308 REASONING. 



dation of it I take to be, that Belief and Disbelief are two dif- 

 ferent mental states, excluding one another. This we know by 

 the simplest observation of our own minds. And if we carry 

 our observation outwards, we also find that light and darkness, 

 sound and silence, motion and quiescence, equality and in- 

 equality, preceding and following, succession and simultane- 

 ousness, any positive phenomenon whatever and its negative, 

 are distinct phenomena, pointedly contrasted, and the one 

 always absent where the other is present. I consider the 

 maxim in question to be a generalization from all these facts. 

 In like manner as the Principle of Contradiction (that one 

 of two contradictories must be false) means that an assertion 

 cannot be both true and false, so the Principle of Excluded 

 Middle, or that one of two contradictories must be true, means 

 that an assertion must be either true or false : either the affir- 

 mative is true, or otherwise the negative is true, which means 

 that the affirmative is false. I cannot help thinking this 

 principle a surprising specimen of a so-called necessity of 

 Thought, since it is not even true, unless with a large qualifi- 

 cation. A proposition must be either true or false, provided 

 that the predicate be one which can in any intelligible sense 

 be attributed to the subject ; (and as this is always assumed 

 to be the case in treatises on logic, the axiom is always laid 

 down there as of absolute truth) . " Abracadabra is a second 

 intention" is neither true nor false. Between the true and the 

 false there is a third possibility, the Unmeaning : and this 

 alternative is fatal to Sir William Hamilton's extension of the 

 maxim to Noumena. That Matter must either have a minimum 

 of divisibility or be infinitely divisible, is more than we can 

 ever know. For in the first place, Matter, in any other than 

 the phenomenal sense of the term, may not exist : and it will 

 scarcely be said that a non-entity must be either infinitely or 

 finitely divisible.* In the second place, though matter, con- 

 sidered as the occult cause of our sensations, do really exist, 



* If it be said that the existence of matter is among the things proved by 

 the principle of Excluded Middle, that principle must prove also the existence 

 of dragons and hippogriffs, because they must be either scaly or not scaly, 

 creeping or not creeping, and so forth. 



