Object Theory Logic and Mathematics: Two Essays by Ernst Mally

Abstract

Presented here are translations of two essays of the Austrian logician, philosopher and experimental psychologist Ernst Mally, originally delivered at the Third International Congress of Philosophy in Heidelberg, Germany. Both essays conclude with discussion between Mally and Kurt Grelling. Mally was a student of Alexius Meinong and a contributor to logical investigations in the field of object theory (Gegenstandstheorie). In these essays, Mally introduces a vital distinction between formal and extra-formal ‘determinations’ (Bestimmungen), and he argues that formal determinations are not part of the identity conditions for intended objects, but provide the basis for a theory of pure logical and mathematical relations. Mally then proceeds to develop a formal logic of formal and extra-formal determinations, whose interrelations of ontic and modal predications provide an analysis of fundamental object theory concepts.

Notes

  ¹ Mally's early development of a proto-deontic logic appears in his 1926; rpt., 1971, pp. 228–324. See Johann Mokre, ‘Gegenstandstheorie – Logik – Deontik’, Einleitung, in Mally 1971, especially pp. 17–18. Wolenski 1998; Morscher 1998; Lokhorst 1999; Weinberger 2001; Lokhorst and Goble 2004.

  ²  Brentano 1973, pp. 88–89. Jacquette 2004, especially pp. 121–124.

  ³  Jacquette 1991, 2006.

  ⁴  Meinong 1904 discusses the (Scholastic) Sein/Bestand distinction in ‘Über Gegenstandstheorie’.

  ⁵  Jacquette 2001.

  ⁶  Mally 1914. Mally's paper is translated with a critical commentary by Jacquette 1989. See Jacquette 1982.

  ⁷  Mally 1908a,b. For the sake of thematic continuity in discussing the topics of the two papers, I refer to Mally's essay appearing on pp. 881–886 as the ‘first’ essay, and that appearing on pp. 862–867 as the ‘second’ essay.

  ⁸  Russell 1956, p. 45.

  ⁹  Meinong 1969–1978, Vol. VI, pp. 176–177. Findlay 1995, p. 176, proposes the English equivalents ‘nuclear’ and ‘extranuclear’ for Meinong's distinction between konstitutorische und ausserkonstitutorische Bestimmungen. Mally in his 1912 ‘Gegenstandstheoretische Grundlagen der Logik und Logistik’ also proposes a distinction between multiple ways in which objects can have properties that provides the basis for an object theory logic that stands as an alternative to his own prior 1908 distinction between formal and extra-formal determinations.

¹⁰  Routley 1981, p. 496. Jacquette 1986; 1996, pp. 80–91. Meinong's concept of the modal moment and watering-down extranuclear properties to nuclear versions is presented in Meinong, Über Möglichkeit und Wahrscheinlichkeit, p. 266. Also Findlay 1995, pp. 103–104.

¹¹ Meinong's solution to Russell's problem of the existent golden mountain is presented in 1969–1978, Vol. V, pp. 278–282.

¹² See Routley 1981, p. 496: ‘…logically important though the modal moment is, the [nuclear – extranuclear] property distinction alone, properly applied, is enough to meet all objections to theories of objects based on illegitimate appeals to the Characterisation Postulate [Routley's version of Meinong's thesis of the Independence of Sosein (so-being) from Sein (being)]. The Meinong whose theory includes an unrestricted Characterisation Postulate is accordingly, like Meinong the super-platonist, a mythological Meinong.’

¹³ As far as I have been able to determine, no jointly authored paper on object theory logic was ever published by Mally and Ameseder. Undoubtedly, the most complete logical treatment of object theory Mally published, although as a solo effort rather than collaboration, is his 1912, and the unpublished Grosses Logikfragment (see note 1 above). The only paper Mally jointly authored with Ameseder was in psychology rather than logic, his 1902. Nor are there any papers in manuscript jointly authored by Mally and Ameseder in the Nachlaß Mally at the Universitätsbibliothek Graz; nor did Mally publish or leave behind any essay with the title referred to in the Congress proceedings, ‘Elementen der Gegenstandstheorie’. Meinong nevertheless also mentions the essay as forthcoming in his Über die Stellung der Gegenstandstheorie im System der Wissenschaften, Alexius Meinong Gesamtausgabe, vol. V, p. 202 (p. VI of the original published text of the Stellung: ‘Vielleicht wird mancher Leser der nachstehenden Untersuchungen nicht ohne alles Interesse davon Kenntnis nehmen, dass die unten S. 3 Anm. 2 erwähnte gemeinsame Arbeit R. AMESEDERS und E. MALLYS inzwischen so rüstig gefördert worden ist, dass ihre Veröffentlichung unter dem Title “Elemente der Gegenstandstheorie” seitens der Dürrschen Verlagsbuchhandlung in Leipzig noch für das laufende Jahr in sichere Aussicht genommen werden konnte (Graz, März 1907)’. (I thank an anonymous journal referee for calling my attention to this reference.) It is tempting to suppose that many of the relevant logical principles might have been contained in the unpublished essay coauthored with Ameseder that Mally mentions in the first essay, but in lieu of a manuscript of their lost paper there is no way to be certain.

¹⁴ I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Academy of the Arts and Sciences (KNAW) for support of this and related research projects in philosophical logic and philosophy of mathematics in 2005–2006.

¹⁵ In Untersuchungen zur Gegenstandstheorie und Erkenntnistheorie, edited by A. Meinong. Leipzig 1904 [Verlag von Johann Ambrosius Barth].

¹⁶ Not inductively; extracting instances through experience from several individual objects.

¹⁷ The designation derives from Meinong, Über die Stellung der Gegenstandstheorie im System der Wissenschaften [On the Place of Object Theory in the System of the Sciences], Leipzig, Barth 1907.

¹⁸ Admittedly, the different ‘special object theories' are then not jointly grasped [mitbegriffen]; they receive special, separate treatment anyway, however, to the extent that this is not already done (as in the case of mathematics).

¹⁹ Compare [Ernst] Schröder, Algebra of Logic [Algebra der Logik], Leipzig, 1890; or [Louis] Couturat, Algebra of Logic [L'Algèbre de la logique]. Scientia, Nr. 24.

²⁰ To us it is indeed not probable, but it is in no way precluded, that this issue may have, but until now unfortunately has not already received as we would have wished a correct treatment in the extensive logical literature.

²¹ Use of the minus-sign does not of course signify the implicit assumption of an arithmetical connection between σ and —σ.

²² In connection with Couturat, as previously cited.

²³ This and the previous proposition embody a contradiction. σσ = —σ · —σ expresses: if being exists, then non-being does not exist (of any arbitrary object) and conversely; —σ · σ = σ · —σ expresses: if non-being exists, then being does not exist, and conversely.

²⁴ For example, if one speaks of the ‘‘exclusion'' [‘‘Ausgeschlossensein''] of a state of affairs.

²⁵ Compare Schröder, previously cited, where clearly the name ‘‘adjunction'' is used as equivalent to ‘‘determination''.

²⁶ It is explicit that a metaphysical presupposition concerning the existence of a ‘‘substance'' [‘‘Substanz''] is in no way included in the alternation of the substrate concept.

The previous remarks appear capable of clarifying and resolving the conflict between the Schröder-isch and the Wundt-ish concept of ‘‘determination''. —Determination is admittedly achieved by means of apposition (adjunction) of determinations to other determinations, but the previous determinations are not determined, that is, defined, by means of a new determination, but rather by means of each ‘‘something'' that confronts all as a general ‘‘substrate''.