History versus hacking on probability

History Printed

of European Ideas, Vol. 8, No. 6, pp. 655-673, in Great Britain

0191-6599/87 $3.00 + 0.00 % ,987 Pergamon Journals Ltd.

1987

HISTORY VERSUS HACKING ON PROBABILITY ROBERTBROWN* I. INTRODUCTION:

HACKING’S

THESES

The history of the problem of induction is a large topic, and the half dozen chapters devoted to it in Ian Hacking’s book The Emergence of Probability’ attracted a corresponding large amount of critical comment from original reviewers of that volume. Larry Laudan, for example, suggested that Hacking had put forward three important ‘historical theses’. The first is that until the midseventeenth century there was no concept of inductive evidence available with which to state the problem of induction. The second is that, in Hacking’s words, The sceptical problem about the future, often called the problem of induction, was first published in 1739, in David Hume’sA Treatise ofHuman Nature. It doubts that any known facts about past objects or events give any reason for beliefs about future objects or events. A similar problem arises also for inference about unremembered past events and unobserved present ones.3 Hacking’s

third historical

thesis is, as he puts it,

that the concept of internal evidence of things is primarily a legacy of the low sciences, alchemy, geology, astrology, and in particular medicine. By default these could deal only in opinio. They could achieve no demonstrations and so had to resort to some other method of proof. The high sciences, such as optics, astronomy, and mechanics, still lusted after demonstration and could, in many cases, seem to achieve it.4 Laudan quite rightly argues that all three of these views are false. But in the course of trying to show this Laudan falls into some dubious claims of his own that nevertheless are interesting enough to be worthy of discussion. One ofthese claims is that if we restrict our attention to those earlier ‘writers who see evidence in terms of the relation between an empirical universal generalisation and its positive instances’, Hacking’s historical views are almost correct. For Laudan agrees with Hacking that with the exception of Bacon there were few writers before the mid-seventeenth century ‘who worried about the degree to which positive instances probabilified generalisations’.5 The reason for this lack of worry, according to Laudan, is that these earlier thinkers were concerned with a more important problem of induction-that of the degree to which confirming instances of a scientific theory provide evidence of its truth. If Hacking had taken account of the difference between probabilifying an empirical generalisation and probabilifying a theoretical statement, he would not, Laudan thinks, have *History of Ideas Unit, Research School of Social Sciences, Australian University, Canberra A.C.T. 2601, Australia.

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assigned to these two problems a common history.6 To this conclusion we can reply that it is true that before Bacon very few writers were explicitly concerned with the probabilification of empirical generalisations. But is it also true that the reason for this is that they were concerned, instead, with the probabilificationwith the verification and falsification-of scientific theories? Or is there another reason? In reviewing The Emergence of Probability Fred Wilson’ raised some different issues, but was led, similarly, to reconstruct their history in the service of an implausible view. Hume’s problem, as Wilson puts it, is this: ‘how, on the basis of observing a constant conjunction in a sample, can we be sure the constant conjunction holds in the population?’ According to Wilson, this problem could not have been formulated until philosophers had given up the belief, common to the Aristotelians, neo-Platonists and Hermeticists, ‘that there are necessary connections that account for regularities among sensible particulars, and that these can be discerned by the mind’.* Once this belief has been rejected, says Wilson, and we realise that there is necessarily a ‘logical gap’ between a sample and the population from which it is drawn, then we can understand that there is no genuine problem of induction and hence no need to look for its solution. We can, and must, resign ourselves to the fact ‘that infallible knowledge of cause and effect is impossible. Which is to say that we must accept, what neither Aristotle, nor the medievals, nor Descartes, nor Leibniz, nor Kant accepted, that human reason is essentiallyfallible’. Thus what makes acceptance of this view possible ‘is not as Hacking suggests, the new concept of probability, but the new metaphysics that denies the existence of necessary connections’.‘The conclusion to which this should lead us, Wilson thinks, is that the emergence of the aleatory (or chance) notion of probability in the mid-seventeenth century can be explained ‘simply by citing the dominant interest in matter-of-observable-fact regularities and in acquiriflg improved knowledge of such regularities’. lo However, the solution cannot be quite that simple. For as we shall see, interest in such regularities by many thinkers long preceded the development of the mathematical theory of chances. Moreover, a belief in the impossibility of infallible knowledge of cause and effect was not, in the case of some medieval writers, either the cause or effect, or the same as, the belief that ‘human reason is essentially fallible’. In any case, there is no more reason to conclude that a belief in such fallibility made possible the development either of statistical or epistemic probability than there is to conclude that an interest in epistemic probability-in determining reasonable degrees of belief-made possible the belief that causal knowledge is fallible. These two conclusions are equally doubtful since each of the two interests or beliefs existed for long periods of time in the absence of the other. Of course if the phrase ‘made possible’ simply means ‘in the circumstances was a necessary but not sufficient condition of’, then the argument alters. But it remains to be shown that we have more reason to think that either interest is a necessary rather than sufficient condition of the other; and this is true whether we take these conditions to be logical or causal. It is clear, then, that Hacking’s theses have produced more confusion than they have dispelled. For the fact that in 1654 Pascal and Fermat began successful work on gambling problems is, as Simon Blackburn wrote in his review of Hacking’s book, ‘certainly not explained by the emergence of a modern attitude to evidence.

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The proof of this is that many people with a firm notion of epistemic probability would be quite unable to solve for themselves the division problem, or the So even if Hacking were correct in his view that Chevalier de Mere’s problem’.” ideas about the two types of probability-degree of confirmation and relative frequency-emerged together in the mid-seventeenth century along with the concurrent development of the notion of inductive evidence, the presence of the latter would not account for the origin and growth of the idea that probability can be interpreted as relative frequency. Yet if the dual concept of probability and the notion of inductive evidence did not develop concurrently, what was their actual history?

II. THE CONCEPT

OF EVIDENCE

It requires no unusual amount of scholarly investigation-in fact we can confine ourselves to common works available in English-to show that well before the seventeenth century there were medieval thinkers who were concerned with the concept of inductive evidence, with inductive scepticism and epistemic probability. On the first point, we have only to recall some of the rules that Avicenna laid down in the eleventh century for determining the effects of medicines. Four of them, in A.C. Crombie’s words, are: (a) ‘The medicine must be free from any extraneous, accidental quality, as, for example, from the heat retained by heated water which by nature was cold’. (b) ‘The experimentation must be done with a simple and not a composite disease, for in the latter case it would be impossible to infer from the cure what was the curing cause in the medicine’. (c) ‘The effect of the medicine must be seen to occur constantly or in many cases, for if this did not happen it was an accidental effect’. (d) ‘The experimentation must be done with the human body, for testing a medicine on a lion or a horse might not prove anything about its effect on man’. **These rules were known to Grosseteste more than a century later when he devised his procedure for obtaining probable knowledge of causal laws-a procedure that was intended to lead the investigator to select among competing hypotheses by deducing their consequences and rejecting those that did not agree with the observed facts.‘) Thus one theory concerning comets was ‘that the tail of the comet was produced by the reflection of the sun’s radiation falling on a planet’. Against this view Grossteste objected both that a transparent terrestial-not celestial-medium would be needed in order for the rays to be seen, and that the view required that the tail of the comet be ‘always extended in the opposite direction to the sun, whereas all reflected rays would go in the opposite direction to the incident rays at equal angles’.14 Now Hacking divides inductive evidence into that ‘for a generalisation or even for a law of nature, gained from particular observation and experiment’, and that obtained from inferring from one particular to another.i5 Given this, it is not clear why Avicenna’s rules and Grosseteste’s remarks on comets are not concerned with the concept of inductive evidence. The former refer to such features of evidence as the frequency with which distinct and specifiable properties are found by experience to exist together, and to the type of causal field in which they occur. The latter refer to the failure of derived consequences to

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match the observed facts. Grosseteste’s recognition of this failure presupposes that he could also recognise successful matching-that he took the direction of the sun’s reflected rays to be evidence of the direction of their incident rays. In general, Grosseteste’s procedure for falsifying hypotheses and generalisations required him to recognise that various factors served as evidence for other factors. He thought, for example, that the sun’s motion could not produce heat because the medium produced no external resistance.r6 So he must have taken the presence of external resistance to a body by its surrounding medium as evidence that any body moving through it would produce heat. This is what Hacking follows Sextus Empiricus in calling an ‘associative sign’, one that, in Hacking’s words, ‘we use to infer what is at present unobservable from what is at present observed’.” Under what circumstances, according to mediaeval writers, could such inferences be properly drawn? Scotus replied that any factor that produces frequently and under varying conditions a uniform and constant reaction permits us to infer with ‘infallible certitude’ the following: ‘first, that the observed effect is proper to that particular agent here and now(quodita est), and secondly, that the same agent will always and everywhere (semper et in omnibus) for making this inference is the selfproduce the same effect’.” The justification evident principle that ‘if an effect occurs frequently it is not produced by chance and its cause therefore will be a natural cause if it is not a free agent’.19 For a natural cause of this kind-one that does not act freely-‘cannot in most instances produce an effect that is the very opposite of what it is by its form ordained to produce’.20 Hence this causal principle amounts to a belief, based on repeated experience, that nature is usually uniform in its operation.21 When the causal principle is joined to a proposition concerning natural factors that are observed to be associated regularly under changing conditions, we are entitled to infer that they are causally related. But since these factors are only contingently related, repeated observation and experience can give us only probable, rather than infallible, knowledge of the actual presence of these factors. The same agent will, except for divine intervention, always produce the same effect. But we may be mistaken in believing that we have been observing the same agent or the same effect. This sort of probable knowledge, says Scotus, is the lowest grade of ‘cognitionis scientificae’.22 These views of Scotus raise, in brief form, two of the questions that we are pursuing here. One is the medieval writers’ understanding of probability. The other is their view of empirical knowledge and of the support available for it. On the first point Hacking has written: For the medieval, evidence short of deduction was not really evidence at all. It was no accident that probability was not primarily a matter of evidence or reason. Probability pertains to opinion, where there was no clear concept of evidence. Hence ‘probability’ had to mean something other than evidential support. It indicated approval or acceptability by intelligent people.23

That these claims do not hold of all medieval thinkers is both well known and easily substantiated. John of Mirecourt, for example, writing in the midfourteenth century, said:

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I do not take ‘probable’ as does the Philosopher [Aristotle], but I call anything which is neither known [scitum] nor believed from the Catholic determined by the church nor stated by such a one whose statement none deny or to assert its opposite. Probable is commonly accustomed described.24

probable faith nor ought to to be so

It is quite clear that John did not believe that probability claims required ‘approval or acceptability by intelligent people’. For he said that while ‘a proposition is not true when faith is in opposition, yet it does not follow that the proposition is not probable. Indeed, the opposites of articles of faith are more probable to us than are the articles themselves’.25 In brief, a proposition can be probable whether or not the majority of people, or wise people, or religious spokesmen, believe it to be true. Nicholaus of Autrecourt, writing at much the same time as John of Mirecourt, argued that belief in probable opinions is distinct from religious belief, and from the certainty produced either by logical truths or by some propositions based on sense experience. For Nicholaus, the probability of these opinions varies, as Julius Weinberg puts it, with ‘our abilities, our present stock ofinformation and the kinds of argument at our disposal’. The result is a state in us of ‘partial belief’ whose degree is dependent upon the persuasiveness of the supporting argument. One kind of probable inference is that which, as a result of our repeated experience over time with specific instances of a set of associated factors, leads us to conclude that a similar association will hold of all future instances of these factors. It is true that Nicholaus thought that the degree of probability of a particular opinion-of ‘a conjecture suggested by the facts but not indubitably certified by them-would be decided by an impartial and intelligent judge’.26 But the judge simply determined what degree of probability the evidence gave to the conjecture; his conclusion did not itself constitute part of the evidence in support of the opinion’s degree of probability. In the same century Jean Buridan, when considering the question whether a projectile is moved by air or by something else, also treated probability as evidential likelihood: But others cavil when they say that the prior part of the motion which produced the projection produces another part of the motion which is related successively and that produces another part and so on up to the cessation of the whole movement. But this is not probable, because the ‘producing something’ ought to exist when the something is made, but the prior part of the motion does not exist when the posterior part exists, as was elsewhere stated. Hence, neither does the prior exist when the posterior is made.27

Later in the same discussion

Buridan

wrote:

And it is probably (verisimile) that that impetus is a quality naturally present and predisposed for moving a body in which it is impressed, just as it is said that a quality impressed in iron by a magnet moves the iron to the magnet. And it is also probable that just as that quality (the impetus) is impressed in the moving body along with motion by the motor; so with the motion it is remitted, corrupted, or impeded by resistance or a contrary inclination.28

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Julius Weinberg has pointed out that by the mid-fourteenth century there were two common senses of the term ‘probable’. One was applied to propositions that were taken to be true by the majority of people or by a select group of wise people. These propositions were believed to be true because they were derivable from premises generally agreed to be plausible. The other sense of ‘probable’ was the frequency sense and was applied to generalisations that held mostly but not always. 29 Hacking is correct in drawing attention to the first sense and incorrect in passing over the second. This is an important omission because the historical basis of Hacking’s argument is that because the first-or testimonial-sense of probability held sway until the seventeenth century, the notion of probable knowledge, and hence of aleatory probability, could not arise. In sum, Hacking’s historical thesis depends upon the frequency sense of probability not being known to such medieval thinkers as John or Mirecourt, Buridan andNicholaus. However, not only was it known to them but they habitually used it in the course of specific arguments. Thus Nicholaus argued: that it can well be held with probability that wherever hotness has being it has equally perfect being, and similarly in the case of coldness, whiteness, and

blackness, and so on, but that it does not everywhere perform its action equally, because of the admixture of its opposite. But two things seem to contribute to the destruction of this probability. After giving his reasons,

Nicholaus

goes on to say:

if two candles were taken altogether equal and alike as to matter, form, etc. (which is not possible, as I intimated above), I would say that at the midpoint, where the lights would meet, there would not be greater light and this would be as true of a thousand as of two. In keeping with this the highly improbable result would seem to follow that if some altogether similar wax were taken and made into a torch, it would not give more light than a small candle.30 Did all medieval writers believe, as Hacking says they did, that ‘evidence short of deduction was not really evidence at all’? Clearly not, for Jean Buridan took issue with Nicholaus of Autrecourt on this very point. Nicholaus had argued that since the existence of one thing cannot be inferred from the existence of another thing, we cannot obtain knowledge of causes through their effects. All certain knowledge is reducible to the first principle (or law of non-contradiction) including the certainties of immediate consciousness. Nicholaus wrote: ‘From the fact that some thing is known to exist, it cannot be inferred evidently, by evidence reduced to the first principle or to the certitude of the first principle, that another thing exists’. The reason is that ‘the consequent would not be really indentical with the antecedent, nor with a part of what is signified by the antecedent’. Hence we could not know the consequence ‘by evidence of the first principle’.31 Buridan replied that a cause is known through its effect because the latter ‘bears a certain likeness’ to the former and can thus ‘represent’ it. He denied that we cannot infer the existence of one thing from that of another, saying that ‘there are almost an infinite number of principles known per se, either through sense or through experience or through inclusion of terms, without it being required that

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they be demonstrated through the first principle’.32 The question from which this dispute had arisen was whether God can produce an effect other than by its natural cause. Nicholaus rejected the view that God could do what nature could not, claiming, as Ernest Moody summarises it, ‘that ifwe admit that an effect can be supernaturally produced without its natural cause, then we have no right to posit natural causes for any effects whatever’.33 Moody goes on to say that the opposing view, represented by such people as Aquinas, Ockham, Bernard of Arezzo and Buridan, argued that the laws of the created world are certainly not logically necessary but have scientific necessity-ex suppositione naturae-require natural evidence, and hence ‘retain an element of probability’.34 Buridan concluded: certain people speak very evilly, seeking

to destroy the natural and the moral sciences on the ground that their principles and conclusions do not for the most part possess absolute evidence, but can become false through possible supernatural instances; for evidence in the unqualified sense is not required for such sciences, but the above mentioned types of evidence, secundum quid or ex suppositione, are

sufficient. Whence it is well said by Aristotle that the accuracy of mathematics is not to be looked for in every science.35 To claim, as Hacking does, that the medieval thinkers in general thought nondeductive evidence to be somehow not genuine is to neglect one of the basic controversies of the fourteenth century: whether scientific knowledge of the created world is to consist only in knowledge of logical and mathematical tautologies or, instead, in empirical hypotheses open to testing by observation and experiment. ‘In truth’, wrote Pierre d’Ailly, ‘it is not at all necessary that an evidence be of the highest order, for evidence admits of various degrees. On this, Paul Vignaux comments: ‘Alongside unconditional evidence, which coincides with that of the principle of noncontradiction, Ailly admits a conditional evidence-evidentia conditionata-which is valid only within the hypothesis of a natural order established and respected by God, being given his general influence and the customary course of nature and the absence of the miraculous’.36 The causal field within which the sciences operate is of this character. For as Vignaux puts the view, how can we ‘require a certainty superior to the probabile in matters essentially dependent on divine liberty’?37 John of Mirecourt held similar opinions to those of d’Ailly on this point. With the exception of my denial of my own existence, all propositions dependent on experience are subject to ‘natural evidence’, that is, ‘evidence by which we give assent to a thing’s existence without any fear of error, this assent being brought about by causes which naturally necessitate our assent’.38 While such propositions are known to us, John says that ‘they are not known to us by the supreme kind of knowledge’. On Frederick Copleston’s interpretation, “‘natural evidence” meant that we naturally assent to the existence of what we sense, though it would be possible for us to be in error, if, that is to say, God were to work a miracle’.” Of John’s phrase ‘causes naturally necessitating assent’, Copleston adds that ‘it looks very much as though he meant that, though we can conceive the possibility of the principle of causality not being true, we are obliged by nature to think and act in the concrete as though it were true ‘.40This was also the view of Nicholaus of

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Autrecourt and, of course, of its much later adherent, David Hume. More generally, what these medieval advocates of the distinction betwen logical and empirical necessity make obvious to us is that they did not believe that infallible knowledge of cause and effect is possible. Not only they but their opponents, such as Nicholaus of Autrecourt, rejected the view that infallible knowledge of this sort is possible. Moreover, as we shall suggest presently, all these thinkers were simply carrying on a traditional view that was much older than they were. Therefore Wilson is mistaken in claiming that medieval thinkers did not believe that ‘human reason is essentially fallible’. He must also be mistaken in suggesting that what made possible the rejection of a belief in human infallibility was the acceptance, in the eighteenth century, of a ‘new metaphysics’, one that denies that ‘there are necessary connections that account for regularities among sensible particulars, and that these can be discerned by the mind’. For the medieval rejection of human infallibility long preceded any acceptance of a new metaphysics by Hume or anyone else in the eighteenth century.

III. THE SCEPTICAL

PROBLEM

OF INDUCTION

Hume’s critique of causality stands at the end of a long tradition of such debates about the relation of cause and effect and, in consequence, of divine intervention in the natural world. It has been widely known since the publication of J.E. Renan’s Averroes et Paverroisme in 1852 that the eleventh-century Persian philosopher, al-Ghazali, the target of Averroes’ criticism, denied that the causal relation is a logically necessary one. In the course of criticising his predecessor, Avicenna, for holding that the causal relation is necessary, al-Ghazali wrote: According to us the connexion between what is usually believed to be a cause and what is believed to be an effect is not a necessary connextion; each of two things has its own individuality and is not the other, and neither the affirmation nor the negation, neither the existence nor the non-existence of the one is implied in the affirmation, negation, existence, and non-existence of the other-e.g. the satisfaction of thirst does not imply drinking, nor satiety eating and so on for all the empirical connexions existing in medicine, astronomy, the sciences, and the crafts.. . it is in God’s power to create satiety without eating. . . and so on.4’ In brief, al-Ghazali argued, as had al-Ashari in the previous century, that God can do everything but the logically impossible. To the objection that such aview leaves it open that if a man ‘left a youth at home, he might find him turned into a

dog; or he might leave ashes and find them turned into musk’, al-Ghazali replied that God has given us the knowledge ‘that He will not do all these possible is the proof that things’, although He can do so. 42 What, asked al-Ghazali, contact with fire causes cotton to burn? There is no other proof, he said, than the observation of burning upon contact; ‘but observation proves only a simultaneity, not a causation, and, in reality, there is no other cause but God’.43 It is because of this common medieval belief in the possibility of divine intervention in the natural world that such thinkers as Scotus held that generalisations based on experience of particular cases cannot be known as certain. Since cause and effect are only related contingently, ‘we have here’, as Scotus said, ‘no knowledge of the

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actual union of the terms but only a knowledge of what is apt to be the case because of the nature of the terms. 44 But if we cannot infer the existence of one thing from that of another, it follows that we must rely on probable arguments rather than deductive proofs. Ockham gives us an explicit definition of ‘efficient cause’: ‘That is the cause of something which, not being posited, the thing does not exist, and being posited, the thing exists’.45 Thus for him a cause is a necessary and sufficient condition of its effect, and this relationship, in any given case, can only be learned from experience. For us to know that A is a cause is for us to know that it bears a specific relationship to an effect, B, since our knowledge that A has a particular causal relationship requires us to know to which things it is so related. Therefore we cannot deduce from our completed knowledge of the essential properties of A that it is either the cause or effect ofB. Ockham wrote: ‘to know a cause insofar as it is a cause presupposes a knowledge of the effect so that knowledge of the thing as being a cause does not cause a knowledge of its effect but rather is the result of knowing its effect’.46 However, while Ockham believes that efficient causes exist and that we learn them through experience, he does not believe that we can logically demonstrate their existence. The reason is the familiar one that omnipotent God could have, and may have, arranged to be the sole cause of any given effect. For Ockham, as for al-Ghazali, all that we can observe in the causal relationship of things is their spatial conjunction and temporal sequence. Barring miracles, this is sufficient for us to learn causes and their effects since the processes of nature, though continguent, are orderly and stable. He, like Scotus, held the view that when it is not impeded a natural cause will produce its effect. Thus we learn of efficient causality by means of our observation of regular succession; but the two are not identical.47 The causative power (virtus causativa) simply shows itself in the existence of regular sequence.48 It has often been remarked that Nicholaus of Autrecourt, in his critique of causation, does not rely only on the argument from God’s omnipotence. He relies, also, on an array of logical and empirical arguments. He says that the appearances of things give us no evidence for the existence of efficient causation, and that for all they show us God may be the only cause. Repetition of experience is merely repetition of appearances. Since the appearances never provide us with evidence of causation, but only of conjunction and sequence, the repetition of appearances cannot increase the probability value of any inductive argument concerning the presence of causation. However, as Weinberg has warned us, ‘This is not to say that a probability does not exist for future events running the same course as past events. But it does imply that the probability will be one of a conjunction of appearances and not of an efficient causation of one thing by another’.49 If the two appearances have been joined together in our past experience, then the occurrence of one of them in the future gives some probability to the occurrence of the other. 5oAs Nicholaus put it, ‘If it was once evident to me when I put my hand to the fire that I became warm, it is now probable to me that if I put my hand to the fire I should become warm.‘s1 What my experience of repeated conjunction of appearances produces in me is a habit of conjecturing that the particular conjunction will hold universally in the future. Each example of such a conjunction strengthens my habitus conjecturativus and thus strengthens my belief in the universality of that conjunction.s2 So all I can

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obtain from these experiences is a conjecture, with some probability, that a causal connection holds between specifiable appearances. Nicholaus applied this conclusion in his criticism of Scotus’s causal principle that whatever occurs in a great many cases from an unfree cause is its natural effect. For in Nicholaus’s view, frequent precedence does not entail invariable precedence, and no amount of experience and repetition can tell us that the latter will occur. The causal principle of Scotus merely assumes as true the very claim that is in question. Because our experience of associated appearances can give us no possible evidence of causation or of a possible mechanism of causation, we must conjecture about the frequency of future conjunctions on the basis of past ones. But this is simply a conjecture, though one with some probability, that future conjunctions will be like those of the past.53 ‘Some probabilities can be inferred’, Nicholaus writes: First, there are the ease and difficulty, painfulness, weariness, which we experience in ourselves when something is somewhere where previously it was not, as when something moves a small or larger stone, or when someone sees the sun or something else.

He goes on to give another

example:

when this whiteness ceases, at the moment of ceasing it is elsewhere, and it does not always appear that it is transferred to a neighboring place. If therefore, this were by way of transference, it would need an agent. And so it is satisfactory to accept as a rather conjectural proposition that it is elsewhere by way of causation, so that it is caused elsewhere.54

Human beings, then, may conjecture, with some probability, that such experiences are evidence of causation. In any case, the starting point of Nicholaus’s criticism is that human beings do not merely make such conjectures. They unjustifiably and firmly believe that appearances are caused and that there are arguments, both logical and empirical, which show this view to be correct. But what the arguments actually show is that we can never have knowledge that any appearance is caused or that causation itself exists. One way in which Hume phrased his sceptical doubts was this: That there is nothing in any object, consider’d in itself; which can afford us a reason for drawing a conclusion beyond it: and That even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience.55

If we take this as an adequate summary of Hume’s ‘sceptical doubts’, then it is clear that they are also largely present in such earlier writers as al-Ghazali, Scotus and Ockham. It is equally clear that causal scepticism is a central feature of the thought of Nicholaus of Autrecourt, and that his habitus conjecturativus is an early version of Hume’s custom and repetition as applied to the idea of causal necessity. For both authors, causal necessity is, in Hume’s words, ‘that propensity which custom produces, to pass from an object to the idea of its usual attendant’. It ‘exists in the mind, not in objects’.56 Hence it cannot be correct to

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claim, as Hacking does, that ‘Hume’s sceptical doubts were unknown before 1739’; and, in consequence, there can be no point in going on to ask, as Hacking does, why this was so. There is one further point. Wilson has written that once we accept the view that human reason is essentially fallible ‘we can then proceed to draw distinctions. So Hume gives an extensive account of reasonable and unreasonable principles upon which to base our expectations (Treatise, 1, III, xii), and for the former lays down the detailed “Rules by which to judge of causes and effects” (Treatise, 1, III, that most of Hume’s Rules were familiar to such xv)‘.57 It is worth mentioning medieval writers as Scotus, Ockham, Grosseteste and Nicholaus of Autrecourt. The first four rules-continguity in space and time, priority of cause, constant conjunction, and same cause, same effect-were medieval commonplaces. The remaining four are to be found, separately, in the works of various writers, Ockham, Grosseteste, Buridan and Nicholaus among them. The significance of this for our purposes is that medieval recognition of these rules indicates that Wilson is mistaken in at least one respect. He claims that Hume’s sceptical problem could not be formulated until the relinquishment of the belief that ‘there are necessary connections that account for regularities among sensible particulars and that these can be discerned by the mind’.5s But Ockham, for example, was both a sceptic about our knowledge of any given causal connection and a believer in such self-evident principles as those of parsimony and the uniformity of nature. These principles were thought by him and other thinkers to be necessary, discernible by the mind, and ‘to account for regularities among sensible particulars’. Yet these principles, far from being replaced by Humean scepticism, were held in conjunction with it-were put forward as a means of limiting its effects. Now the medieval concern with ‘rules for judging of causes and effects’, a concern displayed by Ockham, is compatible both with causal scepticism and with adherence to the necessary principles of inductive science. So the fact that all three sets of ideas-causal scepticism, necessary principles and causal rules-were held concurrently is additional testimony that the presence of rules for judging causes was not dependent on the absence of necessary principles. Moreover, it could also be shown, although it is not important here, that in the history of philosophy a concern with such rules was sometimes present in the absence of causal scepticism. That is, a concern with some of these rules was joined to the belief that causation is a logically necessary relation and that the rules are required in order for us to identify examples of it.

IV. INDUCTION

AND THE

LOW SCIENCES

We have been arguing that Hacking is mistaken in his claim that ‘the concept of internal evidence of things’ did not arise until the mid-seventeenth century. Hacking’s mistaken claim is based on his further view that the notion ofinternal evidence arose from the development of the ‘low sciences’-geology, alchemy, astrology, and medicine-which could not produce demonstrations as the ‘high sciences’ of mechanics, optics and astronomy could on many occasions. Hence the low sciences were restricted to devising methods for the proof of mere

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opinions about nature rather than trying to obtain certain knowledge of its processes. The upshot, says Hacking, was that the low sciences made use of the belief that nature reveals itself in evidential signs that have to be deciphered by the scientific investigator and assigned an appropriate degree of reliability, All this, according to Hacking, was foreign to the high sciences. The question for us here is whether all this, or any part of it, is true. The first qualification to be made of Hacking’s view concerning the difference between the high and low sciences is this: not all medieval thinkers took all, or in some cases any, scientific deduction (demonstration) to supply us with unq~lifiedly necessary truths about nature. Scotus, for instance, argued that since the laws of nature had been freely chosen by God and could be altered at his will, such laws could not be inherently necessary. Instead, the certainty or infallible knowledge given to us by scientific demonstration is simply that a particular kind of agent has an aptitude to yield the same sort of effect in every case. There is no certainty that the effect in question will actually be produced in a given cases9 The aim of demonstrative science ‘is to discover not what is necessary in nature but what is possible or cornpossible’. Thus we can obtain necessary knowledge only about ‘the possibilities of contingent things’.60 Similarly, both Ockham and Nicholas of Autrecourt argued that the conclusions of demonstrative syllogisms are not absolutely certain. The former held that the premises of such syllogisms must be known by primary and evident cognition-by present perception of particulars, for example-and hence the conclusions of these syllogisms are dubitable and can only be known indirectly.6’ The latter author held that since all propositions except the law of non-contradiction and those that record present perceptions could be altered at any time by God, we cannot rely on them to yield certain knowledge of nature.62 We have already seen that Buridan agreed with Nicholaus on this point, but argued that in any case reliable scientific explanations do not require absolute certainty, for probability will do. Hacking does not take account of this point. For Buridan, demonstrative science, as opposed to the much larger body of natural science, is restricted to events and processes that occur all, or at least most, of the time; and their explanation presupposes that no impediments occur. The result, according to Buridan, is that only a small proportion of natural events and processes are suitable for demonstrative explanation. The greater portion are suitable, in Eileen Serene’s words, only for ‘objects of natural science’. She goes on to remark that ‘for Buridan the phenomenon of the lunar eclipse cannot be an object of demonstrative science, nor can the dispositional property of the heavens to have eclipses from time to time’.63 On this point Buridan follows Albertus Magnus who argued that ‘scientific explanations are not absolute, but hypothetical, explaining what happens for the most part (in pluribus), but not without exception’. Hence scientific explanations and predictions are subject to the effects of ‘chance, fortune, human freedom, and divine intervention’; they give us only probable accounts.64 Ockham distinguished universally valid inferences from scientific syllogisms (or demonstrations). Weinberg points out that the following argument, while in Ockham’s view a valid inference, is not thought by him to be a demonstration: ‘(1) This A has caused B. (2) If one member of a species S has a given effect K, then any other member of the species S can cause B under the same

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circumstances. Hence all A’s can cause B’.6’ This is not a demonstration, according to Ockham, because, in Weinberg’s words, ‘A demonstration is a syllogism whose premisses are necessary, essential, etc., and whose middle term is an “intrinsic” middle term, i.e., pertains to the specific subject-matter of the does not have an subject and predicate in question’. The present argument intrinsic middle term ‘because the means was “all members of a species S, etc.“, and this proposition goes beyond the specific subject-matter of the particular subject and predicate’.66 Put more generally, Ockham’s claim-not recognised, apparently, by Hacking-is that inductive arguments from specific cases to universal generahsations are never demonstrations. For all inductive arguments contain a contingent minor premise and a major premise with an extrinsic middle term. But from an argument of two premisses, of which one is contingent, we can validly obtain no more than a contingent conclusion: that is, a conclusion that does not have as high a degree of certainty as that produced by a fully scientific syllogism, e.g. a demonstration in geometry. Aquinas, closely following Aristotle on this point, believes that contingent propositions can only be the object of opinion and not of either fully scientific knowledge or of understanding, although such propositions can give us some degree of certainty.67 Since the sciences of the physical and social world must contain contingent propositions, these sciences cannot give us demonstrative syllogisms concerning universals. Aquinas says that what such sciences as alchemy and medicine must deal with in large numbers are particular events and processes. Not only are these indemonstrable, but ‘if any of them is omitted error will follow’ because of their variability. So while, according to Aquinas, we cannot reasonably look forward to a demonstrative natural science-as Grosseteste, for example, believed that we could68-we can expect to produce sciences of contingent truths, truths that have considerable degrees of certainty.69 Now Hacking’s chief claim here is that ‘the concept of internal evidence of things’ developed primarily from the low sciences, for they could produce no demonstrative knowledge, and ‘so had to resort to some other mode of proof’.‘O One consideration against this claim, in addition to those already given, is that quite commonly the medievals discussed examples from both the high and low sciences in exactly the same way. Thus sometimes examples from optics and mechanics were treated in terms of experimental evidence or common observation, and sometimes as requiring mathematical demonstration. Similarly, examples drawn from botany, geology and medicine were treated by some thinkers as matters of demonstration and by other thinkers as matters of nondemonstrative science. Avicenna thought that we can have demonstrative knowledge that the dried juice of Concolvulus Scammania ‘b>J its nature is purgative of bile’, for the effect occurs so often that it cannot be the effect of chance.” Grosseteste said that we can obtain such knowledge even ofevents that occur not often but only from time to time, as in the case of the eclipse of the moon. For the eclipse occurs whenever its ‘necessitating cause’-the presence of the moon in the earth’s shadow-is present. 72 Ockham argued that scientific knowledge of nature consists in demonstrative syllogisms whose propositions, whether general or singular, are known through experience and cannot themselves be demonstrated; nor are they self-evident. These syllogistic inferences ‘presuppose the common course of nature’ and, as we have noted, give

Robert Brown us knowledge only of aptitudes and powers, not of actual occurrences. Quite a number of medieval thinkers believed that with the progress of scientific knowledge our information about nature would alter in such way that instead of our merely being able to demonstrate that the conclusion of a given syllogism is true, we should eventually learn how to demonstrate, by providing a cause or definition or self-evident principle, why it must be true. We should be able, in Aristotle’s terms, to replace the aposteriori demonstration of the simple fact with an LIpriori demonstration of the reasoned fact. Scotus, for instance, gives as an example of this change the true empirical proposition ‘The moon is frequently eclipsed’. At first, the truth of this proposition, he says, is known only from experience. But if we learn that the earth is an opaque body placed between the moon and its source of light, the sun, we can then deduce our proposition from a self-evident principle, namely ‘that when an opaque body is placed between a visible object and the source of light, the transmission of light to such an object is prevented’. We then know our proposition, Scotus concludes, ‘most certainly by a demonstration of the reasoned fact, for it is known through its cause’.73 Sometimes, however, we must be content with generalisations drawn from experience alone. In such cases we have knowledge, says Scotus, only ‘of what is apt to be the case’, not of whether something is actually the case, for the subject and its attribute may be separated without contradiction.74 Nevertheless, it was a familiar medieval hope, exemplified by Grosseteste, that a logically demonstrative science of all natural processes could be developed. It is certainly true that some medieval thinkers assimilated physical explanations to mathematical proofs and confined the term ‘knowledge’ to conclusions so derived. But it is also true that some thinkers did not: they discussed astronomical hypotheses, for example, in terms of empirical evidence, and thus treated them no differently from hypotheses found in the low sciences. Nicholas Oresme, like Aquinas thought that the ‘appearances’ of the heavenly motions could be saved equally by the hypothesis that the earth rotates daily and by the opposing hypothesis that the heavens rotate while the earth does not. ‘I conclude’, he said, ‘that one could not show by any experience that the heaven was moved with a daily motion and the earth was not moved in this way’.75 He followed Grosseteste in preferring the most economical hypothesis that accounted for the heavenly motions and, according to Copleston, differed from Albert of Saxony and Buridan on precisely this point. They thought that Oresme’s hypothesis would eliminate the motion of the planets. Hence they rejected his view that the earth rotates daily since this view does not account for the established observations of planetary motion. 76This debate on which hypothesis best explains the data of observation clearly concerns what Hacking calls the ‘internal evidence of things’. Yet contrary to his claim, it arises, equally clearly, from a problem in the high sciences rather than the low sciences. In general, discussions of empirical hypotheses arose quite commonly in the high sciences of astronomy, &ptics and mechanics. That they also arose in botany, geology and medicine hardly shows that non-demonstrative methods of scientific proof have a stronger historical connection with the latter fields than with the former. Hacking does not discuss the question of why the low sciences lacked demonstrations whereas the high sciences possessed them. He simply asserts that there was such a difference. But the obvious difference between the two sorts of

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sciences is not only that the high sciences were chiefly theoretical in aim and the low sciences chiefly applied or historical, although Aquinas was correct in remarking that medicine and alchemy lack certainty ‘because of the great number of singulars that must be considered in such sciences’.77 The difference is also that the high sciences actually had some reasonable theories, sometimes mathematically expressible, that could be used in testable explanations whereas the low sciences had no such theories with which to organise their great mass of observations, whether genuine or invented. The practitioners of these sciences were confined to inferring from one particular occurrence to another with the aid of those generalisations that the history of their crafts suggested to them. The natural result was that the large body of observations that might have been used as initial and boundary conditions, if suitable theories had been available, were systemically useless and certainly could not be fitted into the ordinary syllogistic explanation .78 Hence the low sciences could provide relatively few logical demonstrations. Of course the fact that alchemists, astrologers and medical healers were concerned, for the most part, to apply their skills to particular cases, and not merely to types of cases, enlarged the role of their observational data. The best hypotheses would have been idle for this purpose if the initial and boundary conditions did not adequately single out the case in hand and distinguish it from other, somewhat similar, cases-distinguish the causative conditions of John’s illness from that of Joseph’s, for instance. This interest in the specific case, or in the history of a particular event, was much more common in the low sciences than in the high sciences. For the healer, the miner, the engineer, the alchemist were less interested in explanatory principles than in achieving specific results, in particular instances; and for this the practitioneers needed data that discriminated between similar cases. But, then, as Aquinas remarked, ‘there cannot be demonstration of particulars, as we have shown, but only of universals’.79

V. THE EMERGENCE

OF PROBABILITY

Laudan has criticised Hacking for not distinguishing the history of ‘Plebian Induction’ from that of ‘Aristocratic Induction’. The first concerns the question to what degree a particular number of its positive instances ‘constitute evidence for the warranted assertion’ of a universal generalisation. The second concerns the degree to which ‘a certain number of confirming instances’ of a theory ‘constitute evidence for the warranted assertion’ of the theory. The difference is simply, in Laudan’s words, that ‘theoretical statements may have confirming instances (i.e., known, true empirical statements entailed by them), but they do not possess positive instances’.*O Theoretical statements, says Laudan, make not only a testable claim about ‘observable relations’ but also ‘an untestable claim about microstructural processes’. Whereas a generahsation is true if all its ‘possible positive instances’ are true, a theoretical statement can be false even if all its possible confirming instances are true, for it asserts more than their conjunction.*’ For Laudan, the philosophical importance of this distinction is that the two

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forms of induction require different solutions. The problem of Plebian Induction would be solved if we knew that nature was uniform: today’s bread would have to nourish me tomorrow; and fire, having burned me in the past, would do so again. But an established principle of uniformity would not solve the problem of Aristocratic Induction. The reason is that in any given case a theoretical statement asserts more than the sum of its known and true empirical entailments.** However, Laudan’s criticism of Hacking’s historical account is that it limits itself to Plebian Induction and overlooks the history ofAristocratic Induction. When the latter is considered Hacking’s three historical thesescan be falsified. For in contrast to Plebian Induction, there existed a pre-seventeenthcentury concept of aristocratic inductive evidence; ‘a sceptical problem of (aristocratic) inductive evidence long before Hume’; and high, i.e. theoretical, sciences that gave us the concept of ‘the internal evidence of things’.s3 The evidence produced in this paper shows us that Laudan is correct on all three points. But it also shows us that Laudan is mistaken in believing that there was neither a pre-seventeenth-century concept of plebian inductive evidence nor a sceptical problem of plebian inductive evidence long before Hume. From Avicenna to Nicholaus of Autrecourt the problem of inductive scepticism was stated in terms of plebian examples-in terms, that is, of universal generalisations and their positive instances such as fire burning and bread nourishing. The medieval writers’ attempt to state a principle of uniformity-as in Scotus’s claim that ‘whatever occurs in a great many instances by a cause that is not free, is the natural effect of that cause’-was an attempt to bridge the inductive gap betwen observed properties and expected ones: between known cases of scammony producing bile, of herbs that are hot, or of eclipses of the moon, and of predicted future cases. The medieval use of this principle of uniformity was to justify universal generalisations, not theoretical statements. Hence on this point, as on the history of the problem of inductive evidence, and the influence of the two sorts of science, Laudan’s distinction between Plebian and Aristocratic Induction is otiose. All three of Hacking’s historical theses can be disproved without its aid. There are several other corrections to be made to Hacking’s history. One is that our evidence indicates, as we have seen, that the distinction between opinion and knowledge was quite often drawn by medieval thinkers so as to assign some highly probable inferences to the category of knowledge. Thus, contrary to Hacking’s argument, there was no general agreement that the low sciences belonged solely to the realm of opinion and the high sciences solely to that of knowledge. Therefore Hacking’s claim that the sciences were divided in this way cnanot be used as an argument in favour of the conclusion that the concept of probability developed solely from the low sciences and the realm of opinion. Furthermore, contrary both to Hacking, and to Wilson who supports him on this,84 Hacking has not even shown that the concept of probability emerged solely, or even chiefly, from opinio. Another correction is this. Hacking concluded that the two notions of probability, aleatory (or chance) and epistemic, emerged together in this seventeenth century. Wilson had argued that what emerged was only the aleatory concept, connected with dice tossing and ‘the application of statistical reasoning to cases of “contrary causes”‘. The epistemic notion of degrees of assent is

History

versus Hacking

‘parasitic

upon

on Probability

the aleatory

notion’.

671 Wilson

then goes on to write, with italics:

Now, for the ~nd~~ateda~eatoryuses ofprobab~~ityto emerge what ispresupposedis an interest in matter-of-obse~ab~e-fact regularities. It would seem, therefore, that one can account for the emergence of this concept of probability simply by citing the dominant interest in matter-of-observable-fact regularities and in acquiring improved knowledge of such regularities. 85

Yet we have already seen that the epistemic notion of probability in the form of degrees of assent was used by medieval thinkers. So it cannot be historically parasitic upon the emergence of the seventeenth-century aleatory notion. We have also noted the medieval emphasis upon examples of plebian inductive inference, and this amounts to an interest in, and stress upon, ‘matter-ofobservable-fact regularities’. Wilson is correct, therefore, in claiming that the concept of probability that appears in the seventeenth century is not dual but aleatory. Hence Wilson is also correct in thinking that no account is needed ofthe emergence of a dual concept, for no such concept emerged. We are left, then, with the major question of why the aleatory concept did not emerge until the seventeenth century and, connected with this, the (subsidiary) question of why so few thinkers before Bacon ‘worried about the degree to which positive instances probabilified generalisations’. The answer to this second question is surely not that the medievals’ attention was directed at the probabilification of scientific theories (or theoretical statements). For their discussions of probable inference deal with observable regularities and the justification for generalising from observed cases to all possible instances. Given the medievals’ reliance upon a principle of uniformity, the apparent justification obtained by its use seems to have been a substitute for worrying about the degree of probabilification given by positive instances of a generalisation. Lacking any way of measuring degrees of evidential support, at least some of the medieval thinkers relied on falsification to eliminate candidates for generalisation, and on the principle of uniformity to obtain universal generalisations. Against the latter, Nicholaus of Autrecourt argued that the principle assumed the solution that it was supposed to produce. But in the absence of any other answer except that of causal scepticism, it is no surprise that the fuller development of the notion of epistemic probability stagnated and had to wait upon the discovery, in the seventeenth century, of the means of measuring chance probabilities, and wait, also, upon the application of those means to the problem of evidential support. The question of why the aleatory concept did not emerge mathematically until the seventeenth century is more difficult, of course. But it is not even clear that there are good reasons why the concept should have obtained mathematical expression earlier. What is clear, however, is that if there are such reasons Hacking’s book does not describe them. Robert Australian

~~t~ona~ University, Canberra

Brown

Robert Brown

672 NOTES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.

(Cambridge, 1975). L. Laudan, ‘Ex-Huming Hacking’, Erkenntnis 13 (1978) 417-35. Hacking, Emergence of Probability, p.176. Ibid., p.35. Laudan, ‘Ex-Huming Hacking’, p.423. Ibid., p.425. F. Wilson, ‘Critical Noptice’, Canadian Journal OfPhilosophy VIII (1978), 587-97. Ibid., p.595. Ibid. Ibid., p.596. S. Blackburn, Philosophy 51 (1976), 478. A.C. Crombie, Robert Grosseteste and the Origins of Experimental Science (Oxford: Clarendon Press, 1953 and 1971), pp.80-1. Ibid., pp.79-85. Ibid., pp.88-9. Hacking, Emergence of Probability, p.37. Crombie, Robert Grosseteste. p.87, fn.1. Hacking, Emergence of Probability, p.179. P.C. Vier, Evidence andlts Function According to John Duns Scotus (St. Bonaventure, New York: Franciscan Institute, 1951), p.138. A. Wolter, Duns Scotus Philosophical Writings (Edinburgh, 1962), p.109. Ibid. Vier, Evidence, p. 143. Ibid, p.147. Hacking, Emergence of Probability, p.22. J. Weinberg, NichoIaus of Autrecourt (Princeton, 1948), p.120. Ibid., pp.120-1. Ibid., p.126. H. Shapiro, ed., MedievaI Philosophy (New York, 1964), p.534. Ibid., p.535. J. Weinberg, A Short History of Medieval Philosophy (Princeton, 1964) pp.271-2. The Universal Treatise (Milwaukee, 1971), pp.13940. E.A. Moody, ‘Ockham, Buridan, and Nicholas of Autrecourt’, Franciscan Studies 7 (1947), 136. Ibid., p.137. Ibid., p.122. Ibid., p.141. Ibid., p.140. P. Vignaux, Philosophy in the Middle Ages (London, 1959), pp.195-6. Ibid., p.196. F. Copleston, A History of Philosophy, Vol.111, Pt 1 (New York, 1963), p.141. Ibid., p.142. Ibid., p.144. Averroes’ Tahafut AI-Tahafut, Vol.1, trans. and ed. Simon Van Den Bergh (London, 1954), p.316. Ibid., p.324. Ibid., p.317. Wolter, Duns Scotus, p. 111. Weinberg, Short History, p.260. J. Weinberg, Abstraction, ReIation, and Induction (Madison, 1965), p.144.

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41. Weinberg, Short History, p.262; Copleston, History of Philosophy, p.85. 48. Weinberg, Abstraction, pp.1467. 49 Weinberg, Autrecourt, p.68. 50. Ibid., p.112. 5 1. Copleston, History of Philosophy, p. 152. 52. Ibid., p. 70. 53. Weinberg, Short History, p.274; Copleston, History of Philosophy, pp.69-70. 54. Universal Treatise, p.141. 55. A Treatise of Human Nature, ed. E.C. Mossner (Harmondsworth, 1969), Bk I, XII, p.189. 56. Ibid., Book I, XIV, p.216. 57. Wilson, ‘Critical Notice’, p.595. 58. Ibid, p.593. 59. Vier, Evidence, p.148. 60. Eileen Serene, ‘Demonstrative science’, in The Cambridge History of Later Medieval Philosophy, ed. N. Kretzman, A. Kenny and J. Pinborg (Cambridge, 1982), p.510. 61. Ibid., p.514. 62. Ibid., p.515. 63. Zbid., p.516. 64. B.M. Ashley, ‘The nature of natural science’, in AIbert Magnus and the Sciences, ed. J.A. Weisheipl (Toronto, 1980), pp.834. 65. Weinberg, Abstraction, p. 149. 66. Ibid., pp.149-50. 67. Serene, ‘Demonstrative science’, p.505. 68. Ibid., p.503. 69. Ibid., p.506. 70. Hacking, Emergence of Probability, p.35. 71. Weinberg, Abstraction, p. 134. 72. Serene, ‘Demonstrative science’, p.503. 73. Wolter, Duns Scotus, p.110. 74. Ibid., p.111. 75. Copleston, History of Phi/osophy, p.173. 76. Ibid. 77. Serene, ‘Demonstrative science’, p.506, fn.37. 78. Ibid., p.512. 79. Ibid., p.504. 80. Laudan, ‘Ex-Huming Hacking’, pp.419-20. 81. Ibid., p.421. 82. Ibid., pp.420-1. 83. Ibid., p.422. 84. Wilson, ‘Critical Notice’, p.596. 85. Ibid.