Beck was born in the village of Liessau (Lisewo) in the rural district of Marienburg (Malbork) in Royal Prussia, Poland in 1761.
The son of a priest (of Liessau), he studied (after 1783) mathematics and philosophy at the University of Königsberg, where Christian Jakob Kraus, Johann Schultz, and Immanuel Kant were his teachers.
Beck maintains that the real meaning of Kant's theory is idealism; that knowledge of objects outside the domain of consciousness is impossible, and hence that nothing positive remains when we have removed the subjective element.
The value of Beck's exegesis has been to a great extent overlooked owing to the greater attention given to the work of J. G. Fichte.
Beside the three volumes of the Erläuternder Auszug, he published the Grundriss der kritischen Philosophie (1796), containing an interpretation of the Kantian Kritik in the manner of Salomon Maimon.