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# The statement ‘α exists’ proven or otherwise doesn’t say anything about the world; it is just a play on words.
Much akin to the reasoning the analytic/synthetic distinction uses, it is impossible, according to Hume, for a proposition not to fall within the distinction. In Hume’s eyes, such a proposition is would be completely meaningless as failing to . Such a proposition would not be a rational or reasonable endeavour at all.
=== Problem of Induction ===
The problem of induction stems from the reasoning behind causal inference. Given the previous distinction established between relations of ideas and matters of fact the connection must be established by either one or the other. With this in mind, Hume established that causal inference cannot be a relation of ideas, and so must be a matter of fact.
