Both these two modes, viz. the essential but incomplete Definition, and the accidental, or Description, are imperfect; but the Realists' distinction between definition of names and of things is quite erroneous. Their doctrine is now exploded; but many propositions consistent with it alone (e.g. that the science of geometry is deduced from definitions) have been retained by Nominalists, such as Hobbes. Really a definition, as such, cannot explain a thing's nature, being merely an identical proposition explaining the meaning of a word. But definitions of names _known to be names of really existing objects_, as in geometry, include two propositions, one a definition and another a postulate. The latter affirms the existence of a thing answering to the name. The science is based on the postulates (whether they rest on intuition or proof), for the demonstration appeals to them alone, and not on the definitions, which indeed might, though at some cost of brevity, be dispensed with entirely. It has been argued that, at any rate, definitions are premisses of science, _provided_ they give such meanings to terms as suit existing things: but even so, the inference would obviously be from the existence, not of the name which means, but of the thing which has the properties. One reason for the belief that demonstrative truths follow from the definitions, not from the postulates, was because the postulates are never quite true (though in reality so much of them is true as is true of the conclusions). Philosophers, therefore, searching for something more accurately true, surmised that definitions must be statements and analyses, neither of words nor of things, as such, but of ideas; and they supposed the subject-matter of all demonstrative sciences to be abstractions of the mind. But even allowing this (though, in fact, the mind cannot so abstract one property, e.g. length, from all others; it only _attends_ to the one exclusively), yet the conclusions would still follow, not from the mere definitions, but from the postulates of the real existence of the ideas.