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