 The above derivation is an illustrative example of Bolzano’s importation of proof methods from mathematics — such as the methods of indirect proof and of mathematical induction — into philosophy. (For certain reservations concerning these methods cf. WL IV, 269–285.) Nevertheless, this alleged proof for the existence of a true proposition does not reach its goal for a simple reason: The proof is in no way peculiar for truths in the sense of true propositions as Bolzano needs to have it. If successful at all, it would work in the same way also for proving the existence of true judgments or true sentences (understood as linguistic entities). A proof for the existence of at least one truth in itself, i.e., a true proposition, requires premise (2). In premise (2), however, the existence of a proposition is already presupposed since it is shorthand for what can be explicitly stated as: There is a (i.e., at least one) proposition which is the sense of (1). Thus, if we take the derivation as a proof for the existence of at least one true proposition, we will succumb to an obvious petitio principii. By — correctly — requiring the addition of premise (2) to be necessary for the formal correctness of the proof, Bolzano unwittingly displayed its failure due to an informal fallacy. Bolzano himself, however, was convinced that he had correctly and successfully proven that there are “truths in themselves”. From this it follows that there must be propositions, since “truths in themselves” are a certain kind of propositions (WL I, 111 f.). And since in every proposition ideas are contained as its parts, a further consequence is that there are also ideas. For every proposition there is also another proposition that is its propositional negation. The propositional negation of a true proposition is a false proposition. Therefore, among propositions there must also be false ones. They are often overlooked because a special name such as ‘falsehood in itself’ was never introduced “officially” for them and is at least not customary.