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desire the painter to make him the picture of a man, which is as much as to say, of a man in general, he meaneth no more but that the painter should choose what man he pleaseth to draw, which must needs be some of them that are, or have been, or may be, none of which are universal. But when he would have him to draw the picture of the king, or any particular person, he limiteth the painter to that one person he chooseth. It is plain, therefore, that there is nothing universal but names, which are therefore called indefinite.'

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125. "By this imposition of names, some of larger, some of stricter signification, we turn the reckonposed. ing of the consequences of things imagined in the mind into a reckoning of the consequences of appellations." Hence he thinks that though a man born deaf and dumb might by meditation know that the angles of one triangle are equal to two right ones, he could not, on seeing another triangle of different shape, infer the same without a similar process. But by the help of words, after having observed the equality is not consequent on any thing peculiar to one triangle, but on the number of sides and angles which is common to all, he registers his discovery in a proposition. This is surely to confound the antecedent process of reasoning with what he calls the registry, which follows it. The instance, however, is not happily chosen, and Hobbes has conceded the whole point in question, by admitting that the truth of the proposition could be observed, which cannot require the use of words. He expresses

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Logica, his Latin treatise published after the Leviathan. Quomodo autem animo sine verbis tacita cogitatione ratiocinando addere et subtrahere solemus uno aut altero exemplo ostendendum est. Si quis ergo e longinquo aliquid obscurè videat, etsi nulla sint imposita vocabula, habet tamen ejus rei ideam eandem propter quam impositis nunc vocabulis dicit eam rem esse corpus. Postquam autem propius accesserit, videritque eandem rem certo quodam modo nunc uno, nunc alio in loco esse, habebit ejusdem ideam novam, propter quam nunc talem rem ɑnimatam vocat, &c. p. 2.

The demonstration of the thirtysecond proposition of Euclid could leave no one in doubt whether this property were common to all triangles, after it had been proved in a single instance. It

the next sentence with more felicity. "And thus the consequence found in one particular comes to be registered and remembered as an universal rule, and discharges our mental reckoning of time and place; and delivers us from all labour of the mind saving the first, and makes that which was found true here and now to be true in all times and places."

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126. The equivocal use of names makes it often difficult to recover those conceptions for which they The subject were designed "not only in the language of continued. others, wherein we are to consider the drift and occasion and contexture of the speech, as well as the words themselves, but in our own discourse, which being derived from the custom and common use of speech, representeth unto us not our own conceptions. It is, therefore, a great ability in a man, out of the words, contexture, and other circumstances of language, to deliver himself from equivocation, and to find out the true meaning of what is said; and this is it we call understanding."" "If speech be peculiar to man, as for aught I know it is, then is understanding peculiar to him also; understanding being nothing else but conception caused by speech." definition is arbitrary, and not conformable to the usual sense. "True and false," he observes afterwards, "are attributes of speech, not of things; where speech is not, there is neither truth nor falsehood, though there may be error. Hence as truth consists in the right ordering of names in our affirmations, a man that seeks precise truth hath need to remember what every word he uses stands for, and place it accordingly. In geometry, the only science hitherto known, men begin by definitions. And every

is said, however, to be recorded by an ancient writer, that this discovery was first made as to equilateral, afterwards as to isosceles, and lastly as to other triangles. Stewart's Philosophy of Human Mind, vol. ii. chap. iv. sect. 2. The mode of proof must have been different from that of Euclid. And this might possibly lead us to suspect the truth of the tradition. For if the equality of the angles of a triangle to two right angles admitted of any elementary demonstration, such as might occur in the infancy of geometry,

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man who aspires to true knowledge should examine the definitions of former authors, and either correct them or make them anew. For the errors of definitions multiply themselves, according as the reckoning proceeds, and lead men into absurdities, which at last they see, but cannot avoid without reckoning anew from the beginning in which lies the foundation of their errors. . . . . . In the right definition of names, lies the first use of speech, which is the acquisition of science. And in wrong or no definitions lies the first abuse from which proceed all false and senseless tenets, which make those men that take their instruction from the authority of books, and not from their own meditation, to be as much below the condition of ignorant men, as men endued with true science are above it. For between true science and erroneous doctrine, ignorance is in the middle. Words are wise men's counters-they do but reckon by them; but they are the money of fools. "P

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127. "The names of such things as affect us, that is, Names dif- which please and displease us, because all men be posed. not alike affected with the same thing, nor the same man at all times, are in the common discourse of men of inconstant signification. For seeing all names are imposed to signify our conceptions, and all our affections are but conceptions, when we conceive the same thoughts differently, we can hardly avoid different naming of them. For though the nature of that we conceive be the same, yet the diversity of our reception of it, in respect of different constitutions of body and prejudices of opinion, gives every thing a tincture of our different passions. And therefore, in reasoning, a man must take heed of words, which, besides the signification of what we imagine of their nature, have a signification also of the nature, disposition, and interest of the speaker; such as are the names of virtues and vices; for one man calleth wisdom what another calleth fear, and one cruelty what another justice; one prodigality what another magnanimity, and one gravity what another stupidity, &c. And therefore such names can never be true grounds of any ratiocination. No more can metaphors and tropes of speech, but these are less

dangerous, because they profess their inconstancy, which the other do not." Thus ends this chapter of the Leviathan, which, with the corresponding one in the treatise on Human Nature, are, notwithstanding what appear to me some erroneous principles, as full, perhaps, of deep and original thoughts as any other pages of equal length on the art of reasoning and philosophy of language. Many have borrowed from Hobbes without naming him; and in fact he is the founder of the Nominalist school in England. He may probably have conversed with Bacon on these subjects; we see much of that master's style of illustration. But as Bacon was sometimes too excursive to sift particulars, so Hobbes has sometimes wanted a comprehensive view.

128. "There are,' to proceed with Hobbes, "two kinds of knowledge; the one, sense, or knowledge Knowledge. original, and remembrance of the same; the other, science, or knowledge of the truth of propositions, derived from understanding. Both are but experience, one of things from without, the other from the proper use of words in language, and experience being but remembrance, all knowledge is remembrance. Knowledge implies two things, truth and evidence; the latter is the concomitance of a man's conception with the words that signify such conception in the act of ratiocination." If a man does not annex a meaning to his words, his conclusions are not evident to him. "Evidence is to truth as the sap to the tree, which, so far as it creepeth along with the body and branches, keepeth them alive; when it forsaketh them they die; for this evidence, which is meaning with our words, is the life of truth." "Science is evidence of truth, from some beginning or principle of sense. The first principle of knowledge is that we have such and such conceptions; the second, that we have thus and thus named the things whereof they are conceptions; the third is, that we have joined those names in such manner as to make true propositions; the fourth and last is, that we have joined these propositions in such manner as they be concluding, and the truth of the conclusion said to be known."

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129. Reasoning is the addition or subtraction of parcels. "In whatever matter there is room for addition Reasoning. and subtraction, there is room for reason; and where these have no place, then reason has nothing at all to do." This is neither as perspicuously expressed, nor as satisfactorily illustrated, as is usual with Hobbes; but it is true that all syllogistic reasoning is dependent upon quantity alone, and consequently upon that which is capable of addition and subtraction. This seems not to have been clearly perceived by some writers of the old Aristotelian school, or perhaps by some others, who, as far as I can judge, have a notion that the relation of a genus to a species, or a predicate to its subject, considered merely as to syllogism or deductive reasoning, is something different from that of a whole to its parts; which would deprive that logic of its chief boast, its axiomatic evidence. But, as this would appear too dry to some readers, I shall pursue it farther in a note.'

Lev., c. 5.

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Dugald Stewart (Elements of Philosophy, &c., vol. ii. ch. ii. sect. 2) has treated this theory of Hobbes on reasoning, as well as that of Condillac, which seems much the same, with great scorn, as too puerile to admit of (i. e. require) refutation." I do not myself think the language of Hobbes, either here, or as quoted by Stewart from his Latin treatise on Logic, so perspicuous as usual. But I cannot help being of opinion that he is substantially right. For surely, when we assert that A is B, we assert that all things which fall under the class B, taken collectively, comprehend A; or, that B=A+X: B being here put, it is to be observed, not for the res prædicata itself, but for the concrete, de quibus prædicandum est. I mention this, because this elliptical use of the word predicate seems to have occasioned some confusion in writers on logic. The predicate, strictly taken, being an attribute or quality, cannot be said to include or contain the subject. But to return, when we say B=A+X, or B-X-A, since we do not compare, in such a proposition as is here supposed, A with X, we only mean that A=A, or, that a certain part of B is the same as itself. Again, in a particular affirmative, Some A is B, we assert that part of

A, or A-Y, is contained in B, or that B may be expressed by A - Y + X. So also when we say, Some A is not B, we equally divide the class or genus B into A-Y and X, or assert that B-A-Y+X; but, in this case, the subject is no longer A-Y, but the remainder, or other part of A, namely, Y; and this is not found in either term of the predicate. Finally, in the universal negative, No A (neither A-Y nor Y) is B, the A-Y of the predicate vanishes or has no value, and B becomes equal to X, which is incapable of measurement with A, and consequently with either A-Y or Y, which make up A. Now if we combine this with another proposition, in order to form a syllogism, and say that C is A, we find, as before, that A=C+Z; and substituting this value of A in the former proposition, it appears that B=C+Z+X. Then, in the conclusion, we have, C is B; that is, C is a part of C+Z+X. And the same in the three other cases or moods of the figure. This seems to be, in plainer terms, what Hobbes means by addition or subtraction of parcels, and what Condillac means by rather a lax expression, that equations and propositions are at bottom the same, or, as he phrases it better, "l'évidence de rai

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