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 prevented, 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 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.
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 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 is P
it does not follow that it is this P
Ah I think I have it now—
Some S has a complete concrete comprehension
Thus Some Man—is a laugher, a one-eyed man, a cross person, &c.
This cannot be said of