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CHAPTER IV.: Remarks. - Henry Home, Lord Kames, Sketches of the History of Man, vol. 3 
Sketches of the History of Man Considerably enlarged by the last additions and corrections of the author, edited and with an Introduction by James A. Harris (Indianapolis: Liberty Fund, 2007). 3 Vols. Vol. 3.
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Of the Conversion of Propositions.
We have given a summary view of the theory of pure syllogisms as delivered by Aristotle, a theory of which he claims the sole invention. And I believe it will be difficult, in any science, to find so large a system of truths of so very abstract and so general a nature, all fortified by demonstration, and all invented and perfected by one man. It shows a force of genius and labour of investigation, equal to the most arduous attempts. I shall now make some remarks upon it.
As to the conversion of propositions, the writers on logic commonly satisfy themselves with illustrating each of the rules by an example, conceiving them to be self-evident when applied to particular cases. But Aristotle has given demonstrations of the rules he mentions. As a specimen, I shall give his demonstration of the first rule. “Let A B be an universal negative proposition; I say, that if A is in no B, it will follow that B is in no A. If you deny this consequence, let B be in some A, for example, in C; then the first supposition will not be true; for C is of the B’s.” In this demonstration, if I understand it, the third rule of conversion is assumed, that if B is in some A, then A must be in some B, which indeed is contrary to the first supposition. If the third rule be assumed for proof of the first, the proof of all the three goes round in a circle; for the second and third rules are proved by the first. This is a fault in reasoning which Aristotle condemns, and which I would be very unwilling to charge him with, if I could find any better meaning in his demonstration. But it is indeed a fault very difficult to be avoided, when men attempt to prove things that are self-evident.
The rules of conversion cannot be applied to all propositions, but only to those that are categorical; and we are left to the direction of common sense in the conversion of other propositions. To give an example: Alexander was the son of Philip; therefore Philip was the father of Alexander: A is greater than B; therefore B is less than A. These are conversions which, as far as I know, do not fall within any rule in logic; nor do we find any loss for want of a rule in such cases.
Even in the conversion of categorical propositions, it is not enough to transpose the subject and predicate. Both must undergo some change, in order to fit them for their new station: for in every pro-position the subject must be a substantive, or have the force of a substantive; and the predicate must be an adjective, or have the force of an adjective. Hence it follows, that when the subject is an individual, the proposition admits not of conversion. How, for instance, shall we convert this proposition, God is omniscient?
These observations show, that the doctrine of the conversion of propositions is not so complete as it appears. The rules are laid down without any limitation; yet they are fitted only to one class of propositions, to wit, the categorical; and of these only to such as have a general term for their subject.
On Additions made to Aristotle’s Theory.
Although the logicians have enlarged the first and second parts of logic, by explaining some technical words and distinctions which Aristotle has omitted, and by giving names to some kinds of propositions which he overlooks; yet in what concerns the theory of categorical syllo-gisms, he is more full, more minute and particular, than any of them: so that they seem to have thought this capital part of the Organon rather redundant than deficient.
It is true, that Galen added a fourth figure to the three mentioned by Aristotle. But there is reason to think that Aristotle omitted the fourth figure, not through ignorance or inattention, but of design, as containing only some indirect modes, which, when properly expressed, fall into the first figure.
It is true also, that Peter Ramus, a professed enemy of Aristotle, introduced some new modes that are adapted to singular propositions; and that Aristotle takes no notice of singular propositions, either in his rules of conversion, or in the modes of syllogism. But the friends of Aristotle have shewn, that this improvement of Ramus is more specious than useful. Singular propositions have the force of universal propositions, and are subject to the same rules. The definition given by Aristotle of an universal proposition applies to them; and therefore he might think, that there was no occasion to mul-tiply the modes of syllogism upon their account.
These attempts, therefore, show rather inclination than power, to discover any material defect in Aristotle’s theory.
The most valuable addition made to the theory of categorical syllogisms, seems to be the invention of those technical names given to the legitimate modes, by which they may be easily remembered, and which have been comprised in these barbarous verses.
In these verses, every legitimate mode belonging to the three figures has a name given to it, by which it may be distinguished and remembered. And this name is so contrived as to denote its nature: for the name has three vowels, which denote the kind of each of its propositions.
Thus, a syllogism in Bocardo must be made up of the propositions denoted by the three vowels, O, A, O; that is, its major and conclusion must be particular negative propositions, and its minor an universal affirmative; and being in the third figure, the middle term must be the subject of both premises.
This is the mystery contained in the vowels of those barbarous words. But there are other mysteries contained in their consonants: for, by their means, a child may be taught to reduce any syllogism of the second or third figure to one of the first. So that the four modes of the first figure being directly proved to be conclusive, all the modes of the other two are proved at the same time, by means of this operation of reduction. For the rules and manner of this reduction, and the different species of it, called ostensive and per impossible, I refer to the logicians, that I may not disclose all their mysteries.
The invention contained in these verses is so ingenious, and so great an adminicle to the dextrous management of syllogisms, that I think it very probable that Aristotle had some contrivance of this kind, which was kept as one of the secret doctrines of his school, and handed down by tradition, until some person brought it to light. This is offered only as a conjecture, leaving it to those who are better acquainted with the most ancient commentators on the Analytics, either to refute or to confirm it.
On Examples used to illustrate this Theory.
We may observe, that Aristotle hardly ever gives examples of real syllogisms to illustrate his rules. In demonstrating the legitimate modes, he takes A, B, C, for the terms of the syllogism. Thus, the first mode of the first figure is demonstrated by him in this manner. “For,” says he, “if A is attributed to every B, and B to every C, it follows necessarily, that A may be attributed to every C.” For disproving the illegitimate modes, he uses the same manner; with this difference, that he commonly for an example gives three real terms, such as, bonum, habitus, prudentia; of which three terms you are to make up a syllogism of the figure and mode in question, which will appear to be inconclusive.
The commentators and systematical writers in logic, have supplied this defect; and given us real examples of every legitimate mode in all the figures. We acknowledge this to be charitably done, in order to assist the conception in matters so very abstract; but whether it was prudently done for the honour of the art, may be doubted. I am afraid this was to uncover the nakedness of the theory: it has undoubtedly contributed to bring it into contempt; for when one considers the silly and uninstructive reasonings that have been brought forth by this grand organ of science, he can hardly forbear crying out, Parturiunt montes, et nascitur ridiculus mus.21 Many of the writers of logic are acute and ingenious, and much practised in the syllogistical art; and there must be some reason why the examples they have given of syllogisms are so lean.
We shall speak of the reason afterwards; and shall now give a syllogism in each figure as an example.
In this syllogism, the middle term, work of God, is the subject of the major and the predicate of the minor; so that the syllogism is of the first figure. The mode is that called Celarent; the major and conclusion being both universal negatives, and the minor an universal affirmative. It agrees to the rules of the figure, as the major is universal, and the minor affirmative; it is also agreeable to all the general rules; so that it maintains its character in every trial. And to show of what ductile materials syllogisms are made, we may, by converting simply the major proposition, reduce it to a good syllogism of the second figure, and of the mode Cesare, thus:
Here the middle term praise-worthy being the predicate of both premises, the syllogism is of the second figure; and seeing it is made up of the propositions, A, O, O, the mode is Baroco. It will be found to agree both with the general and special rules: and it may be reduced into a good syllogism of the first figure upon converting the major by contraposition, thus:
That this syllogism is conclusive, common sense pronounces, and all logicians must allow; but it is somewhat unpliable to rules, and requires a little straining to make it tally with them.
That it is of the first figure is beyond dispute; but to what mode of that figure shall we refer it? This is a question of some difficulty. For, in the first place, the premises seem to be both negative, which contradicts the third general rule; and moreover, it is contrary to a special rule of the first figure, That the minor should be negative. These are the difficulties to be removed.
Some logicians think, that the two negative particles in the major are equivalent to an affirmative; and that therefore the major proposition, What is not praise-worthy, is not virtuous, is to be accounted an affirmative proposition. This, if granted, solves one difficulty; but the other remains. The most ingenious solution, therefore, is this: Let the middle term be not praise-worthy. Thus, making the negative particle a part of the middle term, the syllogism stands thus:
By this analysis, the major becomes an universal negative, the minor a particular affirmative, and the conclusion a particular negative, and so we have a just syllogism in Ferio.
We see, by this example, that the quality of propositions is not so invariable, but that, when occasion requires, an affirmative may be degraded into a negative, or a negative exalted to an affirmative. Another example:
This is of the third figure, and of the mode Darapti; and it may be reduced to Darii in the first figure, by converting the minor.
By this time I apprehend the reader has got as many examples of syllogisms as will stay his appetite for that kind of entertainment.
On the Demonstration of the Theory.
Aristotle and all his followers have thought it necessary, in order to bring this theory of categorical syllogisms to a science, to demonstrate, both that the fourteen authorised modes conclude justly, and that none of the rest do. Let us now see how this has been executed.
As to the legitimate modes, Aristotle and those who follow him the most closely, demonstrate the four modes of the first figure directly from an axiom called the Dictum de omni et nullo. The amount of the axiom is, That what is affirmed of a whole genus, may be affirmed of all the species and individuals belonging to that genus; and that what is denied of the whole genus, may be denied of its species and individuals. The four modes of the first figure are evidently included in this axiom. And as to the legitimate modes of the other figures, they are proved by reducing them to some mode of the first. Nor is there any other principle assumed in these reductions but the axioms concerning the conversion of propositions, and in some cases the axioms concerning the opposition of propositions.
As to the illegitimate modes, Aristotle has taken the labour to try and condemn them one by one in all the three figures: but this is done in such a manner that it is very painful to follow him. To give a specimen. In order to prove, that those modes of the first figure in which the major is particular, do not conclude, he proceeds thus: “If A is or is not in some B, and B in every C, no conclusion follows. Take for the terms in the affirmative case, good, habit, prudence, in the nega-tive, good, habit, ignorance.” This laconic style, the use of symbols not familiar, and, in place of giving an example, his leaving us to form one from three assigned terms, give such embarrassment to a reader, that he is like one reading a book of riddles.
Having thus ascertained the true and false modes of a figure, he subjoins the particular rules of that figure, which seem to be deduced from the particular cases before determined. The general rules come last of all, as a general corollary from what goes before.
I know not whether it is from a diffidence of Aristotle’s demonstrations, or from an apprehension of their obscurity, or from a desire of improving upon his method, that almost all the writers in logic I have met with, have inverted his order, beginning where he ends, and ending where he begins. They first demonstrate the general rules, which belong to all the figures, from three axioms; then from the general rules and the nature of each figure, they demonstrate the special rules of each figure. When this is done, nothing remains but to apply these general and special rules, and to reject every mode which contradicts them.
This method has a very scientific appearance: and when we consider, that by a few rules once demonstrated, an hundred and seventy-eight false modes are destroyed at one blow, which Aristotle had the trouble to put to death one by one, it seems to be a great improvement. I have only one objection to the three axioms.
The three axioms are these: 1. Things which agree with the same third, agree with one another. 2. When one agrees with the third, and the other does not, they do not agree with one another. 3. When neither agrees with the third, you cannot thence conclude, either that they do, or do not agree with one another. If these axioms are applied to mathematical quantities, to which they seem to relate when taken literally, they have all the evidence that an axiom ought to have: but the logicians apply them in an analogical sense to things of another nature. In order, therefore, to judge whether they are truly axioms, we ought to strip them of their figurative dress, and to set them down in plain English, as the logicians understand them. They amount therefore to this. 1. If two things be affirmed of a third, or the third be affirmed of them; or if one be affirmed of the third, and the third affirmed of the other; then they may be affirmed one of the other. 2. If one is affirmed of the third, or the third of it, and the other denied of the third, or the third of it, they may be denied one of the other. 3. If both are denied of the third, or the third of them; or if one is denied of the third, and the third denied of the other; nothing can be inferred.
When the three axioms are thus put in plain English, they seem not to have that degree of evidence which axioms ought to have; and if there is any defect of evidence in the axioms, this defect will be communicated to the whole edifice raised upon them.
It may even be suspected, that an attempt by any method to demonstrate that a syllogism is conclusive, is an impropriety somewhat like that of attempting to demonstrate an axiom. In a just syllogism, the connection between the premises and the conclusion is not only real, but immediate; so that no proposition can come between them to make their connection more apparent. The very intention of a syllogism is, to leave nothing to be supplied that is necessary to a complete demonstration. Therefore a man of common understanding who has a perfect comprehension of the premises, finds himself under a necessity of admitting the conclusion, supposing the premises to be true; and the conclusion is connected with the premises with all the force of intuitive evidence. In a word, an immediate conclusion is seen in the premises, by the light of common sense; and where that is wanting, no kind of reasoning will supply its place.
On this Theory, considered as an Engine of Science.
The slow progress of useful knowledge, during the many ages in which the syllogistic art was most highly cultivated as the only guide to science, and its quick progress since that art was disused, suggest a presumption against it; and this presump-tion is strengthened by the puerility of the examples which have always been brought to illustrate its rules.
The ancients seem to have had too high notions, both of the force of the reasoning power in man, and of the art of syllogism as its guide. Mere reasoning can carry us but a very little way in most subjects. By observation, and experiments properly conducted, the stock of human knowledge may be enlarged without end; but the power of reasoning alone, applied with vigour through a long life, would only carry a man round, like a horse in a mill who labours hard but makes no progress. There is indeed an exception to this observation in the mathematical sciences. The relations of quantity are so various and so susceptible of exact mensuration, that long trains of accurate reasoning on that subject may be formed, and conclusions drawn very remote from the first principles. It is in this science and those which depend upon it, that the power of reasoning triumphs; in other matters its trophies are inconsiderable. If any man doubt this, let him produce, in any subject unconnected with mathematics, a train of reasoning of some length, leading to a conclusion, which without this train of reasoning would never have been brought within human sight. Every man acquainted with mathematics can produce thousands of such trains of reasoning. I do not say, that none such can be produced in other sciences; but I believe they are few, and not easily found; and that if they are found, it will not be in subjects that can be expressed by categorical propositions, to which alone the theory of figure and mode extends.
In matters to which that theory extends, a man of good sense, who can distinguish things that differ, can avoid the snares of ambiguous words, and is moderately practised in such matters, sees at once all that can be inferred from the premises; or finds, that there is but a very short step to the conclusion.
When the power of reasoning is so feeble by nature, especially in subjects to which this theory can be applied, it would be unreasonable to expect great effects from it. And hence we see the reason why the examples brought to illustrate it by the most ingenious logicians, have rather tended to bring it into contempt.
If it should be thought, that the syllogistic art may be an useful engine in mathematics, in which pure reasoning has ample scope: First, It may be observed, That facts are unfavourable to this opinion: for it does not appear, that Euclid, or Apollonius, or Archimedes, or Hugens, or Newton, ever made the least use of this art; and I am even of opinion, that no use can be made of it in mathematics. I would not wish to advance this rashly, since Aristotle has said, that mathematicians reason for the most part in the first figure. What led him to think so was, that the first figure only yields conclusions that are universal and affirmative, and the conclusions of mathematics are commonly of that kind. But it is to be observed, that the propositions of mathematics are not categorical propositions, consisting of one subject and one predicate. They express some relation which one quantity bears to another, and on that account must have three terms. The quantities compared make two, and the relation between them is a third. Now to such pro-positions we can neither apply the rules concerning the conversion of propositions, nor can they enter into a syllogism of any of the figures or modes. We observed before, that this conversion, A is greater than B, therefore B is less than A, does not fall within the rules of conversion given by Aristotle or the logicians; and we now add, that this simple reasoning, A is equal to B, and B to C; therefore A is equal to C, cannot be brought into any syllogism in figure and mode. There are indeed syllogisms into which mathematical propositions may enter, and of such we shall afterwards speak: but they have nothing to do with the system of figure and mode.
When we go without the circle of the mathematical sciences, I know nothing in which there seems to be so much demonstration as in that part of logic which treats of the figures and modes of syllogism; but the few remarks we have made, shew, that it has some weak places: and besides, this system cannot be used as an engine to rear itself.
The compass of the syllogistic system as an engine of science, may be discerned by a compendious and general view of the conclusion drawn, and the argument used to prove it, in each of the three figures.
In the first figure, the conclusion affirms or denies something of a certain species or individual; and the argument to prove this conclusion is, That the same thing may be affirmed or denied of the whole genus to which that species or individual belongs.
In the second figure, the conclusion is, That some species or individual does not belong to such a genus; and the argument is, That some attribute common to the whole genus does not belong to that species or individual.
In the third figure, the conclusion is, That such an attribute belongs to part of a genus; and the argument is, That the attribute in question belongs to a species or individual which is part of that genus.
I apprehend, that in this short view, every conclusion that falls within the compass of the three figures, as well as the mean of proof, is comprehended. The rules of all the figures might be easily deduced from it; and it appears, that there is only one principle of reasoning in all the three; so that it is not strange, that a syllogism of one figure should be reduced to one of another figure.
The general principle in which the whole terminates, and of which every categorical syllogism is only a particular application, is this, That what is affirmed or denied of the whole genus, may be affirmed or denied of every species and individual belonging to it. This is a principle of undoubted certainty indeed, but of no great depth. Aristotle and all the logicians assume it as an axiom or first principle, from which the syllogistic system, as it were, takes its departure: and after a tedious voyage, and great expence of demonstration, it lands at last in this principle as its ultimate conclusion. O curas hominum! O quantum est in rebus inane!22
On Modal Syllogisms.
Categorical propositions, besides their quantity and quality, have another affection, by which they are divided into pure and modal. In a pure proposition, the predicate is barely affirmed or denied of the subject; but in a modal proposition, the affirmation or negation is modified, by being declared to be necessary, or contingent, or possible, or impossible. These are the four modes observed by Aristotle, from which he denominates a proposition modal. His genuine disciples maintain, that these are all the modes that can affect an affirmation or negation, and that the enumeration is complete. Others maintain, that this enumeration is incomplete; and that when an affirmation or negation is said to be certain or uncertain, probable or improbable, this makes a modal proposition, no less than the four modes of Aristotle. We shall not enter into this dispute; but proceed to observe, that the epithets of pure and modal are applied to syllogisms as well as to propositions. A pure syllogism is that in which both premises are pure propositions. A modal syllogism is that in which either of the premises is a modal proposition.
The syllogisms of which we have already said so much, are those only which are pure as well as categorical. But when we consider, that through all the figures and modes, a syllogism may have one premise modal of any of the four modes, while the other is pure, or it may have both premises modal, and that they may be either of the same mode or of different modes; what prodigious variety arises from all these combinations? Now it is the business of a logician, to shew how the conclusion is affected in all this variety of cases. Aristotle has done this in his First Analytics, with immense labour; and it will not be thought strange, that when he had employed only four chapters in discussing one hundred and ninety-two modes, true and false, of pure syllogisms, he should employ fifteen upon modal syllogisms.
I am very willing to excuse myself from entering upon this great branch of logic, by the judgement and example of those who cannot be charged either with want of respect to Aristotle, or with a low esteem of the syllogistic art.
Keckerman, a famous Dantzican professor, who spent his life in teaching and writing logic, in his huge folio system of that science, published ann. 1600, calls the doctrine of the modals the crux logi-corum. With regard to the scholastic doctors, among whom this was a proverb, De modalibus non gustabit asinus,23 he thinks it very dubious, whether they tortured most the modal syllogisms, or were most tortured by them. But those crabbed geniuses, says he, made this doctrine so very thorny, that it is fitter to tear a man’s wits in pieces than to give them solidity. He desires it to be observed, that the doctrine of the modals is adapted to the Greek language. The modal terms were frequently used by the Greeks in their disputations; and, on that account, are so fully handled by Aristotle: but in the Latin tongue you shall hardly ever meet with them. Nor do I remember, in all my experience, says he, to have observed any man in danger of being foiled in a dispute, through his ignorance of the modals.
This author, however, out of respect to Aristotle, treats pretty fully of modal propositions, shewing how to distinguish their subject and predicate, their quantity and quality. But the modal syllogisms he passes over altogether.
Ludovicus Vives, whom I mention, not as a devotee of Aristotle, but on ac-count of his own judgement and learning, thinks that the doctrine of modals ought to be banished out of logic, and remitted to grammar; and that if the grammar of the Greek tongue had been brought to a system in the time of Aristotle, that most acute philosopher would have saved the great labour he has bestowed on this subject.
Burgersdick, after enumerating five classes of modal syllogisms, observes, that they require many rules and cautions, which Aristotle hath handled diligently; but that as the use of them is not great and their rules difficult, he thinks it not worth while to enter into the discussion of them; recommending to those who would understand them, the most learned paraphrase of Joannes Monlorius upon the first book of the First Analytics.
All the writers of logic for two hundred years back that have fallen into my hands, have passed over the rules of modal syllogisms with as little ceremony. So that this great branch of the doctrine of syllogism, so diligently handled by Aristotle, fell into neglect, if not contempt, even while the doctrine of pure syllogisms con-tinued in the highest esteem. Moved by these authorities, I shall let this doctrine rest in peace, without giving the least disturbance to its ashes.
On Syllogisms that do not belong to Figure and Mode.
Aristotle gives some observations upon imperfect syllogisms: such as, the Enthimema, in which one of the premises is not expressed but understood: Induction, wherein we collect an universal from a full enumeration of particulars: and Examples, which are an imperfect induction. The logicians have copied Aristotle upon these kinds of reasoning, without any considerable improvement. But to compensate the modal syllogisms, which they have laid aside, they have given rules for several kinds of syllogism, of which Aristotle takes no notice. These may be reduced to two classes.
The first class comprehends the syllogisms into which any exclusive, restrictive, exceptive, or reduplicative proposition enters. Such propositions are by some called exponible, by others imperfectly modal. The rules given with regard to these are obvious, from a just interpretation of the propositions.
The second class is that of hypothetical syllogisms, which take that denomination from having a hypothetical proposition for one or both premises. Most logicians give the name of hypothetical to all complex propositions which have more terms than one subject and one predicate. I use the word in this large sense; and mean by hypothetical syllogisms, all those in which either of the premises consists of more terms than two. How many various kinds there may be of such syllogisms, has never been ascertained. The logicians have given names to some; such as, the copulative, the conditional by some called hypothetical, and the disjunctive.
Such syllogisms cannot be tried by the rules of figure and mode. Every kind would require rules peculiar to itself. Logicians have given rules for some kinds; but there are many that have not so much as a name.
The Dilemma is considered by most logicians as a species of the disjunctive syl-logism. A remarkable property of this kind is, that it may sometimes be happily retorted: it is, it seems, like a hand-grenade, which by dextrous management may be thrown back, so as to spend its force upon the assailant. We shall conclude this tedious account of syllogisms, with a dilemma mentioned by A. Gellius, and from him by many logicians, as insoluble in any other way.
Euathlus, a rich young man, desirous of learning the art of pleading, applied to Protagoras, a celebrated sophist, to instruct him, promising a great sum of money as his reward; one half of which was paid down; the other half he bound himself to pay as soon as he should plead a cause before the judges, and gain it. Protagoras found him a very apt scholar; but, after he had made good progress, he was in no haste to plead causes. The master, conceiving that he intended by this means to shift off his second payment, took, as he thought, a sure method to get the better of his delay. He sued Euathlus before the judges; and, having opened his cause at the bar, he pleaded to this purpose. O most foolish young man, do you not see, that, in any event, I must gain my point? for if the judges give sentence for me, you must pay by their sentence; if against me, the condition of our bargain is fulfilled, and you have no plea left for your delay, after having pleaded and gained a cause. To which Euathlus answered. O most wise master, I might have avoided the force of your argument, by not pleading my own cause. But, giving up this advantage, do you not see, that whatever sentence the judges pass, I am safe? If they give sentence for me, I am acquitted by their sentence; if against me, the condition of our bargain is not fulfilled, by my pleading a cause, and losing it. The judges, thinking the arguments unanswerable on both sides, put off the cause to a long day.
[21. ]“Mountains will labour, to birth will come a laughter-rousing mouse”: Horace, Ars poetica, l. 139 (trans. Rushton Fairclough).
[22. ]“O the vanity of mankind! How vast the void in human affairs!”: Persius Flaccus, Satires, I, l. 1 (trans. Ramsay).
[23. ]“Even a donkey will not eat the modes [of syllogisms].”