Comment author:RobinZ
03 October 2012 08:06:04PM
1 point
[-]

I freely concede that a tree falling in the woods with no-one around makes acoustic vibrations, but I think it is relevant that it does not make any auditory experiences.

In retrospect, however, backtracking to the original comment, if "2+2=4" were replaced by "not(A and B) = (not A) or (not B)", I think my argument would be nearly untenable. I think that probably suffices to demonstrate that ArisKatsaris's theory of meaningfulness is flawed.

Comment author:dankane
03 October 2012 08:56:34PM
2 points
[-]

I freely concede that a tree falling in the woods with no-one around makes acoustic vibrations, but I think it is relevant that it does not make any auditory experiences.

How is it relevant? CCC was arguing that "2+2=4" was not true in some universes, not that it wouldn't be discovered or useful in all universes. If your other example makes you happy that's fine, but I think it would be possible to find hypothetical observers to whom De Morgan's Law is equally useless. For example, the observer trapped in a sensory deprivation chamber may not have enough in the way of actual experiences for De Morgan's Law to be at all useful in making sense of them.

Comment author:RobinZ
04 October 2012 04:20:04AM
1 point
[-]

In my opinion, saying "2+2=4 in every universe" is roughly equivalent to saying "1.f3 is a poor chess opening in every universe" - it's "true" only if you stipulate a set of axioms whose meaningfulness is contingent on facts about our universe. It's a valid interpretation of the term "true", but it is not the only such interpretation, and it is not my preferred interpretation. That's all.

Comment author:dankane
06 October 2012 12:27:12AM
*
2 points
[-]

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".

Comment author:RobinZ
06 October 2012 12:56:19AM
2 points
[-]

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.

## Comments (515)

BestI freely concede that a tree falling in the woods with no-one around makes acoustic vibrations, but I think it is relevant that it does not make any auditory experiences.

In retrospect, however, backtracking to the original comment, if "2+2=4" were replaced by "not(A and B) = (not A) or (not B)", I think my argument would be nearly untenable. I think that probably suffices to demonstrate that ArisKatsaris's theory of meaningfulness is flawed.

How is it relevant? CCC was arguing that "2+2=4" was not true in some universes, not that it wouldn't be discovered or useful in all universes. If your other example makes you happy that's fine, but I think it would be possible to find hypothetical observers to whom De Morgan's Law is equally useless. For example, the observer trapped in a sensory deprivation chamber may not have enough in the way of actual experiences for De Morgan's Law to be at all useful in making sense of them.

In my opinion, saying "2+2=4 in every universe" is roughly equivalent to saying "1.f3 is a poor chess opening in every universe" - it's "true" only if you stipulate a set of axioms whose meaningfulness is contingent on facts about

ouruniverse. It's a valid interpretation of the term "true", but it is not the only such interpretation, and it is not mypreferredinterpretation. That's all.*2 points [-]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.