The denial of the "necessary truth" that
the thought now in my mind exists, involves the denial of consciousness.
To the assertion that the evidence of matter of fact, is not so strong
as that of relations of ideas, it may be justly replied, that a great
number of matters of fact are nothing but relations of ideas. If I say
that red is unlike blue, I make an assertion concerning a relation of
ideas; but it is also matter of fact, and the contrary proposition is
inconceivable. If I remember[26] something that happened five minutes
ago, that is matter of fact; and, at the same time, it expresses a
relation between the event remembered and the present time. It is wholly
inconceivable to me that the event did not happen, so that my assurance
respecting it is as strong as that which I have respecting any other
necessary truth. In fact, the man is either very wise or very virtuous,
or very lucky, perhaps all three, who has gone through life without
accumulating a store of such necessary beliefs which he would give a
good deal to be able to disbelieve.
It would be beside the mark to discuss the matter further on the present
occasion. It is sufficient to point out that, whatever may be the
differences, between mathematical and other truths, they do not justify
Hume's statement. And it is, at any rate, impossible to prove, that the
cogency of mathematical first principles is due to anything more than
these circumstances; that the experiences with which they are concerned
are among the first which arise in the mind; that they are so
incessantly repeated as to justify us, according to the ordinary laws of
ideation, in expecting that the associations which they form will be of
extreme tenacity; while the fact, that the expectations based upon them
are always verified, finishes the process of welding them together.
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