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In mathematical/scientific texts, conditions that are true (within context) are said to

  • hold
  • be satisfied
  • obtain

(the last one was news for me)

My question is whether there is nuance in meaning among the three versions or are these completely interchangeable (within this specific meaning referring to conditions) and are meant to be frequently interchanged to avoid repetition.

I did check NGrams for relative frequencies of these, but it doesn't tell me anything about difference in meaning.

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Well, no; you need a dictionary for differences in meaning. – Andrew Leach Jun 5 '13 at 9:10
Or for nuances like these, a lot of examples from accepted authorities (accepted wrt scientific and linguistic accuracy). I'd say, off the top of my head, that the three terms are often interchangeable (and 'apply' is another near-synonym) when talking about physical laws / rules. 'Be satisfied' can also be used when talking about requisite physical conditions etc (the required temperature / pressure ranges for a reaction to proceed, say), and the other three (though rarely 'hold') for talking about any existing physical conditions etc one encounters during observed events. – Edwin Ashworth Jun 5 '13 at 9:33
up vote 3 down vote accepted
  • If a condition holds, it still exists
  • If a condition is satisfied, then all necessary features or qualities are present
  • If a condition obtains, it "exists, is used, or is accepted"

Saying that a condition obtains is more formal and academic, and is marked as such in the dictionary reference cited.

Saying that a condition is satisfied may or may not imply that it wasn't previously.

Saying that a condition holds implies its continued persistence.

However, in the context of trying to say that the condition is true, and continues to be so, all of these terms are more or less interchangeable. I wouldn't vary them simply for the sake of avoiding repetition; I would revise my writing so it wasn't necessary to assert that the condition is true so often.

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