abstract notion of 'triangle.' Abstraction may be performed equally
well in the case of a single object: but the mind would not originally
have known on what points to fix its attention except by a comparison
of individuals.

98. Abstraction too may be performed upon attributes as well as
substances. Thus, having by abstraction already arrived at the notion
of triangle, square, and so on, we may fix our attention upon what
these have in common, and so rise to the higher abstraction of
'figure.' As thought becomes more complex, we may have abstraction on
abstraction and attributes of attributes. But, however many steps may
intervene, attributes may always be traced back to substances at
last. For attributes of attributes can mean at bottom nothing but the
co-existence of attributes in, or in connection with, the same
substances.

99. We have said that abstract terms are so called, as being arrived
at by abstraction: but it must not be inferred from this statement
that all terms which are arrived at by abstraction are abstract. If
this were so, all names would be abstract except proper names of
individual substances. All common terms, including attributives, are
arrived at by abstraction, but they are not therefore abstract terms.
Those terms only are called abstract, which cannot be applied to
substances at all. The terms 'man' and 'human' are names of the same
substance of which Socrates is a name. Humanity is a name only of
certain attributes of that substance, namely those which are shared by
others. All names of concrete things then are concrete, whether they
denote them individually or according to classes, and whether directly
and in themselves, or indirectly, as possessing some given attribute.