EXAMPLE:
1) “Ella” is Darrell’s daughter.
2) “Lilly” is Darrell’s daughter.
3) Therefore, “Noel” is not Darrell’s daughter.
Obviously, “Darrell” could theoretically have had a third daughter named “Noel,” and he does. However, if the primary premise had established that Darrell only had two daughters, then a case could have been made to conclude (3), which of course we now know would have been erroneous.
Calvinists make a Negative Inference Fallacy for the Calvinist doctrine of a Limited Atonement:
1) Jesus died for the “Church.”
2) Jesus died for His “sheep.”
3) Therefore, Jesus died for no one else.
Obviously, Jesus could theoretically have died for more, such as the numerous verses which state that Christ died for “the world.” (John 3:16) Proponents of a Limited Atonement would like to have started with a primary premise that Jesus only died for the elect, but that would be problematic, since that is the conclusion that proponents are instead trying to prove, rather than to simply assert. There is no verse that would afford Calvinists the opportunity to biblically establish a primary premise that Jesus did not die for all, or that Jesus died only for the elect. So Calvinists are thus often found committing a Negative Inference Fallacy in order to argue in defense of a Limited Atonement.