OKASHA ON INDUCTIVE SCEPTICISM

B M L

In a recent paper replying to the inductive sceptic, Samir Okasha says that the Humean argument forinductive scepticism depends on mistakenly construing inductive reasoning as based on a principle ofthe uniformity of nature. I dispute Okasha’s argument that we are entitled to the background beliefson which (he says) inductive reasoning depends. Furthermore, I argue that the sorts of theoreticallyimpoverished contexts to which a uniformity-of-nature principle has traditionally been restricted areexactly the contexts relevant to the inductive sceptic’s argument, and (pace Okasha) are not at allremote from actual scientific practice. I discuss several scientific examples involving such contexts.

In a recent paper,1 Samir Okasha bravely offers a reply to the Humean argumentfor inductive scepticism. Unfortunately for all of us who reason inductively, the replyfails. The reasons for its failure are worthy of discussion.

I

The Humean argument, Okasha says, assumes that any inductive reasoning takesnature to be uniform – in other words, takes unexamined cases to be like examinedcases. The Humean argument then demonstrates that we are not entitled to thispremise: it does not follow deductively from our observations, and we would bereasoning in a circle if we used induction to justify it. Okasha’s initial move is topoint out that inductive arguments do not actually proceed by using a generalprinciple of the uniformity of nature (or any other ‘inductive rule’). Rather theydepend on ‘a vast store of background information’ (p. ). So to justify inductionwe do not need to justify some general principle of the uniformity of nature.

I agree that confirmation theory has come a long way from the models ofHempelian instance confirmation, Goodmanian projection of observed uniformitiesonto unexamined cases, Reichenbach’s straight rule, enumerative induction, and soforth. The Bayesian account leaves plenty of room for background knowledge, butassigns no special place to the belief that unexamined cases will be like examinedcases. Okasha contends that because there is no assumption about contingent

1 S. Okasha, ‘What Did Hume Really Show about Induction?’, The Philosophical Quarterly, (), pp. –.

The Philosophical Quarterly, Vol. , No. April ISSN –

© The Editors of The Philosophical Quarterly, . Published by Blackwell Publishers, Cowley Road, Oxford , UK, and Main Street, Malden, , USA.

features of the world which grounds all of our inductive inferences, there is no wayto construct a Humean argument for inductive scepticism: any such argumentwould have to show that we are not justified in believing some assumption aboutthe world which grounds all of our inductive inferences.

Of course we must not commit the fallacy of quantifier inversion: ‘There is awoman who at all times is pregnant’ is false, but ‘At all times there is a womanwho is pregnant’ may nevertheless be true. Likewise, although there is no singleuniformity-of-nature premise that grounds all inductive inferences, Okasha ap-parently admits that for each inductive inference there is some ‘background inform-ation’ which is needed to support it. In other words, Okasha accepts that one of thethings Hume has demonstrated about induction is that our observations alone,without being supplemented by further logically contingent premises, fail toprobabilify expectations regarding unexamined cases. But then why do these furtherpremises not make inductive inferences vulnerable to a Humean argument forinductive scepticism? That argument could proceed as follows. A given expectationwhich we hold regarding contingent features of unexamined cases is justified, in thelight of various observations we have made, only if we are justified in holding certainbackground beliefs regarding the world’s contingent features. That background in-formation does not follow deductively from our past observations. To use inductivearguments to support those background beliefs is merely to shift the original issue towhatever background beliefs ground these new inductive arguments.

Recognizing this ‘problem of the priors’ (p. ), Okasha argues (p. ) that re-liance upon background information stands less in need of justification than wouldreliance upon a uniformity-of-nature principle:

... all coherent prior probability distributions are equally arbitrary. This implies,obviously, that the actual prior distribution we start with cannot be shown to be‘better’ than any other. But this simply reflects the fact that there is an inevitablyconjectural element, and thus an element of uncertainty, in all empirical enquiry – ifthere were not, it would not be empirical.... Once we accept that the notion of a priordistribution which reflects a state of ignorance is chimerical, then adopting any parti-cular prior distribution does not constitute helping ourselves to empirical informationwhich should be suppressed; it simply reflects the fact that an element of guesswork isinvolved in all empirical enquiry.

Okasha’s argument seems to be that a prior state of opinion embodies no unjustifiedinformation about the world, since any prior opinion embodies some information.But the inductive sceptic should reply that since any prior opinion strong enough tosupport an inductive inference embodies some information, no prior opinion cap-able of supporting an inductive inference is justified.

In other words, Okasha’s argument seems to be that there are no objectivelyneutral priors, so if the inductive sceptic accuses our priors of being unjustified,

we need only ask the sceptic ‘What prior probability do you recommend?’ ... It doesnot beg the question to operate with some particular prior probability distribution ifthere is no alternative to doing so. Only if the inductive sceptic can show that there is

OKASHA ON INDUCTIVE SCEPTICISM

© The Editors of The Philosophical Quarterly,

an alternative, i.e., that ‘information-free’ priors do exist, would adopting someparticular prior distribution beg the question (p. ).

But there is an alternative to operating from a prior opinion strong enough tosupport inductive inferences – in other words, a prior that distributes subjectiveprobability over some claims that are neither logical truths nor logical falsehoods.The alternative is to operate from a prior distribution that embodies no opinionwhatsoever about the way in which the world happens to be arranged. Of coursesuch a prior opinion would not support inductive inferences from our observations.But that is precisely the inductive sceptic’s point. There is no alternative to operatingwith a prior distribution that embodies information about the world, as Okasha says,if we are going to carry out ampliative inferences from our observations. But topresuppose that we are justified in carrying out such inferences is obviously to begthe question against the inductive sceptic.

If the sceptic is asked to recommend a prior probability, he should suggest adistribution that makes no probability assignment at all to any claim about the worldwhich concerns logically contingent matters of fact. (By this, I do not mean theassignment of zero subjective probability to such a claim. That would be to assign it aprobability, namely, zero. Nor do I mean assigning it a vague probability value. Imean making no assignment at all to any such claim, unless we have directlyobserved it to hold.) As Okasha rightly emphasizes (pp. –), the sceptic is notmaking merely the boring point that induction is fallible. The point, rather, is thatregarding predictions about unobserved cases, there is no degree of confidence towhich we are entitled.

Of course I have not shown that there is no argument against the priorprobability distribution favoured by the inductive sceptic. But Okasha has not pro-vided one.

II

Okasha is certainly correct that many inductive inferences do not employ anythinglike a principle of the uniformity of nature. The Bayesian formalism deals neatlywith cases where ordinary background beliefs, rather than some such principle,underwrite ampliative reasoning from our observations, even with cases where thosebackground opinions lead us to regard instances of a generalization as disconfirmingthat generalization.2 However, what if there is no elaborate body of relevant back-ground knowledge to draw upon? In reply to the move made by Hempel, Salmonand others that a uniformity-of-nature principle is to be applied only in ‘theoreticallybarren contexts’, Okasha writes (p. ):

MARC LANGE

© The Editors of The Philosophical Quarterly,

2 For famous examples involving ships lost at sea, patrons checking their hats, andgrasshoppers outside Pitcairn Island, see respectively I.J. Good, ‘The White Shoe is a RedHerring’, British Journal for the Philosophy of Science, (), p. ; R.D. Rosencrantz,Foundations and Applications of Inductive Probability (Atascadero: Ridgeview, ), p. ; and R.G.Swinburne, ‘The Paradoxes of Confirmation – a Survey’, American Philosophical Quarterly, (), pp. –, at p. .

In my view we should be extremely wary of this Salmon–Hempel move. For onething, it is far from clear that the idea of informational neutrality, or of a ‘theoreticallybarren context’, is actually coherent. In any case, Salmon’s and Hempel’s admissionsthat their principles of induction and confirmation only apply from a hypotheticalepistemic starting-point, very different from the one in which we find ourselves in reallife, is an enormous concession. For this is little different from saying that we do notactually follow the principles in question at all.

This is a familiar criticism.3 I do not entirely agree with it.Admittedly, if in a ‘theoretically barren context’ we are supposed to have no

background beliefs at all regarding how the world happens to be, apart from whatwe have directly observed, then such a context is artificial indeed, and it is difficultto see how a ‘principle of the uniformity of nature’, restricted to such conditions,could have any relevance to actual scientific practice. (Nor is it easy to see how sucha principle, applied in such a context, could suffice to make any determinate recom-mendations, in view of the manifold ‘patterns’ which our observations simultaneouslydisplay but which diverge regarding unexamined cases.) However, a ‘theoreticallybarren context’ could simply be one in which scientists’ relevant background know-ledge is extremely impoverished, so sparse, in fact, that it is not at all evident howthey manage to be justified in suspecting that there exist certain sorts of uniformitiesamong all objects of some specified category. Yet apparently it is on the basis of thissuspicion that scientists justly regard their observations of some objects in thatcategory as bearing to a considerable degree upon unexamined cases.

Indeed, the history of science is filled with cases where scientists, despite oper-ating in contexts that were remarkably theoretically barren (in the latter sense), tookuniformities among their observations and justly projected them onto unexaminedcases. Here are three brief examples.

. In Henrietta Leavitt announced her discovery of , variable stars in theSmall Magellanic Cloud. By she had found of those variables on enoughphotographic plates to allow her to plot their light-curves. She remarked that intheir light-curves ‘ ... they resemble the variables found in globular clusters,diminishing slowly in brightness, remaining near minimum for the greater partof the time, and increasing very rapidly to a brief maximum’.4 She then noted a‘remarkable relation’ (p. ): the brighter the star, the longer its period betweenmaxima. She took this evidence ‘to warrant the drawing of general conclusions’(p. ). In Ejnar Hertzsprung took Leavitt’s evidence as justifying the applicationof her period–luminosity ‘law’ to the variables with light-curves of the shapeLeavitt described which had the best-determined motions relative to Earth. (Hetermed the variables with these light-curves ‘Cepheid’ variables, after the starδ Cephei, a well known example.) In , Harlow Shapley projected the period–luminosity law to all known ‘Cepheids’ in the Milky Way, and, most famously,

OKASHA ON INDUCTIVE SCEPTICISM

© The Editors of The Philosophical Quarterly,

3 For an early statement, see J.L. Mackie, ‘The Paradox of Confirmation’, British Journal forthe Philosophy of Science, (), pp. –, at p. .

4 H. Leavitt, ‘Periods of Variable Stars in the Small Magellanic Cloud’, Harvard CollegeObservatory Circular, (), pp. –, at p. .

Edwin Hubble in projected it to the Cepheids he found in the nebula M(which turned out to be the Andromeda galaxy). Yet there was little backgroundknowledge on which to ground these projections; it is difficult to see what evidencethere was that Cepheids in M, for example, were like the Milky Way Cepheids orthe ‘cluster variables’ to which Leavitt referred. (For example, there was no under-standing of the mechanism by which any of these stars varies in its brightness.) Ofcourse background knowledge of a minimal sort played its part. For example, astro-nomers knew the constellation boundaries to be wholly arbitrary, and so, inamassing evidence regarding Cepheids in the Andromeda nebula, astronomerswould have been unjustified in putting greater weight on some Cepheid in virtue ofits lying in the constellation Andromeda rather than in some other constellation.Nevertheless Hertzsprung’s, Shapley’s and Hubble’s inductions are typical of manymethods for determining celestial distances, in that they presuppose that there maywell exist uniformities in certain respects among objects of some specified category(stars, clusters, galaxies, etc.). But in such a theoretically impoverished context theredoes not seem to be sufficient background knowledge to justify suspecting such uni-formities to hold.

. Considering the relative distances of the known planets (Mercury, Venus,Earth, Mars, Jupiter, and Saturn) from the sun, Johann Daniel Titius proposed in that the mean orbital radius r of every planet, both discovered and as yetundiscovered, accords with the equation r = + × n, where the radius of Earth’sorbit is normalized to units and where n is negative infinity for Mercury and , ,, ... for succeeding planets. After William Herschel discovered Uranus in at adistance within % of Titius’ prediction, and following the discovery shortly there-after of the asteroids between Mars and Jupiter (taken as collectively bearing out theprediction of a planet at n = ), Titius’ proposal (often called ‘Bode’s Law’ after itsbetter known advocate, Johann Elert Bode) became widely accepted. For instance,after small discrepancies were discovered in the theoretical predictions of Uranus’motion, the gravitational influence of an undiscovered planet beyond Uranus wasposited as the source of this anomaly. Astronomers invoked the well confirmedTitius–Bode law in order to determine the posited planet’s mean distance from thesun; astronomers then used this parameter in calculating the planet’s orbit, andhence the direction in which they would have to point their telescopes in order toobserve the planet. Though planetary astronomy had an extensive theory derivedfrom Newtonian physics, this background did not supply the basis for Titius’ induc-tive projection.5

. Macroecology is concerned with understanding the division of food and spaceamong species at large spatial and temporal scales. Many hypotheses positinggeneral macroecological patterns have been confirmed on the basis of a few samples,despite the lack of any obvious theoretical backing for the suspicion that uniformitiesof these kinds exist. For instance, as long ago as the mid-s naturalists hadconcluded that biodiversity is greatest in the tropics and diminishes with increasinglatitude, and they had turned to the task of explaining this latitudinal gradient.

MARC LANGE

© The Editors of The Philosophical Quarterly,

5 For the fascinating history and current status of this ‘law’, see M. Nieto, The Titius–BodeLaw of Planetary Distances (Oxford: Pergamon, ).

Similarly, relationships between the mean local abundance, range size and body sizeof continental species have been investigated for many years without any significantcontribution from ecological theory, whether from bioenergetics, speciation andextinction theory, or from niche theory. The body of evidence for some patterns isremarkably sparse considering the confidence with which those patterns are asserted(as suggested by the efforts that have gone into explaining them). For example, thereexist fewer than published empirical studies of Rapoport’s rule, which posits anincrease in geographic range sizes towards higher latitudes, though the originalpaper on the subject has been cited more than times in journals alone.6 Suchcan be the power of uniformity presuppositions, even in the absence of anyelaborate theoretical framework behind them.7

Here we have a wide range of examples: from the olden days to current cutting-edge research; from cases like Leavitt’s, where the hypothesis has (to a considerableextent) stood the test of time, to cases like Titius’, where it has not; from astronomyto biology. It is difficult to see these grand inductions as capable of being under-written entirely by the very meagre background knowledge which had already beenascertained empirically – unless fairly minimal empirical work can somehow warrantscientists in suspecting the existence of a certain sort of uniformity in nature, andthey are entitled to be guided by this suspicion in the absence of anything better.Without some such default, it is difficult to see how these scientists’ high degree ofconfidence in their conclusions could possibly be justified by the scant evidence theyhad available.

To understand how scientists (in cases like the three I have just given) could bejustified in arriving at their grand conclusions, despite their theoretically impover-ished contexts, was surely a crucial part of the task of justifying induction accordingto those philosophers who invoked a principle of the uniformity of nature. ThusKeynes remarked on this point

Apart from analysis, careful reflection would hardly lead us to expect that a con-clusion which is based on no other than grounds of pure induction, defined as I havedefined them as consisting of repetition of instances merely, could attain in this way toa high degree of probability.... When, therefore, our previous knowledge is consider-able and the analogy is good, the purely inductive part of the argument may take avery subsidiary place. But when our knowledge of the instances is slight, we may haveto depend upon pure induction a good deal. In an advanced science it is a last resort –the least satisfactory of the methods. But sometimes it must be our first resort, themethod upon which we must depend in the dawn of knowledge and in fundamentalenquiries where we must presuppose nothing.8

This is the context not only in the three examples I have just given, but also (ofcourse) whenever we are responding to the challenge of the inductive sceptic, sincein so far as we appeal to background knowledge of contingent facts, the sceptic will

OKASHA ON INDUCTIVE SCEPTICISM

© The Editors of The Philosophical Quarterly,

6 See K.J. Gaston, T.M. Blackburn and J.I. Spicer, ‘Rapoport’s Rule: Time for anEpitaph?’, Trends in Ecology and Evolution, (), pp. –.

7 For more, see J.H. Brown, Macroecology (Univ. of Chicago Press, ).8 J.M. Keynes, A Treatise on Probability (London: Macmillan, ), pp. –.

rightly accuse us of begging the question. The sceptic will push the regress everfurther back, demanding the warrant for whatever background knowledge we in-voke, until we reach an extremely impoverished background.

I conclude that to justify induction, we must understand precisely how scientistsin theoretically impoverished contexts nevertheless manage to become entitled tosuspect the existence of various sorts of grand uniformities in nature. This does notmean that there must be some general principle of the uniformity of nature, havingits own special justification, and sufficing to underwrite all inductive inferencescarried out in theoretically barren contexts. Rather it may well be that differentbeliefs underwrite the three inductions I have mentioned. Of course we could termthese ‘background beliefs’. But to do so would suggest that there is no particularmystery to how these beliefs come to be justified – that their warrant is just asevident as the warrant for various background beliefs held in theoretically muchricher contexts. Surely that is mistaken.

Even if there is no special principle of inductive reasoning which applies only intheoretically barren contexts, we must give some fuller account of how, for instance,stellar astronomers were entitled to suspect certain sorts of uniformities among allCepheid variables, despite knowing so little about variable stars. It almost seems as ifit took less empirical work for stellar astronomers a century ago to justify suspectingthat certain conditions in the Andromeda nebula are like those around here than itwould take for me to justify believing that my neighbour’s dog has fleas. To explainwhy, it clearly does not suffice merely to gesture towards ‘background knowledge’.How to explain the epistemic accessibility of these grand uniformities remains amystery to me.

University of Washington, Seattle

MARC LANGE

© The Editors of The Philosophical Quarterly,