If this is the case, then I’m confused as to what you mean by “true”. Let’s consider the statement “In the standard initial configuration in chess, there’s a helpmate in 2″. I imagine that you consider this analogous to your example of a statement about chess, but I am more comfortable with this one because it’s not clear exactly what a “poor move” is.
Now, if we wanted to explain this statement to a being from another universe, we would need to taboo “chess” and “helpmate” (and maybe “move”). The statement then unfolds into the following: ”In the game with the following set of rules… there is a sequence of play that causes the game to end after only two turns are taken by each player” Now this statement is equivalent to the first, but seems to me like it is only more meaningful to us than it is to anyone else because the game it describes matches a game that we, in a universe where chess is well known, have a non-trivial probability of ever playing. It seems like you want to use “true” to mean “true and useful”, but I don’t think that this agrees with what most people mean by “true”.
For example, there are infinitely many true statements of the form “A+B=C” for some specific integers A,B,C. On the other hand, if you pick A and B to be random really large numbers, the probability that the statement in question will ever be useful to anyone becomes negligible. On the other hand, it seems weird to start calling these statements “false” or “meaningless”.
It seems like you want to use “true” to mean “true and useful”, but I don’t think that this agrees with what most people mean by “true”.
You’re right, of course. To a large extent my comment sprung from a dislike of the idea that mathematics possesses some special ontological status independent of its relevance to our world—your point that even those statements which are parochial can be translated into terms comprehensible in a language fitted to a different sort of universe pretty much refutes that concern of mine.
If this is the case, then I’m confused as to what you mean by “true”. Let’s consider the statement “In the standard initial configuration in chess, there’s a helpmate in 2″. I imagine that you consider this analogous to your example of a statement about chess, but I am more comfortable with this one because it’s not clear exactly what a “poor move” is.
Now, if we wanted to explain this statement to a being from another universe, we would need to taboo “chess” and “helpmate” (and maybe “move”). The statement then unfolds into the following:
”In the game with the following set of rules… there is a sequence of play that causes the game to end after only two turns are taken by each player”
Now this statement is equivalent to the first, but seems to me like it is only more meaningful to us than it is to anyone else because the game it describes matches a game that we, in a universe where chess is well known, have a non-trivial probability of ever playing. It seems like you want to use “true” to mean “true and useful”, but I don’t think that this agrees with what most people mean by “true”.
For example, there are infinitely many true statements of the form “A+B=C” for some specific integers A,B,C. On the other hand, if you pick A and B to be random really large numbers, the probability that the statement in question will ever be useful to anyone becomes negligible. On the other hand, it seems weird to start calling these statements “false” or “meaningless”.
You’re right, of course. To a large extent my comment sprung from a dislike of the idea that mathematics possesses some special ontological status independent of its relevance to our world—your point that even those statements which are parochial can be translated into terms comprehensible in a language fitted to a different sort of universe pretty much refutes that concern of mine.