Abstract
But, in consideration of the fact that a completely novel type of mathematical analysis had shot up in a mighty theoretical-technical development during the nineteenth century, and because of the need of making clear the still utterly confused logical sense of this analysis, I saw yet a third and highest task for a formal logic or formal theory of science. It is announced, in the title of § 69 1, as the theory of possible forms of theories or (correlatively) the theory of multiplicities?
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References
Author’s note: “Prolegomena”, p. 247.
Author’s note: This is what is meant by the word “theory” as first introduced (op. cit., § 64) and throughout.
Translator’s note: Changed to materialen (material) in the second edition.
Translator’s note: Changed to the plural in the second edition.
Translator’s note: Inserted in the second edition.
Translator’s note: Inserted in the second edition.
Author’s note: Op. cit., § 70.
Translator’s note: The heading of the section may be translated: “Elucidations pertaining to the idea of tb’ pure theory of multiplicities”.
Author’s note: We must not be led astray here by the Kantian concept of the space-form, a concept that concerns the regional form belonging to actual Nature and to any possible Nature. Here we are dealing with purely analytic forms, “categorial” forms belonging to objects and judgments and abstracted by completely emptying out all their material contents. “The form space”, in the Kantian sense, is the space of Euclid’s geometry, of space-geometry per se. This “space-form” is itself a singularity subsumed under the analytic form “Euclidean multiplicity”.
Author’s note: That is to say, the ideal suggested to mathematicians by the system-form of the Elements, though not formulated by Euclid himself
Translator’s note: Cf. Hermann Hankel, Theorie der komplexen Zahlen [Theory of Complex Numbers], 1867.
Translator’s note: English translation, pp. 204f.
Author’s note: See the preface to my Philosophie der Arithmetik, [p. VIII].
Author’s note: It is a fault of the exposition in the Logische Untersuchungen that this thought was not made central by repeated emphasis, despite the fact that it continuously determines the sense of the whole exposition. A more serious fault of the “Prolegomena” is, by the way, the following:
In connexion with the concept of truth the modalities of truth are not mentioned, and probability is not cited as one of them. When they are taken into account, an enlargement of formal logic becomes necessary: to the effect that, as universal formal possibilities, modal variants of judging and of judgments enter into certainty-or truth-logic — because any such variant can enter into the predicational content of the judgment and, when it does, it must not be regarded as extra-formal. In other words, only the content that goes beyond anything-whatever is the “matter” of judgments, in the sense proper to formal logic; all the forms in which one judges — not only with certainty but also in the mode of possibility, or in other modalities — belong to anything-whatever. A kindred enlargement results from taking into consideration the fact that emotions and volitions also bring modalities of anything-whatever, which are introduced in the same manner into the doxic sphere. (On this last point cf. Ideen, pp. 243ff. [English translation, pp. 531ff.]; also § 50, pp. 135 ff., infra.)
Author’s note: See § 31, [pp. 94 ff.,] supra.
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Husserl, E. (1969). Theory of deductive systems and theory of multiplicities. In: Formal and Transcendental Logic. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-4900-8_5
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DOI: https://doi.org/10.1007/978-94-017-4900-8_5
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