[ The Logic Notebook ]

MS 140: March-December 1867

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 sensenot 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.

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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 representsonly that which fulfils the function of that subject or predicateonly 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.

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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 presentof 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

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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 w ith 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 it s connotation or otherwise. The apodosis on the other hand conveys the content of the representation. And the question whether the proposition is true is the same as whether that content belongs in fact to that sphere. Thus in the proposition—If the shadow of the moon is cast on the earth, the sun is eclipsed—the former clause indicates the circumstances to which the statement made in the latter clause is applicable.

Take now another case. If the motion of the earth in its orbit were suddenly arrested and the perturbative effects of other bodies pre-

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vented, it would fall in a direct line to the sun. Unless the word truth be taken in a quite improper sense, this proposition is true. Yet how? For in this case there are no such circumstances as those indicated, they are even physically impossible, so that this would seem to be a representation like a copy which [ . . .]

1867 Sep. 26

Let x be that of which I know absolutely nothing
Then I do know that I know nothing of x
Therefore x is not x.

I know Greek. Greek is not present to my reminiscence, but occasion will call it up. This then is the essence of knowledge and what no occasion will call up is not known or conceived. I have therefore no conception of the absolutely unknowable.

Now a proposition is true in all its consequences for possible experience that either constitutes the truth of the proposition or it is false in reference to something which cannot be known (in which case the unknowable means something) or else it is devoid of meaning.

A proposition is not devoid of meaning which has true consequences.—

1867 Sep. 27

Every quality which we know of is of course either experienced or inferred from experience. We admit that things may have qualities which we do not know but that is because we may conceive of a state of knowledge in which something more is predicable of them. But do we mean anything if we say that a thing has a quality which cannot be predicated of it; that is which is unknowable and inconceivable? What can we mean by such a statement? We can imagine such a quality for as Berkeley says were we to imagine it, it would not be unimaginable. Can we have any general or relative notion of it? To have a general notion appears to be, having a habit according to which a certain sort of images will arise on occasion, that is having a capacity of imaging the particulars and the sense of this habit. But here such a thing is impossible.

Let us say then that it means nothing to say that a thing has an

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inconceivable quality. An inconceivable quality—one inconceivable by every being and absolutely—is no quality.That which has no qualities is nothing.That which is absolutely inconceivable is nothing.

Sep. 28

To say that a word has meaning is to say that a conception corresponds to it.

To say that we have a general conception of a triangle for instance is to say that upon the occasion of a triangle being presented to the imagination or in experience a certain feeling complicated in a certain way arises. We have no conception therefore of that of which no determination can be presented in the imagination.

Consequently, though we may undoubtedly mean something by the inconceivable we can mean nothing by an absolutely and in itself inconceivable predicate.

Hence such a predicate is no predicate.

To say that we know what a word means is to say not that we can always apply it rightly in fact but that we can always apply it rightly to imagined cases.

On Logical Extension and Comprehension

One term is more extensive than another, when it is predicable of all that the latter is and of more, besides. One term is more comprehensive than another when all the characters predicable of the latter are predicable of it and more beside.

From this it is plain, at once, that the greater the extension the less the comprehension and vice versa.

We may distinguish real and verbal Comprehension and extension; thus "Englishman" is more extensive than "Surly Englishman" since it includes also Englishmen not surly. But if there is any doubt whether any of the latter exist, it is only verbally more extensive.

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So "magnanimous hero" is more comprehensive than "hero" but if there is a doubt whether anything is conveyed by the adjective not already conveyed by the noun then the difference is merely verbal.

A better instance is "man John" and "man."

Confining our attention to Real Comprehension and Extension, we may observe that the predication spoken of may be either

1st such as could be made with no information except the meaning of the word. This I shall term the Essential Extension and Comprehension.

2nd such as could logically be made in a particular supposed state of information. This I shall term the Inferred Extension and Comprehension.

3rd such as could be made if our information were complete. This I shall term the Natural Extension and Comprehension.

Essential Extension and Comprehension

One half of all terms are positive and one half negative. Positive terms are defined, and therefore have an essential Comprehension. But they have no real essential extension. Negative terms are not defined and therefore have no real essential comprehension but they have a real essential extension since it is known that no determinate conception can embrace the whole sphere of being.

Man is a rational animal
Then Whatever is either irrational or not animal is not man

Two terms cannot be equal in essential extension or comprehension because if they were they would have the same meaning. The relation of two terms in essential comprehension or extension may not be measurable on account of the want of distinctness of one or both of those terms.

Oct. 2

There ought to be a proposition relating to universal and particular terms similar to that relating to affirmatives and negatives. My experience of logical symmetries assures me of it.

Perhaps this is it. A particular term will be found generally to have some natural extension, therefore all the extension implied, but

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it will not have a comprehension adequate to limiting its extension as it is limited. On the other hand a universal term, will never have an extension capable of limiting its comprehension as it is limited since new propositions will be discovered.

This is not yet very clear to me. But it would seem that as there is an arbitrariness in the extension of particulars so that we may exclude this or that from its extension so as to be able to predicate of it what we cannot predicate of them, so there is an arbitrary element in the comprehension of the universal so that this or that may be omitted from it so that we can predicate it of (imaginary things) of which we could not predicate them.

I think this is it. In a particular there is no concrete thing which must be included under it; in a universal there is no concrete quality which must be included in it.

If some S is P
it does not follow that this S is P

If S isP
it does not follow that it is thisP

Ah I think I have it now—

SomeS has a complete concrete comprehension
Thus Some Man—is a laugher, a one-eyed man, a cross person, &c.

This cannot be said of Any man which is therefore without concrete comprehension.

On the other hand Some man is not completely defined in extension since it is disjunctive alternative while any man applies definitely to certain things.

Note the meaning of a particular in the predicate. Some S means Either S' S'' S''' &c. select which I please.

Some S is P, that is let me take as my subject one what one I
please of S' S'' S''' &c. and I can make the proposition true.

Now this does not hold for M is some P unless M is completely determined in comprehension just as Any S is P only holds if P has a very wide extension.

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We may therefore say

Oct. 2

2. Of the Effect of a Change of Information

Suppose it is learned that

Any S is P

Then S receives an addition to its comprehension.

P an addition to its extension.

If we looking at an S find it to be P

Some S is P

This adds to the extension of P—supposing we know what S.

Any S is not-P

This adds to the comprehension of S—supposing we know something of not-P.

1867 Nov. 24

I wish to investigate the nature of a simple concept. Such a concept first arises as predicated of some object (occasion of experience)

S is M

On the ground of some previous representation of the object. (Not immediate)

1. entirely knowable. Intuitional. Capable of external existence.

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The predication of the concept is virtually contained in this previous representation.

To say that a simple concept is the immediate apprehension of a quality is but a mode of saying that its meaning is given in the representation which gives rise to it inasmuch as it is as much as to say that that quality is contained in that representation.

1867 Dec. 7

When I conceive a thing as say 'three' or say 'necessary' I necessarily have some concrete object in my imagination. I have some concrete object—'the necessary'. By saying that I have the necessary in my mind, it is not meant that I have all necessary things in mind. Nor that I have simply the character of necessity. For what I am thinking is not necessity but the necessary. Then I must have something which I recognize as a general sign of the necessary. But why should that particular feeling which is a sign of the necessary be a sign of that any more than of anything else? Because such is my constitution. Very true.

When I conceive as say "necessary," I have some singular object present to my imagination. I have not all necessary things separately imaged.

Doubted whether I ever have an absolutely singular object—

Copyright of the Peirce Edition Project 1998