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Does it follow that if I make the statement "X must be consistent with Y" that "Y must be consistent with X"?

I'm hoping to hear this answered from a linguistics perspective, specifically related to information packaging and the use of the modal. I fear that this community may say "this isn't a good English question" just as much as the mathematics community might say "this isn't a good math question."

I've omitted the context here intentionally because the context itself is a bigger can of worms. What we can know from the structure itself: are these equivalent forms, or is this a false equality?

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    It depends totally on what you mean by the predicate (be) consistent. This is not a well-defined term. If what you mean is always a reciprocal relation, the answer is yes. If not, no. This is a logic question, and first you have to define your terms. Carefully. As for the modal, it seems a standard usage; but only with a defined predicate and a defined obligation. – John Lawler Jan 21 '14 at 16:32
  • It's actually a philosophy question. philosophy.stackexchange.com – Chris Sunami Jan 21 '14 at 17:51
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No, it does not follow. The relationship "must be consistent with" can impose an obligation and it can be such that only one half of the relationship is capable of having obligations imposed on it.

For example, "your writing must be consistent with the rules", can mean that you have an obligation to comply with the rules. While "the rules must be consistent with your writing" can mean that the rules have an obligation to conform to your writing, which they don't.

It is also possible that "your writing must be consistent with the rules" can mean that you have an obligation to ensure that your writing and the rules agree, possibly by changing your writing, possibly by changing the rules, but it need not be this way.

It comes down to precisely what "must be consistent with" means in the specific use case we're talking about. They could denote a logically symmetric relationship, but they could also denote an asymmetric relationship.

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