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2 ideas
9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
Full Idea: There is one hypothetical element in the basis of arithmetic, without which none of it would be true: all the numbers are numbers of the same or of equal units. When we talk of forty horse-power, we assume all horses are of equal strength. | |
From: John Stuart Mill (System of Logic [1843], 2.6.3) | |
A reaction: Of course, horses are not all of equal strength, so there is a problem here for your hard-line empiricist. Mill needs processes of idealisation and abstraction before his empirical arithmetic can get off the ground. |
21382 | Things get smaller without end [Anaxagoras] |
Full Idea: Of the small there is no smallest, but always a smaller. | |
From: Anaxagoras (fragments/reports [c.460 BCE], B03), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras II | |
A reaction: Anaxagoras seems to be speaking of the physical world (and probably writing prior to the emergence of atomism, which could have been a rebellion against he current idea). |