There can be no doubt that in a great many cases, perhaps the greater number of cases, alternatives are exclusive as a matter of fact. Any one number is incompatible with any other; one point of time or place is exclusive of all others. Roger Bacon died either in 1284 or 1292; it is certain that he could not die in both years. Henry Fielding was born either in Dublin or Somersetshire; he could not be born in both places. There is so much more precision and clearness in the use of exclusive alternatives that we ought doubtless to select them when possible. Old works on logic accordingly contained a rule directing that the *Membra dividentia*, the parts of a division or the constituent species of a genus, should be exclusive of each other. It is no doubt owing to the great prevalence and convenience of exclusive divisions that the majority of logicians have held it necessary to make every alternative in a disjunctive proposition exclusive of every other one. Aquinas considered that when this was not the case the proposition was actually *false*, and Kant adopted the same opinion.[64] A multitude of statements to the same effect might readily be quoted, and if the question were to be determined by the weight of historical evidence, it would certainly go against my view. Among recent logicians Hamilton, as well as Boole, took the exclusive side. But there are authorities to the opposite effect. Whately, Mansel, and J. S. Mill have all pointed out that we may often treat alternatives as *Compossible*, or true at the same time. Whately gives us an example,[65] “Virtue tends to procure us either the esteem of mankind, or the favour of God,” and he adds--“Here both members are true, and consequently from one being affirmed we are not authorized to deny the other. Of course we are left to conjecture in each case, from the context, whether it is meant to be implied that the members are or are not exclusive.” Mansel says,[66] “*We may happen to know* that two alternatives cannot be true together, so that the affirmation of the second necessitates the denial of the first; but this, as Boethius observes, is a *material*, not a *formal* consequence.” Mill has also pointed out the absurdities which would arise from always interpreting alternatives as exclusive. “If we assert,” he says,[67] “that a man who has acted in some particular way must be either a knave or a fool, we by no means assert, or intend to assert, that he cannot be both.” Again, “to make an entirely unselfish use of despotic power, a man must be either a saint or a philosopher.... Does the disjunctive premise necessarily imply, or must it be construed as supposing, that the same person cannot be both a saint and a philosopher? Such a construction would be ridiculous.” [64] Mansel’s *Aldrich*, p. 103, and *Prolegomena Logica*, p. 221. [65] *Elements of Logic*, Book II. chap. iv. sect. 4. [66] Aldrich, *Artis Logicæ Rudimenta*, p. 104.