Logic Notebook 1865-7

in their practical relevance. Still the burden of proof ceases to be when the side of Common Sense when it is shown to be contradictory or absurd. Now the whole developement of modern philosophy consists in showing that In general, it will lie with a metaphysical theory. But common sense is itself a [co???????] metaphysical theories. And moreover the history of modern philosohpy may be stated in epitome as the awakening of the mind to the unsatisfactoriness of that theory that man feels. It cannot indeed by denied that there is some truth in this; at any rate it is a hypothesis which accounts very prettily with many facts. In particular it accounts for the partial or only partial confirmation which opinions receive from intercourse with the opinions of others. How natural it is to infer from this that they are our opinions and so to get an idea that we are and that because we think. Perhaps we cannot even yet devise any more satisfactory explanation of this fact. But the theory puts an I or a not-I over against each other in absolute opposition or yet so that one determines the other. This being done, the simple process[?], it will be admitted is that these Now immediately when this Scepticism arises as to the validity of this

conception of the determination of anything by another without it, of causality, that is to say. To resolve this problem we have been forced first to consider the object as also de termined by the subject. And this is to encroach already upon the absolute boundary of I & not I. But even this will not do Even the object itself does not determine the subject, but only a false object does it. * * * * * * What shall we finally say then? The theory that now (?) is is incomprehensible \alpha self-contradictory hypothesis? Certainly not. Nay, such a hypothesis is not intellectual by the very definition of the intellect. It cannot be held in a comprehensible form but it may be held. The intellect did not make this hypothesis. The intellect makes no hypotheses , which are incomprehensible. The intellect is not therefore alone concerned in any proposition. But we make it. All that the words convey is something in capable of being made distinct. Hence it is emotional in its own nature. And as an emotion it is justified.

Dec 14. 5r

Hegel makes a great boast of the fact that his logic developes its own method. Mine pursues a rational method of which the logic itself is but the deduction or proof. Moreover I am not forced to make my book unintelligible in order to follow mine, but on the contrary it is the very procedure which perspicuity demands. Another thing; Hegel never deduces the necessity of considering what he considers before considering it; but I never introduce a concept distinction without having deduced the necessity for it.

Dec. 15

When the implication is constant, if two symbols are equal in extension or intension they are equal in both. Neither can be increased relatively to the other in either respect without diminishing it in the other respect. Accordingly,

1. If A and B are coextensive, they are cointensive.
2. Increase the extension of A; you diminish its intension. Hence if A is superordinate to B in extension, it is subordinate in intension.
3. Next add to B an extension which A has not. You take away from it If we had increased the intension of B, we should have produced the same result.
3. Next add to B an extension which A has not. You diminish its intension. You can not however leave it subordinated safe-

ordinate or cointesive with A. And supposing that there is a symbol which denotes any sum of symbols, there will be a symbol C to which both A and B are subordinate in extension. Hence, they will both be superordinate to it in intension and will have in common the intension of C. Hence they will intersect in intension.

If on the other hand we had added to A an intension excluded from B we should have diminished the extension of A without leaving it subordinate superordinate or coextensive with B. And supposing that any sum of intensions has some symbol to connote it, there will be a symbol C to which both A and B are subordinate in intension. Hence they will both be superordinate to it in extension or will intersect it in extension.

4. Next suppose that from the extensions of both A and B we take away that from which they have in common. This will only add to the intension of both as they cannot be subordinate superordinate or cointensive, they will still intersect in intension.

Or suppose they are made to exclude each other in intension then by the same reasoning, they would intersect in extension.

Hence since intersection in either quantity by (3) implies intersection in both it follows that when the suppositions of (3) there can be no exclusion either in extension or intension. But if there is no exclusion there is no coincidence or subordination since these imply exclusion (?) and hence nothing but intersection.

But the intension of C may be the only being which is the Summum Genus and the extension of C' may be only nothing which is the Infima Species. In the former case therefore they may be said to exclude each other in intension and in the latter case to exclude each other in extension. Then we have when information is constant --

If A and B exclude each other both in extension and intension their common extension is nothing and their common intension being.

Let us now change our implication. If we have no implication we shall have no [foundations?] of extension and intension. All connotation will be self-contradictory and all denotation will be obscure.

When implication is at a maximum every class will intersection in extension and intension will be abolished. Consequently subordination will be abolished. Consequently all classes will exclude each other and their common extension will be nothing and their common intension being.