Abstract

As the law of identity is the norm of all affirmation and the law of contradiction the norm of all negation, so is the law of excluded middle a norm for the disjunction, seil, so far as every disjunctive proposition, formed according to this law, is self-evident and necessarily true. While the negative formulation : « No logical proposition is neither true nor false » can be reduced to the law of contradiction, its positive formula : « Every logical proposition is true or false » can not ; it is an original and a priori evidence. This evidence applies to things, not as they are in themselves, but only in their relation to the contemplating mind, i.e. as « objects» for the thinking subject. The objections raised to the law in the course of history have a positive significance ; they do not prove the existence of exceptions to the law, but rather help to determine its real and true contents. So it appears from Aristotle's problem concerning the contingent future, that, though every proposition is true or false and consequently has one of these values, it need not be decided or determined, even in itself, which of these two values a proposition has. Secondly, Aristotle's restriction of the law to actual being, because of the indeterminateness of potentiality, can be met by Windelband's distinction between subjective and objective negation and the additional remark, that the adverb « not » in the formula : « Every thing is A or is not A » has to be conceived in the subjective sense. It is only in this way that the formula becomes equivalent to the law, that every logical proposition is true or false. The same holds good for the indeterminateness of universals, wich caused several authors to restrict the applicability of the principle to individual reality. Finally, as for the difficulty of the mathematical infinite, wich made intuitionists doubt of the reliability of the law and avoid its general use, this does not so much prove the unreliability of the principle as the fact that not every grammatical sentence is a proposition in the logical sense. Only of the proposition in the logical sense can it be truthfully said that it is necessarily true or false