59 ideas
10468 | A metaphysics has an ontology (objects) and an ideology (expressed ideas about them) [Oliver] |
Full Idea: A metaphysical theory hs two parts: ontology and ideology. The ontology consists of the entities which the theory says exist; the ideology consists of the ideas which are expressed within the theory using predicates. Ideology sorts into categories. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §02.1) | |
A reaction: Say 'what there is', and 'what we can say about it'. The modern notion remains controversial (see Ladyman and Ross, for example), so it is as well to start crystalising what metaphysics is. I am enthusiastic, but nervous about what is being said. |
10471 | Ockham's Razor has more content if it says believe only in what is causal [Oliver] |
Full Idea: One might give Ockham's Razor a bit more content by advising belief in only those entities which are causally efficacious. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §03) | |
A reaction: He cites Armstrong as taking this line, but I immediately think of Shoemaker's account of properties. It seems to me to be the only account which will separate properties from predicates, and bring them under common sense control. |
10749 | Necessary truths seem to all have the same truth-maker [Oliver] |
Full Idea: The definition of truth-makers entails that a truth-maker for a given necessary truth is equally a truth-maker for every other necessary truth. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §24) | |
A reaction: Maybe we could accept this. Necessary truths concern the way things have to be, so all realities will embody them. Are we to say that nothing makes a necessary truth true? |
10750 | Slingshot Argument: seems to prove that all sentences have the same truth-maker [Oliver] |
Full Idea: Slingshot Argument: if truth-makers work for equivalent sentences and co-referring substitute sentences, then if 'the numbers + S1 = the numbers' has a truth-maker, then 'the numbers + S2 = the numbers' will have the same truth-maker. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §24) | |
A reaction: [compressed] Hence every sentence has the same truth-maker! Truth-maker fans must challenge one of the premises. |
10676 | The Axiom of Choice is a non-logical principle of set-theory [Hossack] |
Full Idea: The Axiom of Choice seems better treated as a non-logical principle of set-theory. | |
From: Keith Hossack (Plurals and Complexes [2000], 4 n8) | |
A reaction: This reinforces the idea that set theory is not part of logic (and so pure logicism had better not depend on set theory). |
10686 | The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack] |
Full Idea: We cannot explicitly define one-one correspondence from the sets to the ordinals (because there is no explicit well-ordering of R). Nevertheless, the Axiom of Choice guarantees that a one-one correspondence does exist, even if we cannot define it. | |
From: Keith Hossack (Plurals and Complexes [2000], 10) |
23623 | Predicativism says only predicated sets exist [Hossack] |
Full Idea: Predicativists doubt the existence of sets with no predicative definition. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 02.3) | |
A reaction: This would imply that sets which encounter paradoxes when they try to be predicative do not therefore exist. Surely you can have a set of random objects which don't fall under a single predicate? |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
Full Idea: The iterative conception justifies Power Set, but cannot justify a satisfactory theory of von Neumann ordinals, so ZFC appropriates Replacement from NBG set theory. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
A reaction: The modern approach to axioms, where we want to prove something so we just add an axiom that does the job. |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
Full Idea: The limitation of size conception of sets justifies the axiom of Replacement, but cannot justify Power Set, so NBG set theory appropriates the Power Set axiom from ZFC. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 09.9) | |
A reaction: Which suggests that the Power Set axiom is not as indispensable as it at first appears to be. |
10687 | Maybe we reduce sets to ordinals, rather than the other way round [Hossack] |
Full Idea: We might reduce sets to ordinal numbers, thereby reversing the standard set-theoretical reduction of ordinals to sets. | |
From: Keith Hossack (Plurals and Complexes [2000], 10) | |
A reaction: He has demonstrated that there are as many ordinals as there are sets. |
10677 | Extensional mereology needs two definitions and two axioms [Hossack] |
Full Idea: Extensional mereology defs: 'distinct' things have no parts in common; a 'fusion' has some things all of which are parts, with no further parts. Axioms: (transitivity) a part of a part is part of the whole; (sums) any things have a unique fusion. | |
From: Keith Hossack (Plurals and Complexes [2000], 5) |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
Full Idea: The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4) | |
A reaction: This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point. |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
Full Idea: The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3) | |
A reaction: This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him. |
10671 | Plural definite descriptions pick out the largest class of things that fit the description [Hossack] |
Full Idea: If we extend the power of language with plural definite descriptions, these would pick out the largest class of things that fit the description. | |
From: Keith Hossack (Plurals and Complexes [2000], 3) |
10666 | Plural reference will refer to complex facts without postulating complex things [Hossack] |
Full Idea: It may be that plural reference gives atomism the resources to state complex facts without needing to refer to complex things. | |
From: Keith Hossack (Plurals and Complexes [2000], 1) | |
A reaction: This seems the most interesting metaphysical implication of the possibility of plural quantification. |
10669 | Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack] |
Full Idea: If all properties are distributive, plural reference is just a handy abbreviation to avoid repetition (as in 'A and B are hungry', to avoid 'A is hungry and B is hungry'), but not all properties are distributive (as in 'some people surround a table'). | |
From: Keith Hossack (Plurals and Complexes [2000], 2) | |
A reaction: The characteristic examples to support plural quantification involve collective activity and relations, which might be weeded out of our basic ontology, thus leaving singular quantification as sufficient. |
10675 | A plural comprehension principle says there are some things one of which meets some condition [Hossack] |
Full Idea: Singular comprehension principles have a bad reputation, but the plural comprehension principle says that given a condition on individuals, there are some things such that something is one of them iff it meets the condition. | |
From: Keith Hossack (Plurals and Complexes [2000], 4) |
10673 | Plural language can discuss without inconsistency things that are not members of themselves [Hossack] |
Full Idea: In a plural language we can discuss without fear of inconsistency the things that are not members of themselves. | |
From: Keith Hossack (Plurals and Complexes [2000], 4) | |
A reaction: [see Hossack for details] |
10680 | The theory of the transfinite needs the ordinal numbers [Hossack] |
Full Idea: The theory of the transfinite needs the ordinal numbers. | |
From: Keith Hossack (Plurals and Complexes [2000], 8) |
10684 | I take the real numbers to be just lengths [Hossack] |
Full Idea: I take the real numbers to be just lengths. | |
From: Keith Hossack (Plurals and Complexes [2000], 9) | |
A reaction: I love it. Real numbers are beginning to get on my nerves. They turn up to the party with no invitation and improperly dressed, and then refuse to give their names when challenged. |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
Full Idea: The transfinite ordinal numbers are important in the theory of proofs, and essential in the theory of recursive functions and computability. Mathematics would be incomplete without them. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.1) | |
A reaction: Hossack offers this as proof that the numbers are not human conceptual creations, but must exist beyond the range of our intellects. Hm. |
10674 | A plural language gives a single comprehensive induction axiom for arithmetic [Hossack] |
Full Idea: A language with plurals is better for arithmetic. Instead of a first-order fragment expressible by an induction schema, we have the complete truth with a plural induction axiom, beginning 'If there are some numbers...'. | |
From: Keith Hossack (Plurals and Complexes [2000], 4) |
10681 | In arithmetic singularists need sets as the instantiator of numeric properties [Hossack] |
Full Idea: In arithmetic singularists need sets as the instantiator of numeric properties. | |
From: Keith Hossack (Plurals and Complexes [2000], 8) |
10685 | Set theory is the science of infinity [Hossack] |
Full Idea: Set theory is the science of infinity. | |
From: Keith Hossack (Plurals and Complexes [2000], 10) |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
Full Idea: I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro) | |
A reaction: Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude. |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
Full Idea: Numbers cannot be mental objects constructed by our own minds: there exists at most a potential infinity of mental constructions, whereas the axioms of mathematics require an actual infinity of numbers. | |
From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro 2) | |
A reaction: Doubt this, but don't know enough to refute it. Actual infinities were a fairly late addition to maths, I think. I would think treating fictional complete infinities as real would be sufficient for the job. Like journeys which include imagined roads. |
10668 | We are committed to a 'group' of children, if they are sitting in a circle [Hossack] |
Full Idea: By Quine's test of ontological commitment, if some children are sitting in a circle, no individual child can sit in a circle, so a singular paraphrase will have us committed to a 'group' of children. | |
From: Keith Hossack (Plurals and Complexes [2000], 2) | |
A reaction: Nice of why Quine is committed to the existence of sets. Hossack offers plural quantification as a way of avoiding commitment to sets. But is 'sitting in a circle' a real property (in the Shoemaker sense)? I can sit in a circle without realising it. |
10747 | Accepting properties by ontological commitment tells you very little about them [Oliver] |
Full Idea: The route to the existence of properties via ontological commitment provides little information about what properties are like. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §22) | |
A reaction: NIce point, and rather important, I would say. I could hardly be committed to something for the sole reason that I had expressed a statement which contained an ontological commitment. Start from the reason for making the statement. |
10748 | Reference is not the only way for a predicate to have ontological commitment [Oliver] |
Full Idea: For a predicate to have a referential function is one way, but not the only way, to harbour ontological commitment. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §22) | |
A reaction: Presumably the main idea is that the predicate makes some important contribution to a sentence which is held to be true. Maybe reference is achieved by the whole sentence, rather than by one bit of it. |
10719 | There are four conditions defining the relations between particulars and properties [Oliver] |
Full Idea: Four adequacy conditions for particulars and properties: asymmetry of instantiation; different particulars can have the same property; particulars can have many properties; two properties can be instantiated by the same particulars. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
A reaction: The distinction between particulars and universals has been challenged (e.g. by Ramsey and MacBride). There are difficulties in the notion of 'instantiation', and in the notion of two properties being 'the same'. |
10721 | If properties are sui generis, are they abstract or concrete? [Oliver] |
Full Idea: If properties are sui generis entities, one must decide whether they are abstract or concrete. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
A reaction: A nice basic question! I take the real properties to be concrete, but we abstract from them, especially from their similarities, and then become deeply confused about the ontology, because our language doesn't mark the distinctions clearly. |
10716 | There are just as many properties as the laws require [Oliver] |
Full Idea: One conception of properties says there are only as many properties as are needed to be constituents of laws. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §03) | |
A reaction: I take this view to the be precise opposite of the real situation. The properties are what lead to the laws. Properties are internal to nature, and laws are imposed from outside, which is ridiculous unless you think there is an active deity. |
10720 | We have four options, depending whether particulars and properties are sui generis or constructions [Oliver] |
Full Idea: Both properties and particulars can be taken as either sui generis or as constructions, so we have four options: both sui generis, or both constructions, or one of each. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §09) | |
A reaction: I think I favour both being sui generis. God didn't make the objects, then add their properties, or make the properties then create some instantiations. There can't be objects without properties, or objectless properties (except in thought). |
10714 | The expressions with properties as their meanings are predicates and abstract singular terms [Oliver] |
Full Idea: The types of expressions which have properties as their meanings may vary, the chief candidates being predicates, such as '...is wise', and abstract singular terms, such as 'wisdom'. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §02) | |
A reaction: This seems to be important, because there is too much emphasis on predicates. If this idea is correct, we need some account of what 'abstract' means, which is notoriously tricky. |
10715 | There are five main semantic theories for properties [Oliver] |
Full Idea: Properties in semantic theory: functions from worlds to extensions ('Californian'), reference, as opposed to sense, of predicates (Frege), reference to universals (Russell), reference to situations (Barwise/Perry), and composition from context (Lewis). | |
From: Alex Oliver (The Metaphysics of Properties [1996], §02 n12) | |
A reaction: [compressed; 'Californian' refers to Carnap and Montague; the Lewis view is p,67 of Oliver]. Frege misses out singular terms, or tries to paraphrase them away. Barwise and Perry sound promising to me. Situations involve powers. |
10738 | Tropes are not properties, since they can't be instantiated twice [Oliver] |
Full Idea: I rule that tropes are not properties, because it is not true that one and the same trope of redness is instantiated by two books. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
A reaction: This seems right, but has very far-reaching implications, because it means there are no properties, and no two things have the same properties, so there can be no generalisations about properties, let alone laws. ..But they have equivalence sets. |
10739 | The property of redness is the maximal set of the tropes of exactly similar redness [Oliver] |
Full Idea: Using the predicate '...is exactly similar to...' we can sort tropes into equivalence sets, these sets serving as properties and relations. For example, the property of redness is the maximal set of the tropes of redness. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
A reaction: You have somehow to get from scarlet and vermilion, which have exact similarity within their sets, to redness, which doesn't. |
10740 | The orthodox view does not allow for uninstantiated tropes [Oliver] |
Full Idea: It is usual to hold an aristotelian conception of tropes, according to which tropes are present in their particular instances, and which does not allow for uninstantiated tropes. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
A reaction: What are you discussing when you ask what colour the wall should be painted? Presumably we can imagine non-existent tropes. If I vividly imagine my wall looking yellow, have I brought anything into existence? |
10741 | Maybe concrete particulars are mereological wholes of abstract particulars [Oliver] |
Full Idea: Some trope theorists give accounts of particulars. Sets of tropes will not do because they are always abstract, but we might say that particulars are (concrete) mereological wholes of the tropes which they instantiate. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
A reaction: Looks like a non-starter to me. How can abstract entities add up to a mereological whole which is concrete? |
10742 | Tropes can overlap, and shouldn't be splittable into parts [Oliver] |
Full Idea: More than one trope can occupy the same place at the same time, and a trope occupies a place without having parts which occupy parts of the place. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §12) | |
A reaction: This is the general question of the size of a spatial trope, or 'how many red tropes in a tin of red paint?' |
10472 | 'Structural universals' methane and butane are made of the same universals, carbon and hydrogen [Oliver] |
Full Idea: The 'structural universals' methane and butane are each made up of the same universals, carbon and hydrogen. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §07) | |
A reaction: He cites Lewis 1986, who is criticising Armstrong. If you insist on having universals, they might (in this case) best be described as 'patterns', which would be useful for structuralism in mathematics. They reduce to relations. |
10724 | Located universals are wholly present in many places, and two can be in the same place [Oliver] |
Full Idea: So-called aristotelian universals have some queer features: one universal can be wholly present at different places at the same time, and two universals can occupy the same place at the same time. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
A reaction: If you want to make a metaphysical doctrine look ridiculous, stating it in very simple language will often do the job. Belief in fairies is more plausible than the first of these two claims. |
7963 | Aristotle's instantiated universals cannot account for properties of abstract objects [Oliver] |
Full Idea: Properties and relations of abstract objects may need to be acknowledged, but they would have no spatio-temporal location, so they cannot instantiate Aristotelian universals, there being nowhere for such universals to be. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §11), quoted by Cynthia Macdonald - Varieties of Things | |
A reaction: Maybe. Why can't the second-order properties be in the same location as the first-order ones? If the reply is that they would seem to be in many places at once, that is only restating the original problem of universals at a higher level. |
10730 | If universals ground similarities, what about uniquely instantiated universals? [Oliver] |
Full Idea: If universals are to ground similarities, it is hard to see why one should admit universals which only happen to be instantiated once. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
A reaction: He is criticising Armstrong, who holds that universals must be instantiated. This is a good point about any metaphysics which makes resemblance basic. |
10727 | Uninstantiated universals seem to exist if they themselves have properties [Oliver] |
Full Idea: We may have to accept uninstantiated universals because the properties and relations of abstract objects may need to be acknowledged. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
A reaction: This is the problem of 'abstract reference'. 'Courage matters more than kindness'; 'Pink is more like red than like yellow'. Not an impressive argument. All you need is second-level abstraction. |
7962 | Uninstantiated properties are useful in philosophy [Oliver] |
Full Idea: Uninstantiated properties and relations may do some useful philosophical work. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §11), quoted by Cynthia Macdonald - Varieties of Things | |
A reaction: Their value isn't just philosophical; hopes and speculations depend on them. This doesn't make universals mind-independent. I think the secret is a clear understanding of the word 'abstract' (which I don't have). |
10722 | Instantiation is set-membership [Oliver] |
Full Idea: One view of instantiation is that it is the set-membership predicate. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §10) | |
A reaction: This cuts the Gordian knot rather nicely, but I don't like it, if the view of sets is extensional. We need to account for natural properties, and we need to exclude mere 'categorial' properties. |
10744 | Nominalism can reject abstractions, or universals, or sets [Oliver] |
Full Idea: We can say that 'Harvard-nominalism' is the thesis that there are no abstract objects, 'Oz-nominalism' that there are no universals, and Goodman's nominalism rejects entities, such as sets, which fail to obey a certain principle of composition. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §15 n46) | |
A reaction: Personally I'm a Goodman-Harvard-Oz nominalist. What are you rebelling against? What have you got? We've been mesmerized by the workings of our own minds, which are trying to grapple with a purely physical world. |
10726 | Things can't be fusions of universals, because two things could then be one thing [Oliver] |
Full Idea: If a particular thing is a bundle of located universals, we might say it is a mereological fusion of them, but if two universals can be instantiated by more than one particular, then two particulars can have the same universals, and be the same thing. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
A reaction: This and Idea 10725 pretty thoroughly demolish the idea that objects could be just bundles of universals. The problem pushes some philosophers back to the idea of 'substance', or some sort of 'substratum' which has the universals. |
10725 | Abstract sets of universals can't be bundled to make concrete things [Oliver] |
Full Idea: If a particular thing is a bundle of located universals, we might say that it is the set of its universals, but this won't work because the thing can be concrete but sets are abstract. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §11) | |
A reaction: This objection applies just as much to tropes (abstract particulars) as it does to universals. |
10664 | Complex particulars are either masses, or composites, or sets [Hossack] |
Full Idea: Complex particulars are of at least three types: masses (which sum, of which we do not ask 'how many?' but 'how much?'); composite individuals (how many?, and summing usually fails); and sets (only divisible one way, unlike composites). | |
From: Keith Hossack (Plurals and Complexes [2000], 1) | |
A reaction: A composite pile of grains of sand gradually becomes a mass, and drops of water become 'water everywhere'. A set of people divides into individual humans, but redescribe the elements as the union of males and females? |
10678 | The relation of composition is indispensable to the part-whole relation for individuals [Hossack] |
Full Idea: The relation of composition seems to be indispensable in a correct account of the part-whole relation for individuals. | |
From: Keith Hossack (Plurals and Complexes [2000], 7) | |
A reaction: This is the culmination of a critical discussion of mereology and ontological atomism. At first blush it doesn't look as if 'composition' has much chance of being a precise notion, and it will be plagued with vagueness. |
10665 | Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack] |
Full Idea: We can employ Leibniz's Law against mereological atomism. Water is wet, but no water molecule is wet. The set of infinite numbers is infinite, but no finite number is infinite. ..But with plural reference the atomist can resist this argument. | |
From: Keith Hossack (Plurals and Complexes [2000], 1) | |
A reaction: The idea of plural reference is to state plural facts without referring to complex things, which is interesting. The general idea is that we have atomism, and then all the relations, unities, identities etc. are in the facts, not in the things. I like it. |
10682 | The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack] |
Full Idea: The fusion of five rectangles may have a decomposition into more than five parts that are rectangles. | |
From: Keith Hossack (Plurals and Complexes [2000], 8) |
10745 | Science is modally committed, to disposition, causation and law [Oliver] |
Full Idea: Natural science is up to its ears in modal notions because of its use of the concepts of disposition, causation and law. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §15) | |
A reaction: This is aimed at Quine. It might be possible for an auster physicist to dispense with these concepts, by merely describing patterns of observed behaviour. |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles. | |
From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro' | |
A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture? |
10663 | A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack] |
Full Idea: A thought can refer to a particular or a universal or a state of affairs, but it can predicate only a universal and it can affirm only a state of affairs. | |
From: Keith Hossack (Plurals and Complexes [2000], 1) | |
A reaction: Hossack is summarising Armstrong's view, which he is accepting. To me, 'thought' must allow for animals, unlike language. I think Hossack's picture is much too clear-cut. Do animals grasp universals? Doubtful. Can they predicate? Yes. |
10746 | Conceptual priority is barely intelligible [Oliver] |
Full Idea: I find the notion of conceptual priority barely intelligible. | |
From: Alex Oliver (The Metaphysics of Properties [1996], §19 n48) | |
A reaction: I don't think I agree, though there is a lot of vagueness and intuition involved, and not a lot of hard argument. Can you derive A from B, but not B from A? Is A inconceivable without B, but B conceivable without A? |
10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
Full Idea: We might dispense with substantival space, and say that if the distribution of matter in space could have been different, that just means the matter of the Universe could have been shaped differently (with geometry as the science of shapes). | |
From: Keith Hossack (Plurals and Complexes [2000], 9) |