This is something that is often misunderstood by the “casual” reader of the Bible. However, Roy Deaver wrote a great section in a book on this matter.  This section of the article is where we will answer the question “What is inference?” He [Roy Deaver] makes this statement in the book,
 

“Brethren often speak of “inference,” but “inference” relates to “implication.” Inference deals with correct reasoning, but correct reasoning (in this context) with regards to what God has implied. Everything the bible teaches it teaches either explicitly or implicitly. And, that which it teaches implicitly is just as true, just as binding, just as authoritative, as is that which it teaches explicitly.”

Also looking to D.R. Dungan he makes this statement concerning “inference”,
 

“The truth is, it is the logical effort to know the facts in the case, and to ascertain the facts from phenomena. Certain things seem to have been done; were they done or not? May require the best effort of the mind to determine. This is done by associating the whole number of things which are known, and reaching conclusions, in a logical way, as to what else was done or said at the time, or in connection therewith.” (D.R. Dungan, Hermeneutics, pg. 91).

Irving M. Copi made this statement in his book “Introduction to Logic”.
 

“Any inference is the drawing of a conclusion from one or more premises.”

There are many statements of “inference” in the Bible. He that believeth and is baptized shall be saved. . . (Mark 16:16). This is a statement of inference. It does not explicitly state “who” [giving specific names] should be baptized, but it “infers” that anyone that is going to be saved has to be baptized into Christ. D.R. Dungan again states this example of inference.
 

“If we read in the book of Joshua that the conquering army did to certain kings just what they did to the king of Jericho, and we learn that they hanged those kings, though nothing be said about what they did to the king of Jericho at the time they took that city, yet we infer that they hanged him. We have the necessary premises, and can not reach any other conclusion.” (D.R. Dungan, Hermeneutics, pg. 92).

Another example of “inference” is the case of Saul of Tarsus is: By “inference” one can teach that Saul “repented” of his sins, yet we have nowhere in the Bible that it is explicitly stated Saul repented, but by implication we know he did. If (A) it is the case that no person can become a Christian without repenting of his sins; and if (B) it is the case that Saul of Tarsus did become a Christian; then, (C) it is the case that Saul of Tarsus, in becoming a Christian did repent of his sins.  (Luke 13:3, Acts 2:38, and Acts 17:30).   Simply it is that “inference” that is binding because the things that are written in the Bible are “the all inspired words of God” (II Timothy 3:16-17).  Whatever God says specifically or by implication (inference) mankind must abide by. A man once said, “God said it, therefore I believe it” and we thus say, This is certainly true even if by implication.

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