This Article Should Not Be Rejected by Mind

Abstract

If the statement which appears in section I of this article were false, then its antecedent 'the statement in section I of this article is trivially true' would be true, which means that the statement itself would be true; this is a contradiction. Therefore, the statement in section I of this article should be true. If the antecedent were true, the consequent would also have to be true. This does not seem right, however, since Mind is a serious journal which enjoys great prestige, and as such should not accept articles the content of which boils down to a statement which is trivially true (for example, the statement in section I) followed by a commentary (as in this section) proving its trivially true character (which is what we seem to have done up to now), or, even worse, proving that it is not trivially true (which is what we hope to do by the end of this discussion). So, the statement in section I is either false or it is a non-trivial truth; it must in fact be this latter, since, as we have already seen, it cannot be false; consequently it is the antecedent which is false. What is then the truth-value of its consequent? If it were false, this would mean that this article should not be accepted for publication by Mind, and this in spite of the fact that, as we have just seen, its content consists basically of a non-trivial truth, followed by a justification that this is so (sections I and II respectively). But, let us remember, Mind is a magazine of great prestige and, as such, would never reject its duty of accepting for publication all articles on logical analysis which are submitted to it when these articles contain a demonstration of a new and surprising non-trivial truth. In other words, the consequent about which we are talking must be true, and therefore the present article should be accepted for publication by Mind. Mind should not reject it. Somebody might counter-argue by saying that the previous discussion does not make sense, since to introduce at the level of the object language its own concept of 'trivial truth' ('non-trivial truth', 'trivial falsity', 'nontrivial falsity') is just as illegitimate as to introduce merely the concept of