130. A man may reckon without the use of words in particular things, as in conjecturing from the sight False reaof anything what is likely to follow; and if he soning. son consiste uniquement dans l'identité." If we add to this, as he probably intended, non-identity, as the condition of all negative conclusions, it seems to be no more than is necessarily involved in the fundamental principle of syllogism, the dictum de omni et nullo; which may be thus reduced to its shortest terms: "Whatever can be divided into parts, includes all those parts, and nothing else." This is not limited to mathematical quantity, but includes every thing which admits of more and less. Hobbes has a good passage in his Logic on this: Non putandum est computationi, id est, ratiocinationi in numeris tantum locum esse, tanquam homo a cæteris animantibus, quod censuisse narratur Pythagoras, sola numerandi facultate distinctus esset; nam et magnitudo magnitudini, corpus corpori, motus motui, tempus tempori, gradus qualitatis gradui, actio actioni, conceptus conceptui, proportio proportioni, oratio orationi, nomen nomini, in quibus omne philosophiæ genus continetur, adjici adimique potest. But it does not follow by any means that we should assent to the strange passages quoted by Stewart from Condillac and Diderot, which reduce all knowledge to identical propositions. Even in geometry, where the objects are strictly magnitudes, the countless variety in which their relations may be exhibited constitutes the riches of that inexhaustible science; and in moral or physical propositions, the relation of quantity between the subject and predicate, as concretes, which enables them to be compared, though it is the sole foundation of all general deductive reasoning, or syllogism, has nothing to do with the other properties or relations, of which we obtain a knowledge by means of that comparison. In mathematical reasoning, we infer as to quantity through the medium of quantity; in other reasoning, we use the same medium, but our inference is as to truths which do not lie within that category. Thus in the hackneyed instance, All men are mortal; that is, mortal creatures include men and something more, it is absurd to assert, that we only know that men are men. It is true that our knowledge of the truth of the proposition comes by the help of this comparison of men in the subject with men as implied in the predicate; but the very nature of the proposition discovers a constant relation between the individuals of the human species and that mortality which is predicated of them along with others; and it is in this, not in an identical equation, as Diderot seems to have thought, that our knowledge consists. The remarks of Stewart's friend, M. Prevost of Geneva, on the principle of identity as the basis of mathematical science, and which the former has candidly subjoined to his own volume, appear to me very satisfactory. Stewart comes to admit that the dispute is nearly verbal; but we cannot say that he originally treated it as such; and the principle itself, both as applied to geometry and to logic, is, in my opinion, of some importance to the clearness of our conceptions as to those sciences. It may be added, that Stewart's objection to the principle of identity as the basis of geometrical reasoning is less forcible in its application to syllogism. He is willing to admit that magnitudes capable of coincidence by immediate superposition may be reckoned identical, but scruples to apply such a word to those which are dissimilar in figure, as the rectangles of the means and extremes of four proportional lines. Neither one nor the other are, in fact, identical as real quantities, the former being necessarily conceived to differ from each other by position in space, as much as the latter; so that the expression he quotes from Aristotle, iv τουτοῖς ἡ ἰσότης ἑνότης, or any similar one of modern mathematicians, can only refer to the abstract magnitude of their areas, which being divisible into the same number of equal parts, they are called the same. And there seems no real difference in this respect between two circles of equal radii and two such rectangles as are supposed above, the identity of their magnitudes being a distinct truth, independent of any consideration either of their figure or their position. But, however this may be, the identity of the subject with part of the predicate in an affirmative proposition is never fictitious, but real. It means that the persons or things in the one are strictly the same beings with the persons or things to which they are reckons wrong, it is error. But in reasoning on general words, to fall on a false inference is not error, though often compared in the other, though, through some difference of relations, or other circumstance, they are expressed in different language. It is needless to give examples, as all those who can read this note at all will know how to find them. I will here take the liberty to remark, though not closely connected with the present subject, that Archbishop Whately is not quite right in saying (Ele ments of Logic, p. 46), that in affirmative propositions the predicate is never distributed. Besides the numerous instances where this is, in point of fact, the case, all which he justly excludes, there are many in which it is involved in the very form of the proposition. Such are those which assert identity or equality, and such are all definitions. Of the first sort are all the theorems in geometry, asserting an equality of magnitudes or ratios, in which the subject and predicate may always change places. It is true that in the instance given in the work quoted, that equilateral triangles are equiangular, the converse requires a separate proof, and so in many similar cases. But in these the predicate is not distributed by the form of the proposition; they assert no equality of magnitude. The position, that where such equality is affirmed, the predicate is not logically distributed, would lead to the consequence that it can only be converted into a particular affirmation. Thus after proving that the square of the hypothenuse, in all right-angled triangles, is equal to those of the sides, we could only infer that the squares of the sides are sometimes equal to that of the hypothenuse, which could not be maintained without rendering the rules of logic ridiculous. The most general mode of considering the question, is to say, as we have done above, that, in an universal affirmative, the predicate B (that is, the class of which B is predicated) is composed of A the subject, and X, an unknown remainder. But if, by the very nature of the proposition, we perceive that X is nothing, or has no value, it is plain that the subject measures the entire predicate, and vice versâ, the predicate measures the subject; in other words, each is taken universally, or distributed. [A critic upon the first edition has observed, that "nothing is clearer than that in these propositions the predicate is not necessarily distributed ;" and even hints a doubt whether I understood the terms rightly. Edinburgh Review, vol. lxxxii. p. 219. This suspicion of my ignorance as to the meaning of the two commonest words in logic I need not probably repel; as to the peremptory assertion of this critic, without any proof beyond his own authority, that in propositions denoting equality of magnitude, the predicate is not necessarily distributed, if his own reflections do not convince him, I can only refer him to Aristotle's words: TOUTOS irons ivórns; and I presume he does not doubt that in identical propositions of the form, A est A, the distribution of the predicate, or the convertibility of the proposition, which is the same thing, is manifest.-1842.] [Reid observes, in his Brief Account of Aristotle's Logic, that "the doctrine of the conversion of propositions is not so complete as it appears. How, for instance, shall we convert this proposition, God is omniscient?" Sir W. Hamilton, who, as editor of Reid, undertakes the defence against him of every thing in the established logic, rather curiously answers, in his notes on this passage: By saying, An, or The, omniscient is God." (Hamilton's edition of Reid, p. 697.) The rule requires, "An omniscient," a conversion into the particular; but, as this would be shocking, he substitutes, as an alternative, the, which is to take generally or distribute the predicate in the first proposition; and to this the nature of the proposition leads us, as it does in innumerable cases. However, as logical writers, especially the recent, commonly exclude all consideration of the subject-matter of propositions, it may be correct to say, with Archbishop Whately, that, as a rule of syllogism, the predicate is not distributed. Aristotle himself, though he lays this down as a formal rule, does not hesitate to say, that where the predicate is the proprium (dev) or characteristic of the subject, and of nothing else, it may be reciprocated (arrıxarnyogura) with the subject; as if it is the proprium of a man to be capable of learning grammar, all men are capable of being grammarians, and all who are such are men. Topica, i. 4. And in the wellknown passage upon inductive syllogism, Analyt. Prior., I. ii. c. 23, he shows the so called, but absurdity." "If a man should talk to me of a round quadrangle, or accidents of bread in cheese, or immaterial substances, or of a free subject, a free will, or any free, but free from being hindered by opposition, I should not say he were in error, but that his words were without meaning, that is to say, absurd." Some of these propositions, it will occur, are intelligible in a reasonable sense, and not contradictory, except by means of an arbitrary definition which he who employs them does not admit. It may be observed here, as we have done before, that Hobbes does not confine reckoning, or reasoning, to universals, or even to words. Its fre quency. 131. Man has the exclusive privilege of forming general theorems. But this privilege is allayed by another, that is, by the privilege of absurdity, to which no living creature is subject, but man only. And of men those are of all most subject to it, that profess philosophy. . . . For there is not one that begins his ratiocination from the definitions or explications of the names they are to use, which is a method used only in geometry, whose conclusions have thereby been made indisputable. He then enumerates seven causes of absurd conclusions; the first of which is the want of definitions, the others are erroneous imposition of names. If we can avoid these errors, it is not easy to fall into absurdity (by which he of course only means any wrong conclusion) except perhaps by the length of a reasoning. "For all men," he says, by nature reason alike, and well, when they have good principles. Hence it appears that reason is not as sense and memory born with us, nor gotten by experience only, minor premise to be convertible into an universal affirmative, by which alone such a syllogism differs from the logical form called Darapti. But as Aristotle notoriously considers syllogisms in their matter as well as form, the modern writers, who confine themselves to the latter, are not concluded by his authority. Their theory, which not only reduces all logic to syllogism, but all syllogism to a very few rules of form, so that we may learn every thing that can be learned in this art through the letters A, B, and C, without any examples at all, appears as prudence is, but attained by industry, in apt imposing of names, and in getting a good and orderly method of proceeding from the elements to assertions, and so to syllogisms. Children are not endued with reason at all till they have attained the use of speech, but are called reasonable creatures, for the possibility of having the use of reason hereafter. And reasoning serves the generality of mankind very little, though with their natural prudence without science they are in better condition than those who reason ill themselves, or trust those who have done so.' ""X It has been observed by Buhle, that Hobbes had more respect for the Aristotelian forms of logic than his master Bacon. He has in fact written a short treatise, in his Elementa Philosophiæ, on the subject; observing, however, therein, that a true logic will be sooner learned by attending to geometrical demonstrations than by drudging over the rules of syllogism, as children learn to walk not by precept but by habit." Knowledge of fact not derived from reasoning. 132." No discourse whatever," he says truly in the seventh chapter of the Leviathan, “can end in absolute knowledge of fact, past or to come. For as to the knowledge of fact, it is originally sense; and ever after memory. And for the knowledge of consequence, which I have said before is called science, it is not absolute but conditional. No man can know by discourse that this or that is, has been, or will be, which is to know absolutely; but only that if this is, that is; if this has been, that has been; if this shall be, that shall be; which is to know conditionally, and that not the consequence of one thing to another, but of one name of a thing to another name of the same thing. And therefore when the discourse is put into speech and begins with the defini * Lev., c. 5. Citius multo veram logicam discunt qui mathematicorum demonstrationibus, quam qui logicorum syllogizandi præceptis legendis tempus conterunt, haud aliter quam parvuli pueri gressum formare discunt non præceptis sed sæpe gradiendo. C. iv. p. 30. Atque hæc sufficiunt (he says afterwards) de syllogismo, qui est tanquam gressus philosophiæ; nam et quantum necesse est ad cognoscendum unde vim suam habeat omnis argumentatio legitima, tantum diximus ; et omnia accumulare quæ dici possunt, æque superfluum esset ac si quis ut dixi puerulo ad gradiendum præcepta dare velit; acquiritur enim ratiocinandi ars non præceptis sed usu et lectione eorum librorum in quibus omnia severis demonstrationibus transiguntur. C. v. p. 35. tions of words, and proceeds by connexion of the same into general affirmations, and of those again into syllogisms, the end or last sum is called the conclusion, and the thought of the mind by it signified is that conditional knowledge of the consequence of words which is commonly called science. But if the first ground of such discourse be not definitions; or if definitions be not rightly joined together in syllogisms, then the end or conclusion is again. opinion, namely, of the truth of somewhat said, though sometimes in absurd and senseless words, without possibility of being understood." Belief. 133. " Belief, which is the admitting of propositions upon trust, in many cases is no less free from doubt than perfect and manifest knowledge; for as there is nothing whereof there is not some cause, so when there is doubt, there must be some cause thereof conceived. Now there be many things which we receive from the report of others, of which it is impossible to imagine any cause of doubt; for what can be opposed against the consent of all men, in things they can know and have no cause to report otherwise than they are, such as is great part of our histories, unless a man would say that all the world had conspired to deceive him?" Whatever we believe on the authority of the speaker, he is the object of our faith. Consequently when we believe that the Scriptures are the word of God, having no immediate revelation from God himself, our belief, faith, and trust is in the church, whose word we take and acquiesce therein. Hence all we believe on the authority of men, whether they be sent from God or not, is faith in men only. We have no certain knowledge of the truth of Scripture, but trust the holy men of God's church succeeding one another from the time of those who saw the wondrous works of God Almighty in the flesh. And as we believe the Scriptures to be the word of God on the authority of the church, the interpretation of the Scripture in case of controversy ought to be trusted to the church rather than private opinion. 134. The ninth chapter of the Leviathan contains a 2 Lev., c. 7. "Hum. Nat., c. 6. VOL. II. b Lev., c. 7. e Hum. Nat., c. 11. |