A proprium is an attribute derived from the definition:  being either (a) implied in it, or deducible from it, as ’having its three angles equal to two right angles’ may be proved from the definition of a triangle; or (b) causally dependent on it, as being ‘dangerous to flocks’ results from the nature of a wolf, and as ‘moving in an ellipse’ results from the nature of a planet in its relation to the sun.

An accident is a property accompanying the defining attributes without being deducible from them.  The word suggests that such a property is merely ‘accidental,’ or there ‘by chance’; but it only means that we do not understand the connection.

Proprium and Accident bear the same relation to one another as Derivative and Empirical Laws:  the predication of a proprium is a derivative law, and the predication of an accident is an empirical law.  Both accidents and empirical laws present problems, the solution of which consists in reducing them, respectively, to propria and derivative laws.  Thus the colour of animals was once regarded as an accident for which no reason could be given; but now the colour of animals is regarded as an effect of their nature and habits, the chief determinants of it being the advantage of concealment; whilst in other cases, as among brightly coloured insects and snakes, the determinant may be the advantage of advertising their own noxiousness.  If such reasoning is sound, colour is a proprium (and if so, it cannot logically be included in a definition; but it is better to be judicious than formal).

If the colour of animals is a proprium, we must recognise a distinction between Inseparable and Separable Propria, according as they do, or do not, always accompany the essence:  for mankind is regarded as one species; but each colour, white, black or yellow, is separable from it under different climatic conditions; whilst tigers are everywhere coloured and striped in much the same way; so that we may consider their colouring as inseparable, in spite of exceptional specimens black or white or clouded.

The same distinction may be drawn between accidents.  ‘Inhabiting Asia’ is an Inseparable Accident of tiger, but a Separable Accident of lion.  Even the occasional characteristics and occupations of individuals are sometimes called separable accidents of the species; as, of man, being colour-blind, carpentering, or running.

A proprium in the original signification of the term [Greek:  hidion] was peculiar to a species, never found with any other, and was therefore convertible with the subject; but this restriction is no longer insisted on.

Sec. 9.  Any predication of a genus, difference or definition, is a verbal, analytic, or essential proposition:  and any predication of a proprium or accident, is a real, synthetic, or accidental proposition (chap. v.  Sec. 6).  A proposition is called verbal or analytic when the predicate is a part, or the whole, of the meaning of the subject; and the subject being species, a genus or difference is part, and a definition is the whole, of its meaning or connotation.  Hence such a proposition has also been called explicative.  Again, a proposition is called real or synthetic when the predicate is no part of the meaning of the subject; and, the subject being species, a proprium or accident is no part of its meaning or connotation.  Hence such a proposition has been called ampliative.