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‪There is a fairly evident ‪ ‪dilemma for scientific philosophy‪‪—limited here for the sake of simplicity to scientific philosophy of science—in which Carnap found himself, but upon which neither he, nor, unless I am mistaken, his successors and scholars writing about him believed they had to dwell.‪ ‪Either ‪ ‪the philosophy in question is scientific in the same sense the other sciences are, that is to say here that it is itself one of the sciences that it has as objects; one wonders then what more precisely such a scientific philosophy would be like, supposing it were possible. ‪ ‪Or ‪ ‪the philosophy in question is not scientific in the sense the other sciences are, that is to say here that it is the only one which can take them all as objects, but also the only one which it can not take as object; the supposed scientific philosophy of sciences is not then the philosophy of all the science, it is only a philosophy of non­philosophical sciences. ‪‪This dilemma holds for scientific philosophy in general and for that of Carnap in particular, for which it takes a trenchant enough form for one to be able to debate it seriously, especially if one keeps to the scientific philosophy of sciences identified by Carnap, at the time of the ‪ ‪Syntax‪‪, to the syntactical study, or syntax, of the Language of science. The knowledgeable, undisputed, negative answer that it would be appropriate to make in response to the first horn of the dilemma is known: no, an ‪ ‪adequate ‪‪syntax of the Language of Science in this Language itself is ‪ ‪impossible without ‪‪the latter being inconsistent. The following article proposes a formulation and outlines a demonstration of this impossibility in an uncustomary way—using no coding, Gödelian or other, of the elementary syntax of the Language of science within this Language itself—and challenges the criterion of adequacy implied in the demonstration of impossibility in question, again opening up the possibility of escaping from the dilemma while staying firmly on the first horn, whereas Carnap believed, or at least behaved as if he believed, that he had to withdraw it to the second horn.