[1] See the recent exposition of the secular Indian Logic, in its most complete form, as found in a treatise of the twelfth century, in II. Jacobi, "Die indische Logik," in the Nachrichten v. d. Königl. Gesellsch. d. Wissenschaft zu Göttingen, Philol.-hist. Klasse, 1901, fasc. iv. pp. 460-484.
[2] Gesch. d. Logik, i. p. 362.
[3] Hamilton, Fragments philosophiques, French tr. pp. 238-242.
[4] Frantl, "Über Petrus Ramus," in the Sitzungsberichte d. k. bayer. Akad. d. Wissensch., Philol.-hist. Klasse, 1878, ii. pp. 157-169.
[5] De dign. et augm. iv. ch. 2-5.
[6] Ib. ch. 2.
[7] Nov. Org. i., aphorism 14.
[8] It is pertinent to translate here a passage of Hegel, in relation to this Leibnitzian tendency, which is now again becoming fashionable. "The extreme form of this (syllogistic) disconceptualized manner of dealing with the conceptual determinations of the syllogism, is found in Leibnitz, who (Opp. t. ii. p. i) places the syllogism under the calculus of combination. By this means he has calculated how many positions of the syllogism are possible, and thus, by taking count of the differences of positive and negative judgments, then of universal, particular, indeterminate and singular judgments, he has arrived at the result that the possible combinations are 2048, of which, after excluding the invalid, there remain 24 valid. Leibnitz boasts much of the utility possessed by the analysis of combination in finding, not only the forms of the syllogism, but also the connections of other concepts. This operation is the same as that of calculating the number of possible combinations of letters that can be made from an alphabet, or of moves in a game of draughts, or of different hands in a game of hombre, and so on. From which it is clear that the determinations of a syllogism are placed on a level with moves in draughts, or hands in hombre. The rational is taken as something dead, altogether deprived of the concept, and the peculiar character of the concept and its determinations is left out; that is to say, the character that in so far as they are spiritual facts, they are relation, and that, in virtue of this relation, they suppress their immediate determination. This Leibnitzian application of the calculus of combination to the syllogism and to the connection of other concepts is not to be distinguished in any way from the discredited art of Lully, save for the greater methodicalness in calculation of which it gives proof; it resembles that absurdity in every other respect. Another thought, dear to Leibnitz, was included in the calculus of combination. He had nourished this thought in his youth, and notwithstanding its immaturity and superficiality, he never afterwards abandoned it. This was the thought of a universal characteristic of concepts, of a writing, in which every concept should be represented as proceeding from others or as referring to another; almost as though, in a rational connection, which is essentially dialectic, a content should preserve the same determinations that it has when standing alone.
"The calculus of Ploucquet is doubtless supported by the most cogent mode of submitting the relation of the syllogism to calculation. He abstracts in the judgment from the difference of relation; that is to say, from its singularity, particularity and universality, and fixes the abstract identity of subject and predicate, placing them in a mathematical relation. This relation reduces reason to an empty, tautological formation of propositions. In the proposition, 'the rose is red,' the predicate must signify, not red in general, but only the determinate 'red of the rose.' In the proposition, 'all Christians are men,' the predicate must signify only 'those men who are Christians.' From this and from the other proposition, 'Hebrews are not Christians,' follows the conclusion (which did not constitute a good recommendation for this calculus with Mendelssohn): 'hence, Hebrews are not men' (that is to say, they are not those men, who are Christians).
"Ploucquet gives as a consequence of his invention posse etiant rudes mechanice tot am logicam doceri, uti pueri arithmeticam docentur. ita quidem, ut nulla formidine in ratiociniis suis errandi lorqueri, vel fallaciis circumveniri possint, si in calculo non errant. This eulogy of the calculus, to the effect that by its means it is possible to supply uneducated people with the whole of Logic, is certainly the worst that can be said of an invention which concerns logical Science'" (Wiss. d. Logik, iii. pp. 142-43).