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I'm not quite clear as to exactly how how Wittgenstein concludes that metaphysical/non-phenomenal talk is meaningless in his Tractatus. Doesn't a statement like, "God exists" and its propositional content make a claim about the world just like the sentence, "The cat is on the mat"?

To Wittgenstein, what keeps sentences like "God exists" or "Absolute Spirit is perfect" from being meaningful, and why?

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See:

6.41 The sense of the world must lie outside the world. In the world everything is as it is, and everything happens as it does happen: in it no value exists—and if it did exist, it would have no value.

Here W speaks of ethics, but we may apply it also to theology.

6.432 How things are in the world is a matter of complete indifference for what is higher. God does not reveal himself in the world.

6.4321 The facts all contribute only to setting the problem, not to its solution.

6.44 It is not how things are in the world that is mystical, but that it exists.

6.5 When the answer cannot be put into words, neither can the question be put into words. The riddle does not exist. If a question can be framed at all, it is also possible to answer it.

[...] 6.52 We feel that even when all possible scientific questions have been answered, the problems of life remain completely untouched. Of course there are then no questions left, and this itself is the answer.

So, it seems, the "meaningful" (i.e. scientific) questions are those related to the facts in the world. We can "speak of" them with our language and thus - in principle - we can answer them.

But we have here also a distinction between "questions" (the scientific, i.e. legitimate ones) and "problems", that remain untouched by science, like ethics and theology; here is the place for the mystical:

6.522 There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical.

Frankly speaking, the link from the theory of language to the "philosopical" problems that stay outside the language, seems feeble to me.

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