material bodies, as well as to the same in future, will produce expansion; or, in other words, all material bodies expand by heat. The different steps may be thus stated syllogistically :—

(1) Every phenomenon has a cause, the expansion of air and other bodies by heat is a phenomenon; therefore it has a cause.

(2) The invariable antecedent of a phenomenon is the cause of the phenomenon, the application of heat is the invariable antecedent of the phenomenon of expansion in the given instances; therefore the application of heat is the cause of the phenomenon of expansion in the given instances.

(3) The same antecedent or cause will, under the same circumstances, produce the same effect or consequent,—that is, if a certain antecedent produces, under certain circumstances, a certain consequent, then it will, under the same circumstances, produce the same consequent; the antecedent, namely, the application of heat to material bodies, under the circumstances of there being no counteracting agencies, produces the consequent, namely, the expansion of those bodies; therefore the same antecedent, namely, the application of heat to material bodies, under the same circumstances of there being no counteracting agencies, will produce the same consequent, namely, the expansion of those material bodies.

Thus all inductive reasonings, like mathematical (see p. 123), may be reduced to the syllogistic form: usually their conformity to an axiom, principle, law, canon, or rule recognized as true is regarded as a sufficient proof of their validity, even as constituting their validity itself; but in all cases where they are valid, they are capable of being reduced to the syllogistic form. In Physics, for example, conformity to the principles of causation and of uniformity of nature, or to the canons and rules derived from them, is regarded as constituting the validity of the reasonings; but we have seen that, taking the principles or the canons as major premisses, and the data as minor, we can, in all cases, construct syllogisms which have the same conclusions as the reasonings themselves; and the best test of the validity of the reasonings is the possibility of their reduction to the syllogistic

form any weakness in the argument is sure to come to light by this process.

To see clearly what premisses have been assumed, or, on what data-both principles and facts—the conclusion ultimately rests, it is necessary to reduce a reasoning or a train of reasoning to the syllogistic form. In this form every step of the argument will be clearly exhibited and every proposition required to prove the conclusion laid bare, and should there be any error in the process of reasoning, it will be brought to light by the axioms, canons, or rules of Deductive or Syllogistic Logic. Of course, if there be any falsity or fallacy in the ultimate data—if any universal principle or any particular fact has been unwarrantedly assumed-it can not be detected by those axioms, canons or rules; nor can it be detected by the canons and rules of any Logic, as understood by British Logicians. For the particular fact, the ultimate appeal must be made to observation, external or internal; and for the universal principle the appeal is made (1) to the Experience of the Individual, that is, to Repeated Experience and Generalisation (the Empirical or Experiential Theory); or (2) to Intuition, that is, to Immediate Knowledge by the Reason (the Intuitional Theory); or (3) to the Forms and Categories of the Mind (the A-priori or Kantian Theory); or (4) to the Experience of the Race, that is, to Inherited Tendencies and Experience (the Evolutional Theory). The first question can be decided only by the special science to which the fact belongs; and the second question by the science which treats of the origin and nature of universal principles, and which has been variously called Metaphysics, the Science of First Principles, the Science of the more General Laws, &c.

E. THE NATURE AND PROVINCE OF OBJECTIVE LOGIC.

The name 'Objective Logic,' and the thing signified by it, are comparatively new. I intend, therefore, to give here extracts from the writings of Logicians with a view to indicate the nature and province of the thing as conceived by them.

§ 1. Hamilton's View.

"The doctrine...which expounds the laws by which our scientific procedure should be governed, in so far as these lie in the forms of thought, or in the conditions of the mind itself, which is the subject in which knowledge inheres,-this Science may be called Formal, or Subjective, or Abstract, or Pure Logic, The Science, again, which expounds the laws by which our scientific procedure should be governed, in so far as these lie in the contents, materials, or objects, about which Knowledge is conversant, this Science may be called Material, or Objective, or Concrete, or Applied Logic1."

§ 2. Mill's View.

In Mill's writings the name 'objective Logic' rarely, if ever, occurs; but the thing is to be found in abundance. He defines and treats of the thing in his Examination of Hamilton's Philosophy and also in his System of Logic, and expounds and criticises logical doctrines from that point of view. There is, however, a difference between the thing as conceived in the Examination, and the thing as treated of in the Logic. In the former he speaks of concepts, judgments, and reasonings, and requires that they should be right or true, that is, that they should ugree with fact or reality. In the latter he treats of phenomena or facts themselves: names, for instance, stand for things; propositions for relations of things; and arguments are about the relations of those relations. In the Logic he gives up

1 Hamilton's Lectures, Vol. IV. p. 231,

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 existThe 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

ences.

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.

"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