THE SCIENCE OF LOGIC.* WE have noticed in a former
number (October 9, 1869,) a work by Professor Jevons, in which he discussed the metaphysical foundation of the science of reasoning. We have now before us a treatise designed to impart to students of that science a know- ledge of the rules and processes built on this foundation, and to illustrate their application to the important end of producing clear and consistent thought ; and can sincerely recommend it as well adapted to this purpose. It brings before the reader in a concise and very intelligible manner the whole body of recognized logical doctrines, refers them to the great principles, or, so-called, Laws of Thought from which they appear to be derived, furnishes the student of logic with a variety of examples by which he can exercise himself in their use, and indicates the sources where he may find a full discussion of the subjects treated.
The work may be divided into two parts. The first, comprising lessons 1-24, treating of the formal art of logic, explains, very clearly and fully, its technical terms and the rules applied by the systematic logician to test the formal correctness of any conclu- sion from assumed premisses, and states the additions and modifi- cations introduced into the formal system since the days of Arch- bishop Whately by Sir W. Hamilton, Mr. J. S. Mill, Professor Boole, and Professor Jevons, known as the doctrines of Connota- tion, of Extension, and Intension, and the Qualification of the Pre- 4licate ; with the ingenious system of Reasoning by Machinery, by which it has been shown to be possible to substitute for the ordi- nary rules of syllogistic argument a process of systematically arranging and eliminating terms, till there are left those only which will form unobjectionable combinations. The second part, from lesson 25 to 31, followed by two lessons on classification and language, will probably be more attractive than the first to those who do not wish to pass an examination in logic, dealing, as it does, with the principles and methods applied by the great masters of scientific research to extend the dominion of human thought over the field of natural action, and by inductive hypotheses and experimental tests to lift more and more of the veil which hangs over the mysteries of existence.
The execution of both parts, assuming the point of view taken by Professor Jevons to be the true point, deserves high praise. Both are full of information clearly and concisely imparted, and the second part is rich in varied and apposite illustration, drawn from a wide range of scientific knowledge. But, to the point of view itself there seems to us something wanting, namely, the power of showing a reasonable connection between the formal method of inference from assumed premisses, and the application of
• Elementary Lessons in Logic, Deductive and Inductive, with Copious Questiotu, and Examples, and a Vocabulary of Logical Terms. By W. Stanley Jevons, M.A., Professor of Logic, &c., in Owens College, Manchester. London : Macmillan and Co.
the reason to ascertain what premisses ought to be assumed: while, by a change in this point of view, we believe that such a connection may be shown, and that thus the formal science of logic may acquire a degree of interest unattainable by it so long as it appears to be divorced from the processes on which the science of nature rests.
It is well known that the copula commonly used to join terms into propositions, is derived from the verb to be ; " The tree is green ;" " A planet is an opaque body." What does this copula signify? Professor Jevons, following the general current of logical explana- tion, says it signifies agreement. " All acts of reasoning," he tells us, " proceed from certain judgments, and the act of judgment con- sists in comparing two things together, and discovering whether they agree or differ ; that is to say, whether they are identical in any qualities" (p. 121). In our former article we adduced cases where the attempt to resolve reasoning into the perception of agreement or difference involved a complicated process in forming judgments to which we appeared to attain by a much simpler road. And Professor Jevons now supplies a method of illustrating the nature of propositions and syllogisms, first suggested, as he informs us, by the celebrated mathematician Euler, under which they assume a form where the imperfection noticed above in the view taken by the Professor is removed, and the difficulties consequent on it disappear. Take any judgment, say " The tree is green." Is any one who forms such a judgment conscious of an act of thought by which he brings together the notions of tree and green, and pronounces them to " agree "? With what green does the tree agree? Is not green the name for an indefinite number of tints passing from a shade scarcely dis- tinguishable from blue into a shade scarcely distinguishable from yellow? Give to the proposition the most abstract character possible, it is clear that it must mean, the colour of the tree belongs to a group of tints collectively called green. Take it in the more natural concrete use, and the proposition means, the tree is a green thing ; one among an indefinitely numerous class of green objects. Now this relation Euler's mode of present- ing propositions brings to light. " A proposition," he says, " expresses the fact that the things or class of things denoted by the subject is included in and forms part of the class of things denoted by the predicate " (p. 71) ; whence Euler proposed to draw a circle round the name of the pre- dicate, and another smaller circle round that of the subject, and by the position of these circles within or without each other to present the objects comprised in them to the eye in the relations in which they really stand to each other in thought. The illus- tration is most apposite. For the process of Construction, the bringing together of the many into one, and the holding fast the individuals brought together, as parts of the whole thus formed, by a bond furnished by some character common to them all ; this, we conceive to be the all-pervading operation on which the action of thought depends. From the simplest possible mental presenta- tion, the notion of a line as the track left behind by a moving point, to the gigantic imaginations by which the modern scientific thinker binds suns into systems of worlds, everywhere we find the General, the Particular, and the Individual combined to form our terms, and propositions, and groups of propositions. In our Judgments we analyze into their parts the unities which we have thus constructed. In our Syllogisms we bring to light the grounds of our judgments, the bonds by which these unities are held together.
To take an instance, adduced in our former article. The proposi- tion "Mont Blanc is is included in the group of mountains] higher than the Dent de Jaman," is a simple judgment. Liow are we to prove it : how can we satisfy ourselves that Mont Blanc really forms part of this unity ? We appeal to the height of the Dent du Midi, which we are supposed to know exceeds that of the Dent de Jaman, but falls short of Mont Blanc ; and assuming that, if B is higher than A the character of being higher than A belongs to all objects higher than B, conclude that Mont Blanc, being [included in the group of mountains] higher than the D. du Midi, must be (included in the group of those) higher than the D. de Jaman.
It is obvious from this description of the process of reasoning that it is quite independent of the special grounds on which, in any given case, we assign an individual to any particular group. Doubtless, the perception of likeness is a principle very commonly used in forming the uniting bond. In the classification of objects, regarded simply as co-existing phenomena, it is the natural prin- ciple. And since the study of the universe must begin by the formation of groups thus constituted, we must expect to meet with the principle of likeness continually, in the words which bind up for thought its primitive groups. Again, since the parts of every
whole must be like each other in that characteristic by which they are united into a whole, this principle is peculiarly liable to assume, as it has done generally in logic, an undue importance. And hence, as well as from a reason men- tioned below, Professor Jevons, in the effort to give sys- tematic unity to logical science, has been led to treat the perception of identity and difference as the basis of all reasoning, instead of presenting it as one only of many con- ceptions, through which the reason exercises its fundamental faculty of combining plurality into unity. The illustration of this action given above belongs to the most perfect form of syllogism, where we assign an individual thought of as part of a group to that group by means of some characteristic belonging to every member. It is easy to extend the same method of making visible to the eye the processes of thought, to the cases where we endeavour either to combine two characteristics belonging to the same object into a unity by means of that object, or to unite two distinct objects by means of the same characteristic. Thus can be presented, in a form perfectly intelligible, and, as appears to us, of considerable scientific in- terest, all those groups of true syllogisms which compose the three figures alone recognized by Aristotle, to the exclusion of the fourth, which Sir W. Hamilton undertook scientifically to abolish [Discussions, 612], and Professor Jevons admits to be " an imperfect and unnatural form, containing nothing but ill-arranged syllogisms, which would have been better stated in the first figure,"f p. 48. But the conception of the pro- cess of reasoning explained above, does more than merely to clear up the nature of the syllogism. By its means we can bring the syllogistic process into perfect connection with the action of the mind in inductive reasoning, that crux of logical speculation, on which so much ingenuity has been unsatisfactorily applied, in the attempt to explain why we feel justified in assigning to individuals qualities which we have no direct evidence that they possess. The old logicians supposed us to reason in these cases thus : —A, B, C (known cases) are X; D (a new case) is A, B, C, therefore, D is X. The explanation is absurd, argued Dr. Whately. Apply it to the case of a magnet. It makes us argue, A, B, C (the known cases) attract iron ; D (the unknown case) is the known cases, therefore D will attract iron. Now, undoubtedly, as the doctor says, we do not so argue, but argue thus :—What belongs to A, B, C will belong to D ; but A, B, C attract iron ; therefore D will attract iron. Bat why should we argue thus? " I am not called on to explain that," replies Dr. Whately ; "I refer you to the physical sciences ;" as if science underlay thought, and were possible without thinking. Nay, suggested Sir W. Hamilton, we really argue thus :—X, Y, Z are A ; X, Y, Z are B, therefore B is A; or, A contains X, Y, Z; X, Y, Z constitute B; there- fore A contains B. The form is apparently sound ; the difficulty is to apply it to any particular case. For instance : X, Y., Zare magnets ; X, Y, Z attract iron ; therefore magnets attract iron. Clearly this does not justify the conclusion that D, the newly-observed object, will attract iron ; there is wanting a pro- position to connect D with X, Y, Z True, says Mr. J. S. Mill, and this proposition is, " Attribute A is a mark connoting attribute B." Now, unquestionably we do assume that this is the case, but again, as with the explanation given by Dr. Whately, though the fact is indisputable, the "why" is unexplained. But the mystery clears up as soon as the constructive action of our intelligence is appreciated. Every construction must embody some uniting bond ; and the freedom of our imagination refuses to recognize any limits but such as are self-imposed, to the contents which shall be assigned to this bond. We apprehend every object as quails, as a kind of thing with which other things of the same kind may be associated ; hence, to some unity, or class of things, known or unknown before, we refer every object presented to our con- sciousness, or we could not think of it at all. Now, if we refer it to a unity already known to us, we must necessarily assume it to possess all the qualities which we have either taken as the constitu- tive bond of this mental group, or consider to be inseparably asso- ciated with them. The process of Inductive reasoning is no blind instinct of thought, or law imposed upon our minds, as Sir W. Hamilton seems to have supposed (Discussions, 137), but the ever present evidence of their ideal nature, the manifestation of that self-limiting freedom which enables us to translate the accidents of sense into the necessities of reason.$ 1' A set of figures, exhibiting all the possible combinations of true syllogisms Illustrated by this method, is to be found at p. 213 of a book called the Analogy of 'Thought and Nature, published by Williams and Norgate. 1863.
It is usual to speak of a suppressed premiss in inductive reasoning. But what Is really suppressed is, we conceive, two syllogisms, of which the first refers the mew object to some group by means of a characteristic, while the second affirms Of this action logic offers another interesting illustration, in a peculiarity first noticed by Sir W. Hamilton and Professor de Morgan, technically called the Quantification of the Predicate ; that is to say, the fact that our predicates may apply either to more or to fewer objects than our subjects, or may be co-extensive with them. If I say cats are vertebrate animals, I mean cats are included in the class of vertebrates. If I say vertebrate animals are cats, I mean the class of vertebrates includes cats. But if I say equilateral triangles are equiangular, I speak of two properties, of which each implies the other, so that the class of equilateral triangles is identical with that of equiangular triangles.
Now, these differences of meaning are not indicated by the common logical forms. To make these forms perfect, therefore, it has been suggested that logical propositions should embody the general and particular words, 0 all" and " some," and their con- verse, on both sides, and take such shapes as these, "all cats are some vertebrate animals;" "all vertebrate animals are some cats "; " all equiangular triangles are all equilateral triangles." Now, no doubt, the object of producing propositions which can be asserted with complete accuracy, is attainable by this method ; and as part of the art of logic, if logic be considered as a System of Rules by which men may be exercised in close and accurate thinking, we are not disposed to quarrel with it. But to logic considered as the Science of Thought, the notion of quantifying predicates is simply bewildering. It confuses the hypothetical action proper to thought in its inductive phase, when it is tentatively ascertaining to what unities it can refer the multiplicity of natural objects, with its demonstrative action, when it deals boldly with its own con- structions, and instead of inducing ideas upon phenomena, deduces phenomena from ideas. In such propositions as, An equi- lateral triangle is also equiangular ; Mont Blanc is 14,735 feet high ; London is the capital of England ; Honesty is always the best policy ; Virtue alone can give true happiness ; Iron is the cheapest metal (Jevons, 185), we pass from the inductive, or syllogistic phase of thought, where we simply connect the indivi- dual with the general by means of the particular, to the deductive stage, where we identify the individual with some particular deter- mination of the general, and therefore can reason about our subject with a precision of which the syllogistic form is incapable.
The difficulty of bringing under the ordinary syllogistic rules these cases where the predicate is thus equalized with the subject seems to have led Professor Jevons to seek for an explanation of the rules in a modification of the principle of identity (p. 124). But this is to present as the principle of mental action, that which, according to our view, is its result, and thus to obscure the spontaneous testimony of language to the double truth,—the great truth announced by Plato, that knowledge belongs only to the world of ideas,—and the great truth, on which Aristotle acted, and which Bacon formulated, that only by the careful study of natural phe- noma can we attain to the perception of those ideas through which nature can be truly known.
To these great truths language spontaneously bears witness ; by the inductive or syllogistic process, where the subject is included in the predicate, testifying that the road to natural truth lies through observation, hypothesis, and verification ; while in the deductive process, where the subject equals the predicate, she sets before us the goal of ideal certainty, to which in all its in- ductive operations the mind instinctively tends.§ That there is a real science of logic, admitting of being presented in a form attractive to those who are interested in the study of their own minds, when its true principles are disentangled from the mass of artificial formula by which they are commonly obscured, we are persuaded, and hope by the foregoing remarks to have made pro- bable to our readers. And, from the amount of attention devoted to this subject of late years by many thinkers of great ability, we cherish the hope of seeing such a work produced ere long by some one who will bring to its composition as great depth of know- ledge and clearness of expression as distinguish the writings of ' Professor Jevons, if not by the pen of the Professor himself. But the examination of his present work strengthens us in the convic- tion that reasoning does not depend on the perception of identity, and that the attempt to resolve it into this principle must give to logic an artifical character, fatal to its claims to teach the science of thought.
that if it does belong to this group it must possess all the properties common to its members. The same view is taken by the author of the work cited above, who at p. 66 gives what he supposes to be the suppressed syllogisms.
§ It must be observed that although in the deductive judgment the meaning of the copula changes from is [included in] to, is [equal to], the grounds of our judg- ments are as various in the one case as in the other.
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