5.535
So all problems disappear which are connected with such pseudo-propositions.
This is the place to solve all the problems with arise through Russell’s “Axiom of Infinity.”
What the axiom of infinity is meant to say would be expressed in language by the fact that there is an infinite number of names with different meanings.
5.5351
There are certain cases in which one is tempted to use expressions of the form “a=a” or “p⊃p”. As, for instance, when one would speak of the archetype Proposition, Thing, etc. So Russell in the Principles of Mathematics has rendered the nonsense “p is a proposition” in symbols by “p⊃p” and has put it as hypothesis before certain propositions to show that their places for arguments could only be occupied by propositions.
(It is nonsense to place the hypothesis p⊃p before a proposition in order to ensure that its arguments have the right form, because the hypotheses for a non-proposition as argument becomes not false but meaningless, and because the proposition itself becomes senseless for arguments of the wrong kind, and therefore it survives the wrong arguments no better and no worse than the senseless hypothesis attached for this purpose.)
5.5352
Similarly it was proposed to express “There are no things” by “~(∃x).x=x”. But even if this were a proposition—would it not be true if indeed “There were things,” but these were not identical with themselves?
5.54
In the general propositional form, propositions occur in a proposition only as bases of the truth-operations.
5.541
At first sight it appears as if there were also a different way in which one proposition could occur in another.
Especially in certain propositional forms of psychology, like “A thinks, that p is the case,” or “A thinks p”, etc.
Here it appears superficially as if the proposition p stood to the object A in a kind of relation.
(And in modern epistemology (Russell, Moore, etc.) those propositions have been conceived in this way.)
5.542
But it is clear that “A believes that p,” “A thinks p,” “A says p,” are of the form “ ‘p’ says p”: and here we have no coordination of a fact and an object, but a coordination of facts by means of a coordination of their objects.
5.5421
This shows that there is no such thing as the soul—the subject, etc.—as it is conceived in superficial psychology. A composite soul would not be a soul any longer.
5.5422
The correct explanation of the form of the proposition “A judges p” must show that it is impossible to judge a nonsense. (Russell’s theory does not satisfy this condition.)
5.5423
To perceive a complex means to perceive that its constituents are combined in such and such a way.
This perhaps explains that the figure
can be seen in two ways as a cube; and all similar phenomena. For we really see two different facts.
(If I fix my eyes first on the corners a and only glance at b, a appears in front and b behind, and vice versa.)
5.55
We must now answer a priori the question as to all possible forms of the elementary propositions. The elementary proposition consists of names. Since we cannot give the number of names with different meanings, we cannot give the composition of the elementary proposition.
5.551
Our fundamental principle is that every question which can be decided at all by logic can be decided offhand. (And if we get into a situation where we need to answer such a problem by looking at the world, this shows that we are on a fundamentally wrong track.)
5.552
The “experience” which we need to understand logic is not that such and such is the case, but that something is; but that is no experience.
Logic precedes every experience—that something is so.
It is before the How, not before the What.
5.5521
And if this were not the case, how could we apply logic? We could say: if there were a logic, even if there were no world, how then could there be a logic, since there is a world?
5.553
Russell said that there were simple relations between different numbers of things (individuals). But between what numbers? And how should this be decided—by experience?
(There is no preeminent number.)
5.554
The enumeration of any special forms would be entirely arbitrary.
5.5541
How could we decide a priori whether, for example, I can get into a situation in which I need to symbolize with a sign of a 27-termed relation?
5.5542
May we then ask this at all? Can we set out a sign form and not know whether anything can correspond to it?
Has the question sense: what must there be in order that anything can be the case?
5.555
It is clear that we have a concept of the elementary proposition apart from its special logical form.
Where, however, we can build symbols according to a system, there this system is the logically important thing and not the single symbols.
And how would it be possible that I should have to deal with forms in logic which I can invent: but I must have to deal with that which makes it possible for me to invent them.
5.556
There cannot be a hierarchy of the forms of the elementary propositions. Only that which we ourselves construct can we foresee.
5.5561
Empirical reality is limited by the totality of objects. The boundary appears again in the totality of elementary propositions.
The hierarchies are and must be independent of reality.
