We know how to construct worlds with different physics. We do it all the time. Video games, or if you don’t accept that example we can construct a world consisting of 1 bit of information and 1 time dimension. This bit flips every certain increment of time. This universe obviously has different physics than ours.
Also as the other person mentioned, a probability space is the space of all possibilities organized based on whether statement Q is true, which is isomorphic to the space all universes consistent with your previous observations. There is, as far as I am aware, no way to logic yourself into the belief that pi could somehow have a different digit in a different universe, given you use a sufficiently exclusive definition of pi(specifying the curve of the plane the circle is upon being the major example)
We know how to construct worlds with different physics. We do it all the time. Video games, or if you don’t accept that example we can construct a world consisting of 1 bit of information and 1 time dimension. This bit flips every certain increment of time.
Technically true, but irrelevant to the point I’m making.
I was talking about constructing alternative worlds similar to ours to such degree that
I can inhabit either of them
I can be reasonably uncertain which one I inhabit
Both worlds are compatible with all my observations of a particular probability experiment—a coin toss
And yet, despite all of that in one world the coin comes Heads and in the other it comes Tails.
These are the type of worlds relevant for the discussions of probability experiments. We have no idea how to construct them, when talking about empiric uncertainty, and yet we don’t mind, only demanding such level of constructivism when dealing with logical uncertainty, for some reason.
There is, as far as I am aware, no way to logic yourself into the belief that pi could somehow have a different digit in a different universe, given you use a sufficiently exclusive definition of pi(specifying the curve of the plane the circle is upon being the major example)
Accent on sufficiently exclusive definition. Likewise, we can sufficiently exculisvily define a particular coin toss in a particular world and refuse to entertain the framing of different possible worlds : “No, the question is not about an abstract coin toss that could’ve ended differently in different possible worlds, the question is about this coin toss in this world”.
It’s just pretty clear in case of empirical uncertainty, that we should not be doing it, because such level of precision doesn’t capture our knowledge state. So why are we insisting on this level of exclusivity when talking about logical uncertainty?
In other words, this seems as an isolated demand for rigor to me.
We know how to construct worlds with different physics. We do it all the time. Video games, or if you don’t accept that example we can construct a world consisting of 1 bit of information and 1 time dimension. This bit flips every certain increment of time. This universe obviously has different physics than ours. Also as the other person mentioned, a probability space is the space of all possibilities organized based on whether statement Q is true, which is isomorphic to the space all universes consistent with your previous observations. There is, as far as I am aware, no way to logic yourself into the belief that pi could somehow have a different digit in a different universe, given you use a sufficiently exclusive definition of pi(specifying the curve of the plane the circle is upon being the major example)
Technically true, but irrelevant to the point I’m making.
I was talking about constructing alternative worlds similar to ours to such degree that
I can inhabit either of them
I can be reasonably uncertain which one I inhabit
Both worlds are compatible with all my observations of a particular probability experiment—a coin toss
And yet, despite all of that in one world the coin comes Heads and in the other it comes Tails.
These are the type of worlds relevant for the discussions of probability experiments. We have no idea how to construct them, when talking about empiric uncertainty, and yet we don’t mind, only demanding such level of constructivism when dealing with logical uncertainty, for some reason.
Accent on sufficiently exclusive definition. Likewise, we can sufficiently exculisvily define a particular coin toss in a particular world and refuse to entertain the framing of different possible worlds : “No, the question is not about an abstract coin toss that could’ve ended differently in different possible worlds, the question is about this coin toss in this world”.
It’s just pretty clear in case of empirical uncertainty, that we should not be doing it, because such level of precision doesn’t capture our knowledge state. So why are we insisting on this level of exclusivity when talking about logical uncertainty?
In other words, this seems as an isolated demand for rigor to me.