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Husserl on Analyticity and Beyond

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Abstract

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

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Notes

  1. For Quine’s criticism of Carnap’s views on analyticity, see his “Two Dogmas of Empiricism” (1953 [1951], pp. 20–46). For Duhem’s views, see his papers “Quelques réflexions au sujet de la physique expérimentale” (1996a [1892]) and “Examen logique de la théorie physique” (1996b [1913]).

  2. On this point, I must refer the reader to two writings of mine, namely to my recently published paper “La Relevancia de Carnap” (Rosado Haddock 2006b), which is an extensive critical study of the book El Programa de Carnap, edited by Ramón Cirera, Andoni Ibarra and Thomas Mormann, and to my The Young Carnap’s Unknown Master (Rosado Haddock 2008).

  3. See Kant (1993, pp. A150-52, B189-91).

  4. See Sect. 3 of Die Grundlagen der Arithmetik (Frege 1986 [1884]).

  5. See Husserl Hua XVIII and Hua XIX. See on this issue also his Alte und neue Logik (Husserl 2003).

  6. All translations have been made by the present author.

  7. See Carnap (1991 [1922]), especially Chapt. 4.

  8. They are not analytic in Frege’s sense, since they are metalogical statements, thus, not even expressible in Frege’s systems. They are not analytic in Carnap’s sense, since they are not obtained by the analysis of language, even with the help of meaning postulates.

  9. They could be formalized in a metametalanguage that would contain statements about the metalanguage not formalizable in the metametalanguage, and so ad infinitum.

  10. Nonetheless, mereology, which is Lesniewski’s most important logical system and also the one most divergent from classical logic, could very well be considered as a mathematical rather than as a logical theory. In fact, Husserl viewed what later was to be called “mereology” as a mathematical theory and the notions of part and whole as formal-ontological categories, i.e. as fundamental mathematical notions alongside the notions of set, cardinal number, relation, and others.

  11. One could reformulate the definition of analyticity in model-theoretic terminology as follows: A statement S is analytic if the theory T having S as its only axiom has a non-empty class of models and that class is closed under isomorphisms. Theories whose classes of models are closed under isomorphisms are sometimes called abstract. Hence, esentially, a statement S is analytic if the theory having S as its only axiom is abstract.

  12. For Frege’s views, see Frege (1986 [1884]) Sects. 10 and 13–14. For Benacerraf’s criticism see Benacerraf (1983 [1965]).

  13. See my paper “On Antiplatonism and its Dogmas” in Hill and Rosado Haddock (2003), as well as Chap. 2 of my recent book, A Critical Introduction to the Philosophy of Gottlob Frege (Rosado Haddock 2006a) and Chap. 4 of Rosado Haddock (2008).

  14. See Hua III.

  15. I cannot discuss the issue here, but—contrary to what occurs with our corresponding definition of analyticity—the above definition of synthetic a priori statements is certainly not wider than Husserl’s corresponding definition and is much more restrictive than his later usage, which allows for a variety of regional a priori statements. For Husserl’s definition of “synthetic a priori,” see Hua XIX/1, p. 260.

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Correspondence to Guillermo E. Rosado Haddock.

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Rosado Haddock, G.E. Husserl on Analyticity and Beyond. Husserl Stud 24, 131–140 (2008). https://doi.org/10.1007/s10743-008-9038-2

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