When disputing game rules, or rules in general, one often hears the phrase "according to Hoyle". This is an appeal to authority, to a book of game rules first compiled by Edmund Hoyle. These games, such as chess, existed in earlier forms long before he compiled the rules. One might argue that there is an "essence" of chess, and a platonic form or ideal of chess, which pre-existed its discovery by humans. If this were true, how close are we to the ideal? Does it include a modern powerful queen? Castling? Of course, this kind of essentialism sounds silly. We understand the rules of chess were made up by humans, and that appeals to the authority of Hoyle are a matter of convention. There is no possibility of a science of empirical "discovery" of the rules of chess. Note observation of games also would not arrive at the rules, since for instance castling may never occur in the set of observed games. So statements about chess are not provisionally true, pending additional observations.

Geometry can also be viewed as a game played with specified rules. An initial set of postulates is chosen, and from them new theorems are derived. Euclid codified the first set of postulates, and for centuries Euclid was cited as the authority. Geometric figures became key examples in essentialism. Much later, with the invention of non-Euclidean geometry, it was discovered other starting postulates were possible.

The rules of mathematics are much more closely tied to science than the rules of chess, and seem much less arbitrary. Mathematical theorems are not provisionally true in the sense that new experimental data could overturn them. But they are provisionally true in the sense that errors could always be found in the proofs. And a connection between any particular mathematical system and the physical world is always provisional, pending new observations. The most prominent dispute, from the theory of general relativity, is whether the large scale geometry of spacetime is flat (Euclidean geometry) or curved (non-Euclidean). And this contradicts Kant's primary example of synthetic apriori knowledge -- things we know to be true independent of any observation of the world.

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