References
- Willard cites this passage on p. 67 as Husserl's best statement on philosophical method, but he makes no use of it in his discussion of the problem of origin.
- According to Willard “certain numbers larger than 12 are made objects of thought by means of their relation to 12. Twelve itself, conversely, becomes the apperceptive support for the thought of these other numbers; and the epistemic condition of their conceptualization is that we have the concept (are able to think) of 12, and of next larger number, of the next larger again, and so on, and that we actually deploy these concepts when actually thinking of a larger number” (p. 126). I cannot see that this picking out of the number 12 (or of any other arbitrarily selected smallish number) and the successive progress is essential to Husserl's account. In the first part of his Philosophy of Arithmetic, Husserl does not primarily intend to teach us how to achieve a genuine conceptualization of the smaller numbers up to around 12. Rather, he wants to give us insight into the principle of the concept of number and of its structure. It is of course necessary to distinguish the different forms-of-multiplicity, but there is no reason why we should be restricted in this to the device mentioned by Willard.
- On p. 103 Willard claims that, while “cardinals themselves are neither decadal, sexagesimal, nor duodecimal”, concepts of cardinal numbers must fall under some such adjectives. Yet as we have seen, numbers for Husserl are defined in terms of multiplicities with the concatenations of “something and something and something etc.”; hence the concept of the particular number itself is neither decadal, sexagesimal nor relative to any other system of number signs. It is merely that our grasping of larger numbers is made possible by our use of symbolic representations, systems such as the decadal, sexagesimal and so on. This essential function of signs for most of the arithmetical concepts is the reason why signs are relevant for a philosophy of arithmetic, and is why Husserl devoted himself at this time to “The Logic of Signs (Semiotics)” (1891).
- Here his discussion of objectless representation in his review of Twardowski's On the Content and Object of Representation (1894) is, it seems to me, particularly crucial.
- This criticism does not exclude, as convincingly shown by Willard, that Schröder was of great significance for Husserl's early views on the nature of mathematics and logic and that his influence exceeded that of Frege, (cf. “The Question of Frege's Influence”, pp. 118ff.)
- In emphasizing the importance of conceptual objects (Begriffsgegenstände) Husserl refers to J. S. Mill (“The Deductive Calculus and the Logic of Contents”, p. 14). Willard notes that we find the relevant paragraphs in Mill's A System of Logic, Book I, Chap. V.
- The difference between analytic philosophers and Husserl lies in the fact that the former do not say how a sentence can be verified by experience, a problem which, as Husserl shows, can be subject to a great deal of detailed investigation. Willard points out, however, that there is one exception, namely the early work of Sellars, who tried to answer the question of what it is for a sentence to be verified, adopting, as Willard tries to show, a strategy identical to that of Husserl. According to Sellars, a sentence is verified whenever a token of it is “co- experienced” with what it designates, i.e. whenever both are parts of the same person's experience. Since this is possible only for autobiographical sentences expressing sensory experiences, no objective (publicly accessible) sentences can be verified, but at best confirmed.
- In his interpretation, Willard refers to the American New Realists (W. Pitkin, R. B. Perry, etc.), who claim that “immanence” and “transcendence” are compatible. The idea is that a thing is distinct from the “knowledge relation”, that it is only a part of it; it may enter into or go out of the knowledge relation, without being essentially changed. Therefore the intuition which involves such a knowledge relation “could not be what it is without the object being and being what it is” (p. 244); this is of course not true for a mere intention, whose object may not exist.
- Willard offers an interpretation according to which the relationships between the matters of subordinate acts serve in the higher order acts as representing content.
- This concept of intention that has its correlate in the concept of fulfilment should not be confounded with the concept of intention as mere directness towards an object; cf. B. Rang, “Einleitung des Herausgebers”, in: Hua XXII.
- This concept of intention is therefore central for an understanding of the development of the early Husserl: what we miss in the Philosophy of Arithmetic is a theory of symbolic knowledge; this concept seems rather, in the framework of the Philosophy of Arithmetic, to be a contradiction in terms, since knowledge—in contrast to mere correct judgement or representation, cf. “On the Logic of Signs (Semiotics)”—implies authentic presentations, whereas symbolic representations are always blind, and are therefore not knowledge. In the 6th Logical Investigation, however, we find a theory according to which knowledge always involves the use of symbolic intentions that are fulfilled. The Logical Investigations entails therefore the theory of symbolic knowledge, which we miss in the Philosophy of Arithmetic, and this is why the 6th Logical Investigation seems to be the central one.
- I should like to thank Barry Smith for checking the manuscript and the “Deutsche Forschungsgemeinschaft” for a grant for research.