were true, then every particular assertion of the form AP * AQ, would not only be true, but would be an instance of a true formal implication (namely "_x_P * _x_Q") and this, according to the proposed definition, is all that "_x_P entails _x_Q" asserts. If, therefore, it were true, it would again follow that all relational properties must be internal. But that this view also is untrue appears to me perfectly obvious. The proposition that I am in this room does "materially imply" that I am more than five years old, since both are true; and the assertion that it does is also an instance of a true formal implication, since it is in fact true that all the persons in this room are more than five years old; but nothing appears to me more obvious than that the second of these two propositions can _not_ be deduced from the first--that the kind of relation which holds between the premisses and conclusion of a syllogism in _Barbara_ does _not_ hold between them. To put it in another way: it seems to me quite obvious that the properties "being a person in this room" and "being more than five years old" are not related in the kind of way in which "being a right angle" _is_ related to "being an angle," and which we express by saying that, in the case of every term, the proposition that that term is an angle can be deduced from the proposition that it is a right angle. These are the only two suggestions as to the meaning of "_p_ entails _q_" known to me, which, if true, would yield the result that (2) does follow from (1), and that therefore all relational properties are internal; and both of these, it seems to me, are obviously false. All other suggested meanings, so far as I know, would leave it true that (2) does not follow from (1), and therefore that I may possibly be right in maintaining that some relational properties are external. It might, for instance, be suggested that the last proposed definition should be amended as follows--that we should say: "_p_ entails _q_" means "_p * q and_ this proposition is an instance of a formal implication, which is not merely true but _self-evident,_ like the laws of Formal Logic." This proposed definition would avoid the paradoxes involved in Mr. Strachey's definition, since such true formal implications as "all the persons in this room are more than five years old" are certainly not self-evident; and, so far as I. can see, it may state something which is in fact true of _p_ and _q,_ whenever and only when _p_ entails _q._ I do not myself think that it gives the _meaning_ of "_p_ entails _q,_" since the kind of relation which I see to hold between the premisses and conclusion of a syllogism seems to me to be one which is purely "objective" in the sense that no psychological term, such as is involved in the meaning of "self-evident," is involved in its definition (if it has one). I am not, however, concerned to dispute that some such definition of "_p_ entails _q_" as this may be true.