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 my 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 coordinated 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.”
The philosophical I is not the man, not the human body or the human soul of which psychology treats, but the metaphysical subject, the limit—not a part of the world.
6
The general form of truth-function is: [p‾,ξ‾,N(ξ‾)].
This is the general form of proposition.
6.001
This says nothing else than that every proposition is the result of successive applications of the operation N′(ξ‾) to the elementary propositions.
6.002
If we are given the general form of the way in which a proposition is constructed, then thereby we are also given the general form of the way in which by an operation out of one proposition another can be created.
6.01
The general form of the operation Ω′(η‾) is therefore: [ξ‾,N(ξ‾)]′(η‾)(=[η‾,ξ‾,N(ξ‾)]).
This is the most general form of transition from one proposition to another.
6.02
And thus we come to numbers: I define
x=Ω0′x Def. and
Ω ′ Ω ν ′ x = Ω ν + 1 ′ x Def.
According, then, to these symbolic rules we write the series x,Ω′x,Ω′Ω′x,Ω′Ω′Ω′x,… as: Ω0′x,Ω0+1′x,Ω0+1+1′x,Ω0+1+1+1′x,…
Therefore I write in place of “[x,ξ,Ω′ξ]”,
“[Ω0′x,Ων′x,Ων+0′x]”.
And I define:
0 + 1 = 1 Def.
0 + 1 + 1 = 2 Def.
0 + 1 + 1 + 1 = 3 Def.
and so on.
6.021
A number is the exponent of an operation.
6.022
The concept number is nothing else than that which is common to all numbers, the general form of a number.
The concept number is the variable number.
And the concept of equality of numbers is the general form of all special equalities of numbers.
6.03
The general form of the
