What is the opposite of a "false positive"?

There is not simply one "opposite" to a false positive; Wikipedia has a good summary of the types of statistical errors.

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Your question doesn't make sense, logically: the data contains four things, in this context:

  1. true positives
  2. false positives
  3. true negatives
  4. false negatives

If we remove the false positives we're left with

  1. true positives
  2. true negatives
  3. false negatives

This isn't "the opposite of false positives". It's just the data minus the false positives.