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Such knowledge may be of the senses, as the sight of the sun or the sound of thunder; or it may be of the reason, such as that the whole is greater than its parts. We may then enumerate four kinds of things known directly without the help of other knowledge, The percepts of the senses. Truths generally admitted by reason of their self-evidence.
But I do wish to suggest that the feeling of self-evidence in mathematical propositions has to do with the fact that they are concerned with the meanings of symbols, not with properties of the world such as external observation might reveal. Similar considerations apply to the impossibility of a thing being in two places at once, or of two things being in one place at the same time.
But this is just the point in dispute, and to set out with a bare affirmation of it is merely to beg the question and to abandon the discussion. Doubtless, by the mere act of consulting their own consciousness, the fact now in dispute appears to some persons self-evident. But in matters of such high abstraction as this, even the evidence of self-evidence must not be relied upon too implicitly.
There certainly was a change in the owner of the dog with the begging-tray, a change in costume, in countenance, in that indescribable self-evidence which we call "manner." The costume was not that Bohemian attire in which Kenelm had first encountered the wandering minstrel, nor the studied, more graceful garb, which so well became his shapely form during his visit to Luscombe.
Thus there is a continual gradation in the degree of self-evidence of what I remember, and a corresponding gradation in the trustworthiness of my memory.
Truths of perception and some of the principles of logic have the very highest degree of self-evidence; truths of immediate memory have an almost equally high degree. Judgements of intrinsic ethical or aesthetic value are apt to have some self-evidence, but not much.
Their truth is evident to us, and we employ them in constructing demonstrations; but they themselves, or at least some of them, are incapable of demonstration. Self-evidence, however, is not confined to those among general principles which are incapable of proof.
It must be admitted, however, that an exceptional power of observation is needed in order to distinguish, by means of introspection, mere combination of ideas from judgments." Self-evidence. Some of our beliefs seem to be peculiarly indubitable.
Besides, this godly fear carrieth in it self-evidence that the state of the sinner is happy, because possessed with this happy grace. So here, "The Lord taketh pleasure in them that fear him, in them that hope in his mercy."
It seems, however, highly probable that two different notions are combined in 'self-evidence' as above explained; that one of them, which corresponds to the highest degree of self-evidence, is really an infallible guarantee of truth, while the other, which corresponds to all the other degrees, does not give an infallible guarantee, but only a greater or less presumption.
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