Mill boldly affirmed that there might be remote realms in space where 2+2 did not make 4 but some different total, even empiricists may hestitate to concur; and yet Mill's assertion is at least the most obvious empiricist reading of the situation.
Geometry again is regarded by thoroughgoing empiricists as hypothetical.
Thus reason is opposed to sensation, perception, feeling, desire, as the faculty (the existence of which is denied by empiricists) by which fundamental truths are intuitively apprehended.
He definitely repudiates a view often ascribed to him, and certainly advanced by many later empiricists, that the data of geometry are hypothetical.
Some empiricists, on the other hand, suppose that induction only infers probable conclusions which are premises of probable deductions; but they give up all exact science.
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