"When remembering a certain thing as in a certain place, the place and the thing are mentally represented together; while to think of the non-existence of the thing in that place, implies a consciousness in which the place is represented, but not the thing. Similarly, if instead of thinking of an object as colourless, we think of its having colour, the change consists in the addition to the concept of an element that was before absent from it--the object cannot be thought of first as red and then as not red, without one component of the thought being totally expelled from the mind by another. The law of the Excluded Middle, then, is simply a generalization of the universal experience that some mental states are directly destructive of other states. It formulates a certain absolutely constant law, that the appearance of any positive mode of consciousness cannot occur without excluding a correlative negative mode; and that the negative mode cannot occur without excluding the correlative positive mode: the antithesis of positive and negative being, indeed, merely an expression of this experience. Hence it follows that if consciousness is not in one of the two modes it must be in the other."[45] I must here close this supplementary chapter, and with it the Second Book. The theory of Induction, in the most comprehensive sense of the term, will form the subject of the Third. FOOTNOTES: [1] As Sir William Hamilton has pointed out, "Some A is not B" may also be converted in the following form: "No B is _some_ A." Some men are not negroes; therefore, No negroes are _some_ men (_e.g._ Europeans). [2] All A is B } contraries. No A is B } Some A is B } subcontraries. Some A is not B } All A is B } contradictories. Some A is not B } No A is B } also contradictories. Some A is B } All A is B } and No A is B } respectively subalternate. Some A is B } Some A is not B } [3] His conclusions are, "The first figure is suited to the discovery or proof of the properties of a thing; the second to the discovery or proof of the distinctions between things; the third to the discovery or proof of instances and exceptions; the fourth to the discovery, or exclusion, of the different species of a genus." The reference of syllogisms in the last three figures to the _dictum de omni et nullo_ is, in Lambert's opinion, strained and unnatural: to each of the three belongs, according to him, a separate axiom, co-ordinate and of equal authority with that _dictum_, and to which he gives the names of _dictum de diverso_ for the second figure, _dictum de exemplo_ for the third, and _dictum de reciproco_ for the fourth. See part i. or _Dianoiologie_, chap. iv. § 229 _et seqq._ Mr. Bailey, (_Theory of Reasoning_, 2nd ed. pp. 70-74) takes a similar view of the subject.