imagine in the one case a jelly with all the qualities of texture, color, and the like, that an individual object of sense would possess, is much the same as in the other to imagine the heavens filled with foot-rules and tape-measures. There is but one safe procedure in dealing with scientific concepts: to regard them as true so far as they describe, and no whit further. To supplement the strict meaning which has been verified and is contained in the formularies of science, with such vague predicates as will suffice to make entities of them, is mere ineptness and confusion of thought. And it is only such a supplementation that obscures their abstractness. For a mechanical description of things, true as it doubtless is, is even more indubitably incomplete. [Sidenote: The Meaning of Abstractness in Truth.] § 52. But though the abstractness involved in scientific description is open and deliberate, we must come to a more precise understanding of it, if we are to draw any conclusion as to what it involves. In his "Principles of Human Knowledge," the English philosopher Bishop Berkeley raises the question as to the universal validity of mathematical demonstrations. If we prove from the image or figure of an isosceles right triangle that the sum of its angles is equal to two right angles, how can we know that this proposition holds of all triangles? "To which I answer, that, though the idea I have in view whilst I make the demonstration be, for instance, that of an isosceles rectangular triangle whose sides are of a determinate length, I may nevertheless be certain it extends to all other rectilinear triangles, of what sort or bigness soever. And that because neither the right angle, nor the equality, nor determinate length of the sides are at all concerned in the demonstration. It is true the diagram I have in view includes all these particulars; but then there is not the least mention made of them in the proof of the proposition."[140:6]