David Godden's paper is primarily focused on two things. First, it attempts to position Mill's work historically, coming sometime in the 19th century placing it in and around Frege's work on logic and after Kant's 'Critique'. Second, the paper seeks to explain exactly how Mill's logic differs and compares to those of its time, such as Whately's 'Elements of Logic'. The most interesting points about Mill's work is what it says about his empiricism. Mill criticized Whately on several points, including Whately's realist and essentialist account of classification and definition, which conflicted with Mill's own nominalism (9). What this points out to us is that Mill's own philosophy on certain topics is a strongly empiricist one, most interestingly relating to mathematics and logic. Considering the arguments made by rationalists from the 17th to the 19th century which made mathematics out to be some sort of a priori enterprise, Kant's arguments at least brought to question the widely accepted belief that mathematics was a priori and analytic. Indeed, his arguments pointed out something that seemed to be a synthetic nature of mathematical facts. Mill's work took this project a step further, attempting to make mathematics entirely empirical and, indeed, attempted to justify the basis for a synthetic mathematics. Considering my own staunch opposition to the analytic/synthetic distinction I perhaps may be too critical of Mill's project but I will try and temper my concerns. Mill holds that numbers have the remarkable peculiarity that they are propositions concerning all things whatever; all objects, all existences of every kind, known to our experience (22). Numbers are essentially about 'things'. Two, for instance, represents all pairs of things. For relatively small numbers this seems like a clear point. Indeed, it seems to be an oft brought up analogy for what numbers are. However, the analogy generally breaks down when numbers become quite large. For instance, in videos about large amounts of money (hundreds of millions of dollars, say), I have seen graphic representations that demonstrate what this means in terms of something like bananas being stretched around the Earth's equator. It aims to relate numbers to something we have a reference for the general size of a banana - and a rather large figure - the circumference of the Earth at its largest cross-section - to figures that are frequently taken to be beyond human imagination. The analogy attempts to clarify a fact, but still leaves something to be desired. Indeed, Frege asks a very pointed question of Mill's understanding of number, asking "what observed or physical fact is asserted in the definition of the number 777864" (25). Frege also points out that "no one... has ever seen or touched 0 pebbles" (25). Thus, it seems that Mill almost misses the point about what a number is in attempting to reduce them to representations of things. Perhaps Mill would argue that what really matters about the science of number is that it is sufficient to understand small numbers like two or twelve through empirical means, and via a principle of induction we can extend this understanding to other numbers like zero or 777,864. As induction isn't wholly a logical principle on Mill's view, it's hard to understand how induction may serve to ground this understanding or if it justifies the point on what a number is, but instead represents some kind of ad hoc saving of synthetic mathematics. As an aside to all of this, I have a sort of general question about the synthetic/analytic distinction. To what extent are these related to contingency and necessity? It seems that analytic facts are those which are necessary and synthetic those which are contingent. Is this all that the distinction amounts to? Are synthetic propositions nothing over and above contingent facts? ________________________________________________________________________________ Dilyn Corner (C) 2020-2022