The law of the excluded middle

We postulate and consider it self-evident that a test is either finite or infinite. This excludes any third, or middle, possibility, which gave this principle the name of the law of the excluded middle. From this we derive that a prediction may be only true or false. We further derive the law of the excluded middle for arbitrary statements. Consider some statement S which is a generator of predictions. Let us run this generator and define the following refutation process. Each time that a prediction if produced it it replaced by the symbol True if it is true and False if it is false. The first time the symbol False appears in the refutation process, the process ends and succeeds. This process is either finite, or infinite. If it is infinite, the statements S is true, otherwise it is false. No other outcome is possible.