Page:Mind (New Series) Volume 9.djvu/368

354 G. J. STOKES : only question seems to be, at what point shall this transition process cease, and a priori there seems no reason why it should cease, before it has brought the processes and infer- ences of every science within its scope. This is the real difficulty, in attempting to generalise from particular opera- tions a general calculus of functions or operations. Shall it include under it, for example, the symbolism of chemistry ? Such a universal science seems to become as empty of all real content as the old Aristotelian logic. The attempt to evolve in a symbolic calculus certain laws and methods common to a variety of symbols of operation, is apt to leave as a residuum simply the general notions of similarity and difference, connexion and separation. The result is formal logic, and formal logic not brought into any organic con- nexion with the material from which it is evolved. The same problem thus presents itself to the logician and mathematician only viewed from opposite sides. The mathe- matician rises from the conception of particular laws and operations to the conception of the most general laws govern- ing all operations. Logicians begin with the latter, but have not been successful in throwing light on the former. They have either dismissed the forms of mathematical inference as material consequences, or added them on empirically to inductive logic. A tendency has of late arisen to bring some of the forms of mathematical inference under what has been called the logic of relatives, but no satisfactory theory of the relation of such forms of inference to the ordinary logic has been put forward. Jevons seems to regard them as disguised cases of formal inference. De Morgan represents the opposite tendency and rather looks at formal inference itself as a refined residuum of material inference. In reality I believe there exists the closest connexion between all the forms of logical inference and of material inference, but the relation is not one of generalisation. In the theory of the imaginary which we have been discussing, we have only one instance out of many of such connexion. The only writer who has in general attempted to conceive the various categories of objective logic, not only as standing in systematic connexion with one another, but also as organically connected with the forms of subjective logic, is Hegel. His theory of the organic growth of the one from the other is opposed to the view which we are about to indicate, but has in common with it that it does not present the relation as one of mere degree of generality. The connexion of these two systems of forms is too vast a subject to be treated within the limits of this paper. It is only possible to briefly point out the general