- #1

- 915

- 587

- TL;DR Summary
- Finite set of indistinguishables -- is axiom of choice required?

From Wikipedia entry on the Axiom of Choice:

[2] Is there any physical consequence of this axiom, i.e. is there any physics experiment where the calculations to predict the result must incorporate the axiom of choice, even indirectly? Perhaps some experiment involving identical particles, say?

[1] What about aBertrand Russell coined an analogy: for any (even infinite) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection; this makes it possible to directly define a choice function. For aninfinitecollection of pairs of socks (assumed to have no distinguishing features), there is no obvious way to make a function that selects one sock from each pair, without invoking the axiom of choice.

**finite**set of indistinguishable things (e.g. identical socks)? Do we**need**to invoke the axiom?[2] Is there any physical consequence of this axiom, i.e. is there any physics experiment where the calculations to predict the result must incorporate the axiom of choice, even indirectly? Perhaps some experiment involving identical particles, say?