D.A. Carson defines the negative inference fallacy in this way: “It does not necessarily follow that if a proposition is true, a negative inference from that proposition is also true.” D.A. Carson, Exegetical Fallacies (Grand Rapids, MI: Baker Books, 1996), p.101. Consider some examples of this fallacy:
(1) “All the basketball players were exercising at the gym. Therefore, no one else was exercising there.”
(2) “Jeff hates broccoli. Therefore, he likes every other kind of vegetable.”
(3) “Jesus gave an exception for divorce. Therefore, there are no other exceptions for divorce.”
These are all examples of the “negative inference fallacy,” and it does not logically follow. A way to avoid the fallacy is to change or add the word “only” to the major premise of the argument or proposition (i.e. “Only the basketball players…”).