The Concept of the Totalizing Act as Collective Connection: Progenitor of Number

  • Jonathan Kearns Cooper-Wiele
Part of the Phaenomenologica book series (PHAE, volume 112)


The collective connection is discerned in the “thinking-together act.” It is the latter objectified in reflection. This reflective act instigates the debut of the collective connection as a relation among relations, albeit a “peculiar” relation binding its parts into a peculiar whole.


Abstract Representation Number Concept Absolute Content Individual Content Ontic Status 
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  1. 1.
    BZ, 334, 27–31/77, 8–10. The PA passage does not replicate the wording of that in BZ. The respective sections of each, referred to at this point by each (BZ 299, 3–302, 4/PA 17, 28–21, 11) are (except for a few minor alterations) identical.Google Scholar
  2. 2.
    Ibid., 298, 21–24/16, 11–14. The point is essentially the same in the two texts. If anything, the emphasis in PA is placed more on the abstracting act than on the abstractive bases. The act relates itself to the concrete. See 301, 34–35/31, 2–3; 302, 7–8/22, 5–6; 309, 15–19/31, 15–21. In the latter passage Husserl distinguishes between “psychological description” (Beschreibung) of a phenomenon, and the “statement of its meaning” (Bedeutung), and between the objects of the description and statement, i.e., the “phenomenon as such” and that for which it “serves” (dienen), which it “signifies” (bedeuten). The phenomenon is the “foundation (Grundlage) for the meaning.” As such, it is distinct from the latter.Google Scholar
  3. 3.
    Ibid., 301, 38/21, 6. It is the concept of multiplicity which is referred to here as the general representation. The difference between these representations is discussed below in the second section of Chapter 3.Google Scholar
  4. 4.
    Ibid., 299, 3–4/18, 5–6.Google Scholar
  5. 5.
    Ibid., 324, 29–34/56, 17–22. Husserl observes that “difference” (Verschiedenheit) is not a content relation - as similarity is - but rather a “negative judgment” concerning the presence (absence) of such.Google Scholar
  6. 6.
    Ibid., 309, 1–5/30, 24–31, 3. Husserl states that it is this which enters into the corresponding “general concept.”Google Scholar
  7. 7.
    Ibid., 300, 17–25/19, 22–30. What are so present here are the “continuous connections” which define the continuum - regardless of how different the “absolute contents” are case to case. The “concept of the continuum as a whole” arises (entstehen) through reflection on this connection.Google Scholar
  8. 8.
    Ibid., 299, 5–13/18, 3–19. Husserl writes that it is those “characteristics” which are “common” that constitute the general concept.Google Scholar
  9. 9.
    Ibid., 300, 9/19, 14. “Attending” (achten) is employed here as essentially synonymous with the “comparing” of different cases which exhibit the same “continuous connection.”Google Scholar
  10. 10.
    Ibid., 299, 5–13/18, 3–19. Concepts “arise” (entstehen) through this comparison of “specific representations,” also referred to as “individual contents.”Google Scholar
  11. 11.
    Ibid., 314, 17–18/37, 5–6. The PA passage omits, “noticed for itself.” Here it is the spatial order and position of entities which are not noticed and, consequently, do not enter into the concept. Such are “differences” between entities.Google Scholar
  12. 12.
    Ibid., 337, 9–18. The passage is scattered to the far corners of PA. See PA 82, 8; 79, 1–27, especially 18–19. Husserl writes that, in the process of abstracting, there is disregard for the “particular determination” (Beschaffenheit) of the individual objects. “No special interest” is taken in the “peculiarities (Besonderheiten) of contents.” Nevertheless, in the course of such (dis)regarding, the “concrete objects” do not disappear from consciousness. See also BZ 309, 25- 37/PA 31, 26–32, 2, where Husserl links such inattention to distinctions (Unterschieden) to our “intention” to unite contents, cf., BZ 314, 1–9/PA 36, 32–33 (lines 8–9 of BZ are omitted in PA).Google Scholar
  13. 13.
    BZ 300, 32/PA 20, 1. The concept formed in this case is that of a “whole.” See 299, 5–13/18, 3–19.Google Scholar
  14. 14.
    Ibid., 300, 17–25/19, 22–30.Google Scholar
  15. 15.
    Ibid., 337, 24–34. The text of PA diverges from that of BZ before this point (at BZ 337, 9, and PA 82, 8). In another passage not reproduced in PA, i.e., BZ 334, 31- 335, 1 (The immediate context of the passage corresponds roughly to PA 11, A-27. PA 11, 28–80, 6, is essentially an interpolated expansion which rejoins BZ at 335, 34. There are allusions in this expansion to BZ 335, 14–335, 34, as well as an intersection with BZ 337, 13–18 at PA 79, 18–27. Generally this is new material.), Husserl describes the abstraction of concepts of wholes as linked to that of the concepts of their particular modes of connection. As a point of translation, it does not seem that a developed theory of the intuition of essences is implied here, as Willard’s rendering of “Beschaffenheit” (BZ 334, 34) as “essence” suggests (see his translation of BZ in Husserl: Shorter Works [Notre Dame: University of Notre Dame Press, 1981], p. 115; hereafter HSW).Google Scholar
  16. 16.
    BZ 335, 1–1/PA 11, 10–15. The PA text omits “universal,” as a prefix to “concept,” with reference to “multiplicity.”Google Scholar
  17. 17.
    Ibid., 336, 2–13/80, 15–26.Google Scholar
  18. 18.
    Ibid., 336, 21–38/81, 7–30. The PA version is more or less of an expanded paraphrase of its antecedent in BZ. While Husserl emphatically dissociates himself from the view that numbers are deposits in space-time, he observes that the lower number names, e.g., “zwei, drei, vier, etc. belong to the earliest creations of all languages.” In this general regard he refers at PA 83, 25–35 to the “children” and the “wild peoples” and, in a footnote, cites some of the historical and anthropological works on which his views were apparently based.Google Scholar
  19. 19.
    By contrast, the contents of the totality are described as “absolute contents” (BZ 323, 15/PA 55, 1).Google Scholar
  20. 20.
    Ibid., 317, 7–17/45, 27–46, 7. The PA rendition of the passage makes essentially the same and significant point, although Husserl injects a critique of Baumann into it, thus expanding it relative to its antecedent in BZ. cf., PA 42, 23–43, 11. de Boer finds an inconsistency between the two versions which does not seem as apparent as he implies (DHT, p. 33). Husserl states in BZ that “numbers are mental creations (Schöpfungen) insofar as they form the results of activities which we exercise upon the concrete contents”. In PA, he writes that “numbers are pure mental creations (the word “pure” is also used in the sentence in BZ preceding that just cited, and de Boer is correct in noting that Husserl says there that the “designation of numbers as pure mental creations of inner intuition involves an exaggeration and distortion of the true state of affairs”) in a certain manner, and this is actually correct in that the numbers rest on psychical activities which we exercise on the contents.” Arguably, the phrase, “in a certain manner,” is a Husserlian caveat here which de Boer fails to emphasize sufficiently, and that it is analogous in this regard to “insofar” in the BZ passage. If so, it renders the PA version essentially the same in meaning to its BZ antecedent. Husserl proceeds in PA to emphasize as well that while, given these caveats, numbers may be regarded as “mental creations,” they are not entities in space-time. The emphasis of this in BZ in the statement that these are relational concepts, capable of being generated again and again, is omitted in PA. Perhaps this is an indication of Husserl’s increasing uneasiness about identifying numbers with concepts of psychical acts. One ought also consult the entire preceding Section IV of BZ, of which this passage is part, especially BZ 313, 1–34/PA 35, 12–36, 17, and BZ 315, 38–316, 26/PA 44, 6–45, 9. The first passage presents essentially the same arguments in PA, although the wording is altered and the text expanded at points. In denying that number is in any way a “part-phenomenon” in BZ, the term becomes “sensible quality” in PA (BZ 313, S/PA 35, 18–19). In his critique of this general position of Mill and Lange, Husserl speaks of their “defiance” of the “clear evidence (Zeugnis) of inner experience” (Erfahrung; PA 36, 3–4). In the second passage, the two texts are essentially the same in point; Husserl injects more quotations from Baumann in PA. While PA retains the assertion that Baumann’s theory rests on an “erroneous interpretation of the abstraction process” (BZ 316, 21–22/PA 45, 6–7), it omits the next sentence of BZ (316, 22–26): “Neither are they (number concepts) ‘pure mental’ creations of an ‘inner intuition,’ nor can one speak of a finding of the same in the external world, and of a being-together with and in space.” However from what is retained immediately following the passage in BZ, it is clear that this omission signals no change in the theory (as is evident in the discussion of the first passage cited in the first half of this footnote).Google Scholar
  21. 21.
    BZ 316, 27–33/PA 45, 9–14; BZ 298, 10–18/ Roughly, the PA correlate to BZ 298, 7–20, is PA 14, 16–16, 11. This is an expansion of the passage in BZ, although the point of the latter passage is not changed, cf., PA 15, 21–24. In the introduction to BZ Husserl uses the term “Verwendung” (BZ 290, 30–38) when speaking of the “application” of mathematical concepts in (the context suggests) the sciences and their attendant technologies. “To apply” is undoubtedly a more elegant translation of “knüpfen” than “to attach.” The latter rendering is given because it conveys “externality” better in English than the former. Husserl does employ “verwenden” when speaking of language use, and perhaps the implication is that words seem to “clothe” their referents most smoothly.Google Scholar
  22. 22.
    BZ 338, 14–16.Google Scholar
  23. 23.
    BZ 336, 13–15/PA 80, 26–29. For a discussion of the negative judgment which asserts the non-identity of terms, and, while sometimes mistaken for a content relation, is made on the basis of terms but not found among them, see BZ 324, 10–38/PA 55, 35–56, 26.Google Scholar
  24. 24.
    Ibid., 298, 14–18/14, 16–16, 11.Google Scholar
  25. 25.
    See “On the Concept of Number,” HSW, p. 96.Google Scholar
  26. 26.
    BZ 298, 19–24/PA 16, 9–14; and 299, 3–7/18, 5–9. The first PA passage diverges in wording at points, but the central point is the same. Husserl omits in it the characterization of totalities of determinate objects as gathered “indiscriminately” (beliebig) in addition to “arbitrarily” (willkürlich). In the second PA passage, although the wording is somewhat different, the point of its antecedent is retained. In PA Husserl does not emphasize the “from which” abstraction is made in the context of a query (BZ 299, 7/PA 18, 9).Google Scholar
  27. 27.
    Ibid., 327, 6–12/64, 6–12. The PA passage is virtually identical to that of BZ withGoogle Scholar
  28. the exception that Husserl replaces “set” (Menge; BZ 327, 10) with “multiplicity” (PA 64, 9–10).Google Scholar
  29. 28.
    Ibid., 336, 39–337, 18/81, 33–82, 8. The PA passage essentially repeats, with minor changes, the BZ text up until BZ 337, 9. Some of BZ 337, 9–18 is found, or essentially the same point is made, in PA 79, 6–24. As noted above, PA diverges from BZ after BZ 337, 9, and at PA 82, 9.Google Scholar
  30. 29.
    Admittedly a barbarism, the term “contentualization” was suggested by Dorion Cairns. In his Guide for Translating Husserl (The Hague: Martinus Nijhoff, Phaenomenologica, vol. 55, 1973), on p. 74, he writes that “inhaltlich” may be translated “contentual.” It is hoped that its awkwardness will not subvert its indication of what might also be termed “content-status.”Google Scholar
  31. 30.
    Husserl appeals to the high court of “inner experience” for validation of his position on this point (BZ 333, 18–23/PA 73, 25–30). He emphasizes the point in PA by adding that this is a result which “repeatedly intrudes” in the critical discussions of the previous chapters. With regard to “inner experience” see BZ 304, 23–2S/PA 24, 29–34, as well.Google Scholar
  32. 31.
    BZ 299, 26–32/PA 18, 31–37.Google Scholar
  33. 32.
    Ibid., 335, 7–10/77, 16–21.Google Scholar
  34. 33.
    Ibid., 332, n. 1/73, n. 1. Also, as Husserl writes at BZ 317, 4/PA 45, 23, the “totality” of collected objects is simply convertible with the fact that “they are one” in virtue of the act.Google Scholar
  35. 34.
    Ibid., 323, 14–18/54, 39–55, 4.Google Scholar
  36. 35.
    Ibid., 332, 6–16/72, 23–29. As already noted, PA 72, 23–29 recapitulates, almost verbatim, BZ 332, 6–12. However PA omits the passage cited here from BZ 332, 12–16. See Appendix II.Google Scholar
  37. 36.
    BZ 299, 17–19/PA 18, 23–25.Google Scholar
  38. 37.
    BZ 335, 1–7/PA 11, 10–15.Google Scholar
  39. 38.
    See, e.g., his letter to Carl Stumpf (c. 1890) reprinted in Edmund Husserl, Studien zur Arithmetik und Geometrie. Texte aus dem Nachlass (1886–1901), edited by Ingeborg Strohmeyer, Husserliana XXI (The Hague, Boston, Lancaster: Martinus Nijhoff Publishers, 1983), P. 245. Willard maintains that Husserl’s departure from the prevailing assumption that analysis could be arithmeticized, was due to the fortuitous conjunction of his writing the last part of PA dealing with this, and his examination of Schröder’s Vorlesungen über die Algebra der Logik of 1890, in preparation for his review of 1891 of this work. It seems to have been in this general period that Husserl became persuaded that universal arithmetic was not derived from numerical concepts after the manner of symbolic numerical concepts, because it was “a piece of formal logic” and hence, to be applied to numbers. As a “symbolic mechanism,” it “can be assigned different interpretations” and can “thereby, be applied to various distinct (though analogous) conceptual domains, not to that of number alone” (LOK 109). Consequently, insofar as this formal arithmetic, its ad hoc concepts, and the formal logic of which it was part, could no longer be regarded as derivative from, and founded upon, actual number concepts, they could not be regarded as founded at all. His attempt to do so in BZ and PA is, in Willard’s famous characterization of it, “the logic that failed.” It was its failure that turned Husserl in the direction of the research that culminated in the publication of the Logical Investigations.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Jonathan Kearns Cooper-Wiele
    • 1
  1. 1.University of Massachusetts at BostonUSA

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