Yes, I can see. I suppose it makes the logic easier but I wonder if it's accurate.
I'm sorry, but your thinking doesn't make sense. A definition only needs to be valid, there is no notion of "accuracy".
Given the set S of legal states s in chess where white is to move, each s of which has a non-empty set of legal moves M(s), a deterministic strategy for white is a mapping f from S where f(s) is always a member of M(s).
That definition is valid because it determines whether something is a deterministic strategy for white or not.
I think I know what you're saying. It's a way of defining determinism itself. However, determinism isn't shown to define chess and so there seem to be double-standards at play here. You're saying that you can define something into existence. This may be acceptable to mathematicians but then that existence only holds for the specific paradigm and only works if it can be cancelled out at the other end. But here you're making a statement, regarding the nature of chess, which is similar in type to those you condemn from tygxc.
It's far from convincing. You would have to do much better than that.
No, you don't understand.
The definitions of deterministic strategy was made in order to be able to define the value of strategies and positions.
The definition of value of a position was made in order to be able to state a proposition like:
"The value of the position after 1. Nh3 is less than or equal to the value of the position after 1. Nf3".
This is the routine way in which mathematics (and very closely related subjects) are done. You can't shortcut it except if everyone is so familiar with the topics that it is obvious without being said. That is not true in this forum!
I'm sorry, but your thinking doesn't make sense. A definition only needs to be valid, there is no notion of "accuracy".>>
Probably in the same way that it's ok to define 1. e4 e5 2. Ba6 as losing for white. Glad that's sorted, anyway.
No, that is a good example of what is not ok.
Asserting an unresolved proposition as an axiom (which is what you are suggesting - nothing to do with definition, which is about labelling, not truth) may cause inconsistency. To be safe, you need to prove relative consistency. In this case this requires proving the result that you (extremely eccentrically) wish to use as an axiom!
Understand the difference between an axiom, a proposition and a definition?
[Please note that your own posts demonstrate why it is necessary to be precise about these things, rather than what you suggest].