ABSTRACT
The problem of consistency is a peculiarity of the postulational logic. When the principles of logic are accepted on purely intuitive grounds, there can be no question concerning their truth and significance. And if they are both true and significant, they cannot lead to inconsistency. Even in the semi-postulational procedure of logistic there is no need for a proof of consistency. A proof of consistency is a demonstration that with the postulates and rules of the formal system no two theorems can be deduced which contradict one another. Confusion in a discussion of consistency might easily arise if the distinction between postulational logic and postulational mathematics is not brought out. A postulational system is a logic if it contains, besides variables, constant symbols which are interpretable as the propositional connectives “if-then” and “it is false that”, or some equivalents of these, and the logical properties of which are defined by some of the postulates.
