LECT. thing else which cannot otherwise be explained or proved. Lemmata, that is, propositions borrowed from another science in order to serve as subsidiary Lemmata. propositions in the science of which we treat. Finally, Scholia, that is, propositions which only serve as illus- Scholia. trations of what is considered in chief. The clearest and most appropriate examples of these various kinds of propositions are given in mathematics." " a Esser, Logik, § 79, pp. 147, 148.-ED. [Compare Krug, Logik, §§ 67, 68.] XV. DIVISIONS ACCORDING TO INTERNAL FORM. LECT. IN my last Lecture, I terminated the Doctrine of Judgments, and now proceed to that of Reasonings. The act of "When the necessity of the junction or separation of -what. a certain subject-notion and a certain predicate-notion is not manifest from the nature of these notions themselves, but when, at the same time, we are desirous of knowing whether they must be thought as inclusive, or as exclusive, of each other, in this case, we find ourselves in a state of doubt or indecision, from our ignorance of which of the two contradictory predicates must be affirmed or denied of the subject. But this doubt can be dissipated,-this ignorance can be removed, only in one way,-only by producing in us a necessity to connect with, or disconnect from, the subject one of the repugnant predicates. And since, ex hypothesi, this necessity does not, at least does not immediately, arise from the simple knowledge of the subject in itself, or of the predicate in itself, or of both together in themselves; it follows XV. that it must be derived from some external source, LECT. and derived it can only be, if derived, from some other knowledge, which affords us, as its necessary consequence, the removal of the doubt originally harboured. But if this knowledge has for its necessary consequence the removal of the original doubt, this knowledge must stand to the existing doubt in the relation of a general rule; and, as every rule is a judgment, it will constitute a general proposition. But a general rule does not simply and of itself reach to the removal of doubt and indecision; there is required, and necessarily required, over and above, this further knowledge, that the rule has really an application, or, what is the same thing, that the doubt really stands under the general proposition, as a case which can be decided by it as by a general rule. But when the general rule has been discovered, and when its application to the doubt has likewise been recognised, the solution of the doubt immediately follows, and therewith the determination of which of the contradictory predicates must or must not be affirmed of the subject; and this determination is accompanied with a consciousness of necessity or absolute certainty."" A Illustrated simple example will place the matter in a clearer light. ample. When the notion of the subject man is given along with the contradictory predicates free agent and necessary agent, there arises the doubt,-with which of these contradictory predicates the subject is to be connected; for, as contradictory, they cannot both be affirmed of the subject, and, as contradictory, the one or the other must be so affirmed; in other words, I doubt whether man be a free agent or not. The notion man, and the repugnant notions free agent and a Esser, Logik, § 82, p. 153. by an ex XV. LECT. necessary agent, do not, in themselves, afford a solution of the doubt; and I must endeavour to discover some other notion which will enable me to decide. Now, taking the predicate free agent, this leads me to the closely connected notion morally responsible agent, which let it be supposed that I otherwise know to be necessarily a free agent, I thus obtain the proposition, Every morally responsible agent is a free agent. But this proposition does not of itself contain the solution of the doubt, for it may still be asked, does the notion morally responsible agent constitute a predicate which appertains to the notion of man, the subject This question is satisfied, if it is recognised. that the notion man involves in it the notion of a morally responsible agent. I can then say,-Man is a morally responsible agent. These two propositions being thus formed, and applied to the subsisting doubt, the removal of this doubt follows of itself; and in place of the previous indecision, whether man be a free agent or not, there follows, with the consciousness of necessity or absolute certainty, the connected judgment that, Man is also a free agent. The whole process, the whole series of judgments,—will stand thus: The ex ample given Every morally responsible agent is a free agent ; Therefore, man is a free agent. Let us consider in what relation the different consti is a Reason- tuent parts of this process stand to each other. It is ing in the evident that the whole process consists of three no whole of and may be tions and their mutual relations. The three notions may represented by three are, free agent, responsible agent, and man. circles. Their mutual relations are all those of whole and part, -and whole and part in the quantity of exten XV. sion; for the notion free agent is seen to contain LECT. under it the notion responsible agent, and the notion responsible agent to contain under it the notion man. Thus, these three notions are like three circles of three various extensions severally, contained one within another; and it is evident, that the process by which we recognise that the narrowest notion, man, is contained under the widest notion, responsible agent, is precisely the same by which we should recognise the inmost circle to be contained in the outmost, if we were only supposed to know the relation of these together by their relation to the middle A B circle. Let A B C denote the three |