortal term that answers the question 'what kind of thing is this?', and determines its persistence conditions, must answer the question what kinds of entity there are. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.3) | |
| A reaction: [He explicitly refers to David Wiggins here] In other words Wiggins has got it the wrong way round, which is my own view of his theory. Sortal terms don't grow on the trees in the Garden of Eden, available for applications. |
| 15851 | Parts must belong to a created thing with a distinct form [Plato] |
| Full Idea: The part would not be the part of many things or all, but of some one character ['ideas'] and of some one thing, which we call a 'whole', since it has come to be one complete [perfected] thing composed [created] of all. | |
| From: Plato (Parmenides [c.364 BCE], 157d) | |
| A reaction: A serious shot by Plato at what identity is. Harte quotes it (125) and shows that 'character' is Gk 'idea', and 'composed' will translate as 'created'. 'Form' links this Platonic passage to Aristotle's hylomorphism. |
| 14740 | If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one [Sider] |
| Full Idea: This powerful puzzle (known to the Stoics, introduced by Geach, popularised by Wiggins) has a cat Tibbles and a proper part Tib, which is all of Tibbles except the tail. If Tibbles loses her tail, the two were distinct, but they now coincide. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.1) | |
| A reaction: [compressed] Compare a few people leave a football ground, and what was a large part of the crowd becomes the whole of the crowd. Which suggests that there is no problem if cats are like crowds. But we don't like that view of cats. |
| 14752 | Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay [Sider] |
| Full Idea: Presumably it is claimed that the artist 'created' the statue because the object created is essentially a statue, and thus cannot be identified with the unformed lump of clay with which the artist began. | |
| From: Theodore Sider (Four Dimensionalism [2001]) | |
| A reaction: This is based on Burke's views. This is sortal essentialism, rather than my own view of essence as an inner explanatory mechanism or form. If an old abstract sculpture was no longer recognised as a statue, would it necessarily still be a statue? |
| 14743 | The stage view of objects is best for dealing with coincident entities [Sider] |
| Full Idea: There are numerous cases in which there is pressure to admit coincident entities. The best way of coming to grips with this, I think, invokes the stage view. ...In the worm theory, coincident objects are no more mysterious than overlapping roads. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.1) | |
| A reaction: At this point I get nervous if in order to 'get to grips' with a phenomenon which is hard to articulate but obvious to common sense, we have to invoke a rather startling metaphysics that completely upends the common sense we started with. |
| 15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
| Full Idea: At the heart of the 'Parmenides' puzzles about composition is the thesis that composition is identity. Considered thus, a whole adds nothing to an ontology that already includes its parts | |
| From: report of Plato (Parmenides [c.364 BCE]) by Verity Harte - Plato on Parts and Wholes 2.5 | |
| A reaction: There has to be more to a unified identity that mere proximity of the parts. When do parts come together, and when do they actually 'compose' something? |
| 14747 | 'Composition as identity' says that an object just is the objects which compose it [Sider] |
| Full Idea: 'Composition as identity' says that when a thing, x, is composed of some other objects, the ys, then this is a kind of identity between the x and the ys. The industrial-strength version says object x just is the ys. Lewis says it is just an analogy. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.3) | |
| A reaction: I am averse to such a doctrine, as is Leibniz, with his insistence that an aggregate is not a unity. There has to be some sort of principle that bestows oneness on a many. I take this to be structural, and is an elucidation of hylomorphism. |
| 15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
| Full Idea: In 'Parmenides' it is argued that a part cannot be part of a many, but must be part of something one. | |
| From: report of Plato (Parmenides [c.364 BCE], 157c) by Verity Harte - Plato on Parts and Wholes 3.2 | |
| A reaction: This looks like the right way to go with the term 'part'. We presuppose a unity before we even talk of its parts, so we can't get into contradictions and paradoxes about their relationships. |
| 15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
| Full Idea: The whole of which the parts are parts must be one thing composed of many; for each of the parts must be part, not of a many, but of a whole. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: This is a key move of metaphysics, and we should hang on to it. The other way madness lies. |
| 13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
| Full Idea: The One must be composed of parts, both being a whole and having parts. So on both grounds the One would thus be many and not one. But it must be not many, but one. So if the One will be one, it will neither be a whole, nor have parts. | |
| From: Plato (Parmenides [c.364 BCE], 137c09), quoted by Kathrin Koslicki - The Structure of Objects 5.2 | |
| A reaction: This is the starting point for Plato's metaphysical discussion of objects. It seems to begin a line of thought which is completed by Aristotle, surmising that only an essential structure can bestow identity on a bunch of parts. |
| 14757 | Mereological essentialism says an object's parts are necessary for its existence [Sider] |
| Full Idea: Mereological essentialism says that an object's parts are necessary for its existence. ....It is literally never correct to say that an thing survives a change in its parts. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.7) | |
| A reaction: Chisholm is well known for proposing this view. Sider adds a possible toughening clause, that the parts are also sufficient for the object's existence. This is a philosophers' notion of identity, not the normal English language concept. |
| 14727 | Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts' [Sider] |
| Full Idea: Three-dimensionalists say that things have no 'temporal parts', that they 'endure', and that they are wholly present at every moment of their careers. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3) | |
| A reaction: An obvious problem case for being wholly present would be the building and fitting of a large ship, where it might seem to be present before it was wholly present. |
| 14738 | Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism [Sider] |
| Full Idea: Some might even regard inconsistency with time travel as an advantage of three-dimensionalism, as a vindication of a prior belief that time travel is impossible! I see no merit in these claims. | |
| From: Theodore Sider (Four Dimensionalism [2001], 7.2) | |
| A reaction: I do! Sider cheerfully says that there are good reasons to believe that time travel is possible, and then use this possibility to support his four-dimensional view, but I personally doubt his assumption. The evidence for time travel is flimsy and obscure. |
| 14726 | Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time [Sider] |
| Full Idea: Four-dimensionalists say that things have 'temporal parts', that they 'perdure', and that they are spread out over time. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3) |
| 14728 | 4D says intrinsic change is difference between successive parts [Sider] |
| Full Idea: For four-dimensionalists intrinsic change is difference between successive temporal parts. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: This attempts a reply to the commonest criticism of four-dimensionalism - that you can't explain change if you don't have one enduring thing which undergoes the change. I get stuck of the question 'how big (temporally) is a part?'. |
| 14729 | 4D says each spatiotemporal object must have a temporal part at every moment at which it exists [Sider] |
| Full Idea: Four-dimensionalism may be formulated as the claim that, necessarily, each spatiotemporal object has a temporal part at every moment at which it exists. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: If there were tiny quantum gaps between temporal parts, that would presumably ruin the story. On this view an object has to be a 'worm', to be the thing which has the parts. |
| 14730 | Temporal parts exist, but are not prior building blocks for objects [Sider] |
| Full Idea: My four-dimensionalism implies the existence of temporal parts, but not that those parts are more fundamental, nor that the object is 'constructed' from its parts, nor that identity over time is reducible to parts. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: That's a rather negative account of temporal parts, which makes you ask what their positive role could be. Do they contribute anything to our understanding of a temporally extended object? |
| 14731 | Temporal parts are instantaneous [Sider] |
| Full Idea: Unless otherwise noted, I will think of temporal parts as being instantaneous. | |
| From: Theodore Sider (Four Dimensionalism [2001], 3.2) | |
| A reaction: This comes up against all the Augustinian worries about the intrinsic nature of time. How many temporal parts does a typical object possess? Is a third temporal part always to be found between any two of them? How do they 'connect'? |
| 14758 | How can an instantaneous stage believe anything, if beliefs take time? [Sider] |
| Full Idea: How can an instantaneous stage believe anything? Beliefs take time. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.8) | |
| A reaction: Sider's four-dimensionalist answer is that the belief is embodied in the earlier counterparts, making belief a 'highly relational property'. I am not impressed by this answer to the very nice problem which he has raised. It's a problem for 3D, too. |
| 14762 | Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts [Sider] |
| Full Idea: The sensible four-dimensionalist will claim that current temporal parts are caused to exist by previous temporal parts. The laws that govern this process are none other than the familiar laws of motion. | |
| From: Theodore Sider (Four Dimensionalism [2001], 6.3) | |
| A reaction: I keep struggling with the instantaneous natural of temporal parts, and now I find that they have to do the job of being causal relata. When do they do their job? They've gone home before they've finished clocking in. Continuance requires motion? |
| 14741 | The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger [Sider] |
| Full Idea: The Ship of Theseus seems to be a case of 'asymmetric' fission (where one resultant entity has a stronger claim). Many see the continuously rebuilt ship as the stronger candidate, but each candidate, without the other, would be the original ship. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.1) |
| 15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
| Full Idea: Everything is surely related to everything as follows: either it is the same or different; or, if it is not the same or different, it would be related as part to whole or as whole to part. | |
| From: Plato (Parmenides [c.364 BCE], 146b) | |
| A reaction: This strikes me as a really helpful first step in trying to analyse the nature of identity. Two things are either two or (actually) one, or related mereologically. |
| 14754 | If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity [Sider] |
| Full Idea: If someone is in pain at t1 and not at t2, we might restrict Leibniz's Law so as not to apply to 'timebound' properties, ..but this is deeply unsatisfying, ...and forfeits one's claim to be discussing identity. The demands of identity are high. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.5) | |
| A reaction: [on Myro 1986] Sider's response is unsatisfying. It means a thing loses its identity (with itself?) if it has even a tiny fluctuating in its properties. Quantum changes then destroy all notions of identity. English-speakers don't use 'identity' like that. |
| 14763 | Counterparts rest on similarity, so there are many such relations in different contexts [Sider] |
| Full Idea: A counterpart relation is a similarity relation. Since there are different dimensions of similarity, there are different counterpart relations. | |
| From: Theodore Sider (Four Dimensionalism [2001], 6.4) |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
| 222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
| Full Idea: Only a man of very great natural gifts will be able to understand that everything has a class and absolute essence, and an even more wonderful man can teach this. | |
| From: Plato (Parmenides [c.364 BCE], 135a) |
| 225 | The unlimited has no shape and is endless [Plato] |
| Full Idea: The unlimited partakes neither of the round nor of the straight, because it has no ends nor edges. | |
| From: Plato (Parmenides [c.364 BCE], 137e) |
| 233 | Some things do not partake of the One [Plato] |
| Full Idea: The others cannot partake of the one in any way; they can neither partake of it nor of the whole. | |
| From: Plato (Parmenides [c.364 BCE], 159d) | |
| A reaction: Compare Idea 231 |
| 2062 | The only movement possible for the One is in space or in alteration [Plato] |
| Full Idea: If the One moves it either moves spatially or it is altered, since these are the only motions. | |
| From: Plato (Parmenides [c.364 BCE], 138b) |
| 231 | Everything partakes of the One in some way [Plato] |
| Full Idea: The others are not altogether deprived of the one, for they partake of it in some way. | |
| From: Plato (Parmenides [c.364 BCE], 157c) | |
| A reaction: Compare Idea 233. |
| 14725 | Maybe motion is a dynamical quantity intrinsic to a thing at a particular time [Sider] |
| Full Idea: There is an alternative to the Russellian 'at-at' theory of motion, according to which dynamical quantities are intrinsic to times. Whether and how an object is moving at a time is a fact about what that object is like then. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.2) | |
| A reaction: I think I find this quite appealing, because there is too much of a tendency to think of objects as passive and inert, with laws, forces, motions etc. imposed from the outside. But nature is active and dynamic. However, motion can't be wholly intrinsic. |
| 14735 | Space is 3D and lacks a direction; time seems connected to causation [Sider] |
| Full Idea: Unlike time, space has three dimensions and lacks a distinguishing direction; unlike space, time seems to be specially connected with causation. | |
| From: Theodore Sider (Four Dimensionalism [2001], 4.5) | |
| A reaction: These strike me as nice reasons to doubt (what I already prima facie doubt) that there is a single manifold that is 'space-time', for all that twentieth century physics tells us it is so. A century is a mere click of a clock where truth is concerned. |
| 14722 | Between presentism and eternalism is the 'growing block' view - the past is real, the future is not [Sider] |
| Full Idea: Intermediate between the polar opposites of presentism and eternalism is the view (defended by Broad 1923 and Tooley 1997) that the past is real but the future is not. Reality consists of a growing four-dimensional manifold, the 'growing block universe'. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.1) | |
| A reaction: The obvious and plausible basis for this is that statements about the past seem to have truthmakers, but statements about the future lack them. Does a truth always require ontological commitment? Death is cessation of existence. |
| 14756 | For Presentists there must always be a temporal vantage point for any description [Sider] |
| Full Idea: The Presentist acknowledges that no atemporal description of the case can be given; a vantage point must be chosen for any description. | |
| From: Theodore Sider (Four Dimensionalism [2001], 5.5) | |
| A reaction: This is because Presentists are committed to tense, which have to be either explicit or implicit in any sentence. But what of famously 'timeless' truths such as '2 and 2 are 4'? |
| 14724 | Presentists must deny truths about multiple times [Sider] |
| Full Idea: The presentist must deny the truth of everyday claims that concern multiple times taken together. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.2) | |
| A reaction: This rests on the extent to which every truth has an ontological commitment. You can deny the literal existence of multiple times without denying such truths. |
| 14723 | Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance [Sider] |
| Full Idea: The temporal reductionist claims that tensed locutions are indexical - 'present' being the time of utterance etc. This generalises to say that nothing corresponding to tense need be admitted as a fundamental feature of the world. | |
| From: Theodore Sider (Four Dimensionalism [2001], 2.1) | |
| A reaction: [He particular cites Mellor for this view] Highly implausible. I very much doubt whether it is possible to explain the indexicality of a word like 'now' without referring to tenses. Does time only exist when sentences and thoughts occur? |
| 14736 | The B-theory is adequate, except that it omits to say which time is present [Sider] |
| Full Idea: The B-theoretic description of the world is completely adequate except that it leaves out information about which time is present. | |
| From: Theodore Sider (Four Dimensionalism [2001], 4.6) | |
| A reaction: This strikes me as a pretty basic deficiency. How could there a time which lacked a present moment? The present is when things happen. How would it qualify as time at all if it lacked past, present and future? |
| 14734 | The B-series involves eternalism, and the reduction of tense [Sider] |
| Full Idea: The B-series has two components: eternalism - the thesis that all future entities are real - and the thesis of reducibility of tense. | |
| From: Theodore Sider (Four Dimensionalism [2001], 4.2) |
| 234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |
| Full Idea: There must be knowledge of the one, or else not even the meaning of the words 'if the one does not exist' would be known. | |
| From: Plato (Parmenides [c.364 BCE], 160d) |