Let us ask, then, whether, when error occurs and we are convinced of it, in mathematical or logical assertions, experience shows it to have occurred through want of distinctness in our conceptions? Now—excluding the case of reasoning in which symbols are used more or less mechanically, so that error when it occurs is usually due to a casual lapse of memory—I find that Descartes’ view is confirmed by my experience in a certain sense; but not in a sense which tends to establish the adequacy of his criterion. That is, the discovery of any such error seems always to involve the discovery of a past confusion of thought; but, in some cases at least, before the discovery of the error the thought appeared to be quite free from confusion, so that the most conscientious application of the criterion would not have saved me from error. I suppose the experience of others to be similar. Let me take as an illustration a mathematical error of an eminent thinker which I transiently shared.
In an attack on Metageometry (Metaph., book ii., chapter ii.) Lotze, discussing Helmholtz’s fiction of an intelligent being whose life and experience are confined to the surface of a sphere, remarks that such a being, if it moved in a small circle of the sphere, would find that “the meridians known to it from other experiences make smaller angles with its path on the side” towards the pole of the circle, “and greater on the opposite side”. On first reading this sentence I thought I could see clearly the fact as stated; then, on further consideration, I saw that the meridians must cut the small circle at right angles; then—reflecting on my momentary error in order to see how I had been misled—I perceived that the object I had been contemplating in idea was not a true spherical surface, but a confused mixture or tertium quid between such a surface and its projection on a plane. When discovered, the confusion seemed very palpable; but the opposite view had seemed clear and distinct when I agreed with Lotze’s assertion, and I could not doubt that it had seemed so to Lotze himself.
I do not therefore think the Cartesian criterion useless; on the contrary, I believe that I have actually saved myself from error by applying it. But the experience to which Descartes appeals seems to me to show that judgments, universal and particular, often present themselves with an illusory semblance of distinct conception or perception which cannot be stripped from them by direct reflexion; though it often vanishes at once when the judgment is otherwise demonstrated to be erroneous. In the case of perception Descartes expressly recognises this; he speaks (Med., iii.)
