« PreviousContinue »
on either side it is unconsciously, if not expressly, allowed that similars must be similarly treated. Almost the whole of our difficulties in the government of Ireland arise from the different national characters of the Irish and English, which renders laws and institutions suited to the one inapplicable to the other. Yet such is the tendency of indiscriminating public opinion to run in the groove of similarity, that it requires a bold legislator to repeal laws for Ireland which it is not intended or desired to repeal for England.
65. Before closing, I should notice that at some period in the obscurity of the Middle Ages an attempt seems to have been made to assimilate in some degree the logical and mathematical sciences, by inventing a logical canon analogous to the first axiom of Euclid. Between the dictum de omni et nullo of Aristotle, which had so long been esteemed the primary and perfect rule of reason, and the axiom concerning equal quantities, there was no apparent similarity. Logicians accordingly adopted a syllogistic canon which seems closely analogous to the axiom in question, and which was thus stated in the textbook of Aldrich :—
Qua conveniunt in uno aliquo eodemque tertio, ea conveniunt inter şe.
This was supplemented by a corresponding canon concerning terms which disagree :—
Quorum unum convenit, alterum differt uni et eidem tertio, ea differunt inter se.
The excessive subtlety of logical writers of past centuries even led them to invent six separate canons to express the principle which seems to be sufficiently embodied in our one rule. Whately considers two of these canons to be a sufficient rule of reason, which he thus translates :—
If two terms agree with one and the same third, they agree with each other; and
If one term agrees, and another disagrees, with one and the same third, these two disagree with each other.
"No categorical syllogism can be faulty which does not violate these canons: none correct which does." 1
66. Though Wallis spoke of these canons as an innovation in his day, Mr. Mansel has traced them back to the time of Rodolphus Agricola.2 They were well known to Lord Bacon, for he appears to
1 Whately, "Elements of Logic," Book ii. chap. iii. sec. 2. 2 Born 1442; his logical work, "De Inventione Dialecticæ," was printed at Louvain in 1516.
have been greatly struck with the apparent analogy between these canons and the axioms of mathematicians, and he introduces it as an instance of conformity or analogy in his "Novum Organum" in the following passage:
Postulatum mathematicum, ut quæ eidem tertio æqualia sunt, etiam inter se sint æqualia, conforme est cum fabrica syllogismi in logica: qui unit ea quæ conveniunt in medio.
67. It is a truly curious fact in the history of Logic, that these canons should so long have been adopted, and yet that the only form of proposition to which they correctly apply should have been almost wholly ignored until the present century.
It is only when applied to propositions of the form A = B that these canons prevent us from falling into error, but when used with the propositions of the old Aristotelian system they allow the free commission of fallacies of undistributed middle. It has been well pointed out by Mr. Mansel,2 that "these canons are an attempt to reduce all the three figures of syllogism directly to a single principle; the dictum de omni et nullo of Aristotle, which was universally adopted by the scholastic logicians,
1 Book ii. Aphorism 27.
2 Artis Logica Rudimenta, p. 65.
being directly applicable to the first figure only. This reduction, so long as the predicate of propositions has no expressed quantity, is illegitimate; the terms not being equal, but contained one within another, as is denoted by the names major and minor. Hence, as applied to the first figure, the word conveniunt has to express, at one and the same time, the relation of a greater to a less, and of a less to a greater,—of a predicate to a subject, and of a subject to a predicate."
Thus in the syllogism of the mood Barbara,
Metals are elements,
Iron is a metal,
Iron, therefore, is an element,
the terms elements and iron are both said to agree with metals, the third common term, although elements is a wider term, and iron much narrower one, than metals. Nothing can be more unscientific and fallacious than such an application of the same word in two distinct meanings. And if we avoid this fallacy by taking the meaning of the word agreement in the same manner in each premise, we fall into the fallacy of undistributed middle. Thus Metals are elements,
Oxygen is an element,
would conform precisely to the canon, because oxygen agrees with element exactly in the same sense in which metals agree with elements, and yet the result is an untrue and fallacious conclusion. Doubtless this absurdity may be explained away by pointing out that metals and oxygen do not really agree with the same part of the class elements, so that there is no really common third term; but the so-called supreme canon of syllogism is unable to indicate when this is the case and when it is not. Other rules have to be assumed in order to overrule the supreme rule, and these involve the principle of quantification, because they depend upon the inquiry as to what parts of the middle term are identical respectively with the major and minor terms. Yet for centuries logicians failed to acknowledge that identity is at the bottom of the question.
68. To sum up, we may say that the logicians attempted to reconcile logical with mathematical forms of reasoning, by assuming a canon which is true when applied to quantified propositions ; but, as they applied the canon to unquantified propositions, they failed in producing anything but a fallacious appearance of conformity. In the present century logicians have abundantly recognised the importance of quantifying the proposition; but they have either adhered to the old