This paper explores the suppression of ideas within academic scholarship by academics, either by self-suppression or because of the efforts of other academics. Legal, moral, and social issues distinguishing freedom of speech, freedom of inquiry, and academic freedom are reviewed. How these freedoms and protections can come into tension is then explored by a sociological analysis of denunciation mobs who exercise their legal free speech rights to call for punishing scholars who express ideas they disapprove of and condemn. When successful, these efforts, which constitute legally protected speech, will suppress certain ideas. Real-world examples over the past five years of academics who have been sanctioned or terminated for scholarship targeted by a denunciation mob are then explored.