that are characterized by known
properties of which the
elements are related to other such classes.
That things come in
kinds seems a natural assumption of the human mind: For the human
mind, everything is of some kind. Aristotle already made it, quite
explicitly, though he spoke of 'categories'.
It is difficult to be precise about such a fundamental concept, but it
makes sense to insist that such classes as are considered kinds are
characterized by known properties and
indeed also satisfy the following:
Kind(Y) --> (EX)(x)(xeX --> xeY) & (EZ)(x)(xeY --> xeZ)
In other words: One must have some idea of the antecedents and
consequents of a kind, or again in Aristotelian terms: Of species and
genera of a
There is also a more precise form, that involves references to presumed background knowledge, e.g. of relevant conditions and presumptions K, possibly also of a person a or group $, that uses the concepts of proper antecendents or proper consequents, both relative to a and K. Thus one may define proper consequents of P relative K along lines like these:
pc(a,P,K) =def |Q: ( ~(K|-Q) & ~(K|-~Q) & ~(P|-Q) & & ~(P|-~Q) & (K&P |- Q) )
Now one can say P is a kind relative to K if it has a non-empty set of proper consequents relative to K, that is, consequents that do not follow from K or from P alone, nor do the denials of the consequents follow from K or from P alone, but that do follow if both K and P are true, and that thus are, given K, characteristic in a fairly clear sense for whatever is P.