r

we find a diagram of which the following is nearly a

facsimile :

ἡ ουσία

διαιρῆται

εἰς

σῶμα ἀσώματον

ἔμψυχον ἄψυχον

αἰσθητικὸν ἀναίσθητον

μεταβατικὸν ἀμετάβατον

λογικὸν ἄλογον τὸν ἄνθρωπον.

In the above scheme we find the bifurcate principle accurately but not completely applied. Each genus is subdivided into two species, described by a pair of positive and negative terms, so that the species are together equal in extent to the genus. But it will of course be observed that each negative branch is left without further subdivision, so that there is only a single infima species, namely man, instead of thirty-two final branches, as there would be in a theoretically complete system.

This tree was subsequently reproduced in the works of a multitude of logicians in a form which is more complicated and not so good as that of Nicephorus. Thus 'Epitome Logica, Augustæ Vindel.' 1605, p. 118.

r

in the Opuscula' of Aquinas, as quoted by Mansel in his edition of Aldrich's 'Artis Logica Rudimenta,' second edition, p. 31, we find the Tree nearly in the following form:

This example of the bifurcate method, although repeated in almost all compendiums and treatises on logic, attracted no particular attention until the time of Peter Ramus and his followers, who are commonly said to have bestowed so much attention and praise upon it as to be

regarded by some persons as its inventors. The Ramean Tree is a name frequently employed instead of the Porphyrian Tree, or the kλiua, that is, the Ladder of Porphyry, as it was sometimes called by the Greek logicians. Although I have looked through several commentaries upon the Dialectics of Ramus, I do not find that very much is said upon the subject. In the Questions of Frederick Beurhusius", the method of dichotomy is described as 'illa naturalis et antiquissimorum philosophorum præstantissima Dichotomia,' but in none of the works do I find the Tree itself given.

Among modern logicians Jeremy Bentham possesses the great merit of having drawn attention to the logical importance of bifurcate division. His remarks on the subject are contained in that extraordinary collection of digressive, and often almost incomprehensible papers, called Chrestomathias, two of the formidable title-pages of which are given below. The fifth appendix in this work, forming the larger and most important part of the book, consists of an Essay on Nomenclature and Classification. Although written in his later and worse style, this essay is well worth reading, and full of forcible remarks. It may be regarded, I believe, as the first of

r In Petri Rami, Regii Professoris Clariss. Dialectica Libros duos Lutetiæ Anno LXXII, postremo sine Prælectionibus æditos, explicationum Quæstiones: quæ Pædagogiæ Logicæ de Docenda Discendaque Dialectica. Auctore Frederico Beurhusio. Londoni, 1581, p. 120.

s 'Chrestomathia: being a Collection of Papers, explanatory of the Design of an Institution proposed to be set on foot, under the name of the Chrestomathic Day School, or Chrestomathic School, for the extension of the New System of Instruction,' &c. By Jeremy Bentham, Esq., London, 1816.

An Essay on Nomenclature and Classification: including a Critical Examination of the Encyclopædical Table of Lord Bacon, as improved by D'Alembert: and the first lines of a new one grounded on the application of the Logical Principle of Exhaustively Bifurcate Analysis.' London, 1817.

the series of English writings which have, in the present century, made logic a new and progressive science. In Table IV. Bentham gives the Arbor Porphyriana, as exhibited in the course of a college lecture in 1761, calling it the original form. His reading of logic seems to have been restricted to the compendiums of Saunderson and Watts, and it was only after the text was written that he obtained an opportunity of consulting the work of Porphyry, and was surprised to find no diagram therein. He attributes its invention to Peter Ramus, although he had never seen the writings of that logician, and had merely learnt their titles from a dictionary.

In this essay he states in the most powerful way the advantages of the bifurcate method of classification, which had been suggested to him by a chapter in Saunderson's logic and the diagram given in the college course. Although the Tree of Porphyry and the principles of bifurcation had been mentioned by almost all logicians, the utility and excellence of the method, he says (p. 287), had not made itself apparent. Indeed the method was mentioned but to be slighted, or to be made a subject of pleasantry by Reid and Kames. Bentham sufficiently states his own opinion when he speaks (p. 295) of 'the matchless beauty of the Ramean Tree.' After fully showing its logical value as an exhaustive method of classification, and refuting the objections of Reid and Kames, on a wrong ground, as I think, he proceeds to inquire to what length it may be carried. He correctly points out two objections to the extensive use of bifid arrangements, (1) because they soon become impracticably extensive and unwieldy, and (2) because they are uneconomical. In his day the recorded number of different species of plants was 40,000, and he leaves the reader to estimate the immense number of branches and the enormous area of a bifurcate table which should exhibit all these species in

one scheme. He also points out the apparent loss of labour in making any large bifurcate classification; but this he considers to be fully recompensed by the logical value of the result, and the logical training acquired in its execution. Jeremy Bentham, then, fully recognises, as I conceive, the value of the Logical Abecedarium under another name, though he apprehends the limit to its use placed by the finiteness of our mental and manual powers.

Mr. George Bentham has also fully recognised the value of bifurcate classification, both in his Outline of a New System of Logic'" (pp. 105-118), and in his Essai sur la Nomenclature et la Classification.' This latter work consists of a free translation or improved version in French of Jeremy Bentham's 'Essay on Classification.' Further illustrations of the value of the bifurcate method are adduced from the natural sciences, and Mr. Bentham points out that it is really this method which was employed by Lamark and Decandolle in their so-called analytical arrangement of the French Flora. The following table contains an excellent example of bifurcate division, consisting of the principal classes of Decandolle's system, as given by Mr. Bentham in Table No. III. p. 108 of his Essay, the names, however, being translated:

u Concerning the connexion of this work with the great discovery of the quantification of the predicate, I may refer the reader to the remarks and articles of Mr. Herbert Spencer and Professor Thomas Spencer Baynes, in the Contemporary Review' of March, April, and July, 1873, vol. xxi. pp. 490, 796; vol. xxii. p. 318; as also to my own article in answer to Professor Baynes in the same Review for May, 1873, vol. xxi. p. 821. Professor Baynes makes it evident that, when Sir W. Hamilton reviewed Mr. Bentham's work in 1833, he did not sufficiently acquaint himself with its contents. I must continue to hold that the principle of quantification is explicitly stated by Mr. Bentham, and it must be regarded as a remarkable fact in the history of logic that Hamilton, while vindicating, in 1847, his own claims to originality and priority against the scheme of De Morgan, should have overlooked the much earlier and more closely related discoveries of Bentham.