Pages
31
22
of definite individuals called its members, what is the meaning of this compounded existence. It is plain that the idea of a compound is a triadic idea. It implies that there is some sign, or something like a sign, which picks out and unites those members. Now the fact that they are all united in that compound is a quality belonging to them all and to nothing else. There is thus here a reference to a possible sam which does this. Thus, we might as well at once defined a gath as a subject which has but one mode of being which is the existence of a sam. From this fact, that a gath cannot be defined except in terms of a sam, it follows that if by a collection
32
24
be meant, as ordinarily is meant, a gath; while a gath is not distinguished from a sam, it becomes utterly impossible to define what is meant by a collection.
This would not be true if the two clauses of the definition of the sam were two distinct ideas which have to be put together; but it is not so. Secondness involves Firstness, although it can be discriminated from it; and consequently the idea of the existence of that which has an essence, which is simple Secondness, is a decidedly simpler notion than that of existence without essence, or a Secondness discriminated from Firstness. For it is only by a rectification applied to the former notion that the latter can be attained.
33
26
No doubt the easiest way to conceive of the sam is to imagine that you have a common noun, without specifying what noun it is, and to think that that noun signifies some quality which is possessed by anything to which it applies, but is not possessed by anything to which it does not apply. Now you are to imagine a single thing which is composed of parts. Nothing is done to these parts to put them into their places in the whole: their mere existence locates them in the whole. Now think of this rule as describing the whole. If any individual object can properly have that common noun predicated of it, it is a part of the single object called a sam; if not, it is not. That gives you the idea of the sam. Now to get the idea of a gath, you are to consider that
34
28
those individual objects might change their qualities without losing their individual identity; so that limiting ourselves to any instant any individual object which at that instant forms a part of the sam forever forms a part of an object of which no object not at that instant a part of the sam is a part, and this individual composite whole which has nothing to do with the qualities of its members is a gath.
For every gath there must be a corresponding sam. This is what we should ordinarily express by saying that whatever exists is possible. Or, as De Morgan put it, the individuals of whatsoever collection have some
35
30
some quality common to them all that is peculiar to them i.e. possessed by nothing else. Kant, I dare say, would remark that this is a Regulative Principle but that it cannot be proved to be a Constitutive principle. That is, it is proper to assume it, but you cannot prove it is so. But I reply that every principle of logic is a Regulative Principle and nothing more. Logic has nothing to do with Existence. And I should add: Herr Professor Dr. Hofrath Kant, permit me to say that in saying this is not a Constitutive principle you speak of qualities as if they were existent individuals. A quality has no other being in itself than possibility and to say that a quality is possible is to say that it has all the being that in the nature of things a quality could have. If as you say there may be