Or, try this (I read it somewhere in relation to the BT Paradox). Take a balloon and fill it up with gas. So you have a balloon of a certain volume. Now decant the gas into two balloons, and you will get two balloons, each with half the volume of the original. But now reduce the air pressure in the room and you will get two balloons each with the same volume as the original. And keep going. Decant again into 4 balloons and reduce the air density by half again. Voila, 4 balloons of the same volume as the first one. And so on, to infinity.
If this sounds like a cheat to demonstrate the BT Paradox in reality, then maybe it is. But maybe the BT Paradox involves a cheat of a different kind, the dividing volumes up into abstract mathematical infinitesimals.
Except you will not get to infinity, you'll get to internal and external equilibrium pretty damn quickly.
As for BT, I'm, just not sure it's helpful to think about volumes in abstract objects with uncountable porosity.
However, it's not the maths I'm much interested in, it's merely the brute fact that there are things that can be done in the platonic spaces of mathematics and logic that cannot be done anywhere else. I think B-T establishes this (and more importantly, my middle kids, both, unlike me, rather fine mathematicians) assure me that this is the case. As this area is what youngest is doing his Phd on (at Cork) I'm pretty sure I'm on safe ground.
Once established, the philosophical knock on effects of proving that the logical and the physical are not isomorphic are pretty spectacular. It's an accessible route into anomalous monism, it establishes that even in a physical determinism fantasy world, we are bicameral, being potentially determined both logically and physically a fact that introduces some real elbow room...
More importantly, it demonstrates that, even in a respectably naturalistic ontology; that is one with no gaps suitable for hiding a god in, there are irreducibly emergent properties and no matter how fine the dissection, there are things that will be missed from the purely physical stance. Finally, it opens up a class of things that can be added to with more ease once the existence of the class has been demonstrated. Following Aristotle, Wittgenstein, Anscombe and even Dennett, pre 'Real Patterns', I'd like to suggest intentional states as a member of this class...
Because I'm not predictable at all
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