which we here call abstract concepts. Such a definition is more than the explanation of what a name ought to mean (and still further removed from that which it may mean “in reality”); it aims chiefly at describing the matter, i.e. the object thought of, and then assigns to it, as an abbreviated mark, a name which is best chosen arbitrarily as one free from every other meaning. The description is here not merely a statement of limits, which must essentially refer to the comprehension of the concept; but it is as complete as possible a determination of its content, without regard to what the comprehension may be. It is only a make-shift when it is expressed in (not-defined) words of customary usage; science avails itself of this when and in so far as it has no other expressions defined by itself. Sigwart expresses this exactly in the words: “every definition presupposes a scientific terminology”.
Note 1. Like other modern logicians, Sigwart distinguishes from merely analytic definitions “in which the value of a word is expressed by an equivalent formula,” synthetic definitions, “which introduce the term for a new concept”. But he does not notice that all definitions of scientific meaning are, at any rate in intention, synthetic definitions, and must be estimated by this idea; nor that in the postulate of real-definitions we are dealing with nothing else than with these; although he speaks in the context of formulae which “are externally like a nominal definition, but really different from it,” yet he holds (a few pages before) that the concept of the so-called real-definition “has no longer any meaning for us in logic”.
Note 2. The doctrine of Bishop Berkeley that nothing general can be thought, can only be disputed when it has been agreed what is meant by general and by thinking. But when he gives as example (and is followed therein by more recent writers) that we cannot have an idea of a triangle which is neither equilateral nor scalene, etc., then this is indeed true, but proves nothing. For no one will maintain that there is a natural universal idea of the triangle; but concerning the abstract concept triangle this is in fact sufficiently described as a plane surface enclosed by three straight lines, if the concepts of straight and of lines have been previously defined. The different sorts of triangle which are actual in idea or in diagram, are not related to the concept as species to genus, but are copies or realisations of it (in the first and second degree) and as such are, for and with reference to the concept, all of one kind. For the rest they are related to it as isolated experiments to an ideal case thought in abstracto.
