RUSSELL AND MODAL LOGIC
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Russell's criticism of Kant in the Principles ofMathematics (Cambridge University Press, 1903) gives another revealing insjght into his position. According to Russell, the Kantian analysis of the foundations ofnecessity is drastically insufficient. In tracing the source of necessity to the categories and forms of the human understanding, Kant - so Russell holds - merely provides a contingently factual basis that cannot provide an appropriate foothold for necessity proper:
[On the Kantian theory of necessity] we only push one ~tage farther back the region of'mere fact,' for the constitution ofour minds remains still a mere fact. The theory of necessity urged by Kant,
and adopted ... by Lotze, appears radically vicious. Everything is in a sense a mer:e fact. (§ection' 4"30)
The philosopher, Russell seems to imply, is engaged on a quest for the necessity of things that does not permit him to rest content, at any stage, with anything that is a matter of mere fact. Just this attitude lay behind Russell's rejection at this stage ofthe empiricist philosophy ofmathematics ofJohn. Stuart Mill, which would not provide a suitable account of the necessity of mathematical truth.