1867 March 23
I cannot explain the deep emotion with which I open this book again. Here I write but never after read what I have written for what I write is done in the process of forming a conception. Yet I cannot forget that here are the germs of the theory of the categories which is (if anything is) the gift I make to the world. That is my child. In it I shall live when oblivion has me—my body.
This matter of the logical principles of the different kinds of inference is a difficult matter. One way of putting it would be this.
Every symbol denotes certain objects and connotes certain characters. The symbol represents each of those objects to have each of those characters. The symbol may be a false one; it may be that the objects it denotes do not have the characters it connotes. But if S is M in this sense—not merely that M is a name for S but that it is the name of a class of things among which S is and if M is P not merely in the sense that———
then S is P.
Here the principle is that
That which is M is what M is.
Every one of the integrant parts of m is an integrant part of each prime aliquot of m and vice versa.
A purely contentless principle. As a logical principle should be.
Now let us take up the synthetic arguments.
Whatever is a character of every thing denoted by M is a character of M. Whatever has every character of M is denoted by m.
Here are two principles. But they do not apply to induction and hypothesis just as they stand.
Whatever is a common character of many things denoted by M is likely to be a character of m.
That does not quite hit the point. It does not contain the idea that the things must have been taken at random out of those denoted by M.
In what point of view shall we regard this necessity for a random selection?
Suppose we look at the matter thus. Certain things have a certain character in common. It follows that there must be some genus of these things which have the character. We cannot take any genus lower than that which they are selected as belonging to. To take a higher one would involve a perfectly arbitrary proposition.
I am convinced that this is a very awkward way of taking hold of the matter.
Suppose we take it up another way.
For any subject or predicate we can substitute what?
Only that which this subject or predicate represents—only that which fulfils the function of that subject or predicate—only that which the subject or predicate represents to the proposition or to the other terms of it.
Now a subject is a direct symbol of its subject to its predicate and a predicate of its predicate to its subject.
But a subject is also an imperfect representation of that genus from which it has been taken—by which it is determined. It is not a semeion sign of it as I have said—it is an example of it.
A predicate is a representation of the thing of which it is a random character—a copy of it.
This is horribly vague.
1867 March 25
Here is another point of view.
What is the function of a symbol as subject? To stand for certain things. Then if a predicate be true of all the things that it stands for as yet, that is for all which we yet know it to stand for, the symbol may stand as subject provisionally.
The difficulty with this is that it does not represent the synthetic probability of the inference.
It is however a good idea that a random selection is equivalent to all known—the genus of those two would fit that.
We have
M is P in the sense that the actual denotation or things taken under M are P (contingent)
and 2nd in the sense that all possible things taken under M would be P (necessary).
On the same principle
S is M in the senses
1st that S has the qualities taken of M (attributive)
2nd that S has all qualities of M (subsumptive)
Still it may be doubted if Hypothesis proceeds by random selection of qualities of the new predicate.
Then the principle would be
the possible is like most of the actual.
1867 April 1
What is taken—the present—of a class if it has any common character—that character probably belongs to the class, or to the majority of it. And if what is known of the characters of a thing belong to another thing, the second thing has most of the characters of the first, probably.
The reason is that the parts compose the whole and therefore what does not belong to the majority of the whole does not belong to the majority of the parts.
What does not belong to most of the parts does not belong to the parts taken mostly, because the parts to be taken are all the possible parts.
April 12
The distinction must be observed between Induction and Hypothesis as formal operations and between them as leading to truth.
1867 September 24
Let me consider a little about the nature of truth.
First. I notice that if we define an image to be a representation completely determined in content so that in it every attribute is affirmed or denied there is probably no image. And is not this what is requisite to make an image? What is an image? There is a good question for dialectical research.
As it seems to me that the world has not yet exhausted the instruction to be derived from Sophisms I shall undertake some analysis of a collocation of them which seems to me to lead at once to a solution of the darkest questions of metaphysics.
In the first place what is meant by a hypothetical proposition, when is it true? Take this one—If the carotid artery of a man is cut, he will die. Or this—if the shadow of the moon is cast on the earth, there is an eclipse of the sun.
Truth may be defined as the concurrence of the extension and comprehension of a representation which has extension and comprehension independent of one another.
Thus if a representation is a mere likeness (as no human representations are) which stands for nothing except what it happens fully to agree with in characters; it cannot be false of any thing because it only stands for whatever it fully agrees with. And therefore truth has no meaning in reference to it.
So if a representation merely points out certain things and implies nothing of them.
But if a representation at once indicates certain objects and independently implies certain characters, its truth or falsity depends on whether those characters can be predicated of those objects.
This definition is a bad one—it contains a diallele—but it will answer as a preliminary explanation and even sometimes as a test.
[First apply what has been said to a categorical.]
Now in a hypothetical proposition the function of the protasis is to mark the sphere of the representation, which it may do by means of its connotation or otherwise. The apodosis on the other hand conveys the content