The same doctrine is still more distinctly stated by Dugald Stewart. "If by the first principles of a science," says he, "be meant those fundamental propositions from which its remoter truths are derived, the axioms cannot, with any consistency, be called the first principles of mathematics. They have not, (it will be admitted,) the most distant analogy to what are called the first principles of natural philosophy:--to those general facts, for example, of the gravity and elasticity of the air, from which may be deduced, as consequences, the suspension of the mercury in the Torricellian tube, and its fall when carried up to an eminence. According to this meaning of the word, the first principles of mathematical science are, not the _axioms_ but the _definitions_; which definitions hold, in mathematics, precisely the same place that is held in natural philosophy by such general facts as have now been referred to." But the doctrine in question rests upon a firmer basis than that of human authority. Let any man examine the demonstrations in geometry, and attentively consider the principles from which the conclusions of that science are deduced, and he will find that they are _definitions_, and not _axioms_. He will find; that the properties of the triangle are derived from the definition of a triangle, and those of a circle from the definition of a circle. And then let him try his own skill upon the axioms of that science; let him arrange them and combine them in all possible ways; let him compare them together as long as he pleases, and determine for himself, whether they can be made to yield a single logical inference. If the question is thus brought to the test of an actual experience, I think it is not difficult to foresee, that the decision must be in favour of the doctrine of Stewart, and that it will be seen, that no such proposition as that whatever _is, is,_ can even constitute the postulate, or first principle, in any sound argument; and that it is only from general facts, such as are ascertained by observation and experience, that we can derive logical consequences of any kind whatever, either in relation to matter or to mind. If there is any truth in the foregoing remarks, or correctness in the position of Locke and Stewart, it is certainly one of the capital errors of Edwards, as well as of other necessitarians, that he has undertaken to deduce his doctrine from a metaphysical axiom, or identical proposition.