52 ideas
| 16241 | The metaphysics of nature should focus on physics [Maudlin] |
| Full Idea: Metaphysics, insofar as it is concerned with the natural world, can do no better than to reflect on physics. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: I suppose so. Physics only works at one level of description. Metaphysics often works with concepts which only emerge at a more general level than physics. There are also many metaphysical problems which are of no interest to most physicists. |
| 16257 | Kant survives in seeing metaphysics as analysing our conceptual system, which is a priori [Maudlin] |
| Full Idea: The Kantian strain survives in the notion that metaphysics is not about the world, but about our 'conceptual system', especially as what structures our thought about the world. This keeps it a priori, and so not about the world itself. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3) | |
| A reaction: Strawson would embody this view, I suppose. I take our conceptual system to be largely a reflection of (and even creation of) the world, and not just an arbitrary conventional attempt to grasp the world. Analysing concepts partly analyses the world. |
| 16276 | Wide metaphysical possibility may reduce metaphysics to analysis of fantasies [Maudlin] |
| Full Idea: If metaphysical possibility extends more widely than physical possibility, this may make metaphysics out to be nothing but the analysis of fantastical descriptions produced by philosophers. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: Maudlin wants metaphysics to be firmly constrained in its possibilities by what scientific undestanding permits, and he is right. Metaphysics must integrate into science, or wither away on the margins. |
| 16244 | If the universe is profligate, the Razor leads us astray [Maudlin] |
| Full Idea: If the universe has been profligate, then Ockham's Razor will lead us astray. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: That is, there may be a vast number of entities which exist beyond what seems to be 'necessary'. |
| 16255 | The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin] |
| Full Idea: The Razor is good when it councils higher credence to explanations which posit a single cause to multiple events that occur in a striking pattern, over explanations involving coincidental multiple causes. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: This is in the context of Maudlin warning against embracing the Razor too strongly. Presumably inductive success suggests that the world supports this particular use of the Razor. |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| Full Idea: For a set to be 'well-ordered' it is required that every subset of the set has a first element. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| Full Idea: Set theory made a closer study of infinity possible. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| Full Idea: The idea of the 'power set' means that it is always possible to generate a bigger one using only the elements of that set, namely the set of all its subsets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| Full Idea: Axiom of Extension: Two sets are equal if and only if they have the same elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| Full Idea: Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| Full Idea: Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| Full Idea: Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure. |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| Full Idea: Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set. |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| Full Idea: Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset. |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| Full Idea: Axiom of Existence: there exists at least one set. This may be the empty set, but you need to start with something. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers. |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| Full Idea: Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17) | |
| A reaction: Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'. |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| Full Idea: With ordinary finite numbers ordinals and cardinals are in effect the same, but beyond infinity it is possible for two sets to have the same cardinality but different ordinals. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| Full Idea: You can think of an ordinal number as being defined by the set that comes before it, so, in the non-negative integers, ordinal 5 is defined as {0, 1, 2, 3, 4}. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| Full Idea: The 'transcendental numbers' are those irrationals that can't be fitted to a suitable finite equation, of which π is far and away the best known. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| Full Idea: The realisation that brought 'i' into the toolkit of physicists and engineers was that you could extend the 'number line' into a new dimension, with an imaginary number axis at right angles to it. ...We now have a 'number plane'. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.12) |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| Full Idea: It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| Full Idea: As far as Kronecker was concerned, Cantor had built a whole structure on the irrational numbers, and so that structure had no foundation at all. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| Full Idea: Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| Full Idea: The 'continuum hypothesis' says that aleph-one is the cardinality of the rational and irrational numbers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 16243 | The Humean view is wrong; laws and direction of time are primitive, and atoms are decided by physics [Maudlin] |
| Full Idea: The Humean project is unjustified, in that both the laws of nature and the direction of time require no analysis, and is misconceived, in that the atoms it employs do not correspond to present physical ontology. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: I certainly find it strange, or excessively empirical, that Lewis thinks our account of reality should rest on 'qualities'. Maudlin's whole books is an implicit attack on David Lewis. |
| 16271 | Lewis says it supervenes on the Mosaic, but actually thinks the Mosaic is all there is [Maudlin] |
| Full Idea: At base it is not merely, as Lewis says, that everything else supervenes on the Mosaic; but rather that anything that exists at all is just a feature or element or generic property of the Mosaic. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: [Maudlin has just quoted Idea 16210] Correct about Lewis, but Lewis just has a normal view of supervenience. Only 'emergentists' would think the supervenience allowed anything more, and they are deeply misguided, and in need of help. |
| 16273 | If the Humean Mosaic is ontological bedrock, there can be no explanation of its structure [Maudlin] |
| Full Idea: The Humean Mosaic appears to admit of no further explanation. Since it is the ontological bedrock, …none of the further things can account for the structure of the Mosaic itself. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: A very nice point, reminiscent of Popper's objection to essentialism, that he thought it blocked further enquiry, when actually further enquiry was possible. Lewis and Hume seem too mesmerised by epistemology. They need best explanation. |
| 16275 | The 'spinning disc' is just impossible, because there cannot be 'homogeneous matter' [Maudlin] |
| Full Idea: The 'spinning disc' is not metaphysically possible. We have every reason to believe that there is no such thing as 'perfectly homogeneous matter'. The atomic theory of matter is as well established as any scientific theory is likely to be. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: This is a key case for Maudlin, and his contempt for metaphysics which is not scientifically informed. I agree with him. Extreme thought experiments are worth considering, but impossible ones are pointless. |
| 16258 | To get an ontology from ontological commitment, just add that some theory is actually true [Maudlin] |
| Full Idea: The doctrine of ontological commitment becomes a central element in a theory of ontology if one merely adds that a particular theory is, in fact, true | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: Helpful. I don't think the truth of a theory entails the actual existence of every component mentioned in the theory, as some of them may be generalisations, abstractions, vague, or even convenient linking fictions. |
| 16259 | Naïve translation from natural to formal language can hide or multiply the ontology [Maudlin] |
| Full Idea: Naïve translation from natural language into formal language can obscure necessary ontology as easily as it can create superfluous ontological commitment. …The lion's share of metaphysical work is done when settling on the right translation. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: I suspect this is more than a mere problem of 'naivety', but may be endemic to the whole enterprise. If you hammer a square peg into a round hole, you expect to lose something. Language is subtle, logic is crude. |
| 16253 | A property is fundamental if two objects can differ in only that respect [Maudlin] |
| Full Idea: Fragility is not a fundamental physical property, in that two pieces of glass cannot be physically identical save for their fragility. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: Nice. The best idea I have found in Maudlin, so far! This gives a very nice test for picking out the fundamental physical and intrinsic properties. |
| 16263 | Fundamental physics seems to suggest there are no such things as properties [Maudlin] |
| Full Idea: If one believes that fundamental physics is the place to look for the truths about universals (or tropes or natural sets), then one may find that physics is telling us there are no such things. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.2) | |
| A reaction: His prior discussion of quantum chromodynamics suggests, to me, merely that properties can be described in terms of vectors etc., and remains neutral on the ontology - but then I am blinded by science. |
| 16260 | Existence of universals may just be decided by acceptance, or not, of second-order logic [Maudlin] |
| Full Idea: On one line of thought, the question of whether universals exist seems to reduce to the question of the utility, or necessity, of using second-order rather than first-order logic. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: Second-order logic quantifies over properties, where first-order logic just quantifies over objects. This is an extreme example of doing your metaphysics largely through logic. Not my approach. |
| 16277 | Logically impossible is metaphysically impossible, but logically possible is not metaphysically possible [Maudlin] |
| Full Idea: While logical impossibility is a species of metaphysical impossibility, logical possibility is not a species of metaphysical possibility. The logically impeccable description 'Cicero was not Tully' describes a metaphysically impossible situation. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: The context of this is Maudlin attack on daft notions of metaphysical possibility that are at variance with the limits set by science, but he is still conceding that there are types of metaphysical modality. |
| 16249 | A counterfactual antecedent commands the redescription of a selected moment [Maudlin] |
| Full Idea: The purpose of the antecedent of a counterfactual is to provide instructions on how to pick a Cauchy surface (pick a moment in time) and how to generate an altered description of that moment. It is more of a command than an indicative sentence. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: Quite plausible, but the antecedent might contain no description. 'If things had gone differently, we wouldn't be in this mess'. The antecedent might be timeless. 'If pigs had wings, they still wouldn't fly'. |
| 16254 | Induction leaps into the unknown, but usually lands safely [Maudlin] |
| Full Idea: Induction is always a leap beyond the known, but we are constantly assured by later experience that we have landed safely. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: Not philosophically very interesting, but a nice remark for capturing the lived aspect of inductive thought, as practised by the humblest of animals. |
| 16245 | Laws should help explain the things they govern, or that manifest them [Maudlin] |
| Full Idea: A law ought to be capable of playing some role in explaining the phenomena that are governed by or are manifestations of it. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.2) | |
| A reaction: I find this attitude bewildering. 'Why do electrons have spin?' 'Because they all do!' The word 'governed' is the clue. What on earth is a law, if it can 'govern' nature? What is its ontological status? Natures of things are basic, not 'laws'. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 16248 | Evaluating counterfactuals involves context and interests [Maudlin] |
| Full Idea: The evaluation of counterfactual claims is widely recognised as being influenced by context and interest. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: Such evaluation certainly seems to involve imagination, and so the pragmatics can creep in there. I don't quite see why it should be deeply contextual. |
| 16250 | We don't pick a similar world from many - we construct one possibility from the description [Maudlin] |
| Full Idea: It seems unlikely the psychological process could mirror Lewis's semantics: people don't imagine a multiplicity of worlds and the pick out the most similar. Rather we construct representations of possible worlds from counterfactual descriptions. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: I approve of fitting such theories into a psychology, but this may be unfair to Lewis, who aims for a logical model, not an account of how we actually approach the problem. |
| 16268 | The counterfactual is ruined if some other cause steps in when the antecedent fails [Maudlin] |
| Full Idea: A counterexample to the counterfactual approach is that perhaps the effect would have occurred despite the absence of the cause since another cause would have stepped in to bring it about. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: …Hence you cannot say 'if C had not occurred, E would definitely not have occurred'. You have to add 'ceteris paribus', which ruins the neatness of the theory. |
| 16267 | If we know the cause of an event, we seem to assent to the counterfactual [Maudlin] |
| Full Idea: When we think we know the cause of an event, we typically assent to the corresponding Hume counterfactual. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: This is the correct grounding of the counterfactual approach - not that we think counterfactuals are causation, but that knowledge of causation will map neatly onto a network of counterfactuals, thus providing a logic for the whole process. |
| 16269 | If the effect hadn't occurred the cause wouldn't have happened, so counterfactuals are two-way [Maudlin] |
| Full Idea: If Kennedy had still been President in Dec 1963, he would not have been assassinated in Nov 1963, so the counterfactual goes both ways (where the cause seems to only go one way). | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: Maudlin says a lot of fine-tuning has sort of addressed these problems, but that counterfactual causation is basically wrong-headed anyway, and I incline to agree, though one must understand what the theory is (and is not) trying to do. |
| 16247 | Laws are primitive, so two indiscernible worlds could have the same laws [Maudlin] |
| Full Idea: Laws are ontologically primitives at least in that two worlds could differ in their laws but not in any observable respect. ….[21] I take content of the laws to be expressed by equations. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.4) | |
| A reaction: At least that spells out his view fairly dramatically, but I am baffled as to what he thinks a law could be. He is arguing against the Lewis regularity-axioms view, and the Armstrong universal-relations view. He ignores the essentialist view. |
| 16272 | Fundamental laws say how nature will, or might, evolve from some initial state [Maudlin] |
| Full Idea: The fundamental laws of nature appear to be laws of temporal evolution: they specify how the state of the universe will, or might, evolve from a given intial state. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: Maudlin takes both laws of nature and the passage of time to be primitive facts, and this is how they are connected. I think (this week) that I take time and causation to be primitive, but not laws. |
| 16242 | Laws of nature are ontological bedrock, and beyond analysis [Maudlin] |
| Full Idea: The laws of nature stand in no need of 'philosophical analysis'; they ought to be posited as ontological bedrock. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: This is Maudlin's most basic principle, and I don't agree with it. The notion that laws are more deeply embedded in reality than the physical stuff they control is a sort of 'law-mysticism' that needs to be challenged. |
| 16251 | 'Humans with prime house numbers are mortal' is not a law, because not a natural kind [Maudlin] |
| Full Idea: 'All humans who live in houses with prime house numbers are mortal' is not a law because the class referred to is not a natural kind. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.6) | |
| A reaction: Maudlin wants laws to be primitive, but he now needs a primitive notion of a natural kind to make it work. If kinds generate laws, you can ditch the laws, and build your theory on the kinds. He also says no death is explained by 'all humans are mortal'. |
| 16270 | If laws are just regularities, then there have to be laws [Maudlin] |
| Full Idea: On the Mill-Ramsey-Lewis account of laws, I take it that if the world is extensive and variegated enough, then there must be laws. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5.2) | |
| A reaction: A nice point. If there is any sort of pattern discernible in the surface waves on the sea, then there must be a law to cover it, not matter how vague or complex. |
| 16264 | I believe the passing of time is a fundamental fact about the world [Maudlin] |
| Full Idea: I believe that it is a fundamental, irreducible fact about the spatio-temporal structure of the world that time passes. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4) | |
| A reaction: Worth quoting because it comes from a philosopher fully informed about, and heavily committed to, the physicist's approach to reality. One fears that physicists steeped in Einstein are all B-series Eternalists. Get a life! |
| 16265 | If time passes, presumably it passes at one second per second [Maudlin] |
| Full Idea: It is necessary and, I suppose, a priori that if time passes at all it passes at one second per second. …Similarly, the fair exchange rate for a dollar must be a dollar. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4.1) | |
| A reaction: [He is discussing Huw Price on time] This is a reply to the claim that if time passes it has to pass at some rate, and 'one second per second' is ridiculous. Not very convincing, even with the dollar analogy. |
| 16266 | There is one ordered B series, but an infinitude of A series, depending on when the present is [Maudlin] |
| Full Idea: Given events ordered in a B series, one defines an infinitude of different A series that correspond to taking different events as 'now' or 'present'. McTaggart talks of 'the A series' when there is an infinitude of such. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4.3 n11) | |
| A reaction: This strikes me as a rather mathematical (and distorted) claim about the A series view. The A-series is one dynamic happening. Not an infinity of static times lines, each focused on a different 'now'. |