The Greek adjective alogos (ἄλογος) means without reason or logic — composed of the alpha-privative and logos (word, reason). It is applied to animals (irrational creatures) and to behavior that is contrary to sound reasoning.
Peter and Jude both use alogos to describe those who live according to animal instinct rather than divine wisdom (2 Peter 2:12; Jude 10) — like irrational animals, creatures of instinct. The distinguishing mark of a creature made in God's image is the capacity for logos — reason ordered toward God. To abandon reason for instinct is to deny one's dignity as an image-bearer. Wisdom, by contrast, is logos in its highest form: the Word who is God (John 1:1).