The paper aims to reveal an analogy between the algebraic system of formal logic and the algebraic system of formal axiology. Our aim is to correct some previously published formulations of the mentioned system and clarify interconnections between similar but different notions of “formal-logical-contradiction” and “formal-axiological-contradiction”. Corrected definitions of several basic notions are given; a fundamental analogy is established between the algebraic system of formal logic and the algebraic system of metaphysics as formal axiology. Special attention is paid to an unexpected analogy between the role of self-contradiction in the algebra of formal logic and the role of self-termination (suicide) in the algebra of formal axiology. “Self-annihilation in response to what is unacceptable (from the suicide viewpoint)” is a formal-axiological analogue of “the formal-logical proof by reducing the contrary to absurdity”.