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,
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 co-ordination of a fact and an object, but a co-ordination of facts by means of a co-ordination 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 off-hand.
(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 pre-eminent 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.
5.5562
If we know on purely logical grounds, that there must be elementary propositions, then this must be known by everyone who understands propositions in their unanalysed form.
5.5563
All propositions of our colloquial language are actually, just as they are, logically completely in order. That simple thing which we ought to give here is not a model of the truth but the complete truth itself.
(Our problems are not abstract but perhaps the most concrete that there are.)
5.557
The application of logic decides what elementary propositions there are.
What lies in its application logic cannot anticipate.
It is clear that logic may not conflict with its application.
But logic must have contact with its application.
Therefore logic and its application may not overlap one another.
5.5571
If I cannot give elementary propositions a priori then it must lead to obvious nonsense to try to give them
5.6
The limits of my language mean the limits of my world.
5.61
Logic fills the world: the limits of the world are also its limits.
We cannot therefore say in logic: This and this there is in the world, that there is not.
For that would apparently presuppose that we exclude certain possibilities, and this cannot be the case since otherwise logic must get outside the limits of the world: that is, if it could consider these limits from the other side also.
What we cannot think, that we cannot think: we cannot therefore say what we cannot think.
5.62
This remark provides a key to the question, to what extent solipsism is a truth.
In fact what solipsism means, is quite correct, only it cannot be said, but it shows itself.
That the world is my world, shows itself in the fact that the limits of the language (the language which I understand) mean the limits of my world.
5.621
The world and life are one.
5.63
I am the world. (The microcosm)
5.631
The thinking, presenting subject; there is no such thing.
If I wrote a book "The world as I found it", I should also have therein to report on my body and say which members obey my will and which do not, etc. This then would be a method of isolating the subject or rather of showing that in an important sense there is no subject: that is to say, of it alone in this book mention could not be made.
5.632
The subject does not belong to the world but it is a limit of the world.
5.633
Where in the world is a metaphysical subject to be noted?
You say that this case is altogether like that of the eye and the field of sight. But you do not really see the eye.
And from nothing in the field of sight can it be concluded that it is seen from an eye.
5.6331
For the field of sight has not a form like this:
5.634
This is connected with the fact that no part of our experience is also a priori.
Everything we see could also be otherwise.
Everything we describe at all could also be otherwise.
There is no order of things a priori.
5.64
Here we see that solipsism strictly carried out coincides with pure realism. The I in solipsism shrinks to an extensionless point and there remains the reality co-ordinated with it.
5.641
There is therefore really a sense in which the philosophy we can talk of a non-psychological I.
The I occurs in philosophy through the fact that the "world is my world".
