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But is that a falsifiable claim about a proposition, or the identity itself (in those cases where the claim is not false)? The Platonist in me suspects that the

But is that a falsifiable claim about a proposition, or the identity itself (in those cases where the claim is not false)? The Platonist in me suspects that these are different things, though I could probably be induced to change my mind by a persuasive counter-argument.

whatshisface 8y ago
The Platonist idea that mathematical statements correspond to something "out there" in metaphysical space is a great example of an idea that's not falsifiable. However that's not an idea that I would consider part of mathematics.
- mannykannot 8y ago
  That's a good point, though I don't think you have to be a Platonist to think that a claim about a proposition is not the same as that proposition. It occurred to me this morning that one idea, that is looked on with interest by scientifically- and technically-minded people, is that we're living in a simulation. While there are ways that the truth of this might become apparent, I am not sure it is falsifiable, and that might be good reason to ignore it, but it is not simply a meaningless idea.
  - whatshisface 8y ago
    >it is not simply a meaningless idea. When you think of a simulation, you might imagine a programmer, some server racks, and maybe a broader purpose. However you also have to include the possibility that the simulation popped into existence out of nothing, that the simulation is mathematically inevitable, that God created the simulation, that the simulation was created by beings that live in simulation... In so many words, the idea that you live in a simulation leaves as many options open as the idea that you live in the universe. You don't get any claims about how the simulation got there, how it behaves, or even what it is Maybe it is a meaningless idea.
    - mannykannot 8y ago
      Insofar as your objections are meaningful (in particular, I am not so sure about the last), it would seem they could equally be raised about non-simulation physical theories of the universe. Would that make those meaningless? I would think that, on the contrary, the fact that you can raise these objections indicates that the simulation hypothesis is not without meaning, as does Scott Aaronson's argument that it is unfalsifiable[1] (note: he is not saying that that it is meaningless), and as does Bostrom's argument that if it is possible, we are likely in a simulation[2]. [1] https://www.scottaaronson.com/blog/?p=3482 https://www.scottaaronson.com/blog/?p=3482 [2] https://www.simulation-argument.com/simulation.html https://www.simulation-argument.com/simulation.html

whatshisface 8y ago

The Platonist idea that mathematical statements correspond to something "out there" in metaphysical space is a great example of an idea that's not falsifiable. However that's not an idea that I would consider part of mathematics.

mannykannot 8y ago
That's a good point, though I don't think you have to be a Platonist to think that a claim about a proposition is not the same as that proposition. It occurred to me this morning that one idea, that is looked on with interest by scientifically- and technically-minded people, is that we're living in a simulation. While there are ways that the truth of this might become apparent, I am not sure it is falsifiable, and that might be good reason to ignore it, but it is not simply a meaningless idea.
- whatshisface 8y ago
  >it is not simply a meaningless idea. When you think of a simulation, you might imagine a programmer, some server racks, and maybe a broader purpose. However you also have to include the possibility that the simulation popped into existence out of nothing, that the simulation is mathematically inevitable, that God created the simulation, that the simulation was created by beings that live in simulation... In so many words, the idea that you live in a simulation leaves as many options open as the idea that you live in the universe. You don't get any claims about how the simulation got there, how it behaves, or even what it is Maybe it is a meaningless idea.
  - mannykannot 8y ago
    Insofar as your objections are meaningful (in particular, I am not so sure about the last), it would seem they could equally be raised about non-simulation physical theories of the universe. Would that make those meaningless? I would think that, on the contrary, the fact that you can raise these objections indicates that the simulation hypothesis is not without meaning, as does Scott Aaronson's argument that it is unfalsifiable[1] (note: he is not saying that that it is meaningless), and as does Bostrom's argument that if it is possible, we are likely in a simulation[2]. [1] https://www.scottaaronson.com/blog/?p=3482 https://www.scottaaronson.com/blog/?p=3482 [2] https://www.simulation-argument.com/simulation.html https://www.simulation-argument.com/simulation.html