In
lichess.org/forum/team-jomegas-tabia/layered-chess-concepts#3 I talked about some of the axiomatic ideas needed to understand checkmate. Actually there is one more idea needed to understand all of chess, and it is so fundamental that I only mentioned it in passing in #3. That idea is what a "move" is. Here I don't mean "turn"; I mean how you are changing the board on your "turn".
In the rules of chess there is talk of making a "move" when it actually cannot be done; i.e. it is illegal! Here is an example from the FIDE rules:
3.9.2 No piece can be moved that will either expose the king of the same colour to check or leave that king in check.
To understand that sentence you need to know what "moved" means. You'd think that would be simple; it is not. Since you already know the rules of chess, you know that there are "moves" that involving more than removing a single piece from one square and placing it on another square (occupied or not). Castling involves moving two pieces. Promotion involves moving a pawn, possibly with a capture, and then replacing it by another piece. Capturing en passant involves moving a pawn to another square and removing an opponent pawn that is *not* on the destination square! It is not until you have read all the rules of chess that you would finally know what "moved" means in 3.9.2. In other chess variants (say Atomic) the configuration of the board after your "move" can be radically different from what is was before your move.
Consider the case of a back rank mate with a Rook. The mated King cannot "legally move" because *if* it did move (in the sense I'm pointing out) then it would be on a square that *would then* be directly attacked by the Rook. That square may not have been directly attacked by the Rook prior to this attempt of the King to move.
Here is another example:
3.5 When making these moves, the bishop, rook or queen may not move over any intervening pieces.
Clearly the meaning of "moves" and "move" in this sentence not only involves the beginning and ending square of the man but also the squares "intervening".
Once this is realized, it becomes clear that from the beginning of the game the attempted "move" 1.Ng1-Ng3, which a novice beginner might try, has to be accounted for in the rules. It is accounted for by essentially stating which "moves" are legal.
These complications are, of course, academic. An understanding of this is necessary for programming a chess program and for game theoretic investigations as in
lichess.org/forum/team-jomegas-tabia/theoretical-chess?page=2#15. In that post, moves was given as a function
moves: DecisionNodes -> PowerSet(Moves). moves is a function that takes as argument a decision node and returns a set of the moves. Those moves are the allowed moves from that decision node per the rules of SCC.
In other words, the legal moves are given by the function "moves". As I pointed out in the above post, that function and its domain, along with the other sets used to define them, must be defined recursively because of the 3-time repetition rule.
You can marvel at the complexity required to have a chess program produce the legal set of moves for a chess position (at some point in a game), or for a mathematician to create a mathematical model that gives the legal moves, compared to how easily humans communicate the rules that allow us to know the legal moves.