Judgment, Extension, Logical Form

In Kant-Gesellschaft E. V. Walter de Gruyter (ed.), Law and Peace in Kant’s Philosophy / Recht und Frieden in der Philosophie Kants. Walter de Gruyter. 1--139 (2008)
In Kant’s logical texts the reference of the form of the judgment to an “unknown = x” is well known, but its understanding remains far from consensual. Due to the universality of all concepts, the subject as much as the predicate, in the form S is P, is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, particularly in the text on the “logical use of the understanding”, this Kantian interpretation of the subject-predicate relation leads to the question about the relations that must hold between intuition and concept in the judgment. In contrast to intuition, if no concept, due to its universal character, refers immediately to an object, how should we understand the relations of subject and predicate to one another, as well as their relations to intuition, which corresponds to the very special individuality of that object in general = x? In the Kant-Literatur, the relations between intuition and concept in the judgment have been considered in diverse theoretical backgrounds, mainly in Fregean logic and in the logic of Port-Royal. Although so markedly different, these two solutions to the problem above seem to share a common thesis, in so far as they claim, though in different ways, a predicative character to those relations. If the analytic tradition recognizes in the relation between x and the concept S the marks of a propositional function Sx, in turn, the interpretation elaborated from the background of Port-Royal recognizes in this relation the minor premise x is S implicit in the judgment every S is P. This being the case, if it were possible to prove, on the contrary, that the relations between intuition and concept in the judgment could only be of a non-predicative character, then a third solution would be open to us, a solution that could enable us to track down the sense of the conceptions of judgment and logical form in the CPR. In applying this argumentative strategy, it is of the utmost importance to insist on the specificity of Kant’s notion of extension, in order to prove its irreducibility to the Port-Royal notion of extension as well as to the modern one.
Keywords Kant  judgment  object in general  Port-Royal  Fregean logic
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