40 ideas
| 9777 | Kant was the first philosopher [Zizek] |
| Full Idea: From today's perspective it is in a way clear that Kant was the first philosopher. Pre-Kantian philosophy cannot think in his transcendental aspect. | |
| From: Slavoj Zizek (Conversations, with Glyn Daly [2004], §1) | |
| A reaction: It is probably equally plausible to say that Kant was the last philosopher. More thought-provoking than true. |
| 9778 | There is no dialogue in philosophy [Zizek] |
| Full Idea: I think I truly became a philosopher when I realised that there is no dialogue in philosophy. Plato's dialogues are clearly fakes, with one guy talking most of the time. ...Philosophy as an interdisciplinary project is the ultimate nightmare. | |
| From: Slavoj Zizek (Conversations, with Glyn Daly [2004], §1) | |
| A reaction: This goes against all my prejudices in favour of teamwork and mutual criticism (e.g. Idea 1576), but I was a bit shaken by it, and have begun to wonder whether I must just face up to the solitary nature of the enterprise. |
| 9779 | Philosophy is transcendental questioning (not supporting science or constructing ontology) [Zizek] |
| Full Idea: Philosophy can no longer play its traditional roles, giving foundations to science, or constructing general ontology. It should simply fulfil its task of transcendental questioning. | |
| From: Slavoj Zizek (Conversations, with Glyn Daly [2004], §2) | |
| A reaction: I remain unsure what is being recommended, unless it is for philosophy to start asking questions just at the point where everyone else gives up. |
| 4036 | What matters is not how many entities we postulate, but how many kinds of entities [Armstrong, by Mellor/Oliver] |
| Full Idea: Armstrong argues that what matters is not how few entities we postulate (quantitative economy), but how few kinds of entities (qualitative economy). | |
| From: report of David M. Armstrong (Properties [1992]) by DH Mellor / A Oliver - Introduction to 'Properties' §9 | |
| A reaction: Is this what Ockham meant? Armstrong is claiming that the notion of a 'property' is needed to identify kinds. See also Idea 7038. |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 15754 | Without properties we would be unable to express the laws of nature [Armstrong] |
| Full Idea: The ontological correlates of true law-statements must involve properties. How else can one pick our the uniformities which the law-statements entail? | |
| From: David M. Armstrong (Properties [1992], 1) | |
| A reaction: I'm unconvinced about the 'laws', but I have to admit that it is hard to know how to describe the relevant bits of nature without some family of concepts covered by the word 'property'. I'm in favour of taking some of the family into care, though. |
| 4034 | Whether we apply 'cold' or 'hot' to an object is quite separate from its change of temperature [Armstrong] |
| Full Idea: Evading properties by means of predicates is implausible when things change. If a cold thing becomes hot, first 'cold' applies, and then 'hot', but what have predicates to do with the temperature of an object? | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: A clear illustration of why properties are part of nature, not just part of language. But some applications of predicates are more arbitrary than this (ugly, cool) |
| 8535 | To the claim that every predicate has a property, start by eliminating failure of application of predicate [Armstrong] |
| Full Idea: Upholders of properties have been inclined to postulate a distinct property corresponding to each distinct predicate. We could start by eliminating all those properties where the predicate fails to apply, is not true, of anything. | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: This would leave billions of conjunctional, disjunctional and gerrymandered properties where the predicate applies very well. We are all 'on the same planet as New York'. Am I allowed to say that I 'wish' that a was F? He aims for 'sparse' properties. |
| 8537 | Tropes fall into classes, because exact similarity is symmetrical and transitive [Armstrong] |
| Full Idea: Exact similarity is a symmetrical and transitive relation. (Less than exact similarity is not transitive, even for tropes). So the relation of exact similarity is an equivalence relation, partitioning the field of tropes into equivalence classes. | |
| From: David M. Armstrong (Properties [1992], §2) | |
| A reaction: Armstrong goes on the explore the difficulties for trope theory of less than exact similarity, which is a very good line of discussion. Unfortunately it is a huge problem for everyone, apart from the austere nominalist. |
| 8538 | Trope theory needs extra commitments, to symmetry and non-transitivity, unless resemblance is exact [Armstrong] |
| Full Idea: Trope theory needs extra ontological baggage, the Axioms of Resemblance. There is a principle of symmetry, and there is the failure of transitivity - except in the special case of exact resemblance. | |
| From: David M. Armstrong (Properties [1992], §2) | |
| A reaction: [see text for fuller detail] Is it appropriate to describe such axioms as 'ontological' baggage? Interesting, though I suspect that any account of properties and predicates will have a similar baggage of commitments. |
| 8539 | Universals are required to give a satisfactory account of the laws of nature [Armstrong] |
| Full Idea: A reason why I reject trope theory is that universals are required to give a satisfactory account of the laws of nature. | |
| From: David M. Armstrong (Properties [1992], §2) | |
| A reaction: This is the key thought in Armstrong's defence of universals. Issues about universals may well be decided on such large playing fields. I think he is probably wrong, and I will gradually explain why. Watch this space as the story unfolds... |
| 8529 | Deniers of properties and relations rely on either predicates or on classes [Armstrong] |
| Full Idea: The great deniers of properties and relations are of two sorts: those who put their faith in predicates and those who appeal to sets (classes). | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: This ignores the Quine view, which is strictly for ostriches. Put like this, properties and relations seem undeniable. Predicates are too numerous (gerrymandering) or too few (colour shades). Classes can have arbitrary members. |
| 8532 | Resemblances must be in certain 'respects', and they seem awfully like properties [Armstrong] |
| Full Idea: If a resembles b, in general, they resemble in certain respects, and fail to resemble in other respects. But respects are uncomfortably close to properties, which the Resemblance theory proposes to do without. | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: This is a good objection. I think it is plausible to build a metaphysics around the idea of respects, and drop properties. Shall we just talk of 'respects' for categorising, and 'powers' for causation and explanation? Respects only exist in comparisons. |
| 8530 | Change of temperature in objects is quite independent of the predicates 'hot' and 'cold' [Armstrong] |
| Full Idea: To appreciate the implausibility of the predicate view, consider where a thing's properties change. 'Hot' becomes applicable when 'cold' ceases to, ..but the change in the object would have occurred if the predicates had never existed. | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: They keep involving secondary qualities! Armstrong is taking a strongly realist view (fine by me), but anti-realists can ignore his argument. I take predicate nominalism to be a non-starter. |
| 8536 | We want to know what constituents of objects are grounds for the application of predicates [Armstrong] |
| Full Idea: The properties that are of ontological interest are those constituents of objects, of particulars, which serve as the ground in the objects for the application of predicates. | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: Good. This is a reversal of the predicate nominalist approach, and is a much healthier attitude to the relationship between ontology and language. Value judgements will be an interesting case. Does this allow us to invent new predicates? |
| 8531 | In most sets there is no property common to all the members [Armstrong] |
| Full Idea: Most sets are uninteresting because they are utterly heterogeneous, that is, the members have nothing in common. For most sets there is no common property F, such that the set is the set of all the Fs. | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: One might link the interesting sets together by resemblance, without invoking the actual existence of an item F which all the members carry (like freemasons' briefcases). Personally I am only really interested in 'natural' sets. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 15753 | Essences might support Resemblance Nominalism, but they are too coarse and ill-defined [Armstrong] |
| Full Idea: A sophisticated Resemblance theory can appeal to the natures of the resembling things, from which the resemblances flow. The natures are suitably internal, but are as coarse as the things themselves (and perhaps are the things themselves). | |
| From: David M. Armstrong (Properties [1992], 1) | |
| A reaction: Note that this is essentialism as an underpinning for Resemblance Nominalism. His objection is that he just can't believe in essences, because they are too 'coarse' - which I take to mean that we cannot distinguish the boundaries of an essence. |
| 9780 | Consciousness is a malfunction of evolution [Zizek] |
| Full Idea: Consciousness is a kind of mistake, a malfunction of evolution, and out of this mistake a miracle occurred. | |
| From: Slavoj Zizek (Conversations, with Glyn Daly [2004], §2) | |
| A reaction: Rather hard to prove, but actually quite an uplifting thought. If consciousness only evolved so that we could navigate and defend ourselves, our 'higher' activities seem irrelevant. But Zizek's view means we can make them central. Nice. |
| 8533 | Predicates need ontological correlates to ensure that they apply [Armstrong] |
| Full Idea: Must there not be something quite specific about the thing which allows, indeed ensures, that predicates like 'underneath' and 'hot' apply? The predicates require ontological correlates. | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: An interesting proposal, that in addition to making use of predicates, we should 'ensure that they apply'. Sounds verificationist. Obvious problem cases would be speculative, controversial or metaphorical predicates. "He's beneath contempt". |
| 4035 | There must be some explanation of why certain predicates are applicable to certain objects [Armstrong] |
| Full Idea: When we have said that predicates apply to objects, we have surely not said enough. The situation cries out for an explanation. Must there not be something specific about the things which allows, indeed ensures, that these predicates apply? | |
| From: David M. Armstrong (Properties [1992], §1) | |
| A reaction: A nice challenge to any philosopher who places too much emphasis on language. A random and arbitrary (nominalist?) language simply wouldn't work. Nature has joints. |
| 9781 | Tolerance and love are strategies to avoid encountering our neighbours [Zizek] |
| Full Idea: All this preaching about tolerance, love for one's neighbour and so on, are ultimately strategies to avoid encountering the neighbour. | |
| From: Slavoj Zizek (Conversations, with Glyn Daly [2004], §2) | |
| A reaction: I have begun to wonder whether some such motivation underlies the modern obsession with raising huge sums for charity. |
| 8541 | Regularities theories are poor on causal connections, counterfactuals and probability [Armstrong] |
| Full Idea: Regularity theories make laws molecular, with no inner causal connections; also, only some cosmic regularities are manifestations of laws; molecular states can't sustain counterfactuals; and probabilistic laws are hard to accommodate. | |
| From: David M. Armstrong (Properties [1992], §2) | |
| A reaction: [very compressed] A helpful catalogue of difficulties. The first difficulty is the biggest one - that regularity theories have nothing to say about why there is a regularity. They offer descriptions instead of explanations. |
| 8540 | The introduction of sparse properties avoids the regularity theory's problem with 'grue' [Armstrong] |
| Full Idea: Regularity theories of laws face the grue problem. That, I think, can only be got over by introducing properties, sparse properties, into one's ontology. | |
| From: David M. Armstrong (Properties [1992], §2) | |
| A reaction: The problem is, roughly, that regularities have to be described in language, which is too arbitrary in character. Armstrong rightly tries to break the rigid link to language. See his Idea 8536, which puts reality before language. |