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Page 1: Hume's Sceptical Argument Against Reason

Hume's Sceptical Argument Against Reason

Fred Wilson

Hume Studies, Volume 9, Number 2, November 1983, pp. 90-129 (Article)

Published by Hume SocietyDOI: 10.1353/hms.2011.0551

For additional information about this article

Access provided by University of Arizona (23 Aug 2013 12:21 GMT)

http://muse.jhu.edu/journals/hms/summary/v009/9.2.wilson.html

Page 2: Hume's Sceptical Argument Against Reason

HUME'S SCEPTICAL ARGUMENT AGAINST REASON

In the section of the Treatise entitled Of

scepticism with regard to reason Kume considers the mindas reflecting upon its own activities, monitors them asit were, and then adjusts them in accordance withcertain principles and strategies. ^ What it discoversis that in drawing inferences, the mind sometimeserrs. In the light of this knowledge, and in accord-ance with rational principles of epistemic probabili-ties, it adjusts its response to any inference it makesfrom one of certainty to one with epistemic probabilityof a degree somewhat less than certainty. But thisrational adjustment is itself the consequence of aninference, which will be subject to the same qualifi-cations. By repeating this process, it seems that allcertainty reduces to probability and all probability tozero.

Hume's argument begins this way:Our reason must be consider 'd as a kind ofcause, of which truth is the natural effect;but such-a-one as by _ the irruption of othercauses, and by the inconstancy of our mentalpowers, may frequently be prevented. By thismeans all knowledge degenerates into proba-bility; and this probability is greater orless, according to our experience of theveracity or deceitfulness of our understanding,and according to the simplicity or intricacy ofthe question. 2

It is important to be clear on the logical structure ofthis argument. Consider an actual case of inference.This produces a state of belief or affirmation. Humedoes not say that the inference does not produce truth,i.e. , a true belief. But there is the possibility itdoes not. Nor is this a mere logical possibility. Onecan form the hypothesis about causes that this processof reasoning was in fact one which introduced an

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element of error. One does not know that this hypoth-esis is true. But one does know that there is a cer-

tain probability that this causal hypothesis is true;as Hume puts it, it may frequently be true. Knowingthat we have reasoned poorly sometimes (though notalways) in the past, the hypothesis that we have onthis occasion reasoned poorly has a certain probabil-ity, and we know this even though we have not verifiedthe hypothesis for this particular occasion. On thebasis of this unverified but nonetheless somewhat

probable causal hypothesis we must as a matter ofreason reduce the probability we attach to the beliefor affirmation that was produced by the originalinference. This reduction of probability is itself amatter of reasoning, however. Therefore about it,also, one can form the hypothesis that it is erroneous,and that the probability of the original affirmationwas not reduced sufficiently. On the basis of this newhypothesis we must as a matter of reason reduce stillfurther the probability of the first affirmation. Andso on: as I reflect upon my use of reason, all the rulesof logic require a continual diminution, and at last a totalextinction of belief and evidence. (T183) The result here

of the mind applying to its own activities what itdiscovers about itself is its ceasing to make anycausal inferences. Feedback here yields the attitudeof total scepticism, in the sense of rendering itreasonable that one ought totally to suspend judgment.

To be sure, Hume does hold that no one is infact such a total sceptic:

Nature, by an absolute and uncontroulablenecessity has determin 'd us to judge as wellas to breathe and feel; nor can we any moreforbear viewing certain objects in a strongerand fuller light, upon account of theircustomary connexion with a present impres-sion, than we can hinder ourselves fromthinking as long as we are awake, or see the

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surrounding bodies, when we turn cur eyestowards them in broad sunshine. (T183)

Inferences from sample to population cannot but befallible, and this is the best we can do, given thelogical gap between sample and population.Theargument for scepticism with regard to reason concludesnot only that such inferences are fallible, that theymay be wrong, but more strongly that we have thestrongest of reasons for supposing that they are wrong.This is, of course, incompatible with the point Humemakes earlier in the Treatise, when he includes thesection on the Rules by which to judge of causes andeffects, that we can have good (though not infallible)reasons for supposing that certain inferences that maybe wrong are in fact not wrong. Indeed, in the argu-ment we are now looking at Hume seems to be arguingagainst his earlier discussion. This is, of course,not true. As Hume makes clear, his intention is quiteotherwise·.

My intention then in displaying so carefullythe arguments of that fantastic sect [that is,the total sceptics] , is only to make the readersensible of the truth of my hypothesis, thatall our reasonings concerning causes andeffects are deriv 'd from nothing but custom;and that belief is more properly an act of thesensitive, than of the cogitative part of ournatures. (T183)

which means that he must also intend to show how, uponhis principles, the reasoning which leads to the totalextinction of belief and evidence must at some point turnout to be bad reasoning, or, more accurately, to be aform of reasoning it is not rational to pursue. Thereare two questions.The first is:how, psycho-logically, is it possible that reason's extinction ofbelief and evidence cannot be maintained? And the second

is:are the beliefs that destroy this extinction ofbelief and evidence reasonable beliefs?As for the

first, Hume's account is perfectly straight-forward.

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The process of reasoning by which belief and evidenceare extinguished require a high degree of attention. Anew impression then strikes us. This shifts ourattention. Custom has established an association such

that this impression is associated with other ideas.Given Hume's account of causation, this association is,of course, a causal belief. This association is, as amatter of psychological fact, sufficiently strong as toovercome the long train of reasonings designed toattenuate its strength. As for the second question,what it amounts to is whether the conqueringassociation is justified by the long chain ofreasonings. To this second question, the receivedopinion is - that Hume's inference is quite obviouslyerroneous. What I hope to establish is that thisreceived opinion is wrong.

In Part I, I attempt to lay out clearly thelogic of the probabilistic causal reasoning that Humerelies upon in his discussion. In particular,reference will be made to what Hume says elsewhere inthe Treatise about probabilistic causal reasoning. InPart II, I shall look briefly at two versions of thereceived opinion, and conclude that they go no waytowards refuting Hume's argument. Finally, in PartIII, I shall propose a reconstruction of Hume'sargument that, one, is faithful to what Hume says,- two,given certain reasonable assumptions, is probabistic-ally sound, i.e. , the probability does tend to zero;and three, while not explicitly Hume, is historicallyplausible.

If I succeed in showing these things, then Ishall not have shown that Hume's argument that allreasoning is weak is a cogent argument. All I shallhave shown is that Hume's argument is stronger than isgranted by the received opinion. But that willestablish that Hume, on this point at least, is a

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better philosopher than received opinion, allows,and,moreover, that the argument he advances to castdoubton reason is one that is worth refuting. Boththeseconclusions are worth defending.

Part I: Hume's Argument for the Destruction of ReasonIn the argument against reason, Hume is

explicit in taking an inference, that is, an act ofinferring, to be a case of authority, something thattestifies to the truth of the conclusion inferred:

'Tis certain a man of solid sense and longexperience ought to have, and usually has, agreater assurance in his opinions, than onethat is foolish and ignorant, and that oursentiments have different degrees of authority,even with ourselves, in proportion to thedegrees of our reason and experience. In theman of the best sense and longest experience,this authority is never entire; since evensuch-a-one must be conscious of many errors inthe past, and must still dread the like for thefuture.Here then arises a new species ofprobability to correct and regulate the first,and fix its just standard and proportion. Asdemonstration is subject to the controul ofprobability, so is probability liable to anewcorrection by a reflex act of the mind, whereinthe nature of our understanding, and ourreasoning from the first probability become ourobjects. (T182, italics added)

Hume is not alone in making this analogy. Sextus, forone, recognizes that proof, or an argument qua actuallyused, is a kind of sign or testimony to the truth ofwhat is to be proved. But in any case, the analogy isthere, and once it is recognized then one can apply toit the reasoning concerning chains of testimony thatleads to the conclusion that the longer the chain thenthe lower the probability of what is testified to.

Now testimony is explicitly discussed elsewhereby Hume, most notably in his essay Of Miracles. 5 Thecrucial point about testimony is that as a rule

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whenever someone testifies that S_ then S_. But let usspell it out in detail.

We can say that a person a is a truth-testif ierwith respect to sentences £ of a set S_ just in casethat:

(1)(s][s£S:(s is true = s_ is testified to by a) ]where, to say that ¿ is testified to by a is to say,among other things, that if a_ is asked about ^ then aasserts s_. As for the set S, this might be, forexample, sentences the truth-value of which iscalculated by a according to rules of arithmetic, orsentences stating what a_ himself has witnessed, orsentences that ¿ has heard from an accepted authority.In any case-, however, S_ must consist of sentences towhich a^ has some special relation; otherwise, the "ifand only if of (1) would not work. Thus, to say that:

1 £ áis to say something like:

aRs

so that (1) is the law:

(2)(s) [aRs D (S^ is true = £ is testified to by a) ]If we restrict the range of the variable to theappropriate s_ in S_, then (2) may be written more simplyas:

(3)(.§_)[.§ is true = s_ is testified to by a]However, (3) does not capture the idea that it .is onlyas a rule and not invariably that testimony is true.Sometimes even the best of truth-testif iers will mis-

calculate, or mis-observe, or mis-hear, or there willbe a slip in his memory, and so on. Every mind isafflicted with what Hume would call the infirmities of

reason. (3) is thus only conditionally true, holdingonly when certain conditions are present, or, whatamounts to the same, when the infirmities of reason areabsent: in order to infer the truth of a sentence s_ towhich a truth-testif ier a testifies, we must assume

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that in respect to x_ the infirmities of reason do no-afflict a_. Let:

sCa

represent that in respect to s_ the infirmities ofreason do not afflict a_. This means that the law wewant is not (3) but rather:

(4)(^) [£> is true = £> is testified to by a_) = sCa]or, to put it briefly:(41) (F = H) = G

The relative frequency of ^' s that are G will, by (4 1) ,be the relative frequency that jà's are such that F_ = Hobtains with respect to them. In order to find therelative frequency that F_ = B obtains in i>'s, we take asample of S_'s that are H, and note the percentage ofthese that are F_. This percentage can then be used asan estimate of the probability for S_'s that an S thatis H_ is also F. But for s to be H is for a_ to testifyto s_ and for s to be F is for s_ to be true. Kence,this probability is the probability, when a testifiesto something, that what he testifies to is the case.And in turn, this probability that an authority istestifying truly is the amount to which we mustdiminish the degree of certainty with which we affirm asentence when that sentence is testified to by thatauthority.

As for when the authority testifies to thetruth of s_ and s_ is false, then we can "explain away"that failure by citing the presence in this case ofcertain infirmities of reason. If a_ testifies to thetruth of a sentence s and s is false, then we have:(5)s is B

and:

(6)£. is F1 ?From these and (4 ) one can infer that:

(7)S1 is G

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that states that the infirmities of reason are presentin a_ with respect to s . Wepost facto using the argument:

T= (4 1JC = (5) & (7)

in a_ with respect to s . We can now explain (6) ex_ng the

T= (4 1J

E = (6)

We have positive evidence that tends to confirm8

(4). Upon the basis of (4), we can predict thepresence of F_ (truth) on the basis of H (testimony),provided that G is present (infirmities of reason areabsent). However, often it is difficult to discover

gwhether G is in fact present or absent. On someoccasions we can have excellent reasons for inferringthe absence of G, even if that fact cannot be verifiedby observation. This is so in the case of miracles.Here the evidence is so overwhelming that F (truth) isabsent that that we may reasonably infer on the basisof (4) that G is absent, the infirmities of reasonpresent. In other cases, however, we may have noindependent grounds either for affirming or denying thepresence of £. It is under just those conditions thatwe wish to affirm the presence of F_ simply bypredicting it using (4), and the fact of H oftestimony. This inference is not possible unless weknow something about whether G is present or absent.The basis on which to proceed is to attempt to estimatethe frequency with which H' e are F's. If the frequencyof F_'s in H is such and such then, with a certaintydiminished to that amount we may, upon the basis oftestimony, affirm that which is testified to.

Hume discusses this general pattern ofreasoning in the Treatise in the section Of theprobability of causes.Hume considers cases where thesame apparent cause has, at different times, contraryeffects. (T132) For example, my watch works well in

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general and as a rule, but sometimes it does not goright. Or, an authority will in general and as a rulespeak the truth, but sometimes it does not. A peasantwill attribute the stopping of the watch to chance.The artizan, in contrast, guided by the principle thatsame causes have the same effects and different effects

have different causes (Hume's fourth rule by which tojudge of causes and effects) (T173)

easily perceives, that the same force in thespring or pendulum has always the sameinfluence on the wheels; but fails of its usualeffect, perhaps by reason of a grain of dust,which puts a stop to the whole movement.(T132)

The artizan thus uses his causal principles to form thereasonable existential hypothesis that there is ahidden, imperceptible, cause which, when present,accounts for why the mechanism has an effect contraryto its usual effect. Often enough, the artizan'shypothesis will prove correct: he will find the speckof dust, thus confirming his existential hypothesis,and will then remove it to restore the watch to its

normal state. Philosophers generalize from this sortof case:

. . .philosophers observing, that almost in everypart of nature there is contain'd a vastvariety of springs and principles, which arehid,by reason of their minuteness orremoteness, find that 'tis at least possible thecontrariety of events may not proceed from anycontingency in the cause, but from the secretoperation of contrary causes. . . . From theobservation of several parallel instances [thatis,parallel to the watchmaker'sdiscovering the dust that is jamming thewatch mechanism], philosophers form a maxim,that the connexion betwixt all causes andeffects is equally necessary, and that itsseeming uncertainty in some instances proceedsfrom the secret operation of contrary causes. *¦

Thus, since an authority (H) will sometimes yieldcontrary effects, that is, sometimes telling the truth

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(F_) and sometimes not, we can hypothesize a cause (G_)the absence of which is a sufficient condition for the

authority to be speaking the truth.Hume also introduces probabilities into this

context. He has already considered the probabilitiesof chances. (TI, III, XI) Take the case of a man lookingat a die in a box and about to be thrown. This man

concludes that the figure that appears on the mostsides is the most probable. Such a one in a mannerbelieves, that this will lie uppermost; tho' still withhesitation and doubt, in proportion to the number of chances,which are contrary___ (T127) The crucial point in thisman's reasoning is that in the causes (gravity,solidity, a cubical figure, etc.) that determine thedie to fall there is nothing to fix the particular side, eachof which is suppos'd contingent. (T128) Hume is thusadopting the classical definition of 'probability'based on a principle of indifference: chance arisesfrom ignorance of causes, and chances or probabilitiesare equal when our knowledge is indifferent betweenwhich of the several exhaustive and mutually exclusivealternative effects will occur. There are manyproblems with a theory of probability based upon a

1 2principle of indifference. But Hume is at least incompany as good as that of Leibniz and Laplace when headopts this account of probability. Even so, Humewants to insist that judgments of indifference or equalinitial probabilities must be based upon experience.This connects his account most closely to that of thefrequency theorists like von Mises than it does to suchcontemporary exponents of the principle of indifferenceas in Carnap: -4

...tho' chance and causation be directlycontrary, yet 'tis impossible for us to conceivethis combination of chances, which is requisiteto render one hazard superior to another,without supposing a mixture of causes amongthe chances, and a conjunction of necessity in

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some particulars, with a total indifference inothers.1,'here nothing limits the chances,every notion, that the most extravagant fancycan form, is upon a footing of equality ; norcan there be any circumstances to give one theadvantage above another.Thus unless weallow, that there are some causes to make thedice fall, and preserve their form in theirfall, and lie upon some one of their sides, wecan form no calculation concerning the laws ofhazard. (T125-6)

Probability defined in terms of chance providesthe model for estimating the probability that a givencause will have a certain sort of effect when, underthe influence of certain hidden factors, it tends toproduce contrary effects.The same basic principlethat governs causal inference in general applies here:

Tis evident, that when an object is attendedwith contrary effects, we judge of them only byour past experience, and aZvays consider thoseas possible, which we have observ'd to followfrom it. And as past experience regulates ourjudgment concerning the possibility of theseeffects, so it does that concerning theirprobability; and that effect, which has beenthe most common, we always esteem the mostlikely. (T133)

As for the role of probability, what Hume has said inthe context of chance applies equally here: Every pastexperiment may be consider 'd as a kind of chance; it beinguncertain to us, whether the object will exist conformable toone experiment or another: And for this reason every thingthat has been said on the one subject is applicable to both.(T135) But it is always in conformity with the generalcausal principle of "same cause, same effect":

Thus upon the whole, contrary experimentsproduce an imperfect belief,either byweakening the habit, or by dividing andafterwards joining in different parts, thatperfect habit, which makes us conclude ingeneral, that instances, of which we have noexperience, must necessarily resemòie thosewhich we have. (T135)

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We may summarize Hume's account of scepticismwith regard to reason. On this account what the totalsceptic does is apply certain lawful facts abouttestimony to his own reason taken as testifying to thetruth of the conclusions it affirms. What then beginsto happen is just what happens with respect to hearsayin contrast to direct testimony.· the greater thenumber of steps it is from what is to be affirmed theless is the degree of certainty with which thataffirmation can be made. The degree of certainty tendsto diminish towards zero: all "evidence and belief" is

extinguished. But not even this can be affirmed withcertainty. For one has arrived at this conclusion bycases of reasoning, and reason may apply the same sortof reasoning to these cases. In this way, the beliefswhich constitute the very foundation of the reasoningwhich "extinguishes" all "evidence and belief" arethemselves extinguished. All reasoning is undermined.All reasoning is weak including the reasoning that allreasoning is weak.

Part II: Two Critics of Hume

In order to defend Hume's argument as strong,if not sound, it will be necessary to establish thecogency of the probabilistic reasoning that he uses.Before turning to this task, however, it will pay, Ithink, to show that we can already see that defendersof the received opinion, that Hume's argument isworthless, in fact quite miss the mark. I begin withH.A. Prichard.15

Prichard treats Hume as a sceptic. But hefinds that the Treatise, so understood, is tedious, andthat it makes him not sceptical but angry. To besure, Prichard thinks that much of it is clever, but itis the cleverness of ingenuity and perversity. Formyself, I should say that this response should suggest

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to Prichard that his reading of the Treatise isincorrect. Perhaps the arguments appear perversebecause they are construed as aiming at a scepticalconclusion; if construed as directed at a non-scepticalposition, then perhaps they might not look so perverseor merely ingenious! However, Prichard is so convincedof the rationalistic position with respect toknowledge, that he cannot but read Hume as a sceptic —which, of course, Hume j^s, at· least with respect to theobjective necessary connections of the rationalist.But that does not mean Hume is a pyrrhonist with

18respect to our knowledge of causes: to be sceptical ofobjective necessary connections is not to be a scepticwith respect to' causation19— though it is to be afallibilist about the latter,- but, again, to be afallabilist is not to be a sceptic, or, at least, apyrrhonian sceptic.

For the sceptical argument that "extinguishes"all "belief and evidence" Prichard raises three

onobjections. He asserts, in the first place, that itconfuses the limit of a series with a term of theseries. This is no doubt so. The limit of the series

of probabilities is indeed zero, but v/e never actuallyreach that limit. All we ever reach is a fraction;

indeed, if we go on long enough we can reach anyfraction as small as we choose. Still, all we everreach is the vanishingly small and not zero. VJe mustrecognize, however, that this mistake hardly modifiesHume's point: "Vanishingly Small" will do as well as"zero" in undermining belief and evidence. Moreover,given that no mathematician of that age was ever clearon the distinction between zero and the vanishinglysmall, that is, on the nature of infinitesimals, it isa harsh judge indeed that will condemn Hume for asimilar failure of understanding. In fact, we see inPrichard's objection nothing more than a simple failure

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to approach Hume with the sympathy with which oneshould- approach any philosophic classic.

Prichard objects, second, that an infiniteregress cannot arise:

...if we judge that the faculty by which we,considering the nature of two and two, judgeit to make four is infallible only to theextent of three-quarters, we inevitably arejudging as a matter of certainty that twoand two is probably four to the extent ofthree-quarters, and we cannot then takefurther account of the fallibility of ourfaculties, for we have already taken fullaccount of it. 1

But clearly, one has taken full account of thefallibility of our faculties only if the probabilityjudgment _j_s- a matter of certainty. Prichard tells usthat "inevitably" the latter is so. Alas, he gives usno reason for thinking it to be so, and less forthinking that it is inevitable. All we have here isPrichard the rationalist asserting that Hume thefallibilist is wrong; but to assert is not to argue.

Prichard's third point is similar.22 The init-ial judgment must be taken as being certain, since byhypothesis it is rendered probable only by reflectingon the fallibility of our judging faculty. However, ifit _i_s certain, then there is no room for doubt; if itis certain, then it cannot be arrived at by falliblefaculties. Hence, Hume cannot use reflections on thelatter to cast doubt on the former. However, thisobjection goes through only if certainty is a guaranteeof infallibility. In the psychological sense of'certainty', i.e., felt certainty, or as Hume wouldanalyze it, maximum vivacity, there is no guarantee ofinfallibility. There is such a guarantee only if thereis some objective necessary connection between theobject of judgment and the feeling of certainty." ButHume has argued in detail against objective necessaryconnections; the connections between objects or

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in,pressions and ideas are causal and these causalrelationships are all to be given a Humean analysis.Prichard's objection is successful if and only if thereis such, a necessary connection between objects andcertainty will guarantee that judgments of the lattersort are infallible. But he does not argue for such aconnection; he simply assumes it. Again all Prichardhas succeeded in doing is to express his rationalisticdogmatism, while at the same time ignoring Hume'sargued case that all our faculties are fallible.

Prichard may be correct in holding that thearguments of the Treatise are ingenious and perverse.But at least the Treatise gives arguments. Pricharddoes not even do Hume that courtesy.

Another recent critic of Hume's sceptic'sargument is MacNabb, who tells us that:

The argument is plainly sophistical butphrased in such vague terms that it would bea lengthy task to set out all the variouspossible cases covered and explain thefallacy in each. Take one case. I judge (1)that Bucephalus will probably win the 2:30.But then I reflect (2) that I am not a goodjudge of form. Then I reflect (3) that I amnot a very good critic of my own performancesin these matters. The force of (3) is tocounteract (2) and leave (1) unchanged butsubject — as it always should have been —to the proviso "unless I am mistaken." Andhow am I supposed to proceed further in thisregress? Where shall I find evidence of mypowers of criticizing my own criticisms of myjudgments, distinct from the evidence of mypowers of criticizing my own judgments? Ihave reached an assessment of my powers ofpicking up my own mistakes, and beyond thatit is not possible to go. Every further stepis the same step repeated.2^

However, it is (2) rather than (3) which requires us toput (1) under the proviso "unless I am mistaken".26 (3)does not counteract (2), but rather in turn subjectsthe latter to a similar proviso. (3) can then be madesubject to the same proviso. And so on: the regress is

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clearly there. KcNabb tries to break it off by arguingthat the regress requires one to distinguish (a) powersof criticizing one's criticisms of judgments from (b)powers of criticizing judgments, where in fact (a) and(b) are not distinct, since evidence for (b) counts asevidence for (a). This is so: one can succeed in

distinguishing (a) from (b) only by failing to notethat the "criticisms of judgments" mentioned in (a) arethemselves judgments. Thus, the evidence for (a) doescount as evidence for (b) and, more specifically,evidence for either is evidence for "All my judgments[including critical judgments!] are fallible" or to"Each of my judgments is probably to degree m/nmistaken". And once one has this rule then it can be

applied at each stage. It is, to be sure, "the samestep repeated", but nonetheless at each step theprobability decreases.

In fact, Hume's argument is not phrased invague terms. He himself, as we saw, places it in thecontext of an analogy with a chain of testimony. Oncethis is seen then it is not hard, I think, to generateHume's sceptic's regress of probabilities, through someelementary applications of the probability calculus.Critics like Prichard and MacNabb are simply too hastyto judge Hume a sophist *_? read him carefully, letalone try to construct a reasonable interpretation inwhich a regress of probabilities can validly begenerated.

Part III: Hume's Argument Reconstructed

Hume's argument against reason relies uponprobabilistic causal reasoning. To defend it one mustattempt to show that such reasoning is cogent. To dothis will require us to invoke the probability calculusin a way that Hume never did. The reconstruction willhave to be faithful to what Hume does say, that is, the

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argument as we have sketched it in Part I, but sincethe reconstruction will add details that Hume never

provides, it follows that we cannot show that Humereasoned as our reconstruction proposes. The best thatcan be done is to provide a little historical contextsufficient to establish that the reconstruction is not

only faithful to Hume but is also not wildly anachron-istic.

Let us begin, then, by recalling that Hume'sargument construes an inference, i.e. , an act ofinferring, as testifying to the truth of itsconclusion, and by noting that a similar argument aboutchains of testimony and diminution of probabilitiesoccurs in Bentham's Rationale of Judicial Evidence

where he employs what is essentially Hume's argument inorder to exclude hearsay evidence:

All modifications of unoriginal evidence thatare of the nature of, or bear similitude to,hearsay evidence ... have this in common, —that for every remove (mendacity and fraudout of the question) they afford anadditional chance of incorrectness andincompleteness .27

and he continues a little later:

Supposed extra judicially stating ornarrating witnesses may have stood in aseries of any length, one behind another.The causes of untrustworthiness applying toevery human being, and, to every being ofwhich nothing more is known than that he orshe is human, with equal force, — it isevident that, the longer the line of thesesupposed witnesses, the less is the probativeforce of their supposed testimony.2^

Now, Bentham is acknowledged to be the mostsignificant theorist of legal evidence. As oneauthority puts it, "Among the theorists Bentham standsfirst, though possibly not the first in time...."29That by itself establishes, I think, that Hume'sargument is not as implausible as such critics asPrichard and McNabb suggest. On the other hand,

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Bentham, like Hume, provides no reasoning explicitly interms of the probability calculus. The task remains,then, of providing the reconstruction we are aiming at.But Bentham does provide a reminder that testimony andprobabilistic considerations have long beenintertwined, and a suggestion that it is in thiscontext that we should attempt to reconstruct Hume's —and Bentham' s — reasoning.

To this end we may start by noting what happensto the ancient distinction between scientia and opinio

under the impact of the criticisms of Locke and Hume. 30Scientia consisted of infallible and certain knowledgeof objective necessary connections. Opinio consistedof fallible belief based primarily on authority. 31Locke and Hume systematically criticized thetraditional view that there are objective necessaryconnections, that knowledge consists of grasping these,and that demonstrative syllogisms beginning frominfallibly known premisses lay out the ontologicalstructure of the world. After this critique neitherscientia nor the demonstrative syllogism of scientiaremains. But neither does opinio remain. Or, at

least, the dialectical syllogism, which (together withrhetoric) dominated the theory of opinio, comes to bebut a minor part of case-making, that is, case-makingwith respect to what the facts are and how we ought tounderstand them. To be sure, it is an essential part.The rules of formal logic remain to ensure consistency.Nor can they be eliminated, since nothing else is atest of consistency. But they come to be but a part ofthe methodology of empirical science, the logic oftruth. The certainty of intuition and demon-strationin scientia have gone. The only certainty that remainsis such certainty as empirical research can yield.Gone, too, is the probability of opinio. Authority,what justifies premisses as probable, is no longer

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taken as given. The worthiness of an authority becomesjust another empirical hypothesis, to be tested likeall others by empirical research. Hacking has quitecorrectly indicated the origin of the probabilitywithin the context of opinio, attached there to thenotion of acceptable propositions. 32 what he has failedto spell out is that in the context of opinioprobability is connected with a magical idea ofauthority, be it that of the scholastics, the Bible,the Fathers, and Aristotle, or that of the humanists,the purified texts of the ancients, or that of thecommon lawyers, the sworn testimony of witnesses. 33What happens as this magical context erodes is thatprobability — and certainty also — comes to beconnected with the idea of the worth of empiricalevidence with respect to hypotheses about matter-of-observable-fact regularities. Knowledge is no longerscientia but comes to be justified certainty aboutempirical regularities. And where such certainty isnot possible we rely upon what Locke called judgment,and, where the matter is put to us verbally, assent ordissent .34 judgment or assent is prooable35 just in caseit conforms with our past experience and "constantobservation"" or conforms to the testimony of otherswhere, however, the latter is to be evaluated as anyother empirical hypothesis. 3' The syllogism is the testof consistency: "This way of reasoning [the syllogism]discovers no new proofs, but is the art of marshallingand ranging the old ones we have already. "3° Probabil-ity is part of the logic of truth: "...as the conform-ity of our knowledge, as the certainty of observations,as the frequency and constancy of experience, and thenumber and credibility of testimonies do more or lessagree or disagree with it, so is any proposition initself more or less probable. "39 Locke is content tolet it go with "constant observation," no doubt

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trusting the basic rationality of men to normally judgewell, if not always correctly. Hume gave more details.Constant observation often tends to confirm contraryhypotheses. Since confirmed, all are not unworthy ofassent, but since contrary not all can be true. They

40are therefore to be characterized as probable. u Thetask of research is to move from such probabilities tocertainty. The rules are the Rules by which to judge ofcauses and effects, (TI, III, XV), which are, inessentials, the rules of eliminative induction.Bacon's new organon is the logic of truth by which wemove from probability to empirical certainty ( i.e. ,insofar as it can be had).

But why should the "contrary causes" or con-trary hypotheses be called "probable"? Here we mustlook more carefully at the concept of probability.

A mass event consists of a characteristic beingexemplified in each member of a large group or mass ofindividuals or points. All persons in a country at agiven time constitute a mass event; so does the set oftosses of a coin. A second characteristic may be

exemplified by the individuals in this mass event.Thus, dying before a certain interval has elapsed issuch a characteristic for our first mass event, comingup heads is one for our second mass event. Therelative frequency of the exemplif ication of the secondcharacteristic in the mass event exists. That a

certain characteristic is exemplified with such andsuch a relative frequency in a mass event is itself agroup characteristic of the mass event. Some sorts ofmass events are serially ordered, but not others.Populations at a time are not, coin tossings are.Where there is a serial order, and if theexemplifications of the characteristic defining themass event and the exemplifications of the secondcharacteristic satisfy together certain conditions

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(axioms), then one has a random sequence. Where thereis a serial order, one has a sequence of mass events(the first in tosses, the first ? + 1 toss-es, and soon), and therefore a sequence of relative frequencies.Where there is a random sequence then the probabilityof the second characteristic relative to that whichdefines the mass events is the limit of the series of

relative frequencies as the size of the mass eventsincreases to infinity. Consider a certain individualcoin being tossed. The sequence of events, this coinbeing tossed at t_,, this coin being tossed at ¿2»···»is serially ordered. This sequence is random. Thecharacteristic of being tossed at some time or otherdefines a sequence of mass events. Within these massevents the characteristic of coming up heads appearswith a certain relative frequency. We form thehypothesis about the sequence that the limit of therelative frequency as the sequence tends to infinity is1/2; i.e. , that the probability of heads is 1/2. Thishypothesis, if true, is a lawful regularity about thetosses of this particular coin. This hypothesisinvolves mixed quantification. To say £ is the limitof the series of frequencies is to say that for all £ ,there is a number K, such that for every ri> N, where n_is the (ordinal) number of the term in the series, thedifference (neglecting signs) between f (the frequencywhich is the jith term) and £ is less than € , Such alawful regularity enables us to assert that if thesequence of tosses were to be extended indefinitelythen the relative frequency would (in the indicatedsense) converge towards 1/2 as a limit. ¦ The hypothesisis an indicative prediction asserting a matter-of-factregularity about the tosses of a single coin. Thehypothesis can be generalized further, to cover thetosses of all well-balanced coins. The notion of

probability for these cases is a well-defined notion,

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one which in no way violates the empiricist criterionof meaning. There is nothing — or ought to be nothing— in such a criterion which renders unacceptable theidea of extrapolating to limits. The only problem isthat of confirmation. Such extrapolations will, ingeneral, given the notion of limit, involve mixedquantification. The relevant laws will, therefore, beneither conclusively confirmable nor conclusivelyfalsifiable. In the case of probabilities the problemis to figure out what probability a sequence or each ofa set of sequences has, since any initial segment we infact observe is compatible, given the logic of limits,with any probability. But statisticians have in factdeveloped reliable evaluation procedures.

What must be emphasized is that suchprobability statements are statements of matter-of-

observable-fact regularities. To be sure, they are ofa logically complicated sort, but that does not renderthem any the less statements of regularities. Thislogical complication makes the use of induction intheir case more precarious than it is in the case ofnon-probabilistic laws. "But," as Bergmann once putit, "to be precarious in this factual sense does notmean to be precarious or problematic in a philosophicalsense."42 Furthermore, these regularities may or maynot be deducible from non-probabilistic laws. Whetheror not deterministic explanations of probabilistic lawsare possible is a question of fact. Laplace,3 andbefore him Hume,44 thought such laws as those of cointossing could be explained deterministically,- we nowknow this not to be so, that they are irreduciblystatistical, though they can, in a way, be fit into thebasic theoretical framework of classical mechanics.45

The coin-tossing and dice-rolling cases are theparadigm cases of random sequences of events. Therewere in fact problems with defining mathematically the

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notion of random sequence. Von Mises' idea wasunsatisfactory, and WaId and others worked to refineit, without, however, providing a perfectly satis-factory notion. 46 Kolmogorov has developed a differentline of research into the notion of random sequence. 4'As he has emphasized, it is crucial to the idea ofapplying any mathematical theory of probability. 4a

In the coin-tossing case, two outcomes areequally probable. This is the special case of the moregeneral idea of. a lottery, in which tickets are drawnfrom a drum (or balls from an urn). In the latter, theprobability of drawing each ticket is assumed to beequal. If there are N different tickets, then for eachticket the probability of its being drawn during a longseries of draws is 1/N. Just as we have found certainsorts of coin are as a matter of fact such that in a

long series of tosses heads and tails are equallyprobable, so we have found certain sorts of ticketdrawing situations are as a matter of fact lotteries inwhich each outcome is equally probable. Thus, we canassume certain sorts of ticket drawing situations areas a matter of fact lotteries in which each outcome is

equally probable. But we can also assume certainoutcomes are more or less probable than others. Thus,we can assume certain sorts of tickets are more likelyto be drawn than others, or that the probability ofheads is some value other than 1/2. Huygens was ableto reduce the treatment of these cases to the case of

49the fair lottery.

Taking coin-tossing and lotteries as paradigms,it becomes possible to extend the notion of probabilityto the case where, because events are not seriallyordered, we have only frequencies, not probabilities5^The fact that a certain percentage of a population ofsize N, taken at time t,, is male (M), the remainderfemale (F), has, by itself, nothing to do with

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probabilities. One simply has a mass event — thepopulation at t — with another characteristic, M,occurring with a certain frequency in it. Theconnection with probability goes as follows. What iscrucial is that the mass event is an event in a

second-order mass event. In the present case, thissecond-order mass event consists of a group ofpopulations of size N. In each of the mass events inthe second-order mass event, M occurs with a certainrelative frequency. The possibilities are zero M, oneM, ..., NM; i.e. , there are N + 1 possible relativefrequencies. Now write each of these relativefrequencies on a ticket to be put into a lottery. Wecan now draw tiCKets and obtain a series of relativefrequencies. Assume the first-order mass events can beserially ordered. In the present case, we considersuccessive populations of size N. Then, that ordercorresponds to the series of relative frequenciesresulting from the lottery draw provided that we makethe appropriate factual assumptions of relativefrequencies (male to total population) in the second-order mass event. If we assume the frequencies areuniformly distributed in the second-order mass event,then we are assuming each ticket in our "frequencylottery" is equally probable. If we assume otherdistributions then we are assuming certain unequalprobabilities for different tickets in our "frequencylottery." We can reduce this case to the coin tossingcase as follows.

We generate the same sequence of relativefrequencies in another way. One considers a coin withM on one side and F on the other. This is repeatedlytossed. This sequence is divided into segments oflength N. These are, of course, serially ordered. Foreach segment, M occurs with a certain relativefrequency. These frequencies in segments of length N

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correspond to the relative frequencies in the non-serial mass events and to the relative frequenciesyielded by the lottery draws. If we assume the tossesare independent, and that the outcome M has probability£, then the probability of nM and (N - n) F is givenby:51(a) CN£n (1 - £)N - n

Thus, to make an assumption about £ in our sequence ofcoin tosses is equivalent to making the mentionedfactual assumption about the distribution offrequencies in the second-order mass event. In thisway we can speak of probabilities where, strictly, weshould speak of frequencies.

Arbuthnot used this analogy to coin tossingwhen he discussed population statistics and their

52stability. * He assumes the M-F coin is fair, so £ =1/2. He correctly calculates, using the binomialcoefficients, the probabilities of frequencies insegments of length N. (a) represents the jith term ofthe binomial expansion of (£ + £)N where 3 = 1 - £.(C is the binomial coefficent of that term.) If wetake £ to be a "random variable" and (a) to be afunction of it, then we have a binomial distribution ofn_. Thus, Arbuthnot makes the matter of fact assumptionthat the distribution in the second-order mass event of

frequency of males in the first-order mass events(populations of size N) is distributed binomially.This is equivalent to assuming the probabilities in our"ticket lottery" are distributed binomially. Morespecifically, Arbuthnot assumes a binomial distributionin which £ = 1/2. If £ = £ = 1/2, then (a) is equalto:

CNx 1/2N?

As N increases in size the probability of getting anyparticular number n_, i.e. , any particular relativefrequency n/N of males, becomes smaller and smaller.

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Arbuthnot correctly calculates that this probabilitybecomes smaller as N increases, and in particular thatthe probability of an equal number of males and femalesbecomes very small. Equally correctly he infers thatthe probability of obtaining an extreme outcome nevervanishes. Arbuthnot — incorrectly — infers that theroughly equal numbers of M and F is highly improbable,and its occurrence therefore not a "matter of chance"but due to Providence. What Arbuthnot does not ask in

quantitative terms is what the probability of obtainingapproximately the same number of males as females.Bernoulli's limit theorem53 establishes that, as Nbecomes large, the probability tends to unity that thefrequency n/N diverges only slightly from £. Thus,given Arbuthnot's distribution assumption, that £ =1/2, the probability of obtaining populations approx-imately 1/2 males tends to unity. And so, contrary towhat Arbuthnot invalidly inferred, the more or lessconstant regularity of males and females can reasonablybe expected even as a "matter of chance". Actually theproportion of males to population tends over time to beslightly greater than 1/2. Nicholas Bernoullicalculated 54that the observed relative frequencies arewhat one could expect if £ = 18/25, that is, if oneassumed a binomial distribution slightly different fromthat assumed by Arbuthnot.

Bernoulli's limit theorem leads to the

prediction that if a population is large and relativelyconstant in size, then the proportion of males willremain relatively constant. This is, of course, anempirical prediction. It presupposes two empiricalassumptions. One has already been mentioned. This isthe distribution assumption. The other is that, justas the outcomes of the coin tosses are as a matter of

fact independent of each other, so this person being Mmust be independent of that person being f, or, what is

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the same, the sex of the next to be Dorn must as a

matter of fact be independent of the sex of the justborn. These factual assumptions are generalities.Their acceptance is therefore justified in the same wayall other empirical generalities are justified, bytheir predictive success. Only, they are generalitiesinvolving mixed quantification — otherwise they couldnot connect up with probability notions! — and so whatwe deduce as the prediction is an existentiallyquantified statement which cannot be falsified. Theproblems of putting them to the test are essentiallythose of putting the probability laws of coin tossingto the test. They are problems which are technicalones in statistics rather than philosophical.

The use of statistics can be extended from

these cases to the investigation of causal laws.Suppose we know that being F_ sometimes causes H,sometimes not. This is a very simple instance of"contrary causes". In such a case it might bereasonable to suppose some unknown factors exist suchthat when these are present F_ causes H_, when they areabsent F_ does not cause H_. Call these unknown factorsG. (The bar indicates that we have a definite

description of the type of factor, not the name of thetype itself.) We are assuming, then, that the presenceof G is necessary and sufficient for F_ to cause H, or,in symbols:(1)(x)lGx = (Fx = Hx)]

or, equivalently(X)[FjC = (Gx. = Ux.)]

(If this looks like (4 ) from part I, then it isintended to! )

If F_ occurs in a followed by H, we have(2)Fa

and

(3)Ha

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from which we can deduce

(4) Ga

Given (1), we can deduce G is present when E isconsequent upon F-, even though we cannot independentlyidentify G. We can now use this information to explainthe presence of H-, in the pattern with which we are bynow familiar from the preceding section.

The explanation is this:Law: (1)

(E) Initial Conditions: Fa & Ga

Hence: H_aThus, where a medicine brings about recovery some butnot all the time we generally infer its not working isdue to the absence of certain physiological factorsnormally present. Consider the total population andits mutually exclusive subpopulations of size N. G-occurs' with some relative frequency in each of thesubpopulations. If we assume a binomial distributionof these frequencies then we can, as discussed justabove, equivalently speak of the probability of anindividual being ~G.Since £ is present in anindividual if and only if F- = H- is also present, itfollows that if f_ is the relative frequency of G in asubpopulation, then _f is the relative frequency withwhich F- causes H- in that subpopulation; and it followsfurther with reference to the total population that theprobability that an individual is G is the same as theprobability that an individual F- causes H-. If we pickout a subpopu2ation and· bring it about that each memberis F-, then the frequency of H in that subpopulationwill be _f if and only if the relative frequency of G inthat subpopulation is f_. The relative frequency of H_' sin a subpopulation of f_'s yields the relative frequencyof G_'s in'that subpopulation. If we pick several suchsubpopulations of £ — randomly, from the total

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population, so that independence is assured — then wecan use these data to infer statistically theprobability of H' s in the subpopulations of F-' s or,what is the same, the probability of G_'s in the totalpopulation. On the basis of such probability estimateswe can use the technique of Huygens for adjusting ourbeliefs and actions, that a gamble is worth the

55mathematical expectation of that gamble, and adjust ourdegree of assent that this F- will be ñ to theprobability in the total population that being F- causesH.

Obviously, we would prefer to know whatcharacteristic it was that the definite description £denotes. Then we could identify those cases where F-will bring about H and those cases where it won't; wewould not then have to rely upon statistics.Statistics here are the mark of imperfect knowledge,our not knowing the causes we have reason to believeare operating. Probability thus comes to be used —and, given certain factual assumptions are fulfilled(independence, etc.) -- successfully used — where expost facto causal explanations such as (E) areavailable and where we also have reasonable hope todiscover the means (by identifying the property G)necessary for deterministic predictions.

The case described by (1), where G is unknown,is the simplest case of the operation of "contrarycauses", which Hume discussed.56 Sometimes F- bringsabout H, sometimes not. The idea is obviouslygeneralizable. We could, for example, have E_ producingIl sometimes and sometimes H . VJe could then

hypothesize after the fashion of (1) that F-SG- causesH and that F- &~G , or perhaps F-SG causes H .

• ^7Statistics would proceed in much the same way.' It isin this fashion that we come to speak of theprobability of "contrary causes" and of "contrary

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effects" ._____Such a use of 'probability' marks animperfection in our knowledge, a gap in our knowledgeof causally relevant characteristics. It is then thetask of the experimental method, of the methods ofeliminative induction, to fill those gaps in ourknow ledge,_____find out specifically what thecharacteristic G. is, and so eliminate the need forstatistics. However, action often requires us to usewhat knowledge we have, imperfect as it is, beforeresearch can be done to remove its imperfections. Inthat case we must rely upon the imperfect statisticalknowledge — where, one must note, to be imperfect or

Cu

"gappy" is not therefore to fail to be knowledge.When we do act upon statistical knowledge we proceedupon the basis of several matter-of-fact assumptions.On the basis of these judgments we can proceed tocalculate the probability of kinds of particularevents. Our expectation of a particular event of sucha kind is proportioned to the probability, and that isto say that it is to that probability that weproportion the degree to which we assent, prior toobservation, to the proposition that a particular eventwill be of that kind.____In this context, epistemicprobabilities (rational degrees of assent) areproportioned to and presuppose aleatory probabilities.Such rational adjustment of belief to probabilitypresupposes antecedent acceptance of certain inductivegeneralizations.

Now consider these factual assumptions uponwhich the expectations and degrees of assent are based:these assumptions are inductive generalizations. Ofthese, there are essentially two. The one is that Gexists. The other is that it has a certaindistribution. The latter is a matter of mixed

quantification, and partakes of the generalprecariousness of statistical generalizations. In the

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present case it further depends upon the otherassumption that G exists. It is the latter assumptionwhich is crucial. what reason might we have forbelieving G- exists, i.e. , for believing that definitedescription is successful? That amounts to asking whatreason we might have for believing a law of the sort(1) obtains even when we do not know specifically whatG is and therefore could have no confirming instancesupon which to base our judgment. The answer can onlybe: inductive. We might have some more generaltheory, confirmed in other cases, that enables us todeduce in the present case that (1) is true. Thus, ifF_ is a drug to cure (Hj a very specific type of disease(e.g. , swine flu), then a more general theory about agenus of disease (influenza), of which that of ourconcern was a species, might very well lead uscorrectly to affirm (1), without specifyingspecifically, only generically, what are the conditionsG. Or, one might rely upon some very general principleof determinism, as Hume did (T132) when consideringthis very sort of case.

A special case of using statistics was ofspecial importance to early investigators. ' This wasthe case of the worth of testimony. That this shouldbe important in this context was thoroughly natural,since, after all, probability is, as Hacking argues, aconcept which does derive from the context of opinio,the dialectical syllogism, and the reliance upontestimony.

Assume

F_x_ = >i asserts at _t some proposition or otherand

Hx = What >c asserts at t_ is truei.e. , The proposition ? asserts at _t is true

and suppose, for the moment, somewhat simplistically,that a law of the sort (1) holds for this F and H. The

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absence of G at some times rather than others would

then explain why a person sometimes asserts what is nottrue.59 Now, as above, we can use (1) or, actually, (1)quantified over both ? and t_, to estimate theprobability in a sequence of assertings that what isasserted is true.60 Our degree of assent to thestatement that this F- is H- is to be proportioned tothis probability. Given that a asserts something at t,is true. But if:

the proposition a asserts at t.-, = S.then we are, upon a_'s say-so, assenting to theindicated degree to the proposition that £. Theprobability of B in F is the probability of G in thetotal population of all individuals at all times. Itis this probability to which we proportion our assentto S1, and which measures the reliability of ¿'stestimony, the extent to which we may reasonably betupon its correctness.

Suppose now, that:S = Fb

= b asserts S at t-2-2

Given £, we may, as before, assent to £ in proportionthat G is probable in the total population. But we arenot given S_ categorically; we assent to it only to acertain degree. To what degree then should we assentto S--? Obviously we may reasonably expect S2 t0 betrue just to the extent that it is probable that wedraw from the population two G's in a row. Now,according to (a), this probability:„22, ,2-2 2C .£11 - £) = £2 2Since 0 $ £ ^ 1, we will always have £ < £ unless

everyone exemplifies G at all times or no one does atany time. Since, as a matter of fact, none of us tellsonly truths and none only falsehoods, it follows thatthe degree of assent we should attach to S_2 i-s> *·? ^hQcircumstances, always less than that we should attach

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to S , . This is what lies behind the courtroom

evidentiary practice of prohibiting hear-say evidence.On the other hand, consider the probability ofobtaining at least one G- in two draws. By (a), thatis:

C \ £ (1 - £)2_1 = 2£ (1 - p)The probability 2£ (1 - £) is greater than £ just incase £^ 1/2. So, if it is more likely than not that aperson is G, then the probability of getting at leastone G in a draw of two is greater than the probabilityof G. If, therefore, we take two witnesses theprobability that the testimony of at least one iscorrect is greater than the probability when making asingle draw that' the witness' testimony is correct.. Weshould therefore attempt to secure several independentwitnesses to an event: the probability at least one iscorrect is greater than the probability any is correct.So testimony derived from several independent sourcesis better than testimony from a single source —provided that, of course, the probability a person isG, i.e. , a truth-sayer, is greater than 1/2.

Jeremy Bentham was effectively the first 62 toprovide any extended treatment of the rules of evidencein legal situations. He made use of such inferencesas the above, though using only relatively crude

64notions of probability. George Bentham used relativefrequencies to provide some analyses, but notprobabilities. J. S. Mill recognized the relevance of

CfZprobabilities. He also recognized the relevance ofchoosing a population and estimating £ for thatpopulation. To attack the credibility of a witness isto try to place him in a population with respect towhich the probability of G is low, i.e. , with respectto which one assents to what is testified to only witha relatively low degree of assent. Hume's discussionof miracles (EHU, X) is, as Hacking has pointed out,67an

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exemplification of Hume's ideas on probability, appliedspecifically to the case of testimony. His aim is, ofcourse, to attack the credibility of any witness whotestifies to a miracle. It was these same generalprinciples that Jeremy Bentham used to rationalize therules of legal evidence. In an important essay Waldmanhas argued that "...the need for a systematic treatiseon evidence was most pressing after a philosophicaltheory of evidence regarding the practical affairs ofmen had been stated." The philosophical theoryWaldman has in mind is that of the "mitigatedscepticism" of Glanvill, Wilkins, and so on, in whichthe ideal of absolute certainty comes to be replaced bythat of moral certainty, and in which a proposition notabsolutely certain remains acceptable so long as it isnot open to reasonable doubt. But its philosophicalfoundations were given by Locke in his Essay.Essentially, its basis is the rejection of theinfallible knowledge of objective necessaryconnections, the rejection of scientia. Once this goesthe theory of legal evidence must be given a basis inempirical fact.

However, the point here is not to trace thesedevelopments in detail. Rather, it is to note thatBentham and others argue that a regress of probabil-ities tending towards zero occurs in a chain oftestimony. VVe have just argued that this reasoning is,according to the calculus of probabilities, valid. ButHume's Sceptic's argument designed to extinguish allbelief and evidence involves the same regress ofprobabilities ._____We must, therefore, accept thesceptic's argument as valid. Thus, contrary to criticslike Prichard and MacNabb, Hume's argument forscepticism with regard to reason is, if not sound, then atleast very far from the "tissue of sophistries" thatthe received opinion charges it with being. Hume's

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Sceptic's argument is, in short, an argument worthy ofa philosopher, and, if it is unsound, then it is atleast one that is worth refuting.

Fred WilsonUniversity of Toronto

1.Another case of the mind monitoring its ownactivities, and adjusting them to achieve its ownends, is the case of causal reasoning. See F.Wilson, "Hume's Theory of Mental Activity," in D. F.Norton et. al. , McGiIl Hume Studies (San Diego:Austin Hill Press, 19B3).

2.David Hume, A Treatise of Human Mature, ed. L. A.Selby-Bigge (London: Oxford University Press,1888), p. 180.

3.Hume, (T182) speaks of a reflex act of the mind:feedback is a more modern term for the same thing.

4.Sextus Empiricus, works, trans. R. G. Bury(Cambridge: Harvard University Press, LoebClassical Library, 1935). Vol. II, pp. 331-3.

5.D. Hume, Enquiries concerning the Human Under-standing and concerning the Principles of Morals,ed. L. A. Selby-Bigge (London: Oxford, 1902), p.109ff .

6.EHV 111-13; T 181-2.

7.Cf. W. Salmon, Logic, First Edition (EnglewoodCliffs, N.J.: Prentice-Hall, 1963), p. 63ff.

8.EHV 112. It has a physiological basis,- cf. T 60-1.

9.T 311-73.

10. Treatise, I, III, XII. This reasoning is discussedin detail in F. Wilson, "Is There a Prussian Hume?"Hume Studies, 8_ (19.82), pp. 1-18. See also F.Wilson, "Mill on the Operation of Discovering andProving General Propositions," Mill Newsletter, 17(1982), pp. 1-14; and "Kuhn and Goodman:Revolutionary vs. Conservative Science," Philo-sophical Studies, forthcoming.

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11.Ibid. This causal argument can be applied to thecase of testimony, which involves causalconnections (in Hume's sense) and also to thetestimony of reason, for as we saw Hume remark (seefn. 2, above), our reason must be consider'd as a kindof cause, of which truth is the natural effect.

12.Cf. E. Nagel, Principles of the Theory of Proba-bility (Chicago: University of Chicago Press,1939), p. 44ff.

13.Cf. 0. Sheynin, "Newton and the Classical Theory ofProbability," Archives for the History of ExactSciences, 7_ (1970-1), pp. 237-3.

14.Cf. I. Lakatos, "Changes in the Problem ofInductive Logic," in I. Lakatos (ed.), The Problemof Inductive Logic, (Amsterdam: North Holland,1968).

15.H.A. Prichard, "Hume," in his Knowledge and Per-ception (London: Oxford University Press, 1950),pp. 174-99.

16.Ibid., p. 174.

17.Cf. ibid., p. 189ff .

18.Cf. Wilson, "Hume's Theory of Mental Activity".19.Cf. T. Beauchamp and A. Rosenberg, Hume and the

Problem of Causation.

20.Prichard, Knowledge and Perception, pp. 195-6.21.Ibid. , p. 195.

22.Ibid.

23.Cf. D. Lewis, "Moore's Realism" Ch. V, in L. Addisand D. Lewis, Moore and RyIe: Two Ontologists (TheHague: Nijhoff, 1965).

24.Cf. Wilson, "Hume's Theory of Mental Activity."Compare also Hume's account of the causal relationbetween a volition and what the volition intends,in the Enquiry concerning the Human Understanding,Sec. viii.

25.D.G.C. MacNabb, Art. "Hume," in P. Edwards (ed.)Encyclopedia of Philosophy (New York: Macmillan,1967), vol. IV, p. 84.

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26.Compare T. Reid, Essays on the Intellectual Powersof Han, in his works, ed., W. Hamilton (Edinburgh:MacLachlan and Stewart, 1852), Essay vii, Ch. IV,p. 487.

27.J. ¦ Bentham, Rationale of Judicial Evidence, inWorks, ed. J. Bowring (London: 1838-43), Vol. 7,Bk. VI, Ch. Ill, p. 132.

28.Ibid. , Ch. IV, p. 133.

29.G. Nokes, An Introduction to Evidence, FourthEdition (London: Sweet and Maxwell, 1957), p. 23.

30.Cf. F. Wilson, "The Lockean Revolution in theTheory of Science," forthcoming in the festschriftfor R. F. McRae; and "Critical Notice of I.Hacking's The Emergence of Probability," TheCanadian Journal of Philosophy, 8_ (1978), pp. 587-97.

31.For an important discussion of the scientia /opiniodistinction, see I. Hacking, The Emergence ofProbability (London: Cambridge University Press,1975).

32.Cf. Hacking, The Emergence of Probability, pp. 20-4, p. 179.

33.Cf. Wilson, "Critical Notice of I. Hacking's TheEmergence of Probability. "

34.J. Locke, Essay concerning the Human Understanding,ed. A.C. Fraser (New York: Dover, 1959), vol. II,Bk. IV, Ch. XIV.

35.Ibid., Bk. IV, Ch. XIV, sec. 4.

36.Ibid., Bk. IV, Ch. XIV, sec. 6, p. 375.

37.Ibid., Bk. IV, Ch. XVI, secs. 9, 10; Bk. IV, Ch.XX, secs. 17, 18.

38.Ibid. , Bk. IV, Ch. XVII, sec. 6, p. 401.

39.Ibid. , Bk. IV, Ch. XV, sec. 6, p. 367.

40.Cf. Hume, Treatise, I, III, XII.

41.Just as the fact that the ideal gas law arises fromextrapolating to the limit does not render that lawis non-empirical; cf. F. Vi. Sears, An Introductionto Thermodynamics, Second Edition (Cambridge,Mass.,: . Addison-Wesley, 1955), p. 7ff. J. L.

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127.

Kackie, Truth, Probability and Paradox (London:Oxford, 1973), p. 174, makes the same point.

42.G. Bergmann, "Frequencies, Probabilities andPositivism," Philosophy and Phenomenological Re-search, 6> (1945), p. 39.

43.Simon, Marquis de Laplace, A Philosophical Essay onProbabilities, trans. F. Truscott and F. Emory (NewYork: Dover, 1951), p. 4.

44.T I, III, XII, p. 132; I, III, XI.

45.Tiie tossed coins are put into situations ofunstable equilibria, where random smalldisturbances yield random upshots. But theseunstable equilibria can be described in classicalmechanical terms.

46.Cf. P. Martin-Lof, "The Literature on von Mises'Kollective Revisited," Theoria, 34 (1969), pp. 12-37. Also J. L. Mackie, Truth, Probability andParadox, p. 173ff.

47.A. Kolmogorov, "On Tables of Random Numbers,"Sankhya: The Indian Journal of Statistics, seriesA, 25_ (1963), pp. 367-76.

48.A. Kolmogorov, Art. "Probability," in the GreatSoviet Encyclopedia, trans. of the Third Edition,Moscow, 1970 (New York: Macmillan, 1974), vol. 4,pp. 423-4. L. E. Maistrov, Probability Theory,trans. S. Kotz (New York: Academic press, 1974), israther less judicious than is Kolmogorov when hetoo hastily condemns the work of von Mises.

49.Cf. Hacking, The Emergence of Probability, Ch. 11.

50.Cf. Bergmann, "Frequencies, Probabilities, andPositivism. "

51.Cf. Nagel, Principles of the Theory of Probability,p. 34; and, with much ¡nore matheinatical detail, W.Feller, An Introduction to Probability Theory andIts Applications, Third Edition (New York: Wiley,1967), Ch. VI.

52.Cf. Hacking, The Emergence of Probability, p. 167.

53.Feller, An Introduction to Probability Theory andits Applications, Third Edition, pp. 150-3.

54.Cf. Hacking, The Emergence of Probability, pp.167-8.

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55.Ibid. , p. 94.

56.Treatise, p. 132. Hume's talk cf a "secret"operation of causes in this passage is of coursecompatible with his empiricism, and withoperationism.

57.Cf. J. S. Mill, System of Logic, Eighth Edition(London: Lonçmans, 1961), p. 35b, on how we judgethe frequency of causes by the frequency of theireffects. See also F. Wilson, "Goudge's Contribu-tion to the Philosophy of Science," in L. W. Sumner,J. G. Slater and F. Wilson, eds., Pragmatism andPurpose (Toronto: University of Toronto Press,1980) .

58.The notion of "imperfect knowledge" is G.Bergmann 's; see his Philosophy of Science (Kadison:University of Wisconsin Press, 1957), Chapter II.The notion of "gappy" laws is J. Mackie's,- see his"Causes and Conditions," American PhilosophicalQuarterly, _2 (1965). Compare J. S. Mill, System ofLogic, p. 353, where the imperfect nature ofstatistical laws is recognized: we should notsettle for chance when cause is possible.

59.I refer here, of course, to Hume's discussion Ofscepticism with regard to reason; see T180, fn. 2above.

60.Cf. the analysis of the argument from authority inW. Salmon's Logic. Salmon's text is one of the fewto give a decent analysis of the logic of sucharguments.

61.Cf. Nokes, An Introduction to Evidence, FourthEdition, pp. 281-5. To put it in inore detail: withhear-say evidence, the original giver of theevidence is not capable of being cross-examined inthe courtroom, so that these standard proceduresfor discovering the presence of factors tending tobring about the assertion of falsehood are notavailable.

62.Nokes, ibid. , p. 23.

63.J. Bentham, The Rationale of Judicial Evidence, ed.J. S. Mill.

64.Cf. ibid. , Bk. I, Ch. VI, where Bentham proposes ascale on which witnesses might mark the degree ofcertainty of their testimony.

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129.

65.G. Bentham, Outline of a New System of Logic(London: 1827), p. 139ff.

66.System of Logic, p. 354.

67.Hacking, The Emergence of Probability, p. 178.68.T. Waldman, "Origins of the Legal Doctrine of

Reasonable Doubt," Journal of the History of ideas,20. (1959), p. 310.

69.Cf. Locke, Essay concerning Human Understanding,Bk. IV, Ch. XV.