64 ideas
| 4767 | Traditionally, rational beliefs are those which are justified by reasons [Psillos] |
| Full Idea: The traditional conception of Reason is that all beliefs should be justified (that is, backed up by reasons) in order to be rational. | |
| From: Stathis Psillos (Causation and Explanation [2002], §1.6) | |
| A reaction: I think it is the duty of all philosophers to either defend this traditional view, or quit philosophy for some other activity. Rorty suggests hermeneutics. In a democracy, rulers should be continually required to give reasons for their decisions. |
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| Full Idea: If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence. | |
| From: David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind' | |
| A reaction: If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later. |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists. | |
| From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4 | |
| A reaction: [p.476 in Van Heijenoort] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 4810 | Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos] |
| Full Idea: Valid deductive arguments have the property of monotonicity; if the conclusion Q follows from the premises P, then it will also follow if further premises P* are added to P. | |
| From: Stathis Psillos (Causation and Explanation [2002], §9.2.1) | |
| A reaction: For perversity's sake we could add a new premise which contradicted one of the original ones ('Socrates is a god'). Or one premise could be 'I believe..', and the new one could show that the belief was false. Induction is non-monotonic. |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
| From: David Hilbert (On the Infinite [1925], p.200) | |
| A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
| From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
| A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
| From: David Hilbert (On the Infinite [1925], p.195) | |
| A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| Full Idea: Operating with the infinite can be made certain only by the finitary. | |
| From: David Hilbert (On the Infinite [1925], p.201) | |
| A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
| From: David Hilbert (On the Infinite [1925], p.186) | |
| A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence. | |
| From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist' | |
| A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!). |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
| From: David Hilbert (On the Infinite [1925], p.192) | |
| A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
| From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
| 4768 | The 'epistemic fallacy' is inferring what does exist from what can be known to exist [Psillos] |
| Full Idea: The move from what can (or cannot) be known to exist to what does (or does not) exist has been dubbed the 'epistemic fallacy'. | |
| From: Stathis Psillos (Causation and Explanation [2002], §1.6) | |
| A reaction: This should be a standard concept in all philosophical discussion. It is the commonest, simplest, and most profound blunder made by philosophers, and they do it all the time. |
| 14933 | Scientific properties are defined by the laws that embody them [Psillos, by Ladyman/Ross] |
| Full Idea: For Psillos, properties in mature science are defined by the laws in which they feature. | |
| From: report of Stathis Psillos (Scientific Realism [1999]) by J Ladyman / D Ross - Every Thing Must Go 3.5 | |
| A reaction: This is a perfect example of the Humean approach getting everything the wrong way round. Laws are not primitives from which we derive our account of nature - they are generalisations built up from the behaviour of prior properties. |
| 17996 | Powers are claimed to be basic because fundamental particles lack internal structure [Psillos] |
| Full Idea: The argument for fundamental powers is that fundamental particles are simple, without internal structure. Hence they have no parts which can be the bearers of further properties (powers or non-powers) which in turn ground the properties of the particles. | |
| From: Stathis Psillos (What do powers do when they are not manifested? [2006], p.151), quoted by Anna Marmodoro - Do powers need powers to make them powerful? 'The Problem' | |
| A reaction: If a power is basic, what has the power? I think the best answer is that at the fundamental level this is a false dichotomy. If you could zoom in, you would say that basic substance is active in a way that everyday stuff doesn't appear to be. |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
| 4807 | A good barometer will predict a storm, but not explain it [Psillos] |
| Full Idea: There can be predictions without explanations, as when a barometer successfully predicts storms, but on its own it does not explain them. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.8) | |
| A reaction: Actually, barometers contribute to explanations. A reasonable predictor might offer no explanation ('if he's out, she's probably out too'), but an infallible predictor is almost certain to involve causation, which helps a lot in explanation. |
| 4808 | If we say where Mars was two months ago, we offer an explanation without a prediction [Psillos] |
| Full Idea: There can be explanations without predictions, as when we explain a previous position of Mars from its present one, plus a law. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.9) | |
| A reaction: If we don't mind stretching the word, I think we can 'predict' the past, as where I predict the location of an Egyptian tomb from my study of papyruses. |
| 4811 | Induction (unlike deduction) is non-monotonic - it can be invalidated by new premises [Psillos] |
| Full Idea: Unlike deductive arguments, induction is non-monotonic - that is, it can be invalidated by the addition of new premises. | |
| From: Stathis Psillos (Causation and Explanation [2002], §9.2.1) | |
| A reaction: This is a fancy way of stating the obvious, which is that induction is not a type of deduction. Hume is sometimes accused of this false assumption. Presumably induction is rational, even if it is not actually logical. |
| 4812 | Explanation is either showing predictability, or showing necessity, or showing causal relations [Psillos] |
| Full Idea: The three types of explanation are 'epistemic' (the event is expectable because of a law), or 'modal' (the event is necessary because of a law), or 'ontic' (it is shown how the event fits into the world's causal structure). | |
| From: Stathis Psillos (Causation and Explanation [2002], §11.1) | |
| A reaction: Prediction, necessity or causes. It is hard to think of any other way to explain something. Presumably you would exclude necessities if you didn't believe in them. Hume would go for prediction, on the basis of regularities. Personally, I want it all. |
| 4802 | Just citing a cause does not enable us to understand an event; we also need a relevant law [Psillos] |
| Full Idea: Explanation has to do with understanding; just citing a cause would not offer an adequate understanding, unless it was accompanied by the citation of a law that connects the two events. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.2) | |
| A reaction: It is surely undeniable that being told the cause but not the law will increase our understanding. Understanding and explanation come in degrees. Full understanding would require an explanation of the law, and beyond. Any relevant truth helps. |
| 4804 | The 'covering law model' says only laws can explain the occurrence of single events [Psillos] |
| Full Idea: The 'deductive-nomological' model became known as the 'covering law model': its main thesis is that laws and only laws adequately explain the occurrence of singular events. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.2) | |
| A reaction: But presumably you need other events to derive a law, so you could say that a singular event can only be explained if it isn't singular. A regularity pattern would offer a partial explanation, before any law had been derived. |
| 4805 | If laws explain the length of a flagpole's shadow, then the shadow also explains the length of the pole [Psillos] |
| Full Idea: If we use geometry and optics to explain the length of shadow cast by a flag-pole, this seems to be reversible, so that the shadow will explain the length of the pole. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.5) | |
| A reaction: A neat example which presumably implies that an explanation must involve temporal statements. The laws of physics are totally reversible in time, and so will not suffice to explain events on their own. Time's arrow becomes an axiom of explanation? |
| 4395 | There are non-causal explanations, most typically mathematical explanations [Psillos] |
| Full Idea: There are non-causal explanations, most typically mathematical explanations. | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: A crucial basic point, which must be drummed into the minds of ruthless Quinean naturalists, who want to explain everything by quarks and electrons |
| 4806 | An explanation can just be a 'causal story', without laws, as when I knock over some ink [Psillos] |
| Full Idea: Knocking over an ink bottle explains the stain on the carpet, and it is not in doubt because you cannot quote the laws involved; a 'causal story' can give a complete explanation without a law. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.6) | |
| A reaction: But why is he so clumsy, and the bottle so unstable? Was it really (Freudian) an 'accident'? There is no end to complete explanation. But 'I was clumsy this once' and 'I am always clumsy' are equally good explanations. |
| 4404 | Maybe explanation is entirely relative to the interests and presuppositions of the questioner [Psillos] |
| Full Idea: Some philosophers focus on the so-called 'pragmatics of explanation' - that an explanation is an answer to a 'why' question, and the relevant answer will depend on the presuppositions or interests of the questioner. | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: This seems to me right. Explanation is an entirely human business, not a feature of nature, and most explanations will track back to the big bang if you have the patience, but they always terminate because of pragmatic considerations. But fobbing off? |
| 4803 | An explanation is the removal of the surprise caused by the event [Psillos] |
| Full Idea: An explanation amounts to the removal of the initial surprise that accompanied the occurrence of the event. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.2) | |
| A reaction: This is a nice simple point. It makes explanation relative. God requires no explanations, small children require many. The implication is that explanations make events predictable, which means they must either offer inductive generalisations, or laws. |
| 4769 | It is hard to analyse causation, if it is presupposed in our theory of the functioning of the mind [Psillos] |
| Full Idea: There is a problem if causation is the object of our analysis, but is also presupposed (as an empirical principle of human psychology) for the functioning of the mind. | |
| From: Stathis Psillos (Causation and Explanation [2002], §1.7) | |
| A reaction: This doesn't sound like a major problem. If it is, it is presumably impossible to analyse the mind, because a mind is presupposed in the process of analysis. |
| 4770 | Nothing is more usual than to apply to external bodies every internal sensation which they occasion [Psillos] |
| Full Idea: Nothing is more usual than to apply to external bodies every internal sensation which they occasion. | |
| From: Stathis Psillos (Causation and Explanation [2002], §1.8) | |
| A reaction: This is the core of Hume's is/ought claim - what he calls the mind 'spreading itself'. It is a powerful claim. Personally I think we have become TOO sceptical here, and have the delusion that crucial features of nature are created within our minds. |
| 7810 | The 'Eumenides' of Aeschylus shows blood feuds replaced by law [Aeschylus, by Grayling] |
| Full Idea: The 'Eumenides' of Aeschylus tells how the old rule of revenge and blood feud was replaced by a due process of law before a civil jury. | |
| From: report of Aeschylus (The Eumenides [c.458 BCE]) by A.C. Grayling - What is Good? Ch.2 | |
| A reaction: Compare Idea 1659, where this revolution is attributed to Protagoras (a little later than Aeschylus). I take the rule of law and of society to be above all the rule of reason, because the aim is calm objectivity instead of emotion. |
| 4399 | Causes clearly make a difference, are recipes for events, explain effects, and are evidence [Psillos] |
| Full Idea: The platitudes of causation are that 1) causes make a difference (counterfactually or probabilistically), 2) causes are recipes for events, 3) causes explain their effects, and 4) causes are evidence for effects. | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: A nice piece of analysis which offers some problems for anyone (like Russell) who wants to analyse causation completely out of our conceptual scheme. |
| 4400 | Theories of causation are based either on regularity, or on intrinsic relations of properties [Psillos] |
| Full Idea: While Humeans base their theories on the intuition of regularity, their opponents base theirs on the intuition that there is an intrinsic relation between the properties of two particular things involved (like a hammer and a vase). | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: I favour the intrinsic relation of properties view, but this leaves the question of whether we can explain a relation, apart from observing the regularities associated with the properties. |
| 4403 | We can't base our account of causation on explanation, because it is the wrong way round [Psillos] |
| Full Idea: We cannot distinguish between good and bad explanations of some phenomena, unless we first distinguish between causal and non-causal explanations. | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: This seems right, but it pushes us towards the idea that causation is non-analysable, and must be taken as a metaphysically basic axiom. If naturalistic accounts fail, that may be only alternative. |
| 4789 | Three divisions of causal theories: generalist/singularist, intrinsic/extrinsic, reductive/non-reductive [Psillos] |
| Full Idea: The three ways to divide theories on causation are: between generalist and singularist, between intrinsic and extrinsic characterisations of the causal relationship, and between reductive and non-reductive approaches. | |
| From: Stathis Psillos (Causation and Explanation [2002], §4.5) | |
| A reaction: Okay. I vote for singularist, intrinsic and reductive. I'm guessing that that pushes me towards Salmon and Dowe's theory of the 'transfer of conserved quantities', which is certainly reductive, doesn't need regularities in the events, and seems intrinsic. |
| 4790 | If causation is 'intrinsic' it depends entirely on the properties and relations of the cause and effect [Psillos] |
| Full Idea: If causation is taken to be an 'intrinsic' relation, then that c causes e will have to depend entirely on the properties of c and e, and the relations between c and e. | |
| From: Stathis Psillos (Causation and Explanation [2002], §4.5.2) | |
| A reaction: This view would move us towards 'essentialism', that the essences of objects produce the events and the laws, rather than external imposed forces and laws. |
| 4402 | Empiricists tried to reduce causation to explanation, which they reduced to logic-plus-a-law [Psillos] |
| Full Idea: The logical empiricists (esp. Hempel) analysed the concept of causation in terms of causal explanation, and analysed the latter as a species of deductive argument, with one premises stating a universal law (the so-called Deductive-Nomological model). | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: This feels wrong, as deduction seems insufficiently naturalistic, and the assumption of a law as premise seems to beg heaps of questions. |
| 4774 | Counterfactual claims about causation imply that it is more than just regular succession [Psillos] |
| Full Idea: If counterfactual claims can be made about causation, this suggests that there is more to it than mere regular succession. | |
| From: Stathis Psillos (Causation and Explanation [2002], §2.2) | |
| A reaction: Interesting. Even Hume makes counterfactual claims in his first definition of cause, and all claims of causation seem to go beyond the immediate evidence. |
| 4793 | "All gold cubes are smaller than one cubic mile" is a true universal generalisation, but not a law [Psillos] |
| Full Idea: The statement "all gold cubes are smaller than one cubic mile" seems to have all the features demanded of a lawlike statement, yet it can hardly be said to express a law. It is a merely true universal generalisation. | |
| From: Stathis Psillos (Causation and Explanation [2002], §5.3) | |
| A reaction: Nice example. A trickier case is "all cubes of uranium are smaller than one cubic mile", which sounds like part of a law. It suggests a blurred borderline between the two. How much gold is there in the universe? Is that fact a natural necessity? |
| 4397 | Regularity doesn't seem sufficient for causation [Psillos] |
| Full Idea: A rather important objection to Humeanism has been that regularity is not sufficient for causation. | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: Obviously a crucial problem, but the Humean view can defend itself by introducing other constant conjunctions. We don't observe events in isolation, but as part of a pattern of regularities. |
| 4792 | A Humean view of causation says it is regularities, and causal facts supervene on non-causal facts [Psillos] |
| Full Idea: The Humean view depends on the conjunction of two general theses: first, causation is tied to regularity; secondly, causal facts supervene on non-causal facts. | |
| From: Stathis Psillos (Causation and Explanation [2002], §4.5.4) | |
| A reaction: If causation is just regularities, this means it is patterns observed by us, which means causation doesn't actually exist. So Hume is wrong. Singular causation is possible, and needs explanation. |
| 4801 | The regularity of a cock's crow is used to predict dawn, even though it doesn't cause it [Psillos] |
| Full Idea: A regularity can be used to predict a future event irrespective of whether it is deemed causal or not. A farmer can predict that dawn has broken on hearing the cock's crow. | |
| From: Stathis Psillos (Causation and Explanation [2002], §8.1) | |
| A reaction: This seems a highly significant criticism of any view that says regularity leads to causation, which is the basis of induction, which leads to counterfactual claims, and thus arrives a the laws of nature. |
| 4401 | It is not a law of nature that all the coins in my pocket are euros, though it is a regularity [Psillos] |
| Full Idea: It is not a law of nature that all the coins in my pocket are euros, though it is a regularity. | |
| From: Stathis Psillos (Causation and Explanation [2002], Intro) | |
| A reaction: Good example, but it doesn't demolish the regularity view. We should come to conscious minds last. There aren't many other unfailing regularities that are not laws. |
| 4796 | Laws are sets of regularities within a simple and strong coherent system of wider regularities [Psillos] |
| Full Idea: In the 'web-of-laws' approach, laws are those regularities that are members of a coherent system of regularities, in particular, a system that can be represented as a deductive axiomatic system, striking a good balance between simplicity and strength. | |
| From: Stathis Psillos (Causation and Explanation [2002], §5.6) | |
| A reaction: Psillos attribute this view to Mill, Ramsey and Lewis. It is the obvious candidate for a fully developed Humean empiricist system, where regularities reinforce one another. I think laws are found in mechanisms, not in regularities, which are symptoms. |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |
| 4799 | Dispositional essentialism can't explain its key distinction between essential and non-essential properties [Psillos] |
| Full Idea: Many philosophers will find dispositional essentialism unappealing, not least because it seems to fail to explain how (and in virtue of what) there is this supposed fundamental distinction between essential and non-essential properties. | |
| From: Stathis Psillos (Causation and Explanation [2002]) | |
| A reaction: Maybe there is no precise definition, but any idiot can see that some properties of gold are essential (mass) and others non-essential (attractive to jackdaws). It's a fair question, but is this the strongest objection to essentialism? |
| 4780 | In some counterfactuals, the counterfactual event happens later than its consequent [Psillos] |
| Full Idea: In "had the acrobat jumped, there would have been a safety net" the antecedent of the counterfactual (the jumping) is temporally later than the consequent (the installation of the net). | |
| From: Stathis Psillos (Causation and Explanation [2002], §3.3) | |
| A reaction: This blocks anyone (e.g. David Lewis) who tries to define counterfactual claims entirely in terms of a condition followed by a consequence. Nice example. |
| 4791 | Counterfactual theories say causes make a difference - if c hadn't occurred, then e wouldn't occur [Psillos] |
| Full Idea: The counterfactual theory is a non-Humean relation between singular events; the thought is that causation makes a difference - to say that c causes e is to say that if c hadn't occurred, e wouldn't have occurred either. | |
| From: Stathis Psillos (Causation and Explanation [2002], §4.5.4) | |
| A reaction: Helpful. I'm beginning to think that this theory is wrong. It gives an account of how we see causation, and a test for it, but it says nothing about what causation actually is. |