106 J.J. Haldane
me to elaborate my objection. What needs to be accounted for is a natural
transition from the non-conceptual to the conceptual and that is not the same
distinction as one between degrees of conceptual complexity. Doubtless Stone
Age cave dwellers made fewer and less abstract discriminations than a con-
temporary physicist, but that is irrelevant; the point is that the ability to make
any general classifications is a conceptual power.
Let me add a further consideration in this cumulative case against natural-
ism. Thus far I have cast my objections concerning the nature of thought in
terms of the genesis of concepts. However, there is an additional difficulty for
the materialist or physicalist so far as concerns the relation between concepts
and the objects and features that fall under them. Consider again the concept
cat. Setting aside issues having to do with its non-specificity and possible
indeterminacy (e.g. there are significant differences between species of cats
and there may be animals concerning which it is an issue whether they even
are cats) let us say that the extension of this concept (the things of which it is
true), or of the corresponding term ‘cat’ and its equivalents in other languages,
is the set of cats.
Smart discusses the need to allow sets into his otherwise materialist ontology
but I am concerned to argue that in the present case this admission is an
insufficient concession to non-materialism. It is natural to think that the
conceptcat designates not only actual cats but future and ‘counterfactual’ cats.
That is to say, one might contemplate and discuss with others the prospects
for cats in the environment of Chernobyl 30 years hence, or consider
what would have been done with the kittens that Mother Cat might have
had had she not been neutered. Thus there is a problem with the attempt
to give the ‘semantic value’ of this term, or concept, by reference to actual
material objects. Additionally, it is easily imaginable that the members of
the set of actual cats fall under another concept, let us say that of being the
most-common-four-legged-animals-whose-average-weight-is-W, call this
the concept ‘maxifourn’. In this situation the extensions of the concepts cat
andmaxifourn are identical: they have all and only the same members. None-
theless, it is natural to say that the property of being a cat is not the same as
that of being a maxifourn. Little Felix would still be a cat even if, because of
population changes, he were no longer a maxifourn; meanwhile in the same
situation though Derek the dachshund might then be a maxifourn he would
not thereby have become a cat.
The point is clear: concepts distinguish objects in virtue of their properties
and even where two concepts are co-extensive – have all and only the same
instances – the properties they designate may differ. This is so even where the
properties in question are not merely co-extensive but necessarily so, i.e.
where, unlike the cat/maxifourn example, there is no possibility of their exten-
sions diverging. Every triangle is a trilateral and vice versa, and in some manner