42 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. |
| 7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
| Full Idea: Bolzano said the 'laws of thought' (identity, contradiction, excluded middle) are true, but nothing of interest follows from them. Logic obeys them, but they are not logic's first principles or axioms. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], §3) by George / Van Evra - The Rise of Modern Logic | |
| A reaction: An interesting and crucial distinction. For samples of proposed axioms of logic, see Ideas 6408, 7798 and 7797. |
| 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. |
| 9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
| Full Idea: An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'. | |
| From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX | |
| A reaction: The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate. |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
| Full Idea: Bolzano if the father of 'arithmetization', which sought to found all of analysis on the concepts of arithmetic and to eliminate geometrical notions entirely (with logicism taking it a step further, by reducing arithmetic to logic). | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by James Robert Brown - Philosophy of Mathematics Ch. 3 | |
| A reaction: Brown's book is a defence of geometrical diagrams against Bolzano's approach. Bolzano sounds like the modern heir of Pythagoras, if he thinks that space is essentially numerical. |
| 10856 | A truly infinite quantity does not need to be a variable [Bolzano] |
| Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable. | |
| From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10 | |
| A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity. |
| 9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
| Full Idea: Bolzano began the process of eliminating intuition from analysis, by proving something apparently obvious (that as continuous function must be zero at some point). Proof reveals on what a theorem rests, and that it is not intuition. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - Frege philosophy of mathematics Ch.6 | |
| A reaction: Kant was the target of Bolzano's attack. Two responses might be to say that many other basic ideas are intuited but impossible to prove, or to say that proof itself depends on intuition, if you dig deep enough. |
| 17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
| Full Idea: Mathematical proofs are philosophical in method if they do not only demonstrate that a certain mathematical truth holds but if they also disclose why it holds, that is, if they uncover its grounds. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3 | |
| A reaction: I aim to defend the role of explanation in mathematics, but this says that this is only if the proofs are 'philosophical', which may be of no interest to mathematicians. Oh well, that's their loss. |
| 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. |
| 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. |
| 9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
| Full Idea: Bolzano was determined to expel Kantian intuition from analysis, and to prove from first principles anything that could be proved, no matter how obvious it might seem when thought of in geometrical terms. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - The Philosophy of Mathematics 2.3 | |
| A reaction: This is characteristic of the Enlightenment Project, well after the Enlightenment. It is a step towards Frege's attack on 'psychologism' in mathematics. The problem is that it led us into a spurious platonism. We live in troubled times. |
| 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? |
| 22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
| Full Idea: Bolzano took the entities of which truth is predicated to be not propositions in the subjective sense but 'propositions-in-themselves' - objective entities existing independent of our apprehension. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Emp' | |
| A reaction: A serious mistake. Presumably the objective propositions are all true (or there would be endless infinities of them). So what is assessed in the case of error? Something other than the objective propositions! We assess these other things! |
| 17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
| Full Idea: Bolzano conceived of propositions as abstract objects which are structured compounds of concepts and potential contents of judgements and assertions. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3 | |
| A reaction: Personally I think of propositions as brain events, the constituents of thought about the world, but that needn't contradict the view of them as 'abstract'. |
| 12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |
| Full Idea: What I mean by 'propositions' is not what the grammarians call a proposition, namely the linguistic expression, but the mere sense of this expression, is what is meant by proposition in itself or object proposition. This sense can be true or false. | |
| From: Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref?) | |
| A reaction: This seems to be the origin of what we understand by 'proposition'. The disputes are over whether such things exists, and whether they are features of minds or features of the world (resembling facts). |
| 12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |
| Full Idea: We can find the ground of a pure conceptual truth only in other conceptual truths. | |
| From: Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref) | |
| A reaction: Elsewhere he insists that these grounds must be in 'truths', and not just in the attributes of the concepts of involved. This conflicts with Kit Fine's view, that the concepts themselves are the source of conceptual truth and necessity. |