Abstract
We now move on to the debate concerning the true subject of the statement of number. It is indicative of conceptual confusion when discord can prevail on this point, and one can hardly believe how far the opinions of philosophers deviate from one another here. J. St. Mill explains: “The numbers are, in the strictest of senses, names of objects. ‘Two’ is certainly a name of the things which are two: two balls, two fingers, and so on.”1
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Notes
James Mill, Analysis, Vol. II, p. 92n. In the wording of the text (p. 91), James Mill says exactly the opposite of what his son says in the note: “Numbers … are not names of objects. They are names of a certain process; the process of addition; …” The opposition lies, however, only in the words, and is based upon the contrasting signification with which the two Mills use the terms “note” and “connote.” In explaining a few lines later that the names co-designate (“connote”) the things enumerated, James Mill expresses — in a very misleading way, to be sure — the same view as his son: namely, that the numbers are asserted of things. (Moreover, the two also agree in a crudely externalistic conceptualization of the numbers. The process of addition is placed by James Mill (Ibid.) on a level with walking and writing.)
Psychologie als Wissenschaft, Part 2, p. 161. Cp. also the passages cited on p. 148 above from the same work as well as from Ueberweg’s Logik.
Frege, op. cit., p. 59.
Schuppe, Erkenntnistheoretische Logik, p. 410.
[Analysis, Vol. II, p. 93n LE] Cp. e.g., also Logik, Book III, chap, xxiv, § 5 [Gesammelte Werke, Vol. III, p. 342]: “When we call a collection of objects two, three or four, …”
Chr. Sigwart, Logik, Vol. I, p. 168n.
Cp. G. Frege, op. cit., p. 59. LE
When Kerry (“Über Anschauung und ihre psychische Verarbeitung,” Sixth Article, Viertelj. f. wiss. Phil., Vol. 13, 1889, p. 392) says: “Wherever I am to enumerate there must be present a … concept the objects of which I enumerate,” he obviously commits the confusion characterized above. And when he further, as proof, points out that without such a “guiding concept” we “would run the risk of also counting things which we ought not count, and of omitting something which we should have counted in” — thereby is conceded as much as we could ever wish, namely, that one can also count without such a guiding concept, whether it then may be a ‘risky’ counting or not. Already on this basis we cannot concede the soundness of the following definition added on: “I call that psychical effort whereby an object is subsumed under one of the guiding concepts for a proposed enumerative task a positing of the unit.” (p. 394) If I have before me a pile of apples, I do not need to carry out separate subsumptions under the concept apple in order to grasp each one as one apple while enumerating step by step. And what, at most, could that accomplish for me? The confirmation of the fact that each of the things before me is an apple. But that each is one apple, which alone matters, I do not cognize in this way, unless I once again turn away from the generic concept apple and rise purely and simply to the “one.” And as here with the concept of unit, so also in the case of the other elemental arithmetical concepts, I cannot agree with Kerry’s analyses.
Op. cit., p. 64.
This, no doubt, was Frege’s, line of thought.
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Husserl, E. (2003). The Sense of the Statement of Number. In: Philosophy of Arithmetic. Edmund Husserl, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0060-4_10
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