The major premiss is not really part of the argument. Brown saw that there would be a petitio principii if it were. He, therefore, contended that the conclusion in reasoning follows from the minor premiss alone, thus suppressing the appeal to experience. He argued, that to reason is merely to analyse our general notions or abstract ideas, and that, provided that the relation between the two ideas, e.g. of man and of mortal, has been first perceived, we can evolve the one directly from the other. But (to waive the error that a proposition relates to ideas instead of things), besides that this proviso is itself a surrender of the doctrine that an argument consists simply of the minor and the conclusion, the perception of the relation between two ideas, one of which is not implied in the name of the other, must obviously be the result, not of analysis, but of experience. In fact, both the minor premiss, and also the expression of our former experience, must both be present in our reasonings, or the conclusion will not follow. Thus, it appears that the universal type of the reasoning process is: Certain individuals possess (as I or others have observed) a given attribute; An individual resembles the former in certain other attributes: Therefore (the conclusion, however, not being conclusive from its form, as is the conclusion in a syllogism, but requiring to be sanctioned by the canons of induction) he resembles them also in the given attribute. But, though this, and not the syllogistic, is the universal type of reasoning, yet the syllogistic process is a useful test of inferences. It is expedient, first, to ascertain generally what attributes are marks of a certain other attribute, so as, subsequently, to have to consider, secondly, only whether any given individuals have those former marks. Every process, then, by which anything is inferred respecting an unobserved case, we will consider to consist of both these last-mentioned processes. Both are equally induction; but the name may be conveniently confined to the process of establishing the general formula, while the interpretation of this will be called 'Deduction.'
CHAPTER IV.
TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
The minor premiss always asserts a resemblance between a new case and cases previously known. When this resemblance is not obvious to the senses, or ascertainable at once by direct observation, but is itself matter of inference, the conclusion is the result of a train of reasoning. However, even then the conclusion is really the result of induction, the only difference being that there are two or more inductions instead of one. The inference is still from particulars to particulars, though drawn in conformity, not to one, but to several formulæ. This need of several formulæ arises merely from the fact that the marks by which we perceive that an inference can be drawn (and of which marks the formulæ are records) happen to be recognisable, not directly, but only through the medium of other marks, which were, by a previous induction, collected to be marks of them.
All reasoning, then, is induction: but the difficulties in sciences often lie (as, e.g. in geometry, where the inductions are the simple ones of which the axioms and a few definitions are the formulæ) not at all in the inductions, but only in the formation of trains of reasoning to prove the minors; that is, in so combining a few simple inductions as to bring a new case, by means of one induction within which it evidently falls, within others in which it cannot be directly seen to be included. In proportion as this is more or less completely effected (that is, in proportion as we are able to discover marks of marks), a science, though always remaining inductive, tends to become also deductive, and, to the same extent, to cease to be one of the experimental sciences, in which, as still in chemistry, though no longer in mechanics, optics, hydrostatics, acoustics, thermology, and astronomy, each generalisation rests on a special induction, and the reasonings consist but of one step each.
An experimental science may become deductive by the mere progress of experiment. The mere connecting together of a few detached generalisations, or even the discovery of a great generalisation working only in a limited sphere, as, e.g. the doctrine of chemical equivalents, does not make a science deductive as a whole; but a science is thus transformed when some comprehensive induction is discovered connecting hosts of formerly isolated inductions, as, e.g. when Newton showed that the motions of all the bodies in the solar system (though each motion had been separately inferred and from separate marks) are all marks of one like movement. Sciences have become deductive usually through its being shown, either by deduction or by direct experiment, that the varieties of some phenomenon in them uniformly attend upon those of a better known phenomenon, e.g. every variety of sound, on a distinct variety of oscillatory motion. The science of number has been the grand agent in thus making sciences deductive. The truths of numbers are, indeed, affirmable of all things only in respect of their quantity; but since the variations of quality in various classes of phenomena have (e.g. in mechanics and in astronomy) been found to correspond regularly to variations of quantity in the same or some other phenomena, every mathematical formula applicable to quantities so varying becomes a mark of a corresponding general truth respecting the accompanying variations in quality; and as the science of quantity is, so far as a science can be, quite deductive, the theory of that special kind of qualities becomes so likewise. It was thus that Descartes and Clairaut made geometry, which was already partially deductive, still more so, by pointing out the correspondence between geometrical and algebraical properties.