In his Logic (B.  II. c. 2, Sec. 3) Mill gives as the axiom of syllogistic reasoning, instead of the Dictum:  “A thing which co-exists with another thing, which other co-exists with a third thing, also co-exists with that third thing.”  Thus the peculiar properties of Socrates co-exist with the attributes of man, which co-exist with mortality:  therefore, Socrates is mortal.  But, again, he says that the ground of the syllogism is Induction; that man is mortal is an induction.  And, further, the ground of Induction is causation; the law of causation is the ultimate major premise of every sound induction.  Now causation is the principle of the succession of phenomena:  how, then, can the syllogism rest on an axiom concerning co-existence?  On reflection, too, it must appear that ‘Man is mortal’ predicates causation:  the human constitution issues in death.

The explanation of this inconsistency may perhaps be found in the history of Mill’s work.  Books I. and II. were written in 1831; but being unable at that time to explain Induction, he did not write Book III. until 1837-8.  Then, no doubt, he revised the earlier Books, but not enough to bring his theory of the syllogism into complete agreement with the theory of Induction; so that the axiom of co-existence was allowed to stand.

Mill also introduced the doctrine of Natural Kinds as a ground of Induction supplementary, at least provisionally, to causation; and to reasoning about Kinds, or Substance and Attribute, his axiom of co-existence is really adapted.  Kinds are groups of things that agree amongst themselves and differ from all others in a multitude of qualities:  these qualities co-exist, or co-inhere, with a high degree of constancy; so that where some are found others may be inferred.  Their co-inherence is not to be considered an ultimate fact; for, “since everything which occurs is determined by laws of causation and collocations of the original causes, it follows that the co-existences observable amongst effects cannot themselves be the subject of any similar set of laws distinct from laws of causation” (B.  III. c. 5, Sec. 9).  According to the theory of evolution (worked out since Mill wrote), Kinds—­that is, species of plants, animals and minerals—­with their qualities are all due to causation.  Still, as we can rarely, or never, trace the causes with any fullness or precision, a great deal of our reasoning, as, e.g., about men and camels, does in fact trust to the relative permanence of natural Kinds as defined by co-inhering attributes.

To see this more clearly, we should consider that causation and natural Kinds are not at present separable; propositions about causation in concrete phenomena (as distinct from abstract ‘forces’) always involve the assumption of Kinds.  For example—­’Water rusts iron,’ or the oxygen of water combines with iron immersed in it to form rust:  this statement of causation assumes that water, oxygen, iron, and iron-rust are known Kinds.  On the other hand, the constitution of every concrete thing, and manifestly of every organised body, is always undergoing change, that is, causation, upon which fact its properties depend.