49 ideas
| 17651 | Without words or other symbols, we have no world [Goodman] |
| Full Idea: We can have words without a world but no world without words or other symbols. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.3) | |
| A reaction: Goodman seems to have a particularly extreme version of the commitment to philosophy as linguistic. Non-human animals have no world, it seems. |
| 17652 | Truth is irrelevant if no statements are involved [Goodman] |
| Full Idea: Truth pertains solely to what is said ...For nonverbal versions and even for verbal versions without statements, truth is irrelevant. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.5) | |
| A reaction: Goodman is a philosopher of language (like Dummett), but I am a philosopher of thought (like Evans). The test, for me, is whether truth is applicable to the thought of non-human animals. I take it to be obvious that it is applicable. |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| Full Idea: We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michčle Friend - Introducing the Philosophy of Mathematics 2.4 | |
| A reaction: A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions. |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| Full Idea: Gödel proved the classical relative consistency of the axiom V = L (which implies the axiom of choice and the generalized continuum hypothesis). This established the full independence of the continuum hypothesis from the other axioms. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Gödel initially wanted to make V = L an axiom, but the changed his mind. Maddy has lots to say on the subject. |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| Full Idea: The set-theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the senses are for physics. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.271), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 03.4 |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| Full Idea: Gödel proved that the Continuum Hypothesis was not inconsistent with the axioms of set theory. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15 |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| Full Idea: Gödel proved that (if set theory is consistent) we cannot refute the continuum hypothesis, and Cohen proved that (if set theory is consistent) we cannot prove it either. | |
| From: report of Kurt Gödel (What is Cantor's Continuum Problem? [1964]) by William D. Hart - The Evolution of Logic 10 |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| Full Idea: Evidently the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas. | |
| From: Kurt Gödel (What is Cantor's Continuum Problem? [1964], Suppl) | |
| A reaction: Yes! The great modern mathematical platonist says something with which I can agree. He goes on to hint at a platonic view of the structure of the empirical world, but we'll let that pass. |
| 22919 | A thing which makes no difference seems unlikely to exist [Le Poidevin] |
| Full Idea: It is a powerful argument for something's non-existence that it would make absolutely no difference. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 02 'Everything') | |
| A reaction: Powerful, but not conclusive. Neutrinos don't seem to do much, so it isn't far from there to get a particle which does nothing. |
| 17656 | Being primitive or prior always depends on a constructional system [Goodman] |
| Full Idea: Nothing is primitive or derivationally prior to anything apart from a constructional system. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.4c) | |
| A reaction: Something may be primitive not just because we can't be bothered to analyse it any further, but because even God couldn't analyse it. Maybe. |
| 17661 | We don't recognise patterns - we invent them [Goodman] |
| Full Idea: Recognising patterns is very much a matter of inventing or imposing them. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.7) | |
| A reaction: I take this to be false. |
| 17659 | Reality is largely a matter of habit [Goodman] |
| Full Idea: Reality in a world, like realism in a picture, is largely a matter of habit. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.6) | |
| A reaction: I'm a robust realist, me, but I sort of see what he means. We become steeped in unspoken conventions about how we take our world to be, and filter out anything that conflicts with it. |
| 17657 | We build our world, and ignore anything that won't fit [Goodman] |
| Full Idea: We dismiss as illusory or negligible what cannot be fitted into the architecture of the world we are building. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.4d) | |
| A reaction: I'm trying to think of an example of this, but can't. Maybe poor people are invisible to the rich? |
| 17654 | A world can be full of variety or not, depending on how we sort it [Goodman] |
| Full Idea: A world may be unmanageably heterogeneous or unbearably monotonous according to how events are sorted into kinds. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.4a) | |
| A reaction: We might expect this from the man who invented 'grue', which allows you to classify things that change colour with things that don't. Could you describe a bird as 'might have been a fish', and classify it with fish? ('Projectible'?) |
| 17653 | Things can only be judged the 'same' by citing some respect of sameness [Goodman] |
| Full Idea: Identification rests upon organization into entities and kinds. The response to the question 'Same or not the same?' must always be 'Same what?'. ...Identity or constancy in a world is identity with respect to what is within that world as organised. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.4a) | |
| A reaction: And the gist of his book is that 'organised' is done by us, not by the world. He seems to be committed to the full Geachean relative identity, rather than the mere Wigginsian relative individuation. An unfashionable view! |
| 17660 | Discovery is often just finding a fit, like a jigsaw puzzle [Goodman] |
| Full Idea: Discovery often amounts, as when I place a piece in a jigsaw puzzle, not to arrival at a proposition for declaration or defense, but to finding a fit. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.7) | |
| A reaction: I find Goodman's views here pretty alien, but I like this bit. Coherence really rocks. |
| 17658 | Users of digital thermometers recognise no temperatures in the gaps [Goodman] |
| Full Idea: To use a digital thermometer with readings in tenths of a degree is to recognise no temperature as lying between 90 and 90.1 degrees. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.4d) | |
| A reaction: This appears to be nonsense, treating users of digital thermometers as if they were stupid. No one thinks temperatures go up and down in quantum leaps. We all know there is a gap between instrument and world. (Very American, I'm thinking!) |
| 17650 | We lack frames of reference to transform physics, biology and psychology into one another [Goodman] |
| Full Idea: We have no neat frames of reference, no ready rules for transforming physics, biology and psychology into one another. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.2) |
| 17655 | Grue and green won't be in the same world, as that would block induction entirely [Goodman] |
| Full Idea: Grue cannot be a relevant kind for induction in the same world as green, for that would preclude some of the decisions, right or wrong, that constitute inductive inference. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.4b) | |
| A reaction: This may make 'grue' less mad than I thought it was. I always assume we are slicing the world as 'green, blue and grue'. I still say 'green' is a basic predicate of experience, but 'grue' is amenable to analysis. |
| 22926 | In addition to causal explanations, they can also be inferential, or definitional, or purposive [Le Poidevin] |
| Full Idea: Not all explanations are causal. We can explain some things by showing what follows logically from what, or what is required by the definition of a term, or in terms of purpose. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'Limits') | |
| A reaction: Would these fully qualify as 'explanations'? You don't explain the sea by saying that 'wet' is part of its definition. |
| 22932 | We don't just describe a time as 'now' from a private viewpoint, but as a fact about the world [Le Poidevin] |
| Full Idea: In describing a time as 'now' one is not merely describing the world from one's own point of view, but describing the world as it is. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Mystery') | |
| A reaction: If we accept this view (which implies absolute time, and the A-series view), then 'now' is not an indexical, in the way that 'I' and 'here' are indexicals. |
| 17649 | If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman] |
| Full Idea: If there is but one world, it embraces a multiplicity of contrasting aspects; if there are many worlds, the collection of them all is one. One world may be taken as many, or many worlds taken as one; whether one or many depends on the way of taking. | |
| From: Nelson Goodman (Ways of Worldmaking [1978], 1.2) | |
| A reaction: He cites 'The Pluralistic Universe' by William James for this idea. The idea is that the distinction 'evaporates under analysis'. Parmenides seems to have thought that no features could be distinguished in the true One. |
| 22927 | The logical properties of causation are asymmetry, transitivity and irreflexivity [Le Poidevin] |
| Full Idea: The usual logical properties of the causal relation are asymmetry (one-way), transitivity and irreflexivity (no self-causing). | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'Great') | |
| A reaction: If two balls rebound off each other, that is only asymmetric if we split the action into two parts, which may be a fiction. Does a bomb cause its own destruction? |
| 22922 | We can identify unoccupied points in space, so they must exist [Le Poidevin] |
| Full Idea: If the midpoint on a line between the chair and the window is five feet from the end of the bookcase. This can be true, but if no object occupies that midpoint, then unoccupied points exist | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Lessons') | |
| A reaction: We can also locate perfect circles (running through fairy rings, or the rings of Saturn), so they must also exist. But then we can also locate the Loch Ness monster. Hm. |
| 22924 | If spatial points exist, then they must be stationary, by definition [Le Poidevin] |
| Full Idea: If there are such things as points in space, independently of any other object, then these points are by definition stationary (since to be stationary is to stay in the same place, and a point is a place). | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Search') | |
| A reaction: So what happens if the whole universe moves ten metres to the left? Is the universe defined by the objects in it (which vary), or by the space that contains them? Why can't a location move, even if that is by definition undetectable? |
| 22923 | Absolute space explains actual and potential positions, and geometrical truths [Le Poidevin] |
| Full Idea: Absolutists say space plays a number of roles. It is what we refer to when we talk of positions. It makes other things possible (by moving into unoccupied positions). And it explains geometrical truths. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Redundancy') | |
| A reaction: I am persuaded by these, and am happy to treat space (and time) as a primitive of metaphysics. |
| 22928 | For relationists moving an object beyond the edge of space creates new space [Le Poidevin] |
| Full Idea: For the relationist, if Archytas goes to the edge of space and extends his arm, he is creating a new spatial relation between objects, and thus extending space, which is, after all, just the collection of thos relations. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'beyond') | |
| A reaction: The obvious point is what are you moving your arm into? And how can some movements be in space, while others create new space? It's a bad theory. |
| 22931 | We distinguish time from space, because it passes, and it has a unique present moment [Le Poidevin] |
| Full Idea: The most characteristic features of time, which distinguish it from space, are the fact that time passes, and the fact that the present is in some sense unique | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Mystery') | |
| A reaction: The B-series view tries to avoid passing time and present moments. I suspect that modern proponents of the B-series mainly want to unifying their view of time with Einstein's, to give us a scientific space-time. |
| 22917 | Since nothing occurs in a temporal vacuum, there is no way to measure its length [Le Poidevin] |
| Full Idea: Since, by definition, nothing happens in a temporal vacuum, there is no possible means of determining its length. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 02 'without change') | |
| A reaction: This is offered a part of a dubious proof that a temporal vacuum is impossible. I like Shoemaker's three worlds thought experiment, which tests this idea to the limit. |
| 22921 | Temporal vacuums would be unexperienced, unmeasured, and unending [Le Poidevin] |
| Full Idea: Three arguments that a temporal vacuum is impossible: we can't experience it, we can't measure it, and it would have no reason to ever terminate. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Lessons') | |
| A reaction: [summarised] The first two reasons are unimpressive. The interiors of black holes are off limits for us. The arrival of time into a timeless situation may actually have occurred, but be beyond our understanding. |
| 22934 | Time can't speed up or slow down, so it doesn't seem to be a 'process' [Le Poidevin] |
| Full Idea: Processes can speed up or slow down, but surely the passage of time is not something that can speed up or slow down? | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Mystery') | |
| A reaction: If something is a process we can ask 'process of what?', but the only answer seems to be that it's a process of processing. So it is that which makes processes possible (and so, as I keep saying) it is best viewed as a primitive. |
| 22938 | To say that the past causes the present needs them both to be equally real [Le Poidevin] |
| Full Idea: The causal connection between the past and the present seems to require that the past is as real as the present. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'First') | |
| A reaction: Cause and effect need to conjoin in space, but their subsequent separation doesn't seem to be a problem. The idea that causes and their effects must be eternally compresent is an absurdity. |
| 22939 | The B-series doesn't seem to allow change [Le Poidevin] |
| Full Idea: How can anything change in a B-universe? | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Second') | |
| A reaction: It seems that change needs time to move on. A timeless series of varying states doesn't seem to be the same thing as change. B-seriesers must be tempted to deny change, and yet nothing seems more obvious to us than change. |
| 22940 | If the B-universe is eternal, why am I trapped in a changing moment of it? [Le Poidevin] |
| Full Idea: What in the B-universe determines my temporal perspective? I can move around in space at will, but I have no choice over where I am in time. What time I am is something that changes, and again I have no control over that | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'Second') | |
| A reaction: The B-series always has to be asserted from the point of view of eternity (e.g. by Einstein). Yet an omniscient mind would still see each of us trapped in our transient moments, so that is part of eternal reality. |
| 22947 | An ordered series can be undirected, but time favours moving from earlier to later [Le Poidevin] |
| Full Idea: A series can be ordered without being directed (such as the series of integers), …but the passage of time indicates a preferred direction, moving from earlier to later events, and never the other way around. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Hidden') | |
| A reaction: I wonder what 'preferred' means here? It is not just memory versus anticipation. The saddest words in the English language are 'Too late!'. It is absurd to say that being too late is an illusion. |
| 22952 | If time's arrow is causal, how can there be non-simultaneous events that are causally unconnected? [Le Poidevin] |
| Full Idea: An objection to the Causal analysis of time's arrow is that it is surely possible for non-simultaneous events to be causally unconnected. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Seeds') | |
| A reaction: I suppose the events could be linked causally by intermediaries. If reality is a vast causal nexus, everything leads to everything else, in some remote way. It's still a good objections, though. |
| 22951 | If time's arrow is psychological then different minds can impose different orders on events [Le Poidevin] |
| Full Idea: If the Psychological account of time's arrow is correct …then there is nothing to prevent different minds from imposing different orders on the world. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'The mind's') | |
| A reaction: All we need is for two people to disagree about the order of some past events. The idea that we are psychologically creating time's arrow when everyone feels they are its victims strikes me as a particularly silly theory. |
| 22948 | There are Thermodynamic, Psychological and Causal arrows of time [Le Poidevin] |
| Full Idea: The three most significant arrows of time are the Thermodynamic (the direction from order to disorder), the Psychological (from perceptions of events to memories), and the Causal (from cause to effect). | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Three') | |
| A reaction: It would be nice if one of these explained the other two. Le Poidevin rejects the Psychological arrow, and seems to favour the Causal. Since I favour taking time as a primitive, I'm inclined to think that the arrow is included in the deal. |
| 22949 | Presumably if time's arrow is thermodynamic then time ends when entropy is complete [Le Poidevin] |
| Full Idea: One consequence of the Thermodynamic analysis of time's arrow is that a universe in which things are as disordered as they could be would exhibit no direction of time at all, because there would be no more significant changes in entropy. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Three') | |
| A reaction: And presumably time would gradually fizzle out, rather than ending abruptly. If entropy then went into reverse, there would be no time interval between the end and the new beginning. Entropy can vary locally, so it has to be universal. |
| 22950 | If time is thermodynamic then entropy is necessary - but the theory says it is probable [Le Poidevin] |
| Full Idea: The Second Law of Thermodynamics says it is overwhelmingly probable that entropy will increase. This leaves the door open for occasional isolated instances of decrease. But the thermodynamic arrow makes the increase a necessity. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'Three') | |
| A reaction: Le Poidevin sees this as a clincher against the thermodynamic explanation of the arrow. I'm now sure how the Second Law can even be stated without explicit or implicit reference to time. |
| 22953 | Time's arrow is not causal if there is no temporal gap between cause and effect [Le Poidevin] |
| Full Idea: If there is no temporal gap between cause and effect, then the causal analysis of time's arrow is doomed. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 12 'simultaneous') | |
| A reaction: A number of recent commentators have rejected the sharp distinction between cause and effect, seeing it as a unified process (which takes time to occur). |
| 22943 | Instantaneous motion is an intrinsic disposition to be elsewhere [Le Poidevin] |
| Full Idea: Being in motion at a particular time can be an intrinsic property of an object, as a disposition to be elsewhere than the place it is. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'in present') | |
| A reaction: This needs an ontology which includes unrealised dispositions. People trapped in boring meetings have a disposition to be elsewhere, but they are stuck. I think 'power' is a better word here than 'disposition'. The disposition isn't just for 'elsewhere'. |
| 22945 | The dynamic view of motion says it is primitive, and not reducible to objects, properties and times [Le Poidevin] |
| Full Idea: According to the dynamic account of motion, an object's being in motion is a primitive event, not further analysable in terms of objects, properties and times. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'Zeno') | |
| A reaction: [The rival view is 'static'] Physics suggests that motion may be indefinable, but acceleration can be given a reductive account. If time and space are taken as primitive (which seems sensible to me), then making motion also primitive is a bit greedy. |
| 22937 | If the present could have diverse pasts, then past truths can't have present truthmakers [Le Poidevin] |
| Full Idea: If any number of pasts are compatible with the present state of affairs, and it is only the present state of affairs which can make true or false statements about the past, then no statement about the past is either true or false. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 08 'First') | |
| A reaction: He suggests an explosion which could have had innumerable different causes. The explosion could have had different origins, but not sure that the whole of present reality could. Presentists certainly have problems with truthmakers for the past. |
| 22925 | The present is the past/future boundary, so the first moment of time was not present [Le Poidevin] |
| Full Idea: The present is the boundary between past and future, therefore if there was a first moment of time, it could not have been present - because there can be no past at the beginning of time. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 05 'Limits') | |
| A reaction: How about at the start of a race the athletes cannot be running. How about 'all moments of time have preceding moments - apart from the first moment'? |
| 22944 | The primitive parts of time are intervals, not instants [Le Poidevin] |
| Full Idea: Intervals of time can be viewed as primitive, and not decomposable into a series of instants. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'in present') | |
| A reaction: Given that instants are nothing, and intervals are something, the latter are clearly the better candidates to be the parts of time. Is there a smallest interval? |
| 22942 | If time is infinitely divisible, then the present must be infinitely short [Le Poidevin] |
| Full Idea: Assuming time to be infinitely divisible, the present can have no duration at all, for if it did, we could divide it into parts, and some parts would be earlier than others. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'in present') | |
| A reaction: I quite like Aristotle's view that things only have parts when you actually divide them. In modern physics fields don't seem to be infinitely divisible. It's a puzzle, though, innit? |
| 22946 | The multiverse is distinct time-series, as well as spaces [Le Poidevin] |
| Full Idea: The multiverse is not just a collection of distinct spaces, it is also a collection of distinct time-series. | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 11 'Objections') | |
| A reaction: This boggles the imagination even more than distinct spatial universes. |
| 22941 | How could a timeless God know what time it is? So could God be both timeless and omniscient? [Le Poidevin] |
| Full Idea: Could a timeless being now know what the time was? If so, does this show that there must be something wrong with the idea of God as both timeless and omniscient? | |
| From: Robin Le Poidevin (Travels in Four Dimensions [2003], 09 'Questions') | |
| A reaction: This is a potential contradiction between the perfections of a supreme God which I had not noticed before. Leibniz tried to refute such objections, but not very successfully, I think. |