The _idea of_ a dragon is _an idea of_ a thing which breathes flame: The _idea of_ a dragon is _an idea of_ a serpent: Therefore, there is _an idea of_ a serpent, which is _an idea of_ a thing breathing flame. Here the conclusion is true, and also the premises; but the premises are not definitions. They are propositions affirming that an idea existing in the mind, includes certain ideal elements. The truth of the conclusion follows from the existence of the psychological phenomenon called the idea of a dragon; and therefore still from the tacit assumption of a matter of fact.[28] When, as in this last syllogism, the conclusion is a proposition respecting an idea, the assumption on which it depends may be merely that of the existence of an idea. But when the conclusion is a proposition concerning a Thing, the postulate involved in the definition which stands as the apparent premise, is the existence of a thing conformable to the definition, and not merely of an idea conformable to it. This assumption of real existence will always convey the impression that we intend to make, when we profess to define any name which is already known to be a name of really existing objects. On this account it is, that the assumption was not necessarily implied in the definition of a dragon, while there was no doubt of its being included in the definition of a circle. § 6. One of the circumstances which have contributed to keep up the notion, that demonstrative truths follow from definitions rather than from the postulates implied in those definitions, is, that the postulates, even in those sciences which are considered to surpass all others in demonstrative certainty, are not always exactly true. It is not true that a circle exists, or can be described, which has all its radii _exactly_ equal. Such accuracy is ideal only; it is not found in nature, still less can it be realized by art. People had a difficulty, therefore, in conceiving that the most certain of all conclusions could rest on premises which, instead of being certainly true, are certainly not true to the full extent asserted. This apparent paradox will be examined when we come to treat of Demonstration; where we shall be able to show that as much of the postulate is true, as is required to support as much as is true of the conclusion. Philosophers, however, to whom this view had not occurred, or whom it did not satisfy, have thought it indispensable that there should be found in definitions something _more_ certain, or at least more accurately true, than the implied postulate of the real existence of a corresponding object. And this something they flattered themselves they had found, when they laid it down that a definition is a statement and analysis not of the mere meaning of a word, nor yet of the nature of a thing, but of an idea. Thus, the proposition, "A circle is a plane figure bounded by a line all the points of which are at an equal distance from a given point within it,"