2. Dr. Stout’s introduction into a “relational unity” of the third term,—_relatedness_ does not seem to me to remove the difficulties inherent in our problem. And the illustration by which he supports it appears to be unsound. He argues that when my hat is on my head this state of things implies (1) the two related terms, the hat and the head,(2) a relation of _on_ and _under_. (3) the fact that the terms stand in this relation—their relatedness. For (1) and (2) by themselves would be compatible with my hat being on the peg and my head bare. But surely there is here a confusion between the relation of _above_ and _below_, and the very different relation of _on_ and _under_. The latter relation includes, as the former does not, immediate contact as part of its meaning. If there are (1) a hat and a head, and (2) the relation _on_ and _under_—in this sense—between the two, there is surely no need of a third factor to complete the concrete actuality of “hat on head.” If the hat is not actually on the head, then (2), the supposed relation, is not there at all. And if (2) is there the whole fact is already there. In a word, Dr. Stout seems to me to count in the concrete fact of “thing exhibiting related aspects” as a third constituent in itself, precisely as popular Logic sometimes counts in the actual judgment, under the name of _Copula_, as one factor of itself.[98] Then to Dr. Stout’s use of his distinction between the relation and the fact of relatedness, I think it may be replied that it leaves us precisely where we were before. The hat is qualified by being _on_ the head, the head by being _in_ or _under_ the hat, and hat and head together by the relation of _on_ and _under_ between them. But how these various aspects of the fact are to be combined in a single consistent view we are no nearer knowing. 3. _The endless regress._ I think it will be seen from the preceding chapter that in my own view a genuine endless regress is evidence of the falsity of the conception which gives rise to it, and that I hold this on the ground that the endless regress always presupposes the self-contradictory purpose to sum an admittedly infinite series. Hence I could not concur, so far as I can see at present, in Dr. Stout’s distinction between the endless regress which does and that which does not involve self-contradiction. As to his illustration of endless regress of the second kind, the infinite divisibility of space (p. 11), I should have thought that there is no actual endless regress in question until you substitute for infinite divisibility infinite actual _subdivision_, and that when you make this substitution it commits you at once to the self-contradictory completion of an unending task. (Cf. what was said above, § 10, with reference to infinite numerical series.)