New Defender's Study Bible Notes
26:4 Answer not a fool. Proverbs 26:4,5, appears superficially to be in direct contradiction, but obviously the writer did not think of these as conflicting instructions, for he placed them back-to-back.
26:5 Answer a fool. When a person is given to foolish skeptical arguments related to God and His Word, it is a waste of time to argue with him. If, however, he is influencing others and becoming self-important in his delusion, it may be necessary to show up his folly by solid evidence.