sense, that the function of names is but that of enabling us to remember and communicate our thoughts. That they also strengthen, even to an incalculable extent, the power of thought itself, is most true: but they do this by no intrinsic and peculiar virtue; they do it by the power inherent in an artificial memory, an instrument of which few have adequately considered the immense potency. As an artificial memory, language truly is, what it has so often been called, an instrument of thought; but it is one thing to be the instrument, and another to be the exclusive subject upon which the instrument is exercised. We think, indeed, to a considerable extent by means of names, but what we think of are the things called by those names; and there cannot be a greater error than to imagine that thought can be carried on with nothing in our mind but names, or that we can make the names think for us. § 3. Those who considered the dictum de omni as the foundation of the syllogism, looked upon arguments in a manner corresponding to the erroneous view which Hobbes took of propositions. Because there are some propositions which are merely verbal, Hobbes, in order apparently that his definition might be rigorously universal, defined a proposition as if no propositions declared anything except the meaning of words. If Hobbes was right; if no further account than this could be given of the import of propositions, no theory could be given but the commonly received one of the combination of propositions in a syllogism. If the minor premise asserted nothing more than that something belongs to a class, and if the major premise asserted nothing of that class except that it is included in another class, the conclusion would only be that what was included in the lower class is included in the higher, and the result, therefore, nothing except that the classification is consistent with itself, But we have seen that it is no sufficient account of the meaning of a proposition to say that it refers something to, or excludes something from, a class. Every proposition which conveys real information asserts a matter of fact, dependent on the laws of nature, and not on classification. It asserts that a given object does or does not possess a given attribute; or it asserts that two attributes, or sets of attributes, do or do not (constantly or occasionally) co-exist. Since such is the purport of all propositions which convey any real knowledge, and since ratiocination is a mode of acquiring real knowledge, any theory of ratiocination which does not recognise this import of propositions, cannot, we may be sure, be the true one. Applying this view of propositions to the two premises of a syllogism, we obtain the following results. The major premise, which, as already remarked, is always universal, asserts that all things which have a certain attribute (or attributes) have or have not along with it a certain other attribute (or attributes). The minor premise asserts that the thing or set of things which are the subject of that premise have the first-mentioned attribute; and the conclusion is, that they have (or that they have not) the second. Thus in our former example, All men are mortal, therefore Socrates is mortal, the subject and predicate of the major premise are connotative terms, denoting objects and connoting attributes. The assertion in the major premise is, that along with one of the two sets of attributes, we always find the other that the attributes connoted by "man" never exist unless conjoined with the attribute called mortality. The assertion in the minor premise is that the individual named Socrates possesses the former attributes; and it is concluded that he possesses also the attribute mortality. Or if both the premises are general propositions, as→ All men are mortal, All kings are mortal, the minor premise asserts that the attributes denoted by kingship only exist in conjunction with those signified by the word "man." The major asserts as before, that the last-mentioned attributes are never found without the attribute of mortality. The conclusion is, that wherever the attributes of kingship are found, that of mortality is found also. If the major premise were negative, as, No men are omnipotent, it would assert, not that the attributes connoted by "man never exist without, but that they never exist with, those connoted by "omnipotent: from which, together with the minor pre. mise, it is concluded that the same incompatibility exists between the attribute omnipotence and those constituting a king. In a similar manner we might analyse any other example of the syllogism. If we generalise this process, and look out for the principle or law involved in every such inference, and presupposed in every syllogism, the propositions of which are anything more than merely verbal; we find, not the unmeaning dictum de omni et nullo, but a fundamental principle, or rather two principles, strikingly resembling the axioms of mathematics. The first, which is the principle of affirmative syllogism, is, that things which co-exist with the same thing, co-exist with one another: or (still more precisely) a thing which coexists with another thing, which other co-exists with a third thing, also coexists with that third thing. The second is the principle of negative syllogisms, and is to this effect: that a thing which co-exists with another thing, with which other a third thing does not co-exist, is not co-existent with that third thing. These axioms manifestly relate to facts, and not to conventions; and one or other of them is the ground of the legitimacy of every argument in which facts and not conventions are the matter treated of.* § 4. It remains to translate this exposition of the syllogism from the * Mr. Herbert Spencer (Principles of Psychology, pp. 125-7) though his theory of the syllogism coincides with all that is essential of mine, thinks it a logical fallacy to present the two axioms in the text as the regulating principles of syllogism. He charges me with falling into the error, pointed out by Archbishop Whately and myself, of confounding exact likeness with literal identity; and maintains that we ought not to say that Socrates possesses the same attributes which are connoted by the word Man, but only that he possesses attributes exactly like them: according to which phraseology, Socrates and the attribute mortality are not two things co-existing with the same thing, as the axiom asserts, but two things co-existing with two different things. The question between Mr. Spencer and me is merely one of language; for neither of us (if I understand Mr. Spencer's opinions thing, possessed of objective existence; we rightly) believes an attribute to be a real believe it to be a particular mode of naming our sensations, or our expectations of sensation, when looked at in their relation to an external object which excites them. The question raised by Mr. Spencer does not, therefore, concern the properties of any really existing thing, but the comparaposes, of two different modes of using a tive appropriateness, for philosophical purname. Considered in this point of view, the phraseology I have employed, which is that commonly used by philosophers, seems to me to be the best. Mr. Spencer is of opinion that because Socrates and Alcibiades are not the same man, the attribute which constitutes them men should not be called the same attribute; that because the humanity of one man and that of another express themselves to our senses not by the same individual sensations, but by sensations exactly alike, humanity ought to different man. be regarded as a different attribute in every But on this showing, the humanity even of any one man should be considered as different attributes now and which it will then manifest itself to my half-an-hour hence; for the sensations by organs will not be a continuation of my present sensations but a repetition of them; fresh sensations, not identical with, but only exactly like the present. If every general conception, instead of being "the One in the Many," were considered to be as many different conceptions as there are would be no such thing as general lanthings to which it is applicable, there guage. A name would have no general one into the other of the two languages in which we formerly remarked that all propositions, and of course therefore all combinations of propositions, might be expressed. We observed that a proposition might be considered in two different lights; meaning if man connoted one thing when predicated of John, and another though closely resembling thing when predicated of William. Accordingly a recent pamphlet asserts the impossibility of general knowledge on this precise ground. The meaning of any general name is some outward or inward phenomenon, consisting, in the last resort, of feelings; and these feelings, if their continuity is for an instant broken, are no longer the same feelings, in the sense of individual identity. What, then, is the common something which gives a meaning to the general name? Mr. Spencer can only say, it is the similarity of the feelings and I rejoin, the attribute is precisely that similarity. The names of attributes are in their ulti mate analysis names for the resemblances of our sensations (or other feelings). Every general name, whether abstract or concrete, denotes or connotes one or more of those resemblances. It will not, probably, be denied, that if a hundred sensations are undistinguishably alike, their resemblance ought to be spoken of as one resemblance. and not a hundred resemblances which merely resemble one another. The things compared are many, but the something common to all of them must be conceived as one, just as the name is conceived as one, though corresponding to numerically different sensations of sound each time it is pronounced. The general term man as a portion of our knowledge of nature, or as a memorandum for our guidance. Under the former, or speculative aspect, an affirmative general proposition is an assertion of a speculative truth, viz. that whatever has a certain attribute has a certain other attribute. Under the other aspect, it is to be regarded not as a part of our knowledge, but as an aid for our practical exigencies, by enabling us, when we see or learn that an object possesses one of the two attributes, to infer that it possesses the other; thus employing the first attribute as a mark or evidence of the second. Thus regarded, every syllogism comes within the following general formula : Attribute A is a mark of attribute B, The given object has the mark A, therefore The given object has the attribute B. Referred to this type, the arguments which we have lately cited as specimens of the syllogism will express themselves in the following manner : The attributes of man are a mark of the attribute mortality, Socrates has the attributes of man, therefore Socrates has the attribute mortality. And again, The attributes of man are a mark of the attribute mortality, does not connote the sensations derived once from one man, which, once gone, can no more occur again than the same flash The of lightning. It connotes the general type of the sensations derived from all men, and the power (always thought of as one) of producing sensations of that type. And The the axiom might be thus worded: Two types of sensation, each of which co-exists with a third type, co-exist with another; or, Two powers, each of which co-exists with a third power, co-exist with one another. Mr. Spencer has misunderstood me in another particular. He supposes that the co-existence spoken of in the axiom, of two things with the same third thing, means simultaneousness in time. The co-existence meant is that of being jointly attributes of the same subject. The attribute of being born without teeth, and the attri. bute of having thirty-two teeth in mature age, are in this sense co-existent, both being attributes of man, though ex vi termini never of the same man at the same time. * Supra, p. 75. attributes of a king are a mark of the attributes of man, therefore attributes of a king are a mark of the attribute mortality. And, lastly, The attributes of man are a mark of the absence of the attribute omnipotence, attributes of a king are a mark of the attributes of man, The The therefore attributes of a king are a mark of the absence of the attribute signified by the word omnipotent (or, are evidence of the absence of that attribute). To correspond with this alteration in the form of the syllogisms, the axioms on which the syllogistic process is founded must undergo a corresponding transformation. In this altered phraseology, both these axioms may be brought under one general expression, namely, that whatever has any mark, has that which it is a mark of. Or, when the minor premise as well as the major is universal, we may state it thus: Whatever is a mark of any mark, is a mark of that which this last is a mark of. To trace the identity of these axioms with those previously laid down may be left to the intelligent reader. We shall find, as we proceed, the great convenience of the phraseology into which we have last thrown them, and which is better adapted than any I am acquainted with to express with precision and force what is aimed at, and actually accomplished, in every case of the ascertainment of a truth by ratiocination.* *Professor Bain (Logic, i. 157) considers the axiom (or rather axioms) here proposed as a sub-titure for the dictum de omni to posse-s certain advantages, but to be "un. workable as a basis of the syllogism. The fatal defect consists in this, that it is illadapted to bring out the difference between total and partial coincidence of terms, the observation of which is the essential precaution in syllogising correctly. If all the terms were co-extensive, the axiom would flow on admirably; A carries B. all B and none but B; B carries C in the same manner; at once A carries C, without limitation or reserve. But in point of fact, we know that while A carries B, other things carry B also; whence a process of limitation is required, in transferring A to C through B. A (in common with other things) carries B; B (in common with other things) carries C; whence A (in common with other things) carries C. The axiom provides no means of making this limitation; if we were to fo low A literally, we should be led to suppose A and C co-extensive: for such is the only obvious meaning of the attribute A coincides with the attribute C."" It is certainly possible that a careless learner here and there may suppose that if A carries B, it follows that B carries A. But if any one is so incautious as to commit this mistake, the very earliest lesson in the logic of infer nce, the Conversion of Propositions, will correct it. The first of the two forms in which I have stated the axiom is in some degree open to Mr. Bain's criti CHAPTER III. OF THE FUNCTIONS AND LOGICAL § 1. We have shown what is the real nature of the truths with which the Syllogism is conversant, in contradistinction to the more superficial manner in which their import is concism: when B is said to co-exist with A, (it must be by a lapsus calami that Mr. Bain uses the word coincide,) it is possible, meaning to be that the two things are only in the absence of warning, to suppose the found together. But this misinterpretation is excluded by the other, or practical, form of the maxim; Nota nota est nota rei inferring that because a is a mark of b, b ipsius. No one would be in any danger of can never exist without a; that because being in a confirmed consumption is a mark of being about to die, no one dies who is not in a consumption; that because being coal is a mark of having come out of the earth, nothing can come out of the earth except coal. Ordinary knowledge of Eng lish seems a sufficient protection against these mistakes, since in speaking of a mark of anything we are never understood as implying reciprocity. A more fundamental objection is stated by Mr. Bain in a subsequent passage (p. 158). "The axiom does not accommodate itself to the type of Deductive Reasoning as contrasted with Induction-the application of a general principle to a special case. Anything that fails to make prominent this circumstance is not adapted as a foundation for the syllogism." But though it may be proper to limit the term Deduction to the application of a general principle to a special case, it has never been held that Ratiocination or Syllogism is subject to the same limitation; and the adoption of it would excludea gr atamount of valid and conclusive syllogistic reasoning. Moreover, if the dictum de omni makes prominent the fact of the application of a general principle to a particular case, the axiom I propose makes prominent the condition which alone makes that application a real inference. I conclude, therefore, that both forms have their value, and their place in Logic. The dictum de omni should be retained as the fundamental axiom of the logic of mere consistency, often ca led Formal Logic; nor have I ever quarrelled with the use of it in that character, nor proposed to banish it from treatises on Formal Logic. But the other is the proper axiom for the logic of the pursuit of truth by way of Deduction; and the recognition of it can alone show how it is possib e that deductive reasoning can be a road to truth. ceived in the common theory; and forms in philosophy, appears to me what are the fundamental axioms on impossible; but which seem to have which its probative force or conclusive- been either overlooked, or insuffiness depends. We have now to in-ciently adverted to, both by the dequire whether the syllogistic process, fenders of the syllogistic theory and that of reasoning from generals to by its assailants. particulars, is, or is not, a process of inference; a process from the known to the unknown: a means of coming to a knowledge of something which we did not know before. § 2. It must be granted that în every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say, All men are mortal, Socrates is mortal; Logicians have been remarkably unanimous in their mode of answering this question. It is universally allowed that a syllogism is vicious if there be anything more in the conclusion than was assumed in the premises. it is unanswerably urged by the adverBut this is, in fact, to say that nothing saries of the syllogistic theory, that ever was, or can be, proved by syllogism the proposition, Socrates is mortal, which was not known, or assumed to is presupposed in the more general be known, before. Is ratiocination, assumption, All men are mortal: that then, not a process of inference? And we cannot be assured of the mortality is the syllogism, to which the word of all men, unless we are already cerreasoning has so often been represent-tain of the mortality of every indied to be exclusively appropriate, not vidual man: that if it be still doubtreally entitled to be called reasoning ful whether Socrates, or any other at all? This seems an inevitable con- individual we choose to naine, be sequence of the doctrine, admitted by mortal or not, the same degree of all writers on the subject, that a syl- uncertainty must hang over the asserlogism can prove no more than is tion, All men are mortal: that the involved in the premises. Yet the general principle, instead of being acknowledgment so explicitly made, given as evidence of the particular has not prevented one set of writers case cannot itself be taken for true from continuing to represent the syl- without exception, until every shadow logism as the correct analysis of what of doubt which could affect any case the mind actually performs in discover comprised with it, is dispelled by eviding and proving the larger half of the ence aliundè; and then what remains truths, whether of science or of daily for the syllogism to prove? That, in life, which we believe; while those short, no reasoning from generals to who have avoided this inconsistency, particulars can, as such, prove anyand followed out the general theorem thing, since from a general principle respecting the logical value of the syl- we cannot infer any particulars, but logism to its legitimate corollary, have those which the principle itself assumes been led to impute uselessness and as known. frivolity to the syllogistic theory itself, on the ground of the petitio principii which they allege to be inherent in every syllogism. As I believe both these opinions to be fundamentally erroneous, I must request the attention of the reader to certain considerations, without which any just appreciation of the true character of the syllogism, and the functions it per This doctrine appears to me irrefragable; and if logicians, though unable to dispute it, have usually exhibited a strong disposition to explain it away, this was not because they could discover any flaw in the argument itself, but because the contrary opinion seemed to rest on arguments equally indisputable. In the syllogism last referred to, for example, |