ak-nol'-ej (gignosko):

To declare that one recognizes the claims of a person or thing fully established. Both in Old Testament and New Testament expressed by various forms of the word "know" (Proverbs 3:6; Isaiah 61:9; Colossians 2:2 the King James Version). The Psalmist (Psalms 32:5) "acknowledged" his sin, when he told God that he knew the guilt of what he had done. The Corinthians (2 Corinthians 1:14) "acknowledged" Paul and his companions when they formally recognized their claims and authority.

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Bibliography Information
Orr, James, M.A., D.D. General Editor. "Entry for 'ACKNOWLEDGE'". "International Standard Bible Encyclopedia". 1915.