The existence of such a word as all in the premiss, although existing therein merely as a contrivance for reconciling the evidence of the distribution of the middle term with a certain amount of simplicity in the way of terminology, could scarcely fail, in conjunction with some of its other properties, to give it what is here considered an undue amount of importance. It made it look like the opposite to none. Yet this is what it is not. The opposite to none is not-none, or some; the opposite to all is one. In one and all we have the highest and lowest numbers of the individuals that constitute a class. In none and some we have the difference between existence and non-existence. That all is a mere mode of some, has been insisted on by many logicians, denied by few or none. Between all and some, there is, at best, but a difference of degree. Between some and none, the difference is a difference of kind. Some may, by strengthening, be converted into all. No strengthening may obliterate the difference between all and not-all. From this it follows that the logic of none and some, the logic of connexion and disjunction (the logic of two signs), is much more widely different from the logic of part and whole (the logic of three signs) than is usually admitted; the former being a logic of pure quality, the latter a logic of quality and quantity as well.
Has the admixture done good? I doubt whether it has. The logic of pure and simple Quality would, undoubtedly, have given but little; nothing but negative conclusions on one side, and possible particulars on the other. Nevertheless it would have given a logic of the Possible and Impossible.
Again, as at present constituted, the Quantitative logic, the logic of all and some, embraces either too much or too little. All is, as aforesaid, only a particular form of more than none. So is most. Now such syllogisms as—
Most men are fallible,
Most men are rational,
Some men are both frail and fallible;
or,
Some frail things are fallible,
are inadmissible in the Aristotelian paradigms. A claim, however, is set up for their admission. Grant it, and you may say instead of most—
Fifty-one per cent., &c.;
but this is only a particular instance. You may combine any two numbers in any way you like, provided only that the sum be greater than unity. Now this may be arithmetic, and it may be fact; but it is scarcely formal logic; at any rate it is anything but general.
It is the logic of some and its modifications one, all, and anything between one and all, as opposed to the logic of the simple absolute some (some the opposite to none), and a little consideration will show that it is also the logic of the probable, with its modification the proven, (proven is probable, as all is some,) as opposed to the logic of the possible and impossible. Let, in such a pair of propositions as—