someone who already understands the game and gradually introduces me to the rules, intermixed with practice of the perceptual and motor skills involved in playing chess on a board with a particular set of pieces.) But as time goes on, I begin to simply see pawns and knights as capable of particular types of movement, and of the state of play as affording particular types of strategic development. As this progresses, I am clearly developing some type of internalized understanding of chess, involving an applied understanding of the rules. This is not the same as memorizing the rulebook, though I may do that as well. A person can memorize the rulebook without understanding how to apply its principles properly, and one can learn to apply the principles without memorizing the rules. One does end up with some form of understanding that mirrors the rules, but this understanding need not involve any reflection on the rules. They are no longer objects of attention. Rather, we perceive the board through a kind of cognitive template that has been shaped by the rules. We might even say that this sort of no-longer-conscious understanding of chess amounts to have a kind of understanding” that is, one in “chess-shaped – which various types of mental representations and operations have the same abstract form as the principles of the game. Understanding seems to require a mental model of the game, which in turn involves a number of kinds of abilities. At very least these would include a way of representing the board as a geometrically and topologically describable space of possible piece-positions along with an understanding that at most one piece may occupy a square at any one time, representational types for types of pieces and permissive rules for their movement, definition of an initial state, and rules for
someone who already understands the game and gradually introduces me to the rules, intermixed with practice of the perceptual and motor skills involved in playing chess on a board with a particular set of pieces.) But as time goes on, I begin to simply see pawns and knights as capable of particular types of movement, and of the state of play as affording particular types of strategic development. As this progresses, I am clearly developing some type of internalized understanding of chess, involving an applied understanding of the rules. This is not the same as memorizing the rulebook, though I may do that as well. A person can memorize the rulebook without understanding how to apply its principles properly, and one can learn to apply the principles without memorizing the rules. One does end up with some form of understanding that mirrors the rules, but this understanding need not involve any reflection on the rules. They are no longer objects of attention. Rather, we perceive the board through a kind of cognitive template that has been shaped by the rules. We might even say that this sort of no-longer-conscious understanding of chess amounts to have a kind of “chess-shaped understanding” – that is, one in which various types of mental representations and operations have the same abstract form as the principles of the game. Understanding seems to require a mental model of the game, which in turn involves a number of kinds of abilities. At very least these would include a way of representing the board as a geometrically and topologically describable space of possible piece-positions along with an understanding that at most one piece may occupy a square at any one time, representational types for types of pieces and permissive rules for their movement, definition of an initial state, and rules for