452 



Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



The time is coming when no one of two correlatives will be introduced without as full 

 an introduction of the other. Logic abounds in pairs' of which both must enter thought 

 together, but of which one only has been allowed to become prominent in language. Of 

 converse relations, and of contrary (or contradictory) relations, we generally see one embodied, 

 while the other is but as a shadow. Part and whole give a marked instance : our language 

 is familiar with a whole of several parts, but hardly knows such a phrase as ' a part of 

 several wholes'. 



How loosely the subject of correlation is considered may be seen in the case of assertion 

 and denial. In logical writings these are — I do not say defined, but — treated as alter- 

 natives. In the wide world it is generally assumed that all which a person cannot assert he 

 can and will deny : let any one hesitate at affirming, and four out of five of his hearers will 

 report him as having contradicted; and the four will be precisely those who see no use in 

 logic. The books on logic so far favour this inaccuracy that they take no notice of any inter- 

 mediate" between affirmation and negation. The following brief summary will show how 

 easily a sufficient notation of syllogism will enable us to collect all cases of what I shall call 

 indecision. I mean inferential indecision ; in which inability to affirm or deny a conclusion 

 is a necessary consequence of inability to affirm or deny a premise. 



When two premises, A and B, give a conclusion C, it follows from the usual law of 

 opponent reduction, as I call it, that the assertion of either premise, with hesitation at denial 

 of the other, is equal hesitation at denial of the conclusion. For one premise, with denial of 

 the conclusion, is denial of the other premise. Hence any hesitation at affirmation of the 

 contrary of the other premise, is equal hesitation at affirmation of the contrary of the con- 

 clusion. That is to say, there are syllogisms in which assertion and non-denial give non- 

 denial ; there are others in which assertion and non-assertion give non-assertion : of four 

 possible forms these are the most systematic ; each form including the other three. 



The syllogisms of undecided denial, in which assertion and non-denial give non-denial, 

 are precisely those in which assertion and assertion give assertion. Thus ) ) )•) gives )•); or 

 X ) ) T ) ■ ) Z gives X ) ■ ) Z. Assert either X))Y or Y))Z, and refuse to deny the other, 

 and we must refuse to deny X)-)Z. This gives rise to two forms of the other kind. 

 Assert X ) ) Y, and refuse to affirm Y ( ( Z, or assert Y ) •) Z, and refuse to affirm X (. ( Y ; 

 in either case we must refuse to affirm X ( ( Z. 



• Many common words, when they represent material ob- 

 jects, have meaning of which relation to other objects Is an 

 essential part; wlience arises some confusion. An island is 

 land surrounded by water: is the surrounding water a part of 

 the island ? Yes, for no water, no island : no, for if you walk 

 into the water, you quit the island. The ambiguity is easily 

 explained in this case : there is the object named, and the rela- 

 tion by which it is named: the object does not extend into the 

 water, but the droits of the notion do, perhaps as far as those 

 of the crown. Again, what is a box ? Is it a space bounded by 

 an envelope of wood, or is it the envelope itself? Not the first, 

 for we certainly move a box from town to town, which no one 

 can do to a bit of space. And yet, when I asked a little girl what 



would happen if the nails used in fixing a card of address were 

 too long, she answered that they would "get inlo the box, and 

 spoil the things." We get over these ambiguities in common 

 life; but they are sore puzzles in philosophy. 



' "But negation and affirmation must be contradictorily 

 opposed; as Aristotle has expressed it, — 'Between affirmation 

 and negation there is no mean,'" (Hamilton, vi. 636»). True 

 enough so far as this, that of affirmation and negation one 

 must be true and the other false; but not true of enunciation. 

 I may not know which is true and which is false; I may have 

 the courage to avow it, and to follow Hamilton's principle of 

 finding language for all that is in thought. 



