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14. Science / C. Induction / 3. Limits of Induction

[why induction cannot justify generalised truths]

32 ideas
We say 'so in cases of this kind', but how do you decide what is 'of this kind'? [Aristotle]
     Full Idea: When it is necessary to establish the universal, people use the expression 'So in all cases of this kind'; but it is one of the most difficult tasks to define which of the terms proposed are 'of this kind' and which are not.
     From: Aristotle (Topics [c.331 BCE], 157a25)
     A reaction: It is particularly hard if induction is expressed as the search for universals, since the kind presumably is the universal, so the universal must be known before the induction can apply, which really is the most frightful nuisance for truth-seekers.
From the fact that some men die, we cannot infer that they all do [Philodemus]
     Full Idea: There is no necessary inference, from the fact that men familiar to us die when pierced through the heart, that all men do.
     From: Philodemus (On Signs (damaged) [c.50 BCE], 1.3)
     A reaction: This is scepticism about the logic of induction, long before David Hume. This is said to be a Stoic argument against Epicureans - though on the whole Stoics are not keen on scepticism.
If you don't view every particular, you may miss the one which disproves your universal induction [Sext.Empiricus]
     Full Idea: Induction cannot establish the universal by means of the particular, since limited particulars may omit crucial examples which disprove the universal, and infinite particulars are impossible to know.
     From: Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.204)
The instances confirming a general truth are never enough to establish its necessity [Leibniz]
     Full Idea: All the instances which confirm a general truth, however numerous they may be, are not sufficient to establish the universal necessity of this same truth.
     From: Gottfried Leibniz (New Essays on Human Understanding [1704], Pref)
     A reaction: This is Leibniz's standardly rationalist view of induction. We can either say that induction is therefore inadequate, or (a better option) that there isn't much evidence for claims of necessity, and they must be treated with caution.
Reason cannot show why reliable past experience should extend to future times and remote places [Hume]
     Full Idea: The main question on which I would insist is why reliable past experience should be extended to future times, and to other objects, which for ought we know, may be only in appearance similar. …No reasoning can show this.
     From: David Hume (Enquiry Conc Human Understanding [1748], IV.II.30)
Induction can't prove that the future will be like the past, since induction assumes this [Hume]
     Full Idea: It is impossible that any arguments from experience can prove the resemblance of the past to the future, since all these arguments are founded on the supposition of this resemblance.
     From: David Hume (Enquiry Conc Human Understanding [1748], IV.II.32)
Fools, children and animals all learn from experience [Hume]
     Full Idea: It is certain that the most ignorant and stupid peasants - nay infants, nay even brute beasts - improve by experience.
     From: David Hume (Enquiry Conc Human Understanding [1748], IV.II.33)
If we infer causes from repetition, this explains why we infer from a thousand objects what we couldn't infer from one [Hume]
     Full Idea: If after the constant conjunction of two objects (e.g. heat and flame) we are determined by custom alone to expect the one from the appearance of the other,this explains why we can draw an inference from a thousand objects which we couldn't draw from one.
     From: David Hume (Enquiry Conc Human Understanding [1748], V.I.36)
     A reaction: This is Hume's best statement of the problem of the difficulty of demonstration the logic of induction.
All inferences from experience are effects of custom, not reasoning [Hume]
     Full Idea: All inferences from experience are effects of custom, not reasoning.
     From: David Hume (Enquiry Conc Human Understanding [1748], V.I.36)
How does induction get started? [Peirce]
     Full Idea: Induction can never make a first suggestion.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: This seems to lead to the general modern problem of the 'theory-laden' nature of observation. You don't see anything at all without some idea of what you are looking for. How do you spot the 'next instance'. Instance of what? Nice.
Induction can never prove that laws have no exceptions [Peirce]
     Full Idea: Induction can never afford the slightest reason to think that a law is without an exception.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: Part of the general Humean doubts about induction, but very precisely stated, and undeniable. You can then give up on universal laws, or look for deeper reasons to justify your conviction that there are no exceptions. E.g. observe mass, or Higgs Boson.
The worst fallacy in induction is generalising one recondite property from a sample [Peirce]
     Full Idea: The most dangerous fallacy of inductive reasoning consists in examining a sample, finding some recondite property in it, and concluding at once that it belongs to the whole collection.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V)
     A reaction: The point, I take it, is not that you infer that the whole collection has all the properties of the sample, but that some 'recondite' or unusual property is sufficiently unusual to be treated as general.
We can't know if the laws of nature are stable, but we must postulate it or assume it [James]
     Full Idea: That nature will follow tomorrow the same laws that she follows today is a truth which no man can know; but in the interests of cognition as well as of action we must postulate or assume it.
     From: William James (The Sentiment of Rationality [1882], p.39)
     A reaction: The stability of nature is something to be assessed, not something taken for granted. If you arrive in a new city and it all seems quiet, you keep your fingers crossed and treat it as stable. But revolution or coup could be just round the corner.
Chickens are not very good at induction, and are surprised when their feeder wrings their neck [Russell]
     Full Idea: The man who has fed his chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.
     From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6)
     A reaction: A justly famous illustration of Hume's problem of induction, that a vast amount of evidence could still support a false conclusion. If we say 'the future will be like the past', this depends on understanding what was happening in the past.
It doesn't follow that because the future has always resembled the past, that it always will [Russell]
     Full Idea: We have experience of past futures, but not of future futures, and the question is: Will future futures resemble past futures? This question is not to be answered by an argument which starts from past futures alone.
     From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6)
     A reaction: This nicely makes the problem of induction unavoidable, for anyone who preferred not to face the problem. The simple solution is to recognise that the future may NOT resemble the past, for all we know. Actually I think it will, but what was the past like?
We can't prove induction from experience without begging the question [Russell]
     Full Idea: We can never use experience to prove the inductive principle without begging the question.
     From: Bertrand Russell (Problems of Philosophy [1912], Ch. 6)
     A reaction: This highlights why induction is such a big problem for hard-line empiricists, who are reduced to saying that it is a 'dogma', or an unsupported 'natural belief'. And that seems right. All creatures which evolve in a stable universe will do induction.
We can't use the uniformity of nature to prove induction, as that would be circular [Ayer]
     Full Idea: It is often said that we can justify induction by invoking the uniformity of nature, but that principle merely states (in a misleading fashion) the assumption that past experience is a reliable guide to the future.
     From: A.J. Ayer (Language,Truth and Logic [1936], Ch.2)
     A reaction: That is correct, but it seems to me that if you take the uniformity of nature as a provisional unproven axiom, then induction is an account of how rational creatures cope with the situation. If nature ceases to be uniform, our reason cannot cope.
There is no such thing as induction [Popper, by Magee]
     Full Idea: According to Popper, induction is a dispensable concept, a myth. It does not exist. There is no such thing.
     From: report of Karl Popper (The Logic of Scientific Discovery [1934]) by Bryan Magee - Popper Ch.2
     A reaction: This is a nice bold summary of the Popper view - that falsification is the underlying rational activity which we mistakenly think is verification by repeated observations. Put like this, Popper seems to be wrong. We obviously learn from experiences.
Induction aims at 'all Fs', but abduction aims at hidden or theoretical entities [Armstrong]
     Full Idea: Many philosophers of science have distinguished between 'simple induction' - the argument from observed Fs to all Fs - and the argument to hidden or theoretical entities (Peirce's 'abduction').
     From: David M. Armstrong (What is a Law of Nature? [1983], 06.7)
     A reaction: 'Abduction' is (roughly) the same is inference to the best explanation, of which I am a great fan.
If events are unconnected, then induction cannot be solved [Ellis]
     Full Idea: If one believes, as Hume did, that all events are loose and separate, then the problem of induction is probably insoluble.
     From: Brian Ellis (Scientific Essentialism [2001], 8.09)
     A reaction: This points to the essentialist solution of induction - that we can genuinely derive inductive truths if we can inductively identify the essences which give rise to the necessities of further cases. I take that to be a correct account.
Induction is 'defeasible', since additional information can invalidate it [Harman]
     Full Idea: It is sometimes said that inductive reasoning is 'defeasible', meaning that considerations that support a given conclusion can be defeated by additional information.
     From: Gilbert Harman (Rationality [1995], 1.4.5)
     A reaction: True. The point is that being defeasible does not prevent such thinking from being rational. The rational part of it is to acknowledge that your conclusion is defeasible.
Conjunctions explain nothing, and so do not give a reason for confidence in inductions [Harré/Madden]
     Full Idea: 'Going together' is irrelevant as an explanation, and that is precisely why it is useless as a reason for having confidence in inductive inferences.
     From: Harré,R./Madden,E.H. (Causal Powers [1975], 4.I)
     A reaction: I suspect that the deep underlying question is whether the actual world has modal features - that is, are dispositions, rather than mere categorical properties, a feature of the actual. Is this room full of possibilities? Yes, say I.
Hume's atomic events makes properties independent, and leads to problems with induction [Harré/Madden]
     Full Idea: The atomicity of Humean events ensures the sequential independence of properties, ...and this in turn leads to the Humean problem of induction.
     From: Harré,R./Madden,E.H. (Causal Powers [1975], 6.IV)
     A reaction: This strikes me as pretty good analysis of what has gone wrong with the Humean account. As far as I can see, the 'problem' of induction just doesn't occur in scientific essentialism.
Standard induction does not allow for vertical inferences, to some unobservable lower level [Lipton]
     Full Idea: One of the problems of the extrapolation and instantial models of confirmation is that they do not cover vertical inferences, where we infer from what we observe to something at a different level that is often unobservable.
     From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 04 'Attractions')
     A reaction: This is my preferred essentialist view of induction, that we don't just infer that future swans will be white, but also that whiteness is built into the biology of swans. There seems to be predictive induction and explanatory induction.
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
     Full Idea: The claim that no number is greater than a million is confirmed by the first million test cases.
     From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Intro')
     A reaction: Extrapolate from this, and you can have as large a number of cases as you could possibly think of failing to do the inductive job. Love it! Induction isn't about accumulations of cases. It is about explanation, which is about essence. Yes!
Children overestimate the power of a single example [Gelman]
     Full Idea: We suggest that children overestimate the power of a single example.
     From: Susan A. Gelman (The Essential Child [2003], 06 'The role')
     A reaction: This conclusion arises from extensive psychological research. 'My grandma smoked, and she lived to be 97' - adults do this too. Wittgenstein says assuming other minds because of your own is induction from one example!
Children make errors in induction by focusing too much on categories [Gelman]
     Full Idea: Because of their narrow focus, children's sensitivity to categories as the basis of induction is a reasoning bias that, though useful much of the time, results in systematic errors.
     From: Susan A. Gelman (The Essential Child [2003], 06 'The role')
     A reaction: This is the bad sense of 'essentialism' which worries its opponents. Presumably, though, my favoured scientific essentialism will be 'scientific', and avoid this problem. The relation between categories and induction needs to be clear.
If Hume is right about induction, there is no scientific knowledge [Bird]
     Full Idea: If Hume is right about induction then there is no scientific knowledge.
     From: Alexander Bird (Philosophy of Science [1998], Ch.5)
     A reaction: The first step is to recognise that induction is not deductively valid, but that does not make it irrational. If something happens five times, get ready for the sixth. If we discover the necessary features of nature, we can predict the future.
Anything justifying inferences from observed to unobserved must itself do that [Bird]
     Full Idea: Whatever could do the job of justifying an inference from the observed to the unobserved must itself be an inference from the observed to the unobserved.
     From: Alexander Bird (Philosophy of Science [1998], Ch.5)
     A reaction: We must first accept that the unobserved might not be like the observed, no matter how much regularity we have, so it can't possibly be a logical 'inference'. Essences generate regularities, but non-essences may not.
Hume's question is whether experimental science will still be valid tomorrow [Meillassoux]
     Full Idea: Hume's question can be formulated as follows: can we demonstrate that the experimental science which is possible today will still be possible tomorrow?
     From: Quentin Meillassoux (After Finitude; the necessity of contingency [2006], 4)
     A reaction: Could there be deep universal changes going on in nature which science could never, even in principle, detect?
Maybe induction is only reliable IF reality is stable [Mitchell,A]
     Full Idea: Maybe we should say that IF regularities are stable, only then is induction a reliable procedure.
     From: Alistair Mitchell (talk [2006]), quoted by PG - Db (ideas)
     A reaction: This seems to me a very good proposal. In a wildly unpredictable reality, it is hard to see how anyone could learn from experience, or do any reasoning about the future. Natural stability is the axiom on which induction is built.
Nature is not completely uniform, and some regular causes sometimes fail to produce their effects [Mumford/Anjum]
     Full Idea: The uniformity of nature principle, if it means absolute regularity, is simply false; not everyone who smokes gets cancer, not all bread nourishes. Nature is not strictly uniform, even if some things tend to be the case.
     From: S.Mumford/R.Lill Anjum (Getting Causes from Powers [2011], 6.6)
     A reaction: Something wrong here. The examples are high-level and complex. When someone survives smoking, or bread fails to nourish, we don't infer a disruption of uniform nature, we infer some other uniformity that has intervened. Are there natural kinds?