The Import of propositions in the foundations of J. S. Mill’s Inductive Logic

Alexandre Mark Katz Hohn

In his work “A System of Logic: Ratiocinative and Inductive”, J. S. Mill mobilizes diverse foundational pieces to construe - and give warrant to - a thorough, exhaustive, inductive system. This exposition deals with the first of such foundational pieces to be set forth in the referred system, which is the analysis of language. It aims to demonstrate its importance through the question: how can an analysis of language offer a warrant to infer unknown cases from known ones? For Mill, “language is evidently […] one of the principal instruments or helps of thought”, and to not dedicate any attention to it would be like “to become an astronomical observer, having never learned to adjust the focal distance of his optical instrument so as to see distinctly” (CW, 7:19). The first step towards such an endeavor would be to understand the role of names in the composition of propositions, which are, in accordance to Mill’s definition, a representation of our beliefs. Even more so, they are able to convey groundings for truths about the world, as soon as we understand how the subject and predicate (or the two names, connected by a copula, within a proposition) are related to our observations. Thus, Mill states that names are names of things, not ideas, for if they are to convey the meaning of our beliefs, it cannot be that they refer to something that one alone can subjectively idealize; nay, it must pertain to a physical fact, that is, a fact that is observable by all (CW, 7: 25). However, difficulties arise when one tries to define the meaning of names involved in the aforementioned propositions, and this because, being the origin of names fruit of an arbitrary convention, a proposition in that form will not be strictly “susceptible of truth or falsity, but only of conformity or disconformity to usage or convention; and the proof they are capable of, is proof of usage” (CW, 7: 109). However, despite language’s dependency on convention, it must still represent a phenomenon worthy of observation, and accounting for how this dependency does not hinder our knowledge of the world is paramount to ground an inductive validity within the System of Logic. Conventions, then, must be linked to true observations before any inference towards generalization can be made. The trajectory charted for this presentation starts by contextualizing Mill’s anti-intuitionist motivations, which led him to base his logic in an inductive, “ultra-empirical”, anchorage. I then proceed to display its main difficulties, and, finally, how Mill’s analysis of language, with special attention to the import of propositions, relates to the substantiation of his logic, thereupon closing the presentation.