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Formal apophantics, formal mathematics
Formal logic in its delimitation up to now, as apophantic analytics in the broader sense, owes its apriori self-containedness to its concept (the Aristotelian concept) of the judgment-form. One can define this concept also as the determining of all judgments exclusively by their 'syntactical forms", the forms that they, as formations produced by 'syntactical operations", have by apriori necessity. The syntactical form of any judgment can be apprehended purely, in eidetic concepts. To say that it is apprehended purely is to say that the "syntactical stuffs" going into the syntaxes are thought of as indeterminately optional. Thus the pure form-concept of a judgment as such originates: that of a judgment as determined exclusively by syntactical forms that are given and conceptually determinate in the particular case.1 As codeterminant <of the judgment as such> and therefore as pertaining to the form-concept in analytic logic, only the most universal "modal"/variations may also be included, those that any judgment whatever can undergo, regardless of all the syntactical operations that build it or can be performed on it. The concept of modal variation employed here is far from being exhausted by the so-called judgment-modalities.
Husserl Edmund (1969). Formal and transcendental logic, transl. D. Cairns, Nijhoff, Den Haag.
Husserl Edmund (1969). Formal apophantics, formal mathematics, in Formal and transcendental logic, Den Haag, Nijhoff, pp. 72-89.