Bentham did not draw a line of distinction between these sciences; and he seems to have considered the terms almost convertible. It follows that he did not treat the subject of Logic, as it has generally been done, particularly by late writers, as a formal science,‡ teaching the laws of thought, as distinct from those sciences which treat of the matter of thought. How far he would have continued his mixture of the two subjects, after he had made some approach to completeness in his examination of the various departments of mental philosophy, it is difficult to say. He seems to have projected, as already stated, (see p. 10,) a full and searching inquiry into all the qualities and operations of the human mind, including an investigation not only of the laws of thought, but of the materials on which they work. To this end, he more than once set himself down to examine and classify the powers of the mind. He exhibited an intention of pursuing the examination of mental operations with a comprehensive, and, at the same time, most minute anatomy. To this purpose, he divided and subdivided the materials of thought; and being brought by his subdivisions into an analysis of the matter of language and grammar, left, in his fragments on these two subjects, specimens of the minuteness with which he intended to go over the whole field.
His notion of Logic was, that it was the means of getting at the truth, in relation to all departments of human knowledge;* and that it thus was, to use his own expression, the schoolmistress of all the other arts and sciences.† It would seem, then, to be included in his view of the subject, that any system of Logic, which left the student ignorant of the means of ascertaining the truth in regard to any one element of human knowledge, was an imperfect system. If Logic be considered as divided into the Analytic and Dialectic branches, the latter half of the subject was entirely rejected by Bentham; for, viewing dialectics in its original signification of the art of debating, he considered it as an instrument of deception rather than of truth — as a system of rules for enabling the more adroit disputant to defeat the less able. If, however, Logic be divided into the Analytic branch and the Synthetic,‡ he has left behind him traces of his labours in both departments: in the former examining the phenomena which the mind exhibits in the process of acquiring truth; in the latter, constructing instruments to facilitate its discovery.
Perhaps the most remarkable and original feature of the analytic portion of the fragments, is the division of all nouns substantive into names of Real, and names of Fictitious entities; a distinction which he follows out with his usual clearness and consistency, and of which he never, in any of his works, loses sight. If this classification in some measure resemble Aristotle’s division into Primary and Secondary substances, it will be found, on examination, to have a much more comprehensive influence, and, from the manner in which its author employs it, to have a much more important application to the arrangement of the elements of thought. Nouns expressing real entities are names of things of which we predicate the actual existence — such as a ball, a wheel, an impression on the mind, &c. Nouns expressive of fictitious entities, are, all those nouns which do not express such actual existences. The distinction seems to be a pretty obvious one; but the uses which its Author makes of it are novel and important. In our phraseology as to fictitious entities, we borrow the forms of words which have been invented for explaining the phenomena of real entities; and we cannot speak of the former without the actual use, or think of them without the mental use, of these forms of words. Thus motion is a fictious entity. We talk of motion being in a thing, or of a thing being in motion; and in using the preposition in, we borrow a word which was invented to be used upon physical matter. Relation is a fictitious entity — one thing is said to have a relation to another, and in this word have we are obliged to borrow a word constructed for the purpose of intimating corporal possession. The method in which I have my pen, and the method in which logic may have a relation to metaphysics, are two very different ideas; but we cannot express the latter without borrowing the use of those words which were constructed to represent the former. Hence, fictitious entities cannot appear in language, our instrument of thought, except through the use of borrowed words. They have no phraseology of their own, and can have none. Whether they have separate existence or not is a question we have not data for determining: to our minds they are so unreal, that we cannot think of them without clothing them for the time-being in the words which are invented for thinking of real entities.* How far a pursuit of this subject would throw light on the old dispute of the Realists and Materialists — how far misapprehension as to the actual subject of discussion may have arisen from this necessity of borrowing the phraseology of real entities for the purpose of discussing fictitious entities, is an inquiry on which the present writer cannot venture.
The next feature prominently demanding attention in the logical tracts, is the instrument which their Author used for analyzing and laying out his subjects — his exhaustive method of division, on the Dichotomous or Bifurcate plan. He took the hint of this system from the old editions of the Isagoge of Porphyry, in which there is a diagram exhibiting an exemplification of it, commonly attributed to the inventive genius of Porphyry himself, but probably the work of an editor. The dichotomous mode of division is frequently alluded to in the writings of the Aristotelian logicians, and it received considerable attention from Ramus; but it was, like many other instruments of discovery, a mere plaything for the intellect, until it fell into the hands of a man who was able to adapt it to practical service. The Porphyrian tree represents as the centre or trunk a genus generalissimum, from which successive branches issuing carry off some separable quality, until it has gone through as many processes of division as can be applied to it, and leaves in the two last condividends the two most concrete entities which can be comprehended within the general term.
The service which Bentham derived from the study of this diagram, was in its leading him to the conclusion that the only species of division which in its very terms bears to be exhaustive, is a division into two. It may happen that any other division — such as that of the works of nature into the animal, vegetable, and mineral kingdoms, may turn out to be exhaustive: but the object is to find a formula the use of which of itself secures exhaustiveness.
It is only by a division into two parts that logical definition per genus et differentiam can be accomplished. The species is marked off by its possessing the quality of the genus, and some differential quality which separates it from the other species of that genus. It is only by the expression of a difference as between two, that thought and language enable us to say whether the elements of the thing divided are exhausted in the condividends. We can only compare two things together — we cannot compare three or more at one time. In common language we do speak of comparing together more things than two; but the operation by which we accomplish this end is compound, consisting of deductions drawn from a series of comparisons, each relating to only two things at a time. Comparison is the estimate of differences; and language, by giving us the word “between,” as that by which we take the estimate, shows that we can only operate on two things at a time. Thus, if we have a division of an aggregate into three, we cannot give such a nomenclature to these three elements as will show that they exhaust the aggregate. If we say law is divided into penal and non-penal, we feel certain, in the very form of the statement, that we include every sort of law under one or other of these designations; but if we say that law is divided into real, personal, and penal, we cannot be, in the same manner, sure that we include every kind of law. If we wish to proceed farther in the division, and, after dividing the law into penal and non-penal, say the non-penal is divided into that which affects persons and that which does not affect persons, we are sure still to be exhaustive; and this system we can continue with the same certainty ad infinitum.
The system is undoubtedly a laborious and a tedious one, when the subject is large, and the examination minute. The exemplifications which the Author has given in his tables are the produce of great labour, and cover but a limited extent of subject. It was more as a test of the accuracy of the analysis made by the mind when proceeding with its ordinary abbreviated operations, than as an instrument to be actually used on all occasions, that the Author adopted the bifurcate system. As a means of using it with the more clearness and certainty, he recommended the adaptation to it of the Contradictory formula — viz., the use of a positive affirmation of a quality in one of the condividends, and the employment of the correspondent negative in the other. The value of this test, as applicable to any description of argumentative statement, is, in its bringing out intended contrasts with clearness and certainty. It is not necessary that the Differential formula should be actually employed. In its constant use there would be an end to all freedom and variety in style. But it is highly useful, to take the statement to pieces, and try whether its various propositions contain within them the essence of the bifurcate system and the formula; in other words, to see that when differences are explained, or contrasts made, they be clearly applied to only two things at a time, and that the phraseology, instead of implying vague elements of difference, explains distinctly what the one thing has, and what the other has not.*
† The Works referred to in this Section are those in vol. viii. down to p. 357. See also vol. iii. p. 285 et seq.
‡ The single word science is here used, for the sake of brevity, though Bentham, like Whately, considered that Logic was both a Science and an Art.
* Works, vol. viii. pp. 220, 222.
† Ibid. p. 76.
‡ Bentham would not himself have admitted the use of the terms Analysis and Synthesis with this popular acceptation. In a very curious note, (vol. viii. p. 75,) he has shown that the same elements separated in analysis are never the same that are put together in synthesis. The pieces, if they may be so called, with which the process of synthesis is performed, are not the same which result from the process of analysis. “The subject analysed is an aggregate or genus, which is divided into species, those into sub-species, and so on. The only case in which synthesis is exactly opposite and correspondent to, and no more than co-extensive with analysis, is, when between the ideas put together there is that sort of conformity from which the act of putting them together receives the name of generalization.”
* See Works, vol. viii. pp. 119, 126, 195 et seq., 263.
* For an account of the Bifurcate system, see Works, vol. viii. pp. 95, 103, 107, 110, 114, 253.
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