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Sorry if this seems like a silly question. For all statements, is it possible to determine whether they are falsifiable or not? Is it possible to create a statement which we do not know is falsifiable? I.e. is there a statement B such that for any statement A, the statement B "statement A is falsifiable" is itself not falsifiable?

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    To clarify, do you mean not falsifiable now, or not falsifiable in some permanent way? There may be all kinds of statements that we cannot falsify now, but we don't know whether some way to falsify them will become available in future.
    – Bumble
    Oct 8, 2020 at 0:45
  • I'm miserable at math and logic, but I'd think unsolvable math problems or random numbers, or even pi, could be turned into statements where falsifiability is, in principle, not decidable. Oct 12, 2020 at 20:07
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    Are there in-principle unsolvable math problems? Oct 13, 2020 at 21:19

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Yeah, sure. Any proposition about which we don't know whether it is in-principle falsifiable or not is of the kind of propositions you are thinking of. If you ask me for examples...

I'm not sure that this is a legitimate example, but just heuristically, think of the following: the proposition that we live in a simulation. I imagine that if the simulation and its security code were good enough, there would be no possible way for the entities in the simulation to discover by themselves that they live in a simulation, so depending on how good the simulation is, the proposition that we live in a simulation might be unfalsifiable for us, we just don't know.

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    Yes, if you can give an example that would help me understand. Oct 12, 2020 at 2:20
  • @zfj3ub94rf576hc4eegm Well, not sure that this is a legitimate example, but just heuristically, think of the following: the proposition that we live in a simulation. I imagine that if the simulation and its security code were good enough, there would be no possible way for the entities in the simulation to discover by themselves that they live in a simulation, so depending on how good the simulation is, the proposition that we live in a simulation might be unfalsifiable for us, we just don't know. Oct 12, 2020 at 12:16

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