Again, it is by definitions that we can best distinguish between Verbal and Real Propositions. Whether a term predicated is implied in the definition of the subject, or adds something to its meaning, deserves our constant attention. We often persuade ourselves that statements are profound and important, when, in fact, they are mere verbal propositions. "It is just to give every man his due"; "the greater good ought to be preferred to the less"; such dicta sound well—indeed, too well! For 'a man's due' means nothing else than what it is just to give him; and 'the greater good' may mean the one that ought to be preferred: these, therefore, are Truisms. The investigation of a definition may be a very valuable service to thought; but, once found, there is no merit in repeating it. To put forward verbal or analytic propositions, or truisms, as information (except, of course, in explaining terms to the uninstructed), shows that we are not thinking what we say; for else we must become aware of our own emptiness. Every step forward in knowledge is expressed in a real or synthetic proposition; and it is only by means of such propositions that information can be given (except as to the meaning of words) or that an argument or train of reasoning can make any progress.
Opposed to a truism is a Contradiction in Terms; that is, the denying of a subject something which it connotes (or which belongs to its definition), or the affirming of it something whose absence it connotes (or which is excluded by its definition). A verbal proposition is necessarily true, because it is tautologous; a contradiction in terms is necessarily false, because it is inconsistent. Yet, as a rhetorical artifice, or figure, it may be effective: that 'the slave is not bound to obey his master' may be a way of saying that there ought to be no slaves; that 'property is theft,' is an uncompromising assertion of the communistic ideal. Similarly a truism may have rhetorical value: that 'a Negro is a man' has often been a timely reminder, or even that "a man's a man." It is only when we fall into such contradiction or tautology by lapse of thought, by not fully understanding our own words, that it becomes absurd.
Real Propositions comprise the predication of Propria and Accidentia. Accidentia, implying a sort of empirical law, can only be established by direct induction. But propria are deduced from (or rather by means of) the definition with the help of real propositions, and this is what is called 'arguing from a Definition.' Thus, if increasing capacity for co-operation be a specific character of civilisation, 'great wealth' may be considered as a proprium of civilised as compared with barbarous nations. For co-operation is made most effectual by the division of labour, and that this is the chief condition of producing wealth is a real proposition. Such arguments from definitions concerning concrete facts and causation require verification by comparing the conclusion with the facts. The verification of this example is easy, if we do not let ourselves be misled in estimating the wealth of barbarians by the ostentatious "pearl and gold" of kings and nobles, where 99 per cent. of the people live in penury and servitude. The wealth of civilisation is not only great but diffused, and in its diffusion its greatness must be estimated.
To argue from a definition may be a process of several degrees of complexity. The simplest case is the establishing of a proprium as the direct consequence of some connoted attribute, as in the above example. If the definition has been correctly abstracted from the particulars, the particulars have the attributes summarised in the definition; and, therefore, they have whatever can be shown to follow from those attributes. But it frequently happens that the argument rests partly on the qualities connoted by the class name and partly on many other facts.
In Geometry, the proof of a theorem depends not only upon the definition of the figure or figures directly concerned, but also upon one or more axioms, and upon propria or constructions already established. Thus, in Euclid's fifth Proposition, the proof that the angles at the base of an isosceles triangle are equal, depends not only on the equality of the opposite sides, but upon this together with the construction that shows how from the greater of two lines a part may be cut off equal to the less, the proof that triangles that can be conceived to coincide are equal, and the axiom that if equals be taken from equals the remainders are equal. Similarly, in Biology, if colouring favourable to concealment is a proprium of carnivorous animals, it is not deducible merely from their predatory character or any other attribute entering into the definition of any species of them, but from their predatory character together with the causes summarised in the phrase 'Natural Selection'; that is, competition for a livelihood, and the destruction of those that labour under any disadvantages, of which conspicuous colouring would be one. The particular coloration of any given species, again, can only be deduced by further considering its habitat (desert, jungle or snowfield): a circumstance lying wholly outside the definition of the species.
The validity of an argument based partly or wholly on a definition depends, in the first place, on the existence of things corresponding with the definition—that is, having the properties connoted by the name defined. If there are no such things as isosceles triangles, Euclid's fifth Proposition is only formally true, like a theorem concerning the fourth dimension of space: merely consistent with his other assumptions. But if there be any triangles only approximately isosceles, the proof applies to them, making allowance for their concrete imperfection: the nearer their sides approach straightness and equality the more nearly equal will the opposite angles be.
Again, as to the things corresponding with terms defined, according to Dr. Venn, their 'existence' may be understood in several senses: (1) merely for the reason, like the pure genera and species of Porphyry's tree; the sole condition of whose being is logical consistency: or (2) for the imagination, like the giants and magicians of romance, the heroes of tragedy and the fairies of popular superstition; whose properties may be discussed, and verified by appeal to the right documents and authorities (poems and ballads): or (3) for perception, like plants, animals, stones and stars. Only the third class exist in the proper sense of the word. But under a convention or hypothesis of existence, we may argue from the definition of a fairy, or a demigod, or a dragon, and deduce various consequences without absurdity, if we are content with poetic consistency and the authority of myths and romances as the test of truth.
In the region of concrete objects, whose properties are causes, and neither merely fictions nor determinations of space (as in Geometry), we meet with another condition of the validity of any argument depending on a definition: there must not only be objects corresponding to the definition, but there must be no other causes counteracting those qualities on whose agency our argument relies. Thus, though we may infer from the quality of co-operation connoted by civilisation, that a civilised country will be a wealthy one, this may not be found true of such a country recently devastated by war or other calamity. Nor can co-operation always triumph over disadvantageous circumstances. Scandinavia is so poor in the gifts of nature favourable to industry, that it is not wealthy in spite of civilisation: still, it is far wealthier than it would be in the hands of a barbarous people. In short, when arguing from a definition, we can only infer the tendency of any causal characteristics included in it; the unqualified realisation of such a tendency must depend upon the absence of counteracting causes. As soon as we leave the region of pure conceptions and make any attempt to bring our speculations home to the actual phenomena of nature or of human life, the verification of every inference becomes an unremitting obligation.