I am not prepared to deny that, to some mind of a higher order than
ours, each of these errors might be traced to the regular operation of
the laws of actual thinking; in fact we ourselves often do detect, not
only errors of calculation, but the causes of these errors. This,
however, by no means alters our conviction that they are errors, and
that one process of thought is right and another process wrong. I
One of the most profound mathematicians and thinkers of our time, the
late George Boole, when reflecting on the precise and almost
mathematical character of the laws of right thinking as compared with
the exceedingly perplexing though perhaps equally determinate laws of
actual and fallible thinking, was led to another of those points of
view from which Science seems to look out into a region beyond her own
domain.
"We must admit," he says, "that there exist laws" (of thought) "which
even the rigour of their mathematical forms does not preserve from
violation. We must ascribe to them an authority, the essence of which
does not consist in power, a supremacy which the analogy of the
inviolable order of the natural world in no way assists us to
comprehend.
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