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.

Original German:Die Logik erfüllt die Welt; die Grenzen der Welt sind auch ihre Grenzen. Wir können also in der Logik nicht sagen: Das und das gibt es in der Welt, jenes nicht.Das würde nämlich scheinbar voraussetzen, dass wir gewisse Möglichkeiten ausschließen, und dies kann nicht der Fall sein, da sonst die Logik über die Grenzen der Welt hinaus müsste; wenn sie nämlich diese Grenzen auch von der anderen Seite betrachten könnte. Was wir nicht denken können, das können wir nicht denken; wir können also auch nicht sagen, was wir nicht denken können.

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.

I don't know whether this world has a meaning that transcends it. But I know that I cannot know that meaning and that it is impossible for me just now to know it. What can a meaning outside my condition mean to me? I can understand only in human terms. What I touch, what resists me — that I understand. And these two certainties — my appetite for the absolute and for unity and the impossibility of reducing this world to a rational and reasonable principle — I also know that I cannot reconcile them. What other truth can I admit without lying, without bringing in a hope I lack and which means nothing within the limits of my conditions?

The limits of my language mean the limits of my world. (5.6)

[Philosophy] must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards through what can be thought.

... for as the reality of light cannot be proved or described in terms of visible shape, the reality of the infinite cannot be proved in terms of the finite. For this reason every attempt to prove the existence of God by logic is a foregone failure. Logic cannot reach God. It may travel backwards in time from effect to cause, effect to cause, but as long as it stays in time, as it must, it cannot touch the eternal. That which doesn't not begin with the infinite cannot end with it.

The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations.

We here touch one instance of Wittgenstein’s fundamental thesis, that it is impossible to say anything about the world as a whole, and that whatever can be said has to be about bounded portions of the world.

These are the limits of the scientific method and of logic itself, insofar as they must rely on language. Our words are built on the objects of our experience. They have acquired their effectiveness by adapting themselves to the occurrences of our everyday world. But when we approach realities of another scale, these words can become obstacles.

"It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an "illogical" world would look like."

Not all possibilities are open to us. The world is finite; our hopes spill over its rim.

Logic is not a theory but a reflexion of the world.

The logical formula: A is both A and Not-A, corresponds to the mathematical formula: A magnitude can be greater or less than itself. The absurdity of both these propositions shows that they cannot refer to our world. Of course absurdity, as such, is indeed not an index of the attributes of noumena, but the attributes of noumena will certainly be expressed in what are absurdities to us. To hope to find in the world of causes anything logical from our standpoint is just as useless as to think that the world of things can exist in accordance with the laws of a world of shadows or stereometry according to the laws of planimetry. To master the fundamental principles of higher logic means to master the fundamentals of the understanding of a space of higher dimensions, or of the world of the wondrous. In order to approach to a clear understanding of the relations of the multi-dimensional world, we must free ourselves from all the "idols" of our world, as Bacon calls them, i.e., from all obstacles to correct receptivity and reasoning. Then we shall have taken the most important step toward an inner affinity with the world of the wondrous.