,
custom, in order to deny that reason could judge about God, freedom,
and immortality; and if once his principles were granted, he was
certainly well able to deduce his conclusions therefrom, with all
logical coherence. But even Hume did not make his empiricism so
universal as to include mathematics. He holds the principles of
mathematics to be analytical; and if his were correct, they would
certainly be apodeictic also: but we could not infer from this that
reason has the faculty of forming apodeictic judgements in
philosophy also- that is to say, those which are synthetical
judgements, like the judgement of causality. But if we adopt a
universal empiricism, then mathematics will be included.
Now if this science is in contradiction with a reason that admits
only empirical principles, as it inevitably is in the antinomy in
which mathematics prove the infinite divisibility of space, which
empiricism cannot admit; then the greatest possible evidence of
demonstration is in manifest contradiction with the alleged
conclusions from experience, and we are driven to ask, like
Cheselden's blind patient, "Which deceives me, sight or touch?" (for
empiricism is based on a necessity felt, rationalism on a necessity
seen).
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