concepts and judgments, and condemns the theories of predication, which are founded upon ideas of things, and not upon things or phenomena themselves. The Logic, therefore, treats of things and their relations; and it is from this point of view that he finds the Syllogism guilty of the petitio principii, and Immediate Inference as no inference at all. Mill's conception of Logic has thus two phases :-— (1) In the first phase Logic is conceived to treat of concepts, judgments, and reasonings as agreeing with things. (2) In the second phase, Logic is conceived to treat of things or phenomena themselves, and of their relations and correlations. Among English Logicians Mill, in fact, seems to occupy an intermediate position between such Subjective Logicians as Hamilton and Mansel, and such Objective Logicians as Spencer and Lewes1. §3. Spencer's View. "A distinction exists which, in consequence of its highly abstract nature, is not easily perceived, between the science of Logic and an account of the process of Reasoning......The distinction is, in brief, this, that Logic formulates the most general laws of correlation among existences considered as objective; while an account of the process of Reasoning, formulates the most general laws of correlation among the ideas corresponding to those existences. The one contemplates in its propositions, certain connexions predicated, which are necessarily involved with certain other connexions given; regarding all these connexions as existing in the nonego-not, it may be, under the form in which we 1 On the difference between Formal Logic (Hamilton's view) and Material Logic (the first phase of Mill's view of Logic), see Venn, Logic of Chance, 2nd ed. chapter x., Discussion of some of the Principal Views as to the Nature and Province of Logic, Material and Conceptualist." On the difference between the two phases, briefly indicated above, of Mill's conception of Logic, compare Ueberweg's distinction of Logic and Metaphysics. See Logic, §§ 1, 2, 3, 8. know them, but in some form. The other contemplates the process in the ego by which these necessities of connexion come to be recognised. "Why this distinction has eluded observation, it is not difficult to see. Logic on the one hand, and the theory of Reasoning on the other, deal with relations from which all concrete terms are, as far as possible, expelled. They are severally obliged to use some terms (which, however, are by preference symbolic, so that they may express indifferently any kind of existence, attribute, action, or even relation); otherwise the relations dealt with can not be expressed, or distinguished from one another. But they intentionally ignore the natures of the terms, and occupy themselves with the most general dependencies of these most abstract relations. The result is that, in the absence of terms definitely specified as belonging either to the outer world or to the inner world, the two sets of relations, belonging the one to the outer world and the other to the inner world, become indistinguishable. Hence there arises this confusion between Logic, which is as much a division of the science of objective existence as Mathematics, and the theory of Reasoning, which is a division of subjective Science. "To show that the affirmations of Logic refer to the connexions among things considered as existing apart from our consciousness, and not to the correlative connexions among our correlative states of consciousness, we need but to take the case of logical propositions as numerically quantified, in the system of Prof. de Morgan. I quote Mr Mill's condensed statement of the doctrine; for Prof. de Morgan's own statements are so encumbered with details and symbols, that I can not find in his work one that is at once brief and adequate. 666 "From the premises most B's are C's, most B's are A's, it may be concluded with certainty that some A's are C's, since two portions of the class B, each of them comprising more than half, must necessarily in part consist of the same individuals. Following out this line of thought, it is equally evident that if we knew exactly what proportion the 'most' in each of the premises bear to the entire class B, we could increase in corresponding degree the definiteness of the conclusion. Thus if 60 per cent. of B are included in C, and 70 per cent. in A, 30 per cent. at least must be common to both; in other words, the number of A's which are B's, and of C's which are A's must be at least equal to 30 per cent. of the Class B.'1” "......But the clearest proof that relations among objective existences form the subject-matter of Logic, is yielded by the mechanical performance of logical inference. Prof. Jevons has devised a machine of such kind that, its keys being pressed down in proper order in conformity with the premisses of the given logical proposition, the conclusion is presented by the combinations which the machine displays. Here it is undeniable that the relation disclosed is an objective one; and it is equally undeniable that the thing ascertained is, that this objective relation was necessarily involved in those other objective relations which constitute the premisses. We have nothing to do with thought at all. We have to do with inter-dependencies among outer things or agencies. The machine having been set to represent objects and attributes in certain relations, evolves certain necessarily-accompanying relations, such as would otherwise be ascertained by actual examination of the objects and attributes 2." "The propositions of Logic, then, primarily express necessary dependencies of things, and not necessary dependencies of thoughts; and in so far as they express necessary dependencies of thoughts, they do this secondarily-they do it in so far as the dependencies of thoughts have been moulded into correspondence with the dependencies of things. I say advisedly, 'in so far as'; for there are certain absolute unlikeness of nature between the outer dependencies and the inner dependencies which for ever forbid anything more than a symbolic correspondence, as we shall hereafter see more clearly. The greater part 1 Principles of Psychology, 2nd ed. Vol. II. § 302, pp. 87-88. 2 Principles of Psychology, Vol. 1. § 302, p. 90. of the necessary objective correlations are statical, while all the necessary subjective correlations are dynamical; and only in so far as dynamical correlations may be so arranged as to symbolize statical correlations, can the necessary dependencies of Reason be made to parallel the necessary dependencies of Logic1". “................See, then, the inevitable implication. No one questions the fact that while I was using these marbles to exemplify arithmetical truths and geometrical truths, I was contemplating, and was teaching, necessary objective correlations. Can it be that when I used these same marbles to exemplify necessities of correlation among groups and sub-groups, distinguished by certain marks, I passed from the region of objective necessities to the region of subjective necessities? No one will, I think, have the hardihood to assert as much. There is no choice but to leave these most general laws of correlation which Logic formulates, outside along with the laws of numerical correlation and geometrical correlation; or else, bringing them into the mind as laws of thought, to bring with them these mathematical laws as laws of thought in the same sense, and, by other steps equally unavoidable, to merge all objective facts in subjective facts: thus abolishing the distinction between subject and object2". Note. Mr Carveth Read adopts Spencer's view of Logic, with these two qualifications, first, that Logic " 'may very well consider the correlation of ideas among themselves," and second, that Logic "deals only with laws of phenomena.” See Mind, Vol. 11. “On some Principles of Logic," p. 336. For a Critical Notice of Mr Read's "Theory of Logic: an Essay," by Dr Venn, see Mind, Vol. III. p. 539. See also a note on "Matter-of-fact' Logic," by Mr J. N. Keynes, in Mind, Vol. IV. p. 120. For a criticism of Spencer's view of Logic, by Dr Venn, see Mind, Vol. IV., "The Difficulties of Material Logic," p. 35. Dr Venn suggests a view of Logic which seems to correspond to Ueberweg's view and to the first phase of Mill's conception of Logic (see Mill's View). "Instead of regarding Logic as a purely objective 1 Principles of Psychology, Vol. 11. § 302, pp. 90–91. science," says Dr Venn, "we might with more propriety term it a science which gives the rules for converting the subjective into the objective" (Mind, Vol. iv. p. 46). Compare Ueberweg's definition, namely, "Logic is the science of the regulative laws of human knowledge" (Logic § 1), and Mill's view of Logic as "the science of the conditions on which right concepts, judgments, and reasonings depend” (Examination of Hamilton's Philosophy, 4th ed. p. 464). § 4. Lewes's View. "Let us pause for a moment to consider the very different meanings assigned to the word Logic. It commonly stands for: (1) the art of reasoning; (2) the theory of reasoning; (3) Reasoning itself; (4) the laws of mental operation, irrespective of the symbols operated on (Formal Logic); (5) the rules of Proof. "The first of these I hold to be absurd. There is no more an art of Reasoning than there is an art of Breathing, or Digesting. But so little is this understood that even thoughtful writers will be found declaring that we must learn how to reason, as we learn how to fence or to swim. In consequence of this misconception, certain studies, notably Mathematics, are popularly believed to strengthen the Faculty,' to develop the logical powers, to 'invigorate the judgment.' The psychological notions which lie at the basis of such declarations are sadly defective. "The second and third meanings of the word are objectionable because restricting Logic to the process of Ratiocination when the ratios are abstract. This restriction is got rid of in the fourth and fifth meanings, which may be accepted as comprehensive. The fourth designates the universal Logic, it includes all Laws of Grouping (Aéyew means to bind together, to group), and is therefore applicable to Feeling and Thought (in the subjective world), and to Cause (in the objective world). |