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faculty, not the only function of the soul. The soul has passions, pleasures, and pains; it affects the body, and is affected through the bodily organs in ways to which the term knowledge is not applicable; it determines action in its individual capacity; collectively, many souls being cognisant of each other's existence through the senses, and being urged by desire, form those combinations which we term political or social. From the consideration of the soul in these its different capacities arise many sciences ethics, æsthetics, politics, social science, physiological psychology, etc.-all of which sciences together may be called the psychological sciences. Now the science which treats of knowledge-its growth, its laws, its development-is one of these sciences; for to know is one of the functions of the soul-as some think, the supreme function, and that without which any consideration of the rest is futile (the opinion, as is to be supposed, of Schelling and Hegel)-but at any rate, one of the functions.

But now, selecting out of the whole number of the psychological sciences this science, which treats of the development of knowledge, the question arises, Is this science throughout its whole scope to be designated by the title of logic? It is not; and yet it may be entirely surveyed from the logical point of view. But there is also another point of view from which we may look on it. It is clear that we may treat of the development of our knowledge to some extent in a simply historical fashion. We may say, Thus and thus were different branches of knowledge successively added on to our previous stock, without dwelling on the truth and reality of the knowledge thus added, on its conformity with the essential laws of all knowledge. If, on the other hand, we wish to treat of knowledge from the logical point of view, the history of the development of knowledge sinks into minor importance, and is only used to illustrate the essential laws of knowledge. That this distinction is possible to a certain extent is plain from the different character of such a book as Dr. Whewell's History of the Inductive Sciences from any professedly logical treatise, such as that of Mr. Mill. In Dr. Whewell, the principles illustrate the history; in Mr. Mill, the history illustrates the principles. But how far is this distinction, between the science which treats of the logical justification of our knowledge and the science which treats of its historical development, capable of being carried out? This is a question that must be entered upon more fully, if we wish to know the exact relation of logic to metaphysics.

There are then certain portions of our knowledge which have been accumulated within historical times; the faculties by which they have been gained are faculties not possessed to anything like their full extent by the savage or the uncultivated person. Of this class are the physical sciences; and accordingly in the case of the physical sciences we can distinguish very accurately between their logic and their his tory, between the reasons which compel us to believe in them and the actual record of their growth. We can observe the processes of thought, induction and deduction, that secure to us this knowledge: we vitally accept these processes, not merely as principles that have obtained during the past, but as principles that must guide us for the future-in a much more stringent and thorough sense than that in which the principles which underlie any material science may be said to guide our action. By far the larger portion, however, of our knowledge, is acquired so very shortly after our birth, that we lose all recollection of the process by which it was gained. The faculties of sight, hearing, taste, smell, touch; the knowledge of ourselves, our emotions, and feelings; these we are said to possess naturally. But it cannot be doubted by any one who reflects on the subject, that though we, through some mysterious process of inheritance, come into possession of these kinds of knowledge easily and quickly, they were not gained easily or quickly by those who first possessed them. Thought and effort must have been necessary for their acquisition; and in that thought and effort must have been at work universal principles similar to those which gain and secure to us the knowledge which we are now for the first time gathering together. And the very difficult science which treats of this knowledge, which we possess so se curely as to call it elementary and primary, is entitled Metaphysics; and here it is impossible to distinguish between the logic and the historical growth of our knowledge. Why I believe that this chair, this table, this house, stands before me, and, Howl came to this belief, are no doubt two differ ent questions; but to treat them separately is very hard indeed. In general, the Ger man metaphysicians have treated of the former, the logical, question; the English psy chologists of the latter, the historical, to the solution of which they have invoked the aid of physiology. But, in point of fact, it is very difficult to treat of either question satisfactorily, apart from the other. And hence, though logic can in part be studied quite without reference to metaphysics, yet

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there is a part of logic which is closely en- | ever, to hear what previous writers have twined with metaphysics, and at present in- said as to the difference between these two separable from it. sciences.

Mr. Mill is hardly clear enough on the subject. "Of the science," he says, "which expounds the operations of the human understanding in the pursuit of truth, one essential part is the inquiry, What are the facts which are the objects of intuition or consciousness, and what are those which we merely infer? But this inquiry has never been considered a portion of logic. place is in another and a perfectly distinct department of science, to which the name metaphysics more particularly belongs: that portion of mental philosophy which attempts to determine what part of the furniture of the mind belongs to it origi

Its

If we could enter into the mind of an infant, and see it, with a swiftness of thought unparalleled in later life, gather together its knowledge of the material world, of colours, sounds, smells, tastes, feelings, and the connections of these, it is not to be doubted but that the fundamental principles which govern the development of knowledge must be rigorously adhered to; the infant must be a perfect, though unconscious, logician. What, however, is more particularly to be noticed is this: it is not quite certain that these primary processes of the mind are exactly of that nature which can be called induction and deduction, the only logical processes that we can be said fully to un-nally, and what part is constructed out of derstand. Even in our present mathemati- materials furnished to it from without. To cal processes, it is difficult to characterize this science appertain the great and much the method of our knowledge by these debated questions of the existence of matterms; we feel, though we cannot describe, ter; the existence of spirit, and of a distinca difference. It cannot be thought impossi- tion between it and matter; the reality of ble that a further analysis of our logical time and space, as things without the mind, processes, such as that which Hegel at- and distinguishable from the objects which tempted, may be necessary when we come are said to exist in them. . . . To the same to consider the processes of our elementary science belong the inquiries into the nature knowledge. But into the Hegelian logic it of Conception, Perception, Memory, and is impossible to enter here; though it is Belief; all of which are operations of the necessary to point out the relation which it understanding in the pursuit of truth, but bears to the ordinary logic. Such a logic, with which, as phenomena of the mind, or if correctly carried out-and I express no with the possibility which may or may not opinion whether Hegel carried it out cor-exist of analysing any of them into simpler rectly or not-must be more penetrating than ordinary logic. It may appear to contradict ordinary logic; just as to superficial minds the Copernican system appears to contradict the Ptolemaic system. It requires a scientific mind to discern that, in a much more important sense, the Copernican system is the development of the Ptolemaic system. Just so, while the possibility of this deeper logic must be vindicated, and the inquiry into it urged, it is certain that it cannot really be other than the development, through an acuter analysis, of our ordinary logic.

phenomena, the logician as such has no concern. To this science must also be referred the following, and all analogous questions: To what extent our intellectual faculties and our emotions are innate to what extent the result of association: whether God and duty are realities, the existence of which is manifest to us à priori by the constitution of our rational faculty; or whether our ideas of them are acquired notions, the origin of which we are able to trace and explain, and the reality of the objects themselves a question not of consciousness or intuition, but of evidence and reasoning. The province I have endeavoured to present above a of logic must be restricted to that portion correct view of the difference, and at the of our knowledge which consists of infersame time the relation, between logic and ences from truths previously known, whether metaphysics. Logic is the science which those antecedent data be general proposielucidates the fundamental principles that tions, or particular observations and perrun through the whole of our knowledge. ceptions. Logic is not the science of BeMetaphysics is the investigation, at once lief, but the science of Proof or Evidence logical and historical, into a certain portion (vol. i. pp. 7, 8). It may be noticed, by of our knowledge, namely, the elementary the way, that the proposition that "the portion. Thus logic and metaphysics are province of logic must be restricted to that intersecting sciences, though this often es- portion of our knowledge which consists of capes notice, from the fact that the portion inferences," is not quite consistent with the where both intersect is the most abstruse observation which Mr. Mill makes on the portion of either. It will be proper, how-succeeding page, that "the field of logic is

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co-extensive with the field of knowledge."
And the fact is that, though Mr. Mill has a
highly positive and precise idea of what he
does intend to write about (which is indeed
the first necessity in an author), his concep-
tion of the subjects outside his scope-of
what he styles "metaphysics"-is some-
what vague. His metaphysical questions
are a very miscellaneous set. None of
them are meaningless; but the meaning of
many of them is extremely indeterminate;
they are mere tentative expressions, and
can by no means be said to sketch the out-
line of a science. And if it be asked, Do
we not really know some things by intui-
tion, others by inference? and if so, must
not these separate kinds of knowledge be
the subjects of different sciences? it must
be replied, that the division thus stated,
whether theoretically possible or not, is
practically impossible. No fact, no truth,
comes before us, of which it can be said,
This is known to us at once and purely,
without any mental process whatever lead-
ing up to it.
We must take knowledge as
we find it, as a conglomerate. In short,
metaphysics, as the science which treats of
our elementary knowledge, is intelligible;
while if defined as the science of our intui-
tive knowledge, it challenges questions that
are not easily answered.

poses.

is time to consider the science in itself, its present condition, and its prospects.

The most fundamental axiom of logic relates to the sharp separation between truth and falsehood. A judgment, an opinion, a proposition, must be true or not true. This, it may be thought, is sufficiently obvious; but something remains to be said of it. The axiom assumes of course that the judgment or proposition has a clear meaning; that it is a hard solid fact knocking at the doors of the mind and challeng ing entrance; that it is not idle words or fluctuating thought. Indeed, the very terms judgment and proposition do, perhaps, imply this; an unmeaning judgment, an unmeaning proposition, is no real judgment, no real proposition. It should, however, be noticed that, though in logic the distinction between true and false is the most thoroughgoing possible, it is one which a prudent mind will be rather shy of urging sharply on all occasions. The sifting of thought necessary before a clear judgment or proposition can be arrived at is in most cases a great deal more than half the battle in the discovery of truth. Nevertheless, if truth is ever to be attained, we must in all cases come at last to a final decision:-Is this alleged truth true or not true? And therefore the distinction between truth and falsehood is the fundamental distinction of logic.

What I have tried to put forward in loose explanatory fashion in the above paragraph, is technically expressed by logicians in the laws, as they are called, of identity, contradiction, and excluded middle. The law of identity says, A thing is what it is. The law of contradiction says, A thing is not what it is not. The law of excluded middle says, What you think, is either true or not true. These three laws are rightly considered the primary laws of logic.

Much better is the account given by Kant and his followers of the difference between logic and metaphysics. According to them, logic deals with the form, i. e., the universal principles, of thought: metaphysics, with the matter of thought, the actual objects that we know. The definition of logic is indeed unexceptionable: that of metaphysics is more vague; it leaves it still doubtful what kind of inquiry into the matter of thought it is which metaphysics proIf it were answered that metaphysics proposes a historical inquiry into But, how are we to discern truth from the development of our knowledge, this ac- falsehood, to separate corn from chaff, to count of the matter would not very essen-educe a cosmos out of the chaos of sensatially differ from that which has been advanced in the above pages. It would differ from it in two ways only: first, in the total exclusion of logic from the sphere of metaphysics, whereas, according to the account here given, they are in certain parts inextricably entwined; and secondly, in extending metaphysics beyond the region of our elementary knowledge. But Kant's conception of metaphysics was clearly not that of a historical science. The metaphysics of Hamilton had more of a historical character; but the question is one that cannot be pursued further in this place. Here must terminate the investigation into the external relations of logical science; it

tion and opinion, to raise an enduring fabric of knowledge? Logicians have from the first endeavoured to generalize the means by which this is done, and with growing success; though it would be idle to deny that obscurity yet rests on many parts of the subject. Aristotle, the founder of the science, laid down the syllogism as the universal model after which all reasoning pro ceeds, and by which alone certain truth can be attained. What the syllogism is, and what are the different forms of it, is much too well known for it to be necessary to enter into a detailed description here. The general type of it is as follows: What is true of a class, is true of everything con

tained in the class; or, to use Kant's phrase- | did not admit of being reduced to rule and ology, That which stands under the condi- form. Hence, though in many important tion of a rule, stands under the rule itself. respects they classified and extended their But it is clear that this formula presupposes science, there remained this great gap at the that we already know the class, the rule, to base of it still unfilled. which we are to reduce our instance. How, then, is this knowledge acquired? Until we can ascertain this, a very large gap is left open in our theory of knowledge. And certainly it is a very extraordinary example of the readiness of mankind to acquiesce in words, that from Aristotle to Bacon no one should have had any idea but that "classes" -"rules '—were ultimate pieces of knowledge, not requiring to be accounted for, nor obtained by any process whatever, but existing originally in the mind. Bacon, as is well known, instituted a new era, and laid down induction from observation as the great process by which knowledge is accumulated. Now it would be incorrect to suppose that the Aristotelian philosophers had no idea of induction; only, strangely enough, they supposed that this process, which is a good half of the whole method by which we increase our knowledge, and the only part of it by which we gain our knowledge of those "classes" and "rules" which the syllogism presupposes, was only a particular kind of syllogism-was subordinate to the syllogism as a whole. Unfortunately, the Baconian school of thinkers at once despised the syllogism and thought induction too simple a process to stand in need of any philosophizing whatever. Logic was at a discount with them; and, till the present century, no writer who could with any truth be styled a follower of Bacon produced any systematic work on the subject, though there are valuable remarks relating to it in the treatises of Hobbes and Locke. Hence it happened that the greater number of writers on logic still continued to put the syllogism alone in the forefront, and to make induction subordinate to it. Kant, indeed, was more acute. He set down syllogism and induction (" die bestimmende Urtheilskraft" and "die reflectirende Urtheilskraft" he called them) as co-ordinate processes; but the latter process, as not giving immediate, but only gradual and probable knowledge, he was disposed to banish out of the domain of logic, except that its existence was to be formally recognised (Logik, pp. 205-208). Krug did the same; and Hamilton went so far in a backward direction as to make induction a particular kind of syllogism. All these writers thought it impossible to give general laws of induction; it seems to have been tacitly assumed by them, as indeed it was by the followers of Bacon, that probable reasoning

It was reserved for Mr. Mill, in his System of Logic, to give such a view of reasoning as should combine at once syllogism and induction, proving them together to form an entire and complete process of argumentation, of such a nature that either the inductive or syllogistic part of the process may in particular arguments drop out and be unnoticed, though a full view of the argument will express them both. We reason, says Mr. Mill, in every case in which the argument is complete, from particulars to particulars, from like to like. Only, the particular thing from which we reason, and the particular thing to which we reason, being like one another (which is indeed the necessary condition of our being able to argue from one to the other), it follows that some one quality, or group of qualities, must be the same in both; and the particular result which we infer will ensue, must be inferred as a result of the qualities which are the same in both phenomena. Hence, if we choose, we may represent in a general proposition the connection of the antecedent similarity and the inferred result. Instead of writing down our conclusion with respect to the individual phenomenon alone, we may write it down in a general manner: "Such and such qualities will always lead to such and such a result." It is clear, that we are perfectly justified in setting down such a general proposition; for, if we make an inference in one case on the strength of certain observed qualities of a phenomenon, we must be equally justified in drawing the same inference in any other case where the same qualities occur. Now supposing one of these general propositions to have been registered and remembered so long that we forget the particular instances from which it was derived, it may in time be considered a kind of first principle in itself; and we may deduce results from it, without referring to the facts in which it originated. When this takes place, then we have pure syllogistic or deductive reasoning; when, on the other hand, we suppress the general proposition, and argue directly from particulars to particulars, or again, when we argue from particulars to a general, we have pure inductive reasoning. But the full argument would always be from particulars to particulars, expressing at the same time that similarity of marks in the two sets of particulars, which is the ground of inferring a

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like result in either case. To this general | former occasion, will have a tendency to be process of argumentation Mr. Jevons has excited in the consciousness of the infant, given the appropriate name of "the substi- and may perhaps actually be so excited. tution of similars." The infant will observe A, and remember It would be superfluous to dwell at length B. So far we have only an example of on the explanation of the theory; but it memory. But it is a law of human nature should be noticed that a logician who was that we should look forward to the future, more of a mental analyst than Mr. Mill and endeavour to anticipate it. Suppose would lay a stress which Mr. Mill has not then the infant's mind to be at this moment laid on the invariable presence, even in an in a state of expectancy-of looking for argument from particulars to particulars, of ward for something actually to happen a general element of an element capable within the sphere of his cognisance, what of being referred to any case. For, even if will he expect? He cannot expect A, bethe reasoner himself does not so refer it, or cause he is observing A, and what is meant erect the grounds of his conclusion into a by his expecting is, what does he think will general proposition, we, if we analysed his happen when A has disappeared? Now, thoughts, must so refer it for him. And next to A, B occupies the chief place within the psychological question might be raised, his sphere of consciousness; he is at pres whether, in the mind of one who argues ent remembering B. Clearly then, unless from particulars to particulars, there is not some other cause interferes, the infant will always a moment (mostly forgotten after- not merely remember B; he will also exwards) when both particulars as particulars pect B to happen in the concrete, immedi are lost, and the points common to both ately. And in fact, at this stage, his realone come into prominence. Certain it is membrance of B as a past event will not that, in arguing from particulars to particu- be distinguishable from his expectation of lars, we often forget the particular from B as a coming event; his memory, without which we argue; we draw a conclusion so some powerful cause to make him throw rapidly as to forget not merely the argu- back B into that past time in which he first ment, but the very facts which form the observed it, will be swallowed up in his expremises. So that it may seem not im- pectation. Here then, at the outset of conprobable that the actual moment of transi-sciousness, we have the two laws of associa tion from particular to particular is forgotten afterwards.

No student of psychology can fail to notice the analogy between this logical theory of "the substitution of similars" and the psychological theory of "the association of ideas." The difference is that, while the psychological theory affirms merely that when two thoughts have been frequently presented together to the mind the recurrence of one (whether in the shape of observation or memory) tends to make the other recur simultaneously, the logical theory affirms that, when two facts have been frequently presented to the observation together, the recurrence of the one tends to create an expectation of the recurrence of the other. But the two theories are undoubtedly very near akin at their origin; and it may be useful to show how they are related to each other. Let us suppose then an infant whose mind is just awakening to the world around him, and has not yet gained any grasp of facts and their sequences. Let us suppose two facts, A and B, to pass successively, and to be observed by the infant. If, on another occasion, the fact A (that is, a fact precisely similar to A) recurs, and is observed by the infant, then by the law of association, the remembrance of the fact B, as observed on the

tion of ideas, and substitution of similarsthe psychological and logical laws-actually coinciding in their effects. But let us conduct the analysis a little further. The infant, as we left him, was observing A (for the second time) and expecting B. Now suppose B actually to happen this second time. Then the expectation of B will be merged in the observation of it; there will be no sharp line drawn between the two; indeed, memory, expectation, observation, will all three as yet be indistinguishable in the infant's mind. But now suppose A to happen a third time, and to be observed by the infant, who will then have the memory, and at the same time the expectation, of B forced upon him even more strongly than on the previous occasion (from the repetition). But suppose, this third time, that which succeeds A in the observation of the infant to be not B, but C. Then (if B has by this time been strongly enough impressed on his memory) a sense of antagonism will be aroused within his consciousness: expecting B, he will experience C. Thus while C impresses itself most strongly on him, from its im mediate presence, B will still remain within his consciousness, in that faint reflection which we call memory. Here then, for the first time, we have memory divorced from observation; the psychological law of asso

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