GOEDEL’S CRITIQUE OF THE BEGINNING OF HEGELIAN LOGIC AND THE MEANING OF EQUIVALENCE, INCONSISTENCY AN INCOMPLETENESS
G.W. Leibnitz based his whole philosophy and mathematics on the two Laws of Non-Contradiction
and Sufficient Reason. This essay investigates if this approach is still a realistic perspective.
It is quite intuitive to think that, on the one hand, formal or material inconcistency disqualifies a theory, and on the other hand, that every theoretical proposition you make should be justified with sufficient reason. Note that it is no paradox to not demand sufficient reason for everything; but it seems perfectly legitimate to do so. According to Karl Popper, discovering formal and material inconsistencies in other theories can’t establish a new theory. However, the following problem then arises: What is the sufficient reason for the Law of Contradiction and the Law of Sufficient reason? Both wanting and not wanting a sufficient reason for sufficient reason is paradox; thus establishing it demands abandoning the Law of Contradiction. But paradox is the sufficient reason for anything (i.E: Ex contradictione sequitur quod libet) (…).