Letter from a Gentleman (Director's Cut)

1 A Letter from a Gentleman in Dunedin to a Lady in the Country with Remarks on the Meaning of deduction in the celebrated Mr Hume's A Treatise of Human Nature, 3.3.1, and in the discourse of the Eighteenth Century in general. Wherein the various senses of deduction deriv'd from the Best Authors are carefully distinguish'd., and the Consequences for the Study of Ethicks are deduced. To Dr Annette Baier, formerly Professor of Philosophy at the University of Pittsburgh, Distinguished Madam, It is not without timidity that I venture to dispute with an author of your distinction whose knowledge of the Eighteenth Century and of the writings of the late Mr Hume vastly exceeds my own. I should scarce content myself with the old excuse of magis amicus veritas, did I not think that in this instance you had done a literary injustice to the memory of our mutual friend (as I cannot help thinking of Mr Hume); an injustice of some consequence for the understanding of ethicks. In your justly celebrated A Progress of Sentiments and in your recent paper ‘Hume’s Own “Ought” Conclusions, you defend the following assertions: (1) That when Mr Hume suggests that it ‘seems altogether inconceivable’ ‘how a new relation’, ought, or ought not, ‘can be a deduction from others, which are entirely different from it’, he employs ‘deduction’ in the large and liberal sense characteristic of Sherlock Holmes. (2) That in this Hume was following the common custom of his times which employed ‘deduction’ to cover inferences generally, including ampliative inferences, reserving the word ‘demonstration’ for formally valid deductions. (3) That Hume did not mean to suggest that deductions from is and is not to ought and ought not were ‘altogether inconceivable’ but only that this new 2 relation or affirmation ought should be ‘observed and explained’ and that a reason should be given, how this new relation could be a deduction (that is inferr’d) from others, which are entirely different from it. (4) That Hume himself observes and explains this new relation or affirmation, deducing (in a large and liberal sense) ought nots - for example that one ought not to steal - from observations concerning human affairs – such as the need for conventions regarding property. (5) That a small attention to the context of Hume’s remarks would subvert all those vulgar systems of philosophy which exaggerate the fork between fact and value, deriving this claim from Hume’s supposed thesis that it is ‘altogether inconceivable’ that an ought could be derived from an is. I maintain on the contrary (1) That in this celebrated passage, Hume employs ‘deduction’ in the strict sense, according to which if a conclusion B is justly or evidently deduced from a set of premises A, A cannot be true and B false, or B false and the premises A true. (Thus on this matter we disagree both about words and about the propositions that Hume is using those words to express.) (2) That Hume was following the common custom of his times which sometimes employed ‘deduction’ in a strict sense to denote inferences in which the premises cannot be true and the conclusion false, since, in the words of Dr Watts’ Logick, ‘the premises, according to the reason of things, do really contain the conclusion that is deduced from them’; that although Hume sometimes uses ‘demonstrative argument’ as a synonym for ‘deduction’, like most of his contemporaries, he generally reserves the word ‘demonstration’, for deductive inferences in which the premises are both necessary and self-evident. (Thus on this matter, we disagree about words and about the way they were employed.) 3 (3) That Mr Hume did indeed mean to suggest that deductions from is to ought were ‘altogether inconceivable’ since if ought represents a new relation or affirmation, it cannot, in the strict sense, be justly deduced from premises which do not really contain it (Thus we agree on the words that Mr Hume employed but disagree on the meanings that he meant to give them.); (4) That in a large and liberal (or perhaps loose and promiscuous) sense Hume does indeed deduce oughts and ought nots from observations concerning human affairs, but that the deductions in question are not general inferences, but explanations, since in another sense of ‘deduce’, common in the Eighteenth Century, to deduce B from A is to trace B back to A or to explain B in terms of A (Thus on this matter we agree in words but disagree in things.); (5) That a small attention to the context of Hume’s remarks and to the logical notions on which they are based would indeed subvert those vulgar systems of philosophy which exaggerate the distinction between fact and value; for just because it is ‘altogether inconceivable’ that the new relation or affirmation ought should be a deduction from others that are entirely different from it, it does not follow that the facts represented by is and is not are at bottom any different from the values represented by ought and ought not. (Thus on this matter we agree in things but disagree about the reasons for things.) Though the real dispute between us relates to Mr Hume we had better begin with point (2). For if ‘deduction’ was seldom employed to denote inferences in which the conclusion is contained within the premises, it is not very probable that Mr Hume employed it for this purpose. But if ‘deduction’ was sometimes used to denote such inferences, then Mr Hume might have been employing to that end in his celebrated remarks concerning is and ought. 4 But this raises a difficulty. Deductions in the strict sense are also deductions in the liberal sense, since in both cases, the premises give reasons – though not necessarily compelling reasons – for the mind to move from the premise to the conclusion. How then do we distinguish between the two? The clew is to be found in the fictions of Sir Arthur Conan Doyle. As all the world knows, the narrator of these tales is Dr Watson, who is something of a rattle and a character more notable for his courage than his intellect. In A Study in Scarlet, Dr Watson is sceptical about Holmes’s brags about the ‘science of deduction’. But Watson’s doubts are in some measure dispelled by an ocular demonstration of Holmes’ deductive powers. Watson sees ‘a stalwart, plainly dressed individual, walking slowly down the other side of the street’ and wonders what the ‘fellow is looking for’. ‘You mean the retired sergeant of Marines,’ says Holmes. When the individual ascends the stairs to No. 221B, Baker Street in order to deliver a message, Holmes’ deduction proves to be correct – the man is indeed a retired sergeant of Marines, currently employed as a commissionaire. As Holmes explains to Watson, he deduced this conclusion from the following premises: that the man had a great blue anchor tattooed on the back of his hand, a circumstance which ‘smacked of the sea’; that he had a military carriage, with regulation side whiskers, suggesting not a sailor but a marine; that although he was apparently not a gentleman, he had an air of command (to be gathered from the way he held his head and swung his cane); and that he appeared to be a steady, respectable, middle-aged man – from which premises Holmes deduced that he was a retired sergeant of Marines. Now what can we say of this deduction? It is evident, to begin with, that the inference is ampliative. The conclusion though it may have been rationally deduced was not really or even virtually contained within the premises. That the man was a sergeant of marines was a new truth which went well beyond the truths about his appearance that Holmes and Watson were already possessed of. Secondly the premises that Holmes had observed could have been true and the conclusion that he deduced could have been false. The man’s air of command might have been due to his gentlemanly status, if, for example, he had been a secret agent who had stooped to conquer the enemies of the Empire by assuming the character of a commissionaire. Finally (and in consequence of the foregoing) the conclusion could have been false and the premises true. Had the man proved not to be a retired sergeant of Marines, 5 Holmes would not have been forced to conclude that he did not have an anchor tattooed on the back of his hand; that he did not have military carriage or regulation side whiskers; or that he did not appear to be a steady, respectable, middle-aged man with a certain air of command. Had the premises really contained the conclusion, and the conclusion been proved to be false, at least some the premises would likewise have had to be false. This allows us to distinguish deductions in the strict sense from deductions in the large. Deductions in the large sense, but not in the strict, are ampliative since the conclusions are not contained within the premises; they are inconclusive, since the premises can be true and the conclusion false; and they are not reversible, since the falsehood of the conclusion need not betoken the falsehood of any of the premises. Conversely a deduction in the strict sense (but not in the large) is not ampliative, the conclusion being contained within the premises; it is conclusive, since the premises cannot be true and the conclusion false; and it is reversible, the falsehood of the conclusion betokening the falsehood of at least some of the premises. In the words of Dr Watts, ‘From truth nothing but truth can follow but what is true; whensoever, therefore, we find a false conclusion drawn from premises which seem to be true, there must be some fault in the deduction or inference; or else one of the premises is not true in the sense in which it used in that argument’ (Watts, Logick 2.3, p. 301). Thus a man is employing ‘deduction’, ‘deduce’ and the like in the strict rather than the liberal sense, if the inferences which he denotes by that term, are, or are thought to be, non-ampliative, conclusive and reversible. Thus far deduction; but what of demonstration? Here, at least, I defer to the authority of Dr Johnson whose opinions on this topic scarcely differ from those of Hume. Just as deductions in the strict sense are a species of deductions in the large. so demonstrations are a sub-species of deductions in the strict sense. According to Dr Johnson’s Dictionary, to demonstrate a proposition is to prove [it] with the highest degree of certainty; to prove in such a manner as reduces the opposing position to evident absurdity whilst a demonstration is the highest degree of deducible or argumentative evidence; the strongest degree of proof; such proof as not only evinces the position proved to be true but shews the contrary position to be absurd and impossible. Hume, perhaps surprisingly, agrees: ‘When a demonstration convinces 6 me of any proposition, it not only makes me conceive the proposition, but also makes me sensible, that 'tis impossible to conceive any thing contrary.’(Abstract18/653) Thus a demonstration is a demonstrative argument or a deduction in the strict sense in which the premises are not only necessary but self-evident (since there might be necessary truths which were not evident to us and which would therefore not afford ‘the strongest degree of proof’). If the premises are both necessary and self-evident (such that the contrary position is absurd or impossible) and if the premises cannot be true and the conclusion false, then we have indeed achieved the highest degree of deducible or argumentative evidence of which human reason is perhaps capable, though the possibility of a slip in a long chain of reasoning means that the premises themselves are more evident still. Dr Owen objects that if a demonstration were understood as a deductively valid argument with necessarily true premises – which is what I have ventured to propose – then any combination of necessary propositions would rise to the dignity of a demonstration . An argument is deductively valid – that is, a deduction in the strict sense – if the premises cannot be true and the conclusion false. But if the conclusion is necessarily true, then the premises cannot be true and the conclusion false, since the conclusion cannot be false. Thus any argument with a necessarily true conclusion will be deductively valid, and any deductively valid argument with a necessarily true premises will qualify as a demonstration, though the premises may have as little to do with the conclusion as the conclusion has to do with the premises. Hume could not have subscribed to such an absurd and useless notion. Hence, whatever he meant by ‘demonstration’ he did not mean a deduction (in the strict sense), with necessarily true premises. (Owen (1999) Hume’s Reason, pp. 90-91) This argument proves too much. For if Hume could not have meant by ‘demonstration’ a deductively valid argument with necessarily true premises, then no man of sense could have meant such a thing. Yet it is evident that men of sense, and even genius, have meant precisely this. Let me begin with the late Bishop of Cloyne: Fourthly, by a diligent observation of the phenomena within our view, we may discover the general laws of Nature, and from them deduce the other phenomena, I do not say demonstrate; for all deductions of that kind depend on a supposition that 7 the Author of Nature always operates uniformly, and in a constant observance of those rules we take for principles: which we cannot evidently know. (Berkeley Principles of Human Knowledge, §107.) The good bishop’s meaning is plain. By a diligent observation of the phenomena – that is by an induction – we arrive at certain laws of nature, such as the incomparable Sir Isaac Newton’s inverse square law. Once these have been arrived at we can (with the aid of certain assumptions) deduce other phenomena such as the periodic return of Halley’s Comet. But though the phenomena in question be never so justly deduced from the laws and initial assumptions, yet the deductions never amount to demonstrations since the premises from which they are derived are neither necessary – since they depend on God’s good pleasure – nor evident – since we cannot know that God will persist in His present purposes. But by thus distinguishing demonstration from deduction, Dr Berkeley makes it sufficiently plain that for him a demonstration is a deduction in which the premises are both necessary and selfevident. Dr Reid concurs. In every step of demonstrative reasoning, the inference is necessary, and we perceive it to be impossible that the conclusion should not follow from the premises. In probable reasoning, the connection between the premises and the conclusion is not necessary, nor do we perceive it to be impossible that the first should be true while the last is false …. It was, I think, the opinion of all the ancients, that demonstrative reasoning can be applied only to truths that are necessary, and not to those that are contingent. In this, I believe, they judged right. Of all created things, the existence, the attributes, and consequently the relations resulting from those attributes, are contingent. They depend upon the will and power of him who made them. These are matters of fact, and admit not of demonstration. (Reid, Essays on the Intellectual Powers of Man, 7.1, pp. 544-545.) Thus for Reid a demonstration is an inference in which it is impossible that the premise should be true while the conclusion is false and in which the premises themselves are necessary. I will only add that Reid gives the impression here that there cannot be a demonstrative or deductive argument, wherein the premises 8 themselves are either contingent or false, a view which was very far from being his real opinion1. Thus both Dr Reid and Bishop Berkeley conceive of demonstration as a deduction in the strict sense, wherein the premises cannot be true and the conclusion false, but with this addition, that the premises themselves must be necessary and selfevident. Now, it is the opinion of Dr Owen, that they are thereby committed to the view that any combination of necessary propositions constitutes a demonstration. But though Reid and Berkeley both believed that ‘2 + 2 = 4’ and ‘The Deity exists’ were necessary propositions, neither of them supposed that the one could be deduced from the other, at least not without the aid of additional premises! Were they perhaps unaware of this consequence of their opinions or is Dr Owen mistaken about the Eighteenth Century notion of logical consequence? Dr Owen’s error consists in confounding a necessary with a sufficient condition. If an inference is deductively valid, the premises cannot be true and the conclusion false. But it does not follow that if the premises cannot be true and the conclusion false, the inference is deductively valid. In the Eighteenth Century as now, some further condition had to be met. Dr Owen, I suspect, supposes, that the only possible condition could be syntactic, for example that the inference should conform to rules of Aristotelian syllogistic. But Berkeley, Hume and Reid would all have acknowledged demonstrations that do not conform to the dictates of Aristotle so none of them can have accepted such a constraint. (To do so would have smacked of the pedantry the ‘scholastic headpieces’ for whom they professed a perhaps unmerited contempt2.) But in the Eighteenth Century, as now, there was a further semantic condition that a valid deduction was expected to meet, a condition that I have hinted at already. Following the great Tarski, we would nowadays say that an inference is only deductively valid if there is no interpretation of the non-logical vocabulary according to which the 1 One might also quote in this connection Gershom Carmichael’s Brevisculae Intoductio ad Logicam (1722): ‘Every perfect argument (such as all, in intention, seem to be) which is constructed according to the rules laid down above, if it rests on true premises, yields a true conclusion, and if it rests on certain premises, yields a certain conclusion; this is called demonstration.’ 2 In fact the ‘scholastick headpieces’ knew full well that there were deductively valid arguments that did not conform to Aristotle’s rules. See Broadie (1993) An Introduction to Medieval Logic, 2nd edn. 9 premises are true and the conclusion false3 . Thus it is not true (as Dr Owen seems to think) that, for a logician of our, perhaps, degenerate age, an inference is automatically valid if the conclusion is necessarily true. On a Tarskian conception of consequence, an inference will be automatically valid if the conclusion is true however the non-logical vocabulary is interpreted, that is, if it is a truth of logic. But there are many necessary truths that are not truths of logic. Thus it does not follow from Tarski’s conception of consequence that any combination of necessary propositions constitutes a deductively valid argument. In the Eighteenth Century the learned subscribed to different constraint on consequence, which, vague and metaphorical though it undoubtedly was, was not without significance. It was moreover a constraint on demonstrations of which Hume was well aware, having ‘passed through the ordinary course of education with success’. For the ordinary course of education at Edinburgh comprehended the Latin lectures of Colin Drummond, then Professor of Logic. These were thrown into the form of a logical catechism: Q Cur Mens semper necessitatur ad Conclusionem Inferendam? Why is the mind always necessitated to infer a conclusion? R Quia Conclusio Virtualiter continetur In Praemissis. Because the conclusion is virtually contained in the premises. The idea that the conclusion of a valid inference is ‘contained’ within the premises is was common in the 17th and 18th Centuries and was accepted in one form or another by Hobbes, Geulinx, Arnauld and Nicole. Dr Watts – who was able on occasion to avert his eyes from the wondrous cross on which the Prince of glory died in order to apply himself to logic4 – employs this idea to get over a difficulty, evident to every discerning mind, that there are valid arguments – indeed arguments valid in virtue of their form - that do not comply with rules of Aristotle’s Syllogistic. ‘Though this sort 3 Though in axiomatic reasoning – which is the sort of thing that Reid, at least, has in mind – we would also impose a syntactic constraint. B would only be a consequence of A in the system S if the inference conformed to the rules of deduction enshrined in the system S. Tarski’s conception of consequence is more general, and, in a sense, more relaxed. 4 Dr Watts was not only a logician but a hymnist of note whose sacred songs now resound not only in the modest Conventicles of Dissent but in the stately Cathedrals of the Established Church. 10 of argument is confessed to be entangled or confused, and irregular, if examined by the simple rules of syllogisms; yet there is a great variety of arguments used in books of learning and in common life, whose consequence is strong and evident, and which must be ranked under this head’ (Watts Logick, p. 282). After listing several such arguments, he goes on ‘Now the force of these arguments is so evident and conclusive, that although the form of the syllogism be never so irregular, yet we are sure the inferences are just and true; for the premises, according to the reason of things, do really contain the conclusion that is deduced from them, which is a neverfailing test for true syllogisms as we shall show hereafter’ (Watts Logick, p. 284). Applying this never-failing test to the inference from ‘2 + 2 = 4’ to ‘The Deity exists’, it is plain that however so necessary they both may be, the one is not contained within the other, and thus that the argument is neither a ‘true syllogism’ nor yet a demonstration. Thus one can conceive of a demonstration as a deductively valid argument with necessary and self-evident premises without admitting the consequence that any combination of necessary truths achieves the dignity of a demonstration. Having distinguished between deductions and demonstrations and between deductions in the strict sense and deductions in the large, I can now defend the opinion of which I have already given strong hints – that the words ‘deduce’, ‘deduction’ etc were sometimes used in the strict sense in the Eighteenth Century. In fact they were employed in at least four distinct senses (excepting their use in Arithmetick): Sense 1 (modern): A deduction is an inference in which the conclusion B necessarily follows from the (possibly contingent or even false) set of premises A, because the conclusion B is in some sense ‘contained’ within at least one of the premises. To deduce B from A is to make such an inference. Deductions in this sense include syllogistic inferences, mathematical demonstrations and analytic inferences such as the inference from ‘Harry is a bachelor’ to ‘Harry is unmarried’. 11 Sense 2: To deduce B from A is to infer B from A in the Sherlock Holmsian sense in which the inferences involved can be, and often are, ampliative. A deduction is simply an inference. Sense 3: To deduce B from A is trace B back to A, or to explain B in terms of A. A deduction is such a tracing back or explanation. Sense 4: To deduce is to explain or set forth methodically. A deduction is simply a methodical exposition. It is not a matter of dispute between us that in the Eighteenth Century ‘deduce’ was often used in the second, large and liberal sense. Thus the incomparable Sir Isaac Newton remarks in his in his Opticks that ‘the main business of natural philosophy is to argue from phaenomena, without feigning hypotheses, and to deduce causes from effects till we come to the very first cause, which certainly is not mechanical’. Despite his contempt for feigned hypotheses and despite his evident desire to ground his theories in observation and experiment, it cannot be denied that when a cause is deduced from an effect, the proposition describing the effect could be true and the proposition describing the supposed cause, false (though happily this was seldom the case with Sir Isaac’s deductions)5 . Thus when Sir Isaac deduces he sometimes deduces in the large and liberal sense. When Bishop Butler deduces, he likewise deduces in Sense 2. A man can as little doubt whether his eyes were given him to see with as he can doubt of the truth of the science of optics, deduced from ocular experiments. (Butler Sermons 2, p. 48, BM 395) For it is evident to all, and would have been evident to Butler, that the science of optics cannot be logically deduced from ocular experiments. 5 A point he came to realize: ‘Although the arguing from Experiments and Observations by Induction be no Demonstration of general Conclusions; yet it is the best way of arguing that the Nature of Things admits of’. Newton, Opticks. 12 When Mr Gibbon deduces, he often infers 6, and when he infers, his inferences are seldom confined within the narrow constraints of deductive logic. [That Eusebius had ‘related whatever might redound to the glory, and suppressed all that could tend to the disgrace, of religion’] is the fair deduction from two remarkable passages in Eusebius, l. viii. c. 2, and de Martyr. Palestin. c. 12. (Gibbon, D&F, 3.16/83.) Let Gibbon’s deduction be never so fair, it was not a deduction in the strict sense. For that distinguished prelate, the bishop Caesarea. might have ‘indirectly confessed’ to literary principles that he did not practice, allowing himself a licence to distort the truth in the interests of religion, whilst retaining the habit of historical veracity. Hence Gibbon’s premises might have been true and his conclusion false. The philosophers of Greece deduced their morals from the nature of man rather than from that of God. (Gibbon D&F, 1.2/37.) Though the philosophers of Greece deduced their oughts and ought nots from ‘observations concerning human affairs’ rather than propositions about ‘the being of a God’, there is no suggestion (nor was it in fact the case) that these inferences were deductive in the strict sense of the word. The last of my loose and promiscuous deductions comes from Mr Hume himself: From the memorable revolutions, which passed in England during this period, we may naturally deduce the same useful lesson, which Charles himself, in his later years, inferred; that it is dangerous for princes, even from the appearance of necessity, to assume more authority, than the laws have allowed them. (Hist. 5.59/545) Whether Charles I did indeed deduce this useful lesson from the memorable revolutions to which he was subject is perhaps a sentiment open to doubt, but if he did so, he can hardly have done it by logic alone (as Hume himself was at pains to point 6 I count 68 instances of ‘deduce’ and ‘deduction’ in three distinct electronic texts of Gibbon’s – Decline and Fall, the Autobiography and the Vindication – of which 29 are inferences, none of them deductive in the strict sense. NB. References are to the 12 volume Bury edn, with the volume and chapter number and a page reference following a forward slash. 13 out); hence we must conclude that this deduction, if it existed, was a deduction in the large and liberal sense. But did anyone ever deduce in Sense 1? I have already supplied some evidence that they did from the writings of Dr Watts, Dr Reid and Bishop Berkeley. You beg leave to doubt this Madam, basing your skepticism on Dr Johnson’s definition of ‘deduce’ in his celebrated Dictionary, that is to form a regular chain of consequential propositions, which suggests Sense 2) rather than Sense 1). Dr Johnson was addicted to deduction both in the large sense and the strict, but the idea of deduction did not excite his intellectual propensities. (It is notable that despite his copious borrowings from Watts’ Logick – Howells notes ‘hundreds of examples and definitions‘ – when it comes to deduction Dr Watts in entirely neglected.) Nevertheless, some of Dr Johnson’s associated definitions do suggest that ‘deduce’ was on occasion used in the strict sense. ‘Deduction’ is defined as a consequential collection; consequence; proposition drawn from principles premised, whilst ‘consequence’ is defined as 3) a proposition collected from the agreement of other previous propositions; deduction; conclusion or 4) the last proposition of a syllogism; as in what is commanded by our Saviour is our duty; prayer is commanded; therefore prayer is our duty. Thus a ‘deduction’ can be a ‘consequence’ and a ‘consequence’ can be the last proposition of a syllogism. However that may be, an instance of deduction in the strict sense can be found in the correspondence of David Hume. As we have seen, a deduction in the strict sense is non-ampliative, conclusive and reversible. And in a letter to Hume, Dr Reid employs the verb ‘deduce’ in precisely this sense. But whether I have any success in this attempt or not, I shall always avow myself your Disciple in Metaphysicks. I have learned more from your writings in this kind than from all others put together. Your system appears to me not onely coherent in all its parts, but likeways justly deduced from principles commonly received among Philosophers: Principles, which I never thought of calling in question, untill the conclusions you draw from them in the Treatise of Human Nature made me suspect them. (Letters, 1.201n/376, Reid, 2002, Letter 21, p. 31) 14 Reid’s generous but critical compliment is clear. Hume justly deduces certain conclusions from principles commonly received among Philosophers. This is his great achievement. These conclusions appear to Reid to be false, and therefore, since the conclusions are indeed justly deduced – since the principles do really contain the conclusions that are deduced from them – if the conclusions are false the commonly received principles must be false also. Reid makes a similar observation about Berkeley in his Essays on the Intellectual Powers The principle from which this important conclusion [that all those bodies which compose the mighty frame of the world, have not any subsistence without a mind] is obviously deduced, is laid down in the first sentence of his principles of knowledge as evident; and indeed it has always been acknowledged by Philosophers … If this be true; then, indeed, the existence of a material world must be a dream that has imposed upon all mankind from the beginning of the world … supposing this principle to be true, Berkeley’s system is impregnable. No demonstration can be more evident than his reasoning from it. Whatever is perceived is an idea, and an idea can only exist in a mind. It has no existence when it is not perceived; nor can there be any thing like an idea, but an idea. (Reid, EIP 2.10/141-142.) [Note that both the demonstration and the deduction start from premises which Reid takes to be not only false but contingently so. It might be that we never perceived anything except ideas but in fact these are not the only objects of perception.] Berkeley’s ‘demonstration’, however so evident it may be, is not, in Reid’s opinion, a true demonstration since the principles from which it is deduced are not themselves self-evident, a consideration that came to Dr Reid’s attention, probably after reading Hume: If I may presume to speak my own sentiments, I once believed this doctrine of ideas so firmly, as to embrace the whole of Berkeley’s system in consequence of it; till, finding other consequences to follow from it, which gave me more uneasiness than the want of a material world, it came into my mind, more than forty years ago, to put the question, What evidence have I for this doctrine, that all the objects of my knowledge are ideas in my own mind? From that time to the present, I have been candidly and impartially, as I think, seeking for the evidence of this principle, but can find none, excepting the authority of Philosophers. (Reid, EIP 2.10/142.) 15 It is evidently Reid’s opinion that deductions in the narrow sense are reversible, a principle he not only implicitly employed but explicitly embraced: A syllogism which leads to a false conclusion, must be vicious, either in matter or in form: for from true principles nothing but the truth can be justly deduced. If the matter be faulty, that is if either of the premises be false, that premise must be denied by the defendant. (Reid, Logic, p. 137.) And this, of course, is what he is doing in his responses to Berkeley and Hume. Reid also subscribed to the principle that the conclusion of a strict deduction is contained within the premises, a principle he employs in his critique of Aristotelian logic: In reasoning by syllogism, from general principles we descend to a conclusion virtually contained in them. The process of induction is more arduous; being an ascent from particular premises to a general conclusion. The evidence of such conclusions is not demonstrative but probable …[but] we can have no other for general principles which are contingent in their nature, and depend upon the will and ordination of the maker of the world (Reid, Logic, 146). It is perhaps worth remarking Dr Reid was a close contemporary of Mr Hume’s, born one year earlier, a circumstance that is perhaps obscured for us by the fact that the youthful Hume wrote his great Treatise when he was still in his twenties whereas Dr Reid deferred publication of his greatest works until he was over seventy years old and had become too deaf to teach. But despite the late date at which Reid’s works were published, the ‘deductions’ of the aged Dr Reid are not entirely unrelated to the ‘deductions’ of the youthful Mr Hume. Whether Hume himself employed ‘deduce’ and ‘deduction’ in Sense 1), is a topic I shall defer for the present, but I flatter myself that I have sufficiently proved that he might have done so, since others employed ‘deduce’ in this strict and logical sense. But what of senses 3) and 4)? If we turn again to the luminous pages of Gibbon, we find that despite his many inferences, ‘deduce’ and ‘deduction’ are more often employed in these latter two senses. Sometimes Gibbon deduces B from A by tracing B back to A, sometimes he deduces B from A by explaining B in terms of A and 16 sometimes he deduces something by narrating an episode or setting things forth in a clear and perspicuous manner. (According to Dr Johnson one meaning of ‘deduce’ is to lay [things] down in a regular order so that the following shall naturally rise from the foregoing.) For example: It is the design of this, and of the two succeeding chapters, to describe the prosperous condition of [the Roman] empire; and afterwards, from the death of Marcus Antoninus, to deduce the most important circumstances of its decline and fall; a revolution which will ever be remembered, and is still felt by the nations of the earth. (Gibbon, D&F, 1.1/1.) Mr Gibbon is not inferring the most important circumstances of the empire’s decline and fall from anything else, nor is he tracing them back to or explaining in them in terms of any other facts or circumstances – rather his purpose in these chapters is simply to lay down those circumstances in a regular and perspicuous order, a purpose in which he abundantly succeeds. But the following passage illustrates the way that these various senses can insensibly blend into one another: From the age of Constantine to that of Clovis and Theodoric, the temporal interests both of the Romans and Barbarians were deeply involved in the theological disputes of Arianism. The historian may therefore be permitted respectfully to withdraw the veil of the sanctuary; and to deduce the progress of reason and faith, of error and passion from the school of Plato, to the decline and fall of the empire. (Gibbon, D&F, 3.21/338.) This deduction is primarily a setting forth, but it is also in some measure a tracing back. Mr Gibbon proposes to narrate the story of the theological disputes of Arianism, but he is also tracing back that memorable heresy to its origins in the school of Plato. Indeed, by tracing back the disputes about Arianism to the speculations of Plato, he is giving that philosopher a causal role, however slight, in the decline and fall of the Roman Empire, and explaining that event as due in some degree to the extraordinary passion for theological faction that possessed both the Romans and the Barbarians in that disputatious age. Sometimes, however, Mr Gibbon’s tracings back are not explanations but tracings back only. Thus: 17 Toxotius, the husband of Paula, deduced his royal lineage from Aeneas, the father of the Julian line. (Gibbon D&F, 5.31/201) . Toxotius may have traced his royal lineage back to the great Aeneas, but this deduction was not an explanation in any serious sense of the word. Sometimes however, the idea of explanation predominates: The motives of [Constantine’s] conversion, as they may variously be deduced from benevolence, from policy, from conviction, or from remorse, and the progress of the revolution, which, under his powerful influence and that of his sons, rendered Christianity the reigning religion of the Roman empire, will form a very interesting and important chapter in the present volume of this history. (Gibbon D&F 3.16/75.) Here the motives of Constantine’s conversion to Christianity are to be explained in terms of benevolence, policy, conviction, and remorse. There is, to be sure, an element of tracing back in this, but the question that Gibbon is endeavouring to answer is this: What cause or causes led Constantine to convert? Gibbon is seeking an explanation of that momentous event, deducing it, in this sense, from that emperor’s passions, dispositions, desires and beliefs. All these species of deduction are likewise to be found in Hume. Sometimes deduction is a setting forth: Accurate and regular argument, indeed, such as is now expected of philosophical enquirers, naturally throws a man into the methodical and didactic manner; where he can immediately, without preparation, explain the point at which he aims; and thence proceed, without interruption, to deduce the proofs on which it is established. (DNR Pam. to Herm. 0.1/127.) Here the proofs are deduced by being laid down in a regular order so that the following shall naturally rise from the foregoing. Sometimes deduction is a tracing back. Thus Richard of York 18 stood near the throne, and addressing himself to the house of peers … gave them a deduction of his title by descent; mentioned the cruelties by which the house of Lancaster had paved their way to sovereign power, [and] insisted on the calamities which had attended the government of Henry. (Hume, Hist, 2.21/447.) Plainly the Duke of York’s deduction, though part of an argument, was not itself an inference but a mere tracing back. Sometimes deduction is a tracing back with strong overtones of explanation. But as qualities, which tend only to the utility of their possessor, without any reference to us, or to the community, are yet esteemed and valued; by what theory or system can we account for this sentiment from self-love, or deduce it from that favourite origin? There seems here a necessity for confessing that the happiness and misery of others are not spectacles entirely indifferent to us? (Hume, EMP, 6.1.22/243.) Hume is endeavouring to prove that it is difficult, if not impossible, to explain our approbation of qualities useful or agreeable to the person himself (but not others) on the assumption that we are solely motivated by self-love. But the deduction that he deems to be impossible is clearly an explanation, not an inference, a setting forth or a mere tracing back. One might perhaps object that in distinguishing betwixt deductions as inferences and deductions as explanations, I am making a distinction without a difference. When Sir Isaac Newton explains the motion of Mars he does so by inferring those motions from a collection of premises to do with the mass of the Sun, the laws of gravitation and inertia and the position of that planet within the mighty frame of the Solar System. Thus, at least for Sir Isaac, the two species of deduction – deduction as inference and deduction as explanation – come to much the same thing. But although some explanations can perhaps be recast as inferences in which the fact to be explained figures as the conclusion of a respectable argument, most explanations fall far short of this lofty ideal. Let us take, for example, Mr Gibbon’s deduction of Constantine’s conversion from ‘benevolence, policy, conviction, and remorse’. If we converted this analytic explanation into a synthetic inference it would prove a very 19 lame and inconclusive affair, so much so as to scarcely merit the name of argument. Likewise Dr Mandeville’s deduction of morality from the sentiment of self-love. So although in some cases the two species of deduction coincide, in most they are effectively distinct. I now return to a topic I deferred some pages back – did Mr Hume employ deduction in its strict and logical sense? You think not Madam, citing in your support the authority of Dr Owen: Suppose demonstrations were deductively valid arguments with necessarily true premises. We would then expect Hume at least to acknowledge the class of deductively valid arguments with contingent premises. But Hume rarely talks of deduction and its cognates at all. Where he does he is using ‘deduction’ in its standard 18th Century sense of ‘argument’ (Owen (1999) p.90). From this we can conclude not that Dr Owen has not read Hume, nor that he has not read him with due care and attention, but that he has not employed the helps and avails of modern technology, specifically an electronic text with a word search capability. Had he condescended to do so, he might perhaps have discovered that leaving out Arithmetic, ‘deduction’ and its cognates – ‘deduce’, deduced’, ‘deductions’ and ‘deducing’ – occur twenty-eight times in the writings of Mr Hume; that five of these deductions are tracings back or explanations rather than inferences or arguments; that one, and maybe two, are expositions; that of the one-and-twenty inferences, though most are merely arguments, several are ambiguous between deductions in the large sense and deductions in the strict; that, leaving aside the supposed deductions from is to ought, there are at least two deductions in the strict sense in Hume; and that in these inferences at least some of the premises are contingent. I doubt not but these consequences will at first sight be receiv'd without difficulty, as being evident deductions from principles, which we have already established, and which we have often employ'd in our reasonings. This evidence both in the first principles, and in the deductions, may 20 seduce us unwarily into the conclusion, and make us imagine it contains nothing extraordinary, nor worthy of our curiosity. But tho' such an inadvertence may facilitate the reception of this reasoning, 'twill make it be the more easily forgot; for which reason I think it proper to give warning, that I have just now examin'd one of the most sublime questions in philosophy, viz. that concerning the power and efficacy of causes; where all the sciences seem so much interested. Such a warning will naturally rouze up the attention of the reader, and make him desire a more full account of my doctrine, as well as of the arguments, on which it is founded. (T, 1.3.14..2/156.) Hume is endeavoring to rouze up those sleepy readers who have not been sensible that he has just said something of interest and importance. The consequence that he believes himself to have deduced is that the idea of a necessary connection betwixt cause and effect is copied from the impression of heightened expectation that we feel when we anticipate the effect following the experience of a constant conjunction between like causes and like effects. Although this conclusion can be deduced from well-established principles (particularly the principle that our ideas are either copies or combinations of copies of our impressions), an inattentive reader might not be sensible of its true significance and that it is both extraordinary and worthy of our curiosity There are three reasons for thinking that these ‘evident deductions’ are supposed to constitute a demonstrative argument, that is a deduction in the strict sense of the word: a) that Hume uses the word ‘evident’ which Locke (like other writers of the period) often employs to distinguish those deductions which are demonstrative from those which are not; b) Hume’s cocksure self-confidence that his argument is ‘perfectly unanswerable’ (T, 1.3.14.19/164) which ampliative deductions generally are not; and c) that his reasoning can indeed be recast as a deductively valid argument (a reconstruction confirmed by his subsequent elaborations of the argument in the rest of the section, especially T, 1.3.14.22 /165-6: i) Every idea is derived from at least one impression. ii) We have the idea of a necessary connection. 21 iii) The only impression from which we could have derived the idea of a necessary connection is the impression of heightened expectation etc. iv) Therefore, the idea of a necessary connection is derived from the impression of heightened expectation etc. Indeed, it is not just the main argument that can be recast as a piece of deductive reasoning in the strict sense. The arguments for premises i) and iii) are also deductively valid. The argument for i) is this: either every idea is derived from at least one impression or some ideas are innate or reason alone can give rise to an original idea; but no ideas are innate (‘the principle of innate ideas … has already been refuted and is now almost universally rejected in the learned world’, T,1.3.14.6/158) and (as has been ‘sufficiently explain’d) ‘reason alone can never give rise to an original idea’ (T,1.3.14.5/157); therefore every idea is derived from at least one impression. The argument for premise iii) is this: the only impressions from which we could have derived the idea of a necessary connection are impressions of sensation or an impression of reflection, namely the impression of heightened expectation etc; the idea of necessary connection is not derived from impressions of sensation; therefore the only impression from which we could have derived the idea of a necessary connection is an impression of reflection, namely the impression of heightened expectation etc. As for premise ii), it needs no argument, since Hume takes it to be self-evident. Thus, as the context makes plain, Hume’s ‘evident deductions’ are meant to be deductively valid inferences. Nor is this all. The premises from which Hume’s ‘evident deductions’ are derived are all of them contingent. As a matter of fact, none of our ideas are innate but there is nothing self-contradictory about the hypothesis of innate ideas, which means that premise i) might be false, and is, therefore contingent. We do have the idea of a necessary connection, but to employ modern idiom, we might have been ‘wired up’ not to have it, which means that premise ii) is likewise contingent. And when Hume says, in effect, that the only possible impression from which the idea of a necessary 22 connection could have been derived is the impression of heightened expectation etc, the ‘possibility’ in question is natural possibility rather than logical possibility or conceivability. No contradiction follows from the negation of premise iii), which means that this premise too is contingent. The three premises are among the experimentally confirmed ‘facts’ on which Hume’s attempt to introduce the experimental method of reasoning into moral subjects is founded. Thus deduction is being used in the narrow sense even though the premises from which Hume’s conclusions are deduced are psychological contingencies. It was Mr Hume’s belief that ‘when any opinion leads to absurdities, it is certainly false’ (EHU, 8.2.26/96 This is only true if the inferences which lead from the opinion to the absurdities are deductively valid. If the absurd conclusion is derived via an ampliative inference, this may cast doubt on the original opinion from which it was inferred but it certainly does not follow, that it is ‘certainly false’. This is evident from the very notion of an ampliative inference wherein the premises can be true and he conclusion false – or even absurd – since the conclusion is not really, or even virtually, contained within the premises. Thus, contrary to Dr Owen, Mr Hume at least ‘acknowledge[d] the class of deductively valid arguments’ with premises that, being false, could not be necessarily true. But perhaps the class that Mr Hume acknowledged contained only arguments with necessarily false premises? Consider this: I pretend not to have obviated or removed all objections to this theory, with regard to necessity and liberty … It may be said, for instance, that, if voluntary actions be subjected to the same laws of necessity with the operations of matter … The ultimate Author of all our volitions is the Creator of the world, who first bestowed motion on this immense machine, and placed all beings in that particular position, whence every subsequent event, by an inevitable necessity, must result. Human actions, therefore, either can have no moral turpitude at all … or if they have any turpitude, they must involve our Creator in the same guilt, while he is 23 acknowledged to be their ultimate cause and author. …. And we must therefore conclude, either that [the actions of men] are not criminal, or that the Deity, not man, is accountable for them. But as either of these positions is absurd and impious, it follows, that the doctrine, from which they are deduced, cannot possibly be true, as being liable to all the same objections. An absurd consequence, if necessary, proves the original doctrine to be absurd; in the same manner as criminal actions render criminal the original cause, if the connexion between them be necessary and inevitable. (EHU 8.2.32/100.) Here again, Hume seems to embrace the principle that some deductions are reversible; that if a conclusion is false or absurd then there must be something false or absurd about the premises from which it is ‘deduced’. This principle only holds if the consequence is deduced in the strict and logical sense. For, as we have already established, in an ampliative inference the conclusion can be false and the premises true. If Sherlock Holmes ‘deduces’ from a man’s neglected appearance that his wife no longer loves him, and if it transpires that she loves him dearly him but neglects his appearance out of feminist principle, we do not conclude that he is in fact dressed with elegance and propriety. But if the connection between the premises and an absurd and impious consequence ‘be necessary and inevitable’, the doctrine from which that conclusion is ‘deduced’ ‘cannot possibly be true’. Hume’s ‘theory with regard to necessity and liberty’ entails the absurd consequence that the Creator, who is wholly good, is the author of sin. Therefore it ‘cannot possibly be true’. But having seemingly embraced this principle, Hume apparently resiles from it in the concluding paragraph of this section. The second objection admits not of so easy and satisfactory an answer; nor is it possible to explain distinctly, how the Deity can be the mediate cause of all the actions of men, without being the author of sin and moral turpitude. These are mysteries, which mere natural and unassisted reason is very unfit to handle; and whatever system she embraces, she must find herself involved in inextricable difficulties, and even contradictions, at 24 every step which she takes with regard to such subjects. To reconcile the indifference and contingency of human actions with prescience; or to defend absolute decrees, and yet free the Deity from being the author of sin, has been found hitherto to exceed all the power of philosophy. Happy, if she be thence sensible of her temerity, when she pries into these sublime mysteries; and leaving a scene so full of obscurities and perplexities, return, with suitable modesty, to her true and proper province, the examination of common life; where she will find difficulties enow to employ her enquiries, without launching into so boundless an ocean of doubt, uncertainty, and contradiction! (EHU, 8.2.36/103.) Hume’s argument seems to be that his ‘theory with regard to necessity and liberty’ should not be rejected simply because we can deduce from this hypothesis the false and absurd consequence that God is the author of Sin. Why not? Because ‘whatever system [Reason] embraces when she pries into these sublime mysteries, she must find herself involved in inextricable difficulties, and even contradictions’. Since every system with regard to liberty and necessity leads to inextricable difficulties, and even contradictions, Hume’s theory should not be rejected because it has, or seems to have, this absurd and impious consequence. But if this deduction is not reversible, which seems to be Mr Hume’s opinion, it appears that he is not employing ‘deduce’ in its strict and logical sense. This appearance is an appearance only. Mr Hume was being as candid as he dared, but he was careful to combine candour with discretion, leaving it to the attentive reader to deduce his real opinion, that if we combine the hypothesis of a Deity with Hume’s ‘theory with regard to necessity and liberty’ we can indeed deduce the absurd and impious consequence that God is the author of sin. Or, if we confine ourselves to the premises that Hume explicitly embraces – namely his theory, with regard to necessity and liberty together with some obvious truisms about moral responsibility – we can deduce the conclusion that if God existed, then he would be the author of sin. However, since God does not exist, the contradiction of a Deity who is both wholly beneficent and the Author of those sins which he punishes with 25 what our manners are pleased call ‘Divine Justice’, cannot be laid at Hume’s door. Hume’s theory only leads to absurdities when combined with the claim that God exists, a hypothesis he does not feel the need of. Nay more, his rhetoric hints at a reductio. If we conjoin Hume’s ‘theory with regard to necessity and liberty’ with he hypothesis of Divine Existence, we can deduce the absurd consequence that a wholly good God is the author of sin. But ‘when [a set of] opinion[s] leads to absurdities, [one of them] is certainly false’. And since Hume’s theory is true, the hypothesis of Divine existence is false. One might object that when the arrow of modus tollens strikes it should strike down Hume’s ‘theory with regard to necessity and liberty’ rather than the hypothesis of a Deity. Confident as he is in his theory, Mr Hume cannot suppose it to be demonstrable. His arguments, however specious, do not ‘make us sensible, that 'tis impossible to conceive any thing contrary’ (Abstract,18/653,) But if we conjoin the hypothesis of a Deity with the alternative system – the theory of the Arminians which affirms the ‘indifference and contingency of human actions’ (EHU. 8.2.36/103) – it is difficult to ‘reconcile’ this hypothesis with ‘prescience’, or, in plain terms, we find that we can deduce the absurd consequence that an omniscient Deity does not foreknow the future. Thus what Hume is hinting at is a dilemma. Either we have the liberty of indifference or we do not. If we do and God exists, we can deduce the absurd conclusion that an all-knowing Deity is ignorant of the future. If we do not and God exists, we can deduce the equally absurd conclusion that a wholly beneficent Deity is the author of sin. So whether we have the liberty of indifference or no, the hypothesis of a Deity leads to an absurdity. And ‘when any opinion leads to absurdities, it is certainly false’. However that may be, I flatter myself that I have sufficiently established the following points: that Hume sometimes uses ‘deduction’ in the strict and logical sense; and that (contrary to Dr Owen) Hume ‘acknowledges the class of deductively valid arguments with contingent premises’. For to say nothing of his arguments on the nature of causality, he takes it to be a necessary consequence of his theory regarding liberty and necessity, when conjoined with the hypothesis of God’s existence, that God is the author if sin. The second premise is in his opinion false, though perhaps not contingently so, but the first is true but contingent. For it is 26 founded on matters of fact or experience, facts about the human mind and its workings which might, perhaps have been otherwise and facts about the world, which might perhaps have been framed in a more loose and irregular manner. We have no innate ideas but though it be false, there is no contradiction in this supposition, in which case we might have had an idea of causality as something other than constant conjunction. Causes and effects succeed each other in the human mind as elsewhere, but it might have been otherwise and the opposite idea implies no contradiction, from which we can deduce that its truth (if it is true) is a contingent affair. ! I cannot forbear adding to these reasonings two further observations, a) that a diligent student such as Mr Hume certainly ought to have been aware of deductive arguments with contingent premises, since he had been informed of their existence by his logic teacher, Professor Drummond. and b) that a student of Leibniz’s Theodicy (which we know Hume to have been) could scarcely have been unaware of such deductions, since they play a prominent part in that author’s defence of the Deity. First Drummond: Q [In a syllogism] does the conclusion follow from the premises necessarily?R Yes. Q How many kinds of necessity are there? R Two — necessity of the consequent and [necessity] of the consequence.Q What is necessity of the consequent?R That which depends on the necessity of the connection of the terms [in the consequent]. Q To which syllogisms does this property belong? R To necessary ones. Q What is necessity of the consequence? R That which arises from the due arrangement of terms. Q In which syllogisms is this necessity found? R In all syllogisms. Q Can there be a syllogism without necessity of the consequence? 27 R No, but there are many without necessity of the consequent. (Drummond, 1724). Thus there are many syllogisms – that is, deductions in the strictest sense – in which the consequence is necessary but the consequent is not. And that is a circumstance that can only occur if at least one of the premises is contingent. As for the celebrated Monsieur Leibniz, the Appendix to the Theodicy contains a section ‘Summary of the Controversy Reduced to Formal Arguments’ containing eleven formally valid arguments which purport to prove either that there is no God or that He is not just. Of these, seven have contingent premises (Leibniz, 1985, pp 377-392). One might add that if, as is commonly supposed, Hume was acquainted with Sextus Empiricus, he would have been aware of the stock syllogisms of the Stoics, such as ‘If it is day it is light: but it is not light; therefore it is not day’. In this inference, as in many others cited by Empiricus, at least one of the premises is contingent (Mates, 1996, pp. 158-160). But what of the deductions from ‘is’ to ‘ought’? In denying, or perhaps questioning, such deductions, was Hume denying or questioning them in the loose sense or the strict? I flatter myself that I have sufficiently proved that he might have meant ‘deduction’ in the strict sense, but if we cannot deduce an ought from an is, we certainly cannot deduce meant from might have meant. There are however several marks which strongly suggest that Hume was using ‘deduction’ in its strict and logical sense. Let us begin with Mr Hume’s language. It is notable that in this much-cited passage Hume speaks the language of logic, employing words, or senses of words, which he seldom or never employs except to make a logical point. Though there is a good deal of copulation in the works of Mr Hume – eight instances of ‘copulation’ and one of ‘copulate‘ – but in every other instance the words denote the union of the sexes. (‘Is it more certain that two flat pieces of marble will unite together, than that two young savages of different sexes will copulate?’). It is in this passage alone that he talks of copulations of propositions, meaning, by this, the verb by which the subject and the predicate are connected in an affirmative or negative proposition. Every text and every course of instruction on formal logic, from 1600 through to 1750 28 devoted much space to the copula,7 a word which was seldom employed in any other connection8. And it is surely a very reasonable presumption that when Hume employs a logical term of art, it is a logical observation that he wishes to make. But this phrase ‘copulations of propositions’ is not the only one which smacks of formal logic. Hume also speaks of the ‘new relation or affirmation’ expressed by ought or ought not. Though the term ‘affirmation’ was sometimes employed outside the schools, it flourished especially in the logic texts where a distinction between affirmative and negative propositions was of prime importance. Hume tends to use it, especially in his philosophical works, when discussing demonstration and deduction or when he 7 Thus for example Drummond, Compendium Logicae: Q.What are these three things that a proposition requires called? R.Subject, predicate and copula. ….. Q What is the copula? R It is that by which judgment is expressed … Q Quid est Forma Propositionis? What determines the form of a proposition? R The copula. Q What is a complex proposition classified by form? R One whose copula is complex, as in “I affirm the earth to be round” … Q What is a modal proposition? R. Those in which [something] is not barely asserted either to be or not to be, but they apply the copula with some modification. 8Hobbes refers to the copula many times (I make it about twenty) but all but all but three of these references come from his Computatio Sive Logica and even in these, he is discussing what would nowadays think of as philosophical logic. Neither Locke nor Berkeley composed a formal Logic and the consequence is that neither mentions the copula once. Although the copula puts in an appearance in his Logicae Compendium, Hutcheson never mentions it in the works on moral philosophy on which his fame principally rests. Although a Professor of Logic, Dr Smith did not have occasion to refer to the copula once, perhaps because he preferred to lecture on Rhetoric and Belles Letters rather than the Logic of the Schools. In his massive Decline and Fall, Gibbon alludes to the copula only once, and even then his point is that ‘the copulative particle’ can be used to make nice logical distinctions between heresy and orthodoxy. [‘The substance of an orthodox, or an heretical, creed may be expressed by the difference of a disjunctive, or a copulative, particle’.(Gibbon, D&F, 3.21/397).] 29 wants to make nice distinctions of meaning and content 9. I freely grant that ‘new relation or affirmation’ does not smell as strongly of logic as ‘copulations of propositions’, since except in formal logic nobody feels the need to discuss the copula whereas we often have occasion to affirm this or that and to discuss our affirmations. Nevertheless, Hume’s employment of this phrase suggests not only that he was thinking about logic but that he had a particular logic book in mind, namely L’Art de Penser of Arnauld and Nicole. Those distinguished authors explain that ‘the verb is nothing than a word whose principal function is to signify an affirmation ‘and that ‘the verb in itself ought to have no other use than to indicate the connection the mind makes between the two terms of a proposition’. However, ‘only the verb “to be” … retains this simplicity [and people] almost always join other significations to 9 For in that proposition, an object is the same with itself, if the idea expressed by the word object were noways distinguished from that meant by itself; we really should mean nothing, nor would the proposition contain a predicate and a subject, which, however, are imply’d in this affirmation. (T 1.4.2.26/200) All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation, which is either intuitively or demonstratively certain. (EHU 4.1.1/25.) That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction, than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind. (EHU 4.1.2/23-26.) We say, for instance, that the vibration of this string is the cause of this particular sound. But what do we mean by that affirmation? We either mean, that this vibration is followed by this sound, and that all similar vibrations have been followed by similar sounds: Or, that this vibration is followed by this sound, and that upon the appearance of one, the mind anticipates the senses, and forms immediately an idea of the other. We may consider the relation of cause and effect in either of these two lights; but beyond these, we have no idea of it. (EHU 7.2.29/77.) Are there any marks of a distributive justice in the world? If you answer in the affirmative, I conclude, that, since justice here exerts itself, it is satisfied. If you reply in the negative, I conclude, that you have then no reason to ascribe justice, in our sense of it, to the gods. If you hold a medium between affirmation and negation, by saying, that the justice of the gods, at present, exerts itself in part, but not in its full extent; I answer, that you have no reason to give it any particular extent, but only so far as you see it, at present, exert itself. (EHU 11.22/141-142.) The approbation or blame, which then ensues, cannot be the work of the judgment, but of the heart; and is not a speculative proposition or affirmation, but an active feeling or sentiment. (EPM App 1 11/290.) 30 affirmation in the same word’. (Arnauld and Nicole, LAT, Part 1. ch.2 /79.) Now Hume’s vulgar moralists are doing something very like this. Their premises are connected by an is or an is not, the copula which retains its original simplicity, but their conclusions are connected by an ought or an ought not. And this joins ‘other significations’ – a new ‘relation or affirmation’ – to the simple substantive ‘to be’ . But however that may be, I hope I have sufficiently proved that Hume is speaking the language of logic, and if he is speaking the language of logic, then it is highly probable that when he denies or questions the possibility of Is/Ought deductions it is logical deductions that he wishes to deny or question. I have I hope removed some rubbish out my way by establishing that ‘deduction’ was sometimes used to denote logically valid arguments, and that Hume himself employed it in this sense. I have proved furthermore that in this celebrated passage Hume speaks the language of logic. But I come now to an argument which I flatter myself is quite decisive. If Hume meant ‘deduction’ in the large and ampliative sense, then so far from making a true or even a sensible observation, he would have said something foolish and evidently false. But Hume was not given to folly and when his opinions are false it is seldom that they are evidently so. Therefore it is improbable that he meant ‘deduction’ in its large and ampliative sense. Why so? Because Hume says that, it ‘seems altogether inconceivable, how this new relation [ought or ought not] can be a deduction from others, which are entirely different from it’. But if Hume meant ‘deduction’ in its large and ampliative sense this would not seem inconceivable in the least. When Sherlock Holmes deduces from the stranger’s appearance that he is a retired sergeant of marines, this is definitely a ‘new relation or affirmation’ something that is decidedly not contained within the premises. But though Holmes’ deductive powers may cause some surprise, we can easily conceive (especially after we have been instructed by Sir Arthur) how this new relation or affirmation (that the man is a retired sergeant of marines) could be a deduction (in the large and liberal sense) from others which are entirely different from it. If Hume had employed ‘deduction’ in its large and ampliative sense it would not have even seemed inconceivable that this new relation or affirmation ought could be a deduction from other propositions connected with an is or an is not.. For it is only if ‘deduction’ is employed in its strict sense that ‘the premises, according to the reason 31 of things, [must] really contain the conclusion that is deduced from them’. Since it did indeed seem inconceivable, he cannot have employed ‘deduction ‘ in its large and ampliative sense. When he spoke of what seemed to be inconceivable and what needed to be ‘observed and explained’ Hume was offering a challenge that he did not expect to be met. Nor did anyone try to meet it. Though there is much in the Treatise to cause controversy and though it managed, after a while, to excite a murmur not only amongst the zealots but even amongst moderate men, the one close contemporary who condescended to notice the Is/Ought passage did not dispute Hume’s thesis that an ought cannot be justly derived from an is. After quoting Hume’s demand that ‘a reason should be given why this new relation (ought) should be a deduction from others which are entirely different from it’, Reid goes on to reply that ‘this is to demand a reason for what does not exist. The first principles of of morals are not deductions. They are self-evident; and their truth is perceived without reasoning or deduction. And moral truths that are not self-evident are deduced, not from relations quite different from them but from the first principles of morals.’ Thus Reid seems to think that the first principles of morals cannot be deductions, for if they were, the oughts involved would be derived, from premises that did not contain them, and deductions involving such new relations or affirmations are fallacious. Nor is it surprising that Reid should have endorsed Hume’s thesis, since it is simply an instance of a principle to which he himself subscribed, namely that in reasoning by syllogism [that is deductively] we descend to a conclusion virtually contained in [the premises]. (Reid, Logic, 146.) Hence if ought represents a new relation or affirmation – that is if it appears in the conclusion but in the premises – the deduction cannot be just. Here indeed is a barrier to inference or deduction, but only to deductions in the strictest sense of the word, namely inferences in which, as Professor Drummond put it, the conclusion follows from the premises ‘not materially but formally, since [there is] no new material is in the conclusion which is not in the premises, but the terms are merely arranged in a different way’. (Drummond, 1724). This is a barrier which ampliative inferences can surmount with ease, but only by sacrificing the assurance, that logic confers, that the premises cannot be true and the conclusion false. 32 Nonetheless, tho’ Hume erects no barrier to ampliative inferences from is to ought, such deductions are seldom to be met with in the Treatise. I agree with you Madam that in Treatise, 3.2, Hume deduces oughts and ought nots from observations concerning human affairs, but I deny that those deductions are in the main inferences. ‘Obligations to respect others’ property, [to] keep promises, [to] obey magistrates [and to] keep marriage vows’, are indeed deduced from human conventions which arise in order to remedy certain inconveniences, which proceed from the concurrence of certain qualities of the human mind – such as selfishness and limited generosity – and the situation of external objects – such as their easy change, joined to their scarcity in comparison of the wants and desires of men (T, 3.2.16/494). But when Hume deduces these obligations, he deduces them in much the same sense that Gibbon deduces the motives of Constantine’s conversion ‘from benevolence, from policy, from conviction, or from remorse’. The deductions in question are tracings back or explanations, deductions in Sense 3. ‘When the neglect or nonperformance of [an action] displeases us after a [certain] manner, we say that we lie under an obligation to perform it’ (T, 3.2.5.4/517). Thus to say that I have an obligation to respect another’s property, to keep a promise or to obey the government is to say that the neglect or the non-performance of such actions would arouse a sentiment of disapprobation in an informed and impartial spectator, a conception that Hume probably derived from Hutcheson: ‘When we say one is obliged to an Action, we ... mean … That every Spectator, or he himself upon Reflection, must approve his Action, and disapprove his omitting it, if he considers fully all its Circumstances’ (Hutcheson, 2002, p. 146). But if an act is obligatory because its nonperformance would arouse a sentiment of disapprobation, to infer that an action is obligatory from ‘observations concerning human affairs’ is to infer from such observations that the action would arouse such a sentiment. Unless he is propounding a reductio, when a philosopher infers, he proceeds from what is known to what is less known, or at least from what is known to what requires further proof. But for Hume our propensities to approve or disapprove do not stand in need of proof or justification, nor can philosophy call them into question unless they depend on 33 mistaken beliefs10. When it comes to morality ‘the opinions of men ... carry with them a peculiar authority, and are, in a great measure, infallible. [Since] the distinction of moral good and evil is founded on the pleasure or pain which results from the view of any sentiment or character; ... there is just so much vice or virtue in any character as every one places in it’ (T, 3.2.8.8./546-7). In this instance Hume exaggerates his real opinion concerning the moral infallibility of mankind. If the view from which pleasure and pain results is dependent on the delusive glosses of superstition and false religion, or on mistaken opinions concerning history or political economy, there may indeed be more or less vice or virtue in an action or character than every one places in it. .Thus the monkish virtues are vices despite the sentiments of the pious, and the jealously of trade is not a political virtue despite the sentiments of the mercantilists, (EPM, 9.1.13/270, Essays, 2.6.) Indeed the monkish virtues and the jealousy of trade would continue to be vicious even if we were all deceived by the delusive glosses of false religion or misled by the sophistries of mercantile economists. Nonetheless, when our opinions concerning matters of fact are correct our moral opinions cannot err since they are founded on the sentiments that we feel when contemplating the facts. And we cannot be mistaken about our feelings. But where there is no need for discovery nor yet for further proof, inference has no place, nor is there any need to infer the truths of morals from propositions less certainly known. As Hume himself observes ‘our judgments concerning the origin of any vice or virtue, [are] not so certain as those concerning their degrees’ (T, 3.2.8.8./547,). Hume does not begin with the need for conventions and infer from thence the existence of obligations. Rather, he takes our obligations for granted, founded, as they are, on sentiments which we are all supposed to feel, and endeavours to trace them back to inconveniences caused by qualities of the human mind (such as lust or limited generosity) and to the situation of external objects (or in the case of the feminine obligation to chastity ‘a trivial anatomical observation’), which men learn to solve by the artifice of convention. Once the conventions have arisen, we annex the sentiments of approbation and disapprobation to the performance or non-performance 10 ‘Have the gods forbid self-murder? An ATHENIAN allows, that it ought to be forborn. Has the Deity permitted it? A FRENCHMAN allows that death is preferable to pain and infamy.’ (EPM, Dialogue, 35/335.) Hume maintains that self-murder need not be forborn by arguing with more sophistry than success, that even if He exists, the Deity has not forbidden it (Essays, 3.8). 34 of the relevant actions through the operations of sympathy. These are the causes of which our obligations are the effects. But Hume does not reason from the causes to the effects but from the effects to the causes. Hence his deductions of our duties are not inferences from observations concerning human affairs to conclusions concerning duties but attempts to trace back our duties to their origins in human nature. You observe very justly Madam, that in the in the EPM we find no recasting, even in an amended form, of Hume’s supposed ‘Law’ forbidding inference from ‘is’ to ‘ought’ (3.1§2). But some deductions from claims about human nature to the principles of morality are denied in the EPM, and the deductions that are denied in the EPM afford us some clew as to the deductions that are affirmed in the Treatise. ‘This deduction of morals from self-love’, says Hume, ‘is an obvious thought, and has not arisen wholly from the wanton sallies and sportive assaults of the sceptics’ (EPM, 5.1.6/215). But obvious as it may be (especially to readers of Mandeville), Hume goes on to argue that we must ‘renounce the theory, which accounts for every moral sentiment by the principle of self-love’. Instead we should ‘allow, that the interests of society are not, even on their own account, entirely indifferent to us, … that every thing, which contributes to the happiness of society recommends itself directly to our approbation and good-will, [and that this is] a principle, which accounts, in great part, for the origin of morality (EPM, 5.2.17/19). Thus the deduction that is denied is an attempt to explain our moral sentiments as due to the modifications of self-love and the deduction that is affirmed is a better explanation that accounts for the origin of morality by tracing it back to sympathy and the sentiment of humanity. Hume’s attempts in the Treatise to deduce our duties from our passions and the conventions that arise to palliate their effects are deductions of a similar nature. Finally I come to point (5). There are those philosophers who suppose that if it is indeed inconceivable that the new affirmation ought can be a deduction from others that are entirely different from it, then the facts represented by is and is not must be at bottom entirely distinct from the values represented by ought and ought not. It is because they deny any fundamental distinction betwixt facts and values that some philosophers maintain that it is indeed possible to deduce affirmations concerning ought from premises that are utterly devoid of that expression. Such philosophers deny the consequent when they ought to be questioning the consequence. Mr Hume is 35 reliant on the principle that in a strict deduction the conclusion follows from the premises ‘not materially but formally, since there is no new material is in the conclusion which is not in the premises’, a principle in which he was instructed at the University of Edinburgh. It is the absence of moral matter in the premises not the fundamental nature of the values expressed in the conclusion that prohibits the inference from is to ought. Why then does Hume make so much of a logical observation, supposing that it might subvert the all the vulgar systems of morality? Because the vulgar systems are those which purport to demonstrate the truths of morality. Hume endeavors to prove, with but indifferent success, that, with the exception of certain trifling propositions, no moral truth is self-evident. But the truths of morality might yet be demonstrable if they could be deduced (in the strict sense) from non-moral premises, that is premises devoid of moral matter. It is logic alone that prohibits such deductions, just as it prohibits any inference whatsoever in which the matter of the conclusion is not contained within the premises. If a wild philosopher, an ornithological Dr Clarke, had maintained, with every excess of pious declamation, that truths about tom-tits were demonstrable, how might Hume have replied? He would have answered, I suggest, that (with certain trifling exceptions) no proposition concerning tom-tits is self-evident, not even the assertion that they are birds, since there is no contradiction in the supposition that they might prove on inspection to be cunningly disguised bats or the artificial creations of an ingenious craftsman. observation. And he might have added to this reasoning the following ‘In this gentleman’s demonstrations I have always remark’d, that he proceeds for some time in the ordinary way of reasoning, and establishes the being of a God, or makes observations concerning avian affairs; when of a sudden I am surpriz’d to find, that instead of such predicates as ‘is one of God’s creatures’, ‘is a bird’ or ‘eats insects’, I continually meet with the predicate ‘is a tom-tit’ or ‘is not a tom-tit’. . This change is imperceptible; but is, however, of the last consequence. For as this ‘is a tom-tit’, or ‘is not a tom-tit’, expresses some new conception or affirmation, ’tis necessary that it shou’d be observ’d and explain’d; and at the same time that a reason should be given, for what seems altogether inconceivable, how this new predicate can be a deduction from others, which are entirely different from it. But as the gentleman does not commonly use this precaution, I shall presume to 36 recommend it to the readers; and am persuaded, that this small attention wou’d subvert his vulgar system of demonstrative ornithology, and let us see, that the character of tom-tits is to be derived from experience, not perceiv’d by abstract reason.’ Had there been such a wild philosopher, I say, and if Hume had responded in this way, would anyone with any logical capacity have concluded that (at least in Hume’s opinion) tom-tits are not birds? No more should we conclude from his observations concerning is and ought that (at least in Hume’s opinion) values are not facts. I remain, Dear Madam, Your most Humble and Obedient Servant etc.