Taking for granted that much of the content of Frege’s works is ontology (1.1), our problem is not whether or not in Frege there is ontology, but rather to pursue further the analysis of those aspects of Frege’s thought which call for a comparison with traditional ontology.


Classical Ontology Modern Logic Ontological Dimension Foundational Research Universal Substance 
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  1. 1.
    A rich critical history of the problem of the two metaphysics is to be found in Owens [1], Part 1, Chapter 1. The author records the different views since the Greek commentators until our times.Google Scholar
  2. 2.
    Aristotle [2], F, 3, 1005a, 22: cí7raat yâe vmciexec aolç ojacv âíld’ov yevst rtri… is the reason given for counting the “axioms” as part of the philosophia prima.Google Scholar
  3. 3.
    For the appearance of this name, cf. Ferrater Mora [1], where the use of “ontology” before Wolff is studied.Google Scholar
  4. 4.
    Pichler [1].Google Scholar
  5. 5.
    Scholz-Hasenjaeger [1], p. 13 below, and note. For Legniewski, cf. Luschei [1], p. 28. By “foundational research” I simply refer to the following text of Frege: “Wenn ich die Arithmetik mit einem Baume vergleiche, der sich oben in eine Mannigfaltigkeit von Methoden und Lehrsätzen entfaltet, während die Wurzel in die Tiefe strebt, so scheint mir der Wurzeltrieb, in Deutschland wenigstens, schwach zu sein. Selbst in einem Werke, das man dieser Richtung zuzählen möchte, der Algebra der Logik des Herrn E. Schröder, gewinnt doch bald der Wipfeltrieb wieder die Oberhand, bevor noch eine größere Tiefe erreicht ist…” (GRG I, p. X III ).Google Scholar
  6. 6.
    Signo s es litera initiale de vocabulo graeco eau (Peano [1], I, § 1).Google Scholar
  7. 7.
    The subject-matter of logic is for Frege die Gesetze des Wahrseins which are the logical laws, only secondarily the Schlußregeln (cf. Bartlett [1], p. 3). “Logic” is said also to contain such subjects as Verneinung (negation), Subsumption, Unterordnung (subordination), Identität… (UGG2 (III), p. 428). If Frege speaks here of “logical” relations he is merely the victim of a situation he himself helped to destroy (cf. Chapters 5 and 7). For “ontology” in modern philosophy, let us consider the following text of Baumgarten: “Ontologia [= die Grundwissenschaft, says the author in a footnote] (ontosophia, metaphysica, metaphysica universalis, architectonica, philosophia prima) est scientia praedicatorum entis generaliorum” (Baumgarten [1], § 4). Or the well known definition of Wolff: “Quoniam Ontologia de ente in genere agit, ea demonstrare debet, quae onmibus entibus sive absolute sive sub data quadam conditione conveniunt” (Wolff [1], § 8).Google Scholar
  8. 8.
    Baumgarten [1], sectio VIII of “praedicata relativa entis” is devoted to “signum et signatum”.Google Scholar
  9. 9.
    Jacoby [1] and [2].Google Scholar
  10. 10.
    For example, FUB, p. 17, GRG I, p. 7.Google Scholar
  11. 11.
    Heidegger [1]: “Was ist demnach ein Ding? Ein Kern, um den viele wechselnde Eigenschaften herumliegen, oder ein Träger, dem diese Eigenschaften aufliegen, etwas, was anderes besitzt, an sich hat. Wie wir es auch drehen und wenden, der Bau der Dinge zeigt sich so…” (p. 25). “Was ist also ein Ding? Antwort: Ein Ding ist der vorhandene Träger vieler an ihm vorhandener und dabei wechselnder Eigenschaften… Die überlieferte Wesensbestimmung der Dingheit des Dinges können wir in den bekannten und geläufigen Titeln festhaltenGoogle Scholar
  12. 12.
    diese Sätze [logical laws] sprechen von nichts anderem als von Individuen und Eigenschaften“ (Scholz-Hasenjaeger [1], p. 13). The same is implied by Hilbert-Ackermann [1], p. 50; Lorenzen [1], § 1, etc., etc.Google Scholar
  13. 13.
    The absolute separation of “logic” and “reality” is expressed with particular force by Clauberg, who acknowledges (in agreement with tradition) that both disciplines (logic and metaphysics) are equally universal, but “inter Metaphysicae ac Logicae subiectum infinita est distantia, quatenus nullum esse reale commune habent” (quoted in Ferrater Mora [1], p. 39–40).Google Scholar
  14. 14.
    On the authenticity of Categoriae see De Rijk [2].Google Scholar
  15. 15.
    Let us consider Jungius’ paraphrase of the Aristotelian text: “Secunda Divisio. Entium, sive eorum, quae sunt, quaedam de Subjecto dicuntur, in Subjecto vero nullo sunt, ut Substantiae Universales, sive Genera vel Species Substantiae, ut homo, animal, corpus. Quaedam in Subjecto sunt, de Subjecto vero nullo dicuntur, ut Accidentia praedicamentalia singularia, ut haec superficies, hic color, haec Virtus. Quaedam et de Subjecto dicuntur, et in Subjecto sunt, ut accidentia universalia, sive Genera et Species Accidentium praedicamentalium ut Superficies, color nigrities, sapor, dulcedo. Quaedam neque de Subjecto dicuntur, neque in Subjecto sunt, ut Substantiae singulares sive individuae, ut Socrates, Cicero, Bucephalus” (Jungius [1], p. 16). Boethius calls the division of entities into ten categories the divisio maxima, the present classification into four classes of entities the divisio parvissima. But unfortunately Boethius does not provide further explanations as to how both divisions and how the two fundamental relations (singular-universal, substance-accident) should be combined (Boethius [1]).Google Scholar
  16. 16.
    Cf. Prantl [1], Vol. I, p. 685. Also Boethius [1]. We find the square in such important editions as Averroes [1] and Pacius [3].Google Scholar
  17. 17.
    Ioannes a Sto. Thoma [1], p. 476: “Atque ita in hoc tertio antepraedicamento distinguit Aristoteles duplex genus entium, scilicet substantiam et accidens, et duplex genus intentionum, scilicet universalitatis et singularitatis.”Google Scholar
  18. 18.
    Fernandez-Garcia [1]: distinctio ens-res. It is interesting to consider also the following earlier text: “Thus the word `thing’ may admit of a wider extension, whereby it may apply to universals, even though Aristotle says that the latter are to be understood as abstracted from particular things in such a way that they would have no existence in the absence of the aforesaid” (John of Salisbury [1], p. 140 = Book II, Ch. 20).Google Scholar
  19. 19.
    ev vnoxsq vw elvat.Google Scholar
  20. 20.
    xaO’ vrcoxctuévov 2,syecOat.Google Scholar
  21. 21.
    Aristotle [1], 2a, 19–27.Google Scholar
  22. 22.
    to be predicated univocally“, Aristotle [1], 3a, 33; 3b, 9; cf. Simplicius [1], p. 52.Google Scholar
  23. 23.
    Belongs to“ (approximately).Google Scholar
  24. 24.
    Separately“ (approximately).Google Scholar
  25. 25.
    The possibility of sometimes predicating the name will actually develop into a wider theory of predication (cf. Section 4.2).Google Scholar
  26. 26.
    Aristotle [I], 2a, 27–34.Google Scholar
  27. 27.
    Subiectum in praesentia non sumitur eodem modo; cum enim asseritur aliquid dici de subiecto, accipitur subiectum pro subiecto praedicationis; at cum dicitur, aliquid esse in subiecto, usurpatur pro subiecto inhaesionis“ (Gasconius [1], II, 67a). Cf. Simplicius [1], p. 53, 25.Google Scholar
  28. 28.
    For example, 3a, 7–15.Google Scholar
  29. 29.
    Aristotle [1], Chapter 5, in particular 3a, 7–32.Google Scholar
  30. 30.
    Cf. Jungius’ paraphrase (quoted above) and especially Boethius [1].Google Scholar
  31. 31.
    This is clear in Aristotle [1], lb, 13; lb, 20–24; 2b, 19 and especially the passage 3a, 33–3b, 10.Google Scholar
  32. 32.
    The term avlcßeßrlxdç does not appear in Categoriae but we follow tradition, for example, Boethius [1]. Cf. also Van Auben [1], 399–400.Google Scholar
  33. 33.
    This is not clear in the basic text (la, 20—lb, 10) but it is obvious in 2b, l-3. “Tam primae quam secundae substantiae subiiciuntur accidentibus”, says Pacius [2], cap. 3, n. 3. This is a fundamental point in traditional ontology whose effects on traditional logic may be easily foreseen. If properties (accidents) inhere in man as well as in this man, one may presume that they will also be said of man as well as of this man. Do individual accidents inhere also in universal substances? The basic text (la, 20–1b, 10) does perhaps allow this (taking for example “vg” in la, 26 as a universal). But thereby we would be forcing the text in a question which is precisely the weak point of Aristotelian ontology: singularity-universality in accidents.Google Scholar
  34. 34.
    Aristotle [1], 3b, 17.Google Scholar
  35. 35.
    T6 xaû’ ixaarov (2a, 35–2b, 3); âroua xai liv deuBu4i (lb, 6); iítqua (3a, 35). The individuality of members of a9 is explicitly assigned by lb, 6 and 4a, 14–17. 11a, 20–36 cannot be used for this because there râ xdB lxaara seems rather to designate subordinate concepts.Google Scholar
  36. 36.
    For the meaning of these terms cf. Bonitz [1], articles xaBdAov and ovaia. Universal is described not only by means of “being predicable of” but also by the Greek term vnaegeiv; this is the origin of the traditional double characterization of universals as being said de multis and being in multis, “universale in praedicando” and “universale in essendo”. The definition of EU in Categoriae (cf. Section 1.2) still serves to characterize the opposition substance—accident in the main Aristotelian works, except that now accidents may always, not only sometimes, be said of their substances. (This corresponds to a predication theory different from that of Categoriae, cf. Section 4.2.)Google Scholar
  37. 37.
    Aristotle [1], Perihermeneias, 7, 17a, 38–40, boldly divides to pragmata into universals and singulars, but the only examples given are man and Callias. In Aristotle [4], B, 3, 195b, 13–15, we may be momentarily attracted by the fact that such terms as “genus”, “individual”, “accident” appear together, but this is useless for the purposes of the present research because there the term “accident” means rather what is incidental. Aristotle [2], B, 6, 1003a, 7ff. illustrates the distinction universal—singular by means of Socrates, animal, man. Aristotle [2], A, 6, 1015b, 16–34, actually refers to both dimensions but the distinction universal—singular is considered only for substances.Google Scholar
  38. 38.
    Perhaps the most significant passage exemplifying this is Aristotle [2], Z, 1: the main opposition there is between substance and non-substance; if some hint at universality—singularity is to be found, this concerns only substances. Aristotle [2], P, 2, contains also an important formulation of the metaphysical program. The dominant opposition is again ousia vs. non-ousia, but it is impossible to find an explicit or adequate reference to the other dimension.Google Scholar
  39. 39.
    Aristotle [2], N, 2, 1089b, 20–28. We quote Ross’ paraphrase: “In the categories other than substance there is another problem as to how things are many; no doubt, since they do not exist apart, they are many through the substratum taking on many qualities, amp;c.; but there must be a matter for each category, only it cannot be one existing apart from substance” (Vol. II, p. 469). Cf. also: “The special difficulty attaching to the minor categories is that of assigning to each a matter which shall render plurality possible without being separable from substance…” (Ibid., p. 477).Google Scholar
  40. 40.
    It may be inferred from such passages as Aristotle [2], A, 5, 1071a, 20 (until the end) that accidents are individuals because (a) universals do not exist (1071a, 19) and (b) if substances would disappear, all other things would likewise disappear, which means that accidents do exist (when substances exist). The same could be inferred from the first lines of A plus Pseudo-Alexander’s commentary (in Aristotle [2.1], Vol. II, p. 643, note 1). But this tends simply to confuse the reader. Sometimes accidents are individual, real entities; sometimes they are predicated of substances, i.e., they are universals. (Of course, examples of accidents being predicated of substances are to be found everywhere in the main Aristotelian works, apart from Categoriae’s peculiar first pages; that is in fact the standard, in opposition to Categoriae, Aristotelian predication theory; cf. Section 4.2.)Google Scholar
  41. 41.
    Tricot (in Aristotle [2.1], Vol. 1, p. 289, note 1) depending on Alexander and Bonitz; Ross (in Aristotle [2], Vol. 1, p. 323) also depending on Alexander. For the second point, Ross in Aristotle [2], Vol. 1, p. LXXXVII; also Ross’ commentary on Metaphysics I, 1054, b, 35, where an expression equivalent to “Porphyrian tree” appears, but where, as in Porphyry, complete obscurity reigns as to which are the bases of the accidental Porphyrian trees. De Rijk [1], p. 70–71, deals with the present question, and he affirms that the reason is to be found in the peculiarities of “the” Aristotelian theory of predication. But “the” Aristotelian theory which he means is that of Analytica Posteriora, and moreover a theory which Aristotle seems to propose only incidentally (“if we are to legislate”). Therefore, the predication theory meant by De Rijk does not seem to explain — as he suggests — why Aristotle is silent about singular—universal in accidents. Owens [1] does not appear to consider at all the problem of singularity—universal- ity in accidents. This is all the more significant as this study is especially concerned with universal—singular relations (but apparently only in the substantial domain). A particular case is Scholz, who approached classical texts on ontology from a perspective of modern predicate-calculus. May “huparchein” always be translated into contemporary predicate-theoretical standards? (cf. Scholz—Hasenjaeger [1], p. 13, note). One may conjecture that Scholz, according to such an approach, would have translated the famous “non est accidens accidenti” (Metaphysics, F, 4) with “there are no predicates of predicates”. But this, especially from the point of view of the whole tradition, would be a most questionable version. Also, in Scholz [2] it is said (p. 140) that to define the existence of classes as their non-emptiness is to be Aristotelian rather than Platonist; this may be correct in itself, but Scholz supports his statement by evoking such Aristotelian theses as “ta pathe do not exist apart from substances”. Now, does “pathe” designate individual or universal accidents? Scholz’s well-known comparison of old ontology with modern logic should perhaps be re-examined; in doing so the two ontological dimensions should be taken into account. Owen [1] is a recent discussion related to the ontological square. The author stresses that the Aristotelian texts do not sufficiently support the thesis that individual accidents cannot be found in more than one subject. This thesis is viewed by the author as “a dogma” originating with Aristotle’s interpreters. The author also stresses that such a dogma entails many difficulties. But the absence of the dogma in Aristotle raises in fact even more difficulties, which are not accounted for by Owen [1].Google Scholar
  42. 42.
    GRG II, § 151 (in the analysis of contents).Google Scholar
  43. 43.
    Cf. Sections 2.61 and 6.4.Google Scholar
  44. 44.
    Cf. Section 1.2, note 17.Google Scholar
  45. 45.
    Cf. Sections 1.45 and 1.46.Google Scholar
  46. 46.
    In the Renaissance I include the second scholastics. (For this term “second scholastics”, cf. Giacon [1]. For the usual “restricted” conception of“Medieval philosophy”, cf. De Wulf [1], n. 15 and 449.)Google Scholar
  47. 47.
    Porphyry [1], Isagoge, 2a, 5–13. Aaron [1], Section 2, finds it strange that Porphyry poses the problem (of universals) in terms of thing-universals only (thing-universals as opposed to qualities or relations). Actually within the framework of a strict Aristotelianism it would be strange to find somebody paying attention to the problem of universals within the accidental domain. It is indeed strange to find so many authors (especially in the Middle Ages) stressing the singular—universal question in the case of accidents. Incidentally, Aaron [1] makes extensive use of the opposition thing—universal and qualities or relations (pp. 3ff, 26, 33, 36, 40, 104, 176, 191, 217–8, 234, 237), but the connection of this modern-philosophy terminology to its source — the ontological square — is not clear. (The author gives one reference to Categoriae’s individuality of accidents on p. 10.)Google Scholar
  48. 48.
    Algazel [1], Tract. primus, div. prima, div. secunda. The second section of the divisio secundo is entitled: “Universale non potest habere plura singularia nisi unumquodque discernatur ab alio.” This involves something akin to the principle of indiscernibles, but with an awareness of the two dimensions of classical ontology.Google Scholar
  49. 49.
    For example: “Ich will einen allgemeinen Satz vorausschicken: alle Substanzen oder Accidenzen oder auch Attribute von Substanzen and Accidenzen mit denen man in dieser Hinsicht auf ihn [God] hinweist, sind weder in großem noch in kleinem Umfange auf den Schöpfer anwendbar” (Kaufmann [1], p. 54).Google Scholar
  50. 50.
    In like manner, and with due proportion, those quantities and qualities which are individually present in primary substances may also be called “primary”, while those quantities which are abstracted from particular things by an analogous process [quadam ratione similitudinis] may be termed “secondary”. The same holds with the other predicaments“ (John of Salisbury [1], p. 161 = Chapter 3, Book 3).Google Scholar
  51. 51.
    Ibid., p. 156.Google Scholar
  52. 52.
    Schütz [1], article “accidens”, b), third line.Google Scholar
  53. 53.
    Ubi notandum est quod natura non se habet ad suppositum sicut universale ad singulare, quia in accidentibus etiam invenitur singularitas sine ratione suppositi et in substantia nostra natura assumpta est a Verbo, secundum Damascenum, non tarnen suppositum nostrae naturae“ (Duns Scotus [1], p. 558). Also: ”Quia ita impossibile videtur unum accidens esse in duobus subiectis, sicut unam formam substantialem esse in duobus materiis“ (quoted by Fernandez Garcia [1], p. 745, effata: ”Accidentis unius unum est subiectum“; referring to Op. Oxon. III dist. I, q. 2, n. 4).Google Scholar
  54. 54.
    Baudry [1].Google Scholar
  55. 55.
  56. 56.
    Uno modo idem est [Ockham is explaining the meanings of “finesse”] quod inhaerere realiter sicut accidens inest subiecto et forma materiae. Alio modo idem est quod praedicari.“Google Scholar
  57. The term “finesse” will be enthusiastically adopted by Leibniz (Couturat [1], p. 10).Google Scholar
  58. 57.
    Paulus Venetus [1], tract. 1, cap. XVI, de praedicamentis.Google Scholar
  59. 58.
    This is an interesting background, which may be taken into account in regard to the famous Berkeley discussion of the idea of triangle.Google Scholar
  60. 59.
    Gasconius [1], II, 55b. Cf. De Natura Accidentis in Aquinas [2].Google Scholar
  61. 60.
    Suarez [1], 39, 1, 1 and 16; cf. the text quoted above in note 50.Google Scholar
  62. 61.
    Pacius [2], cap. 2, n. 16 and 20.Google Scholar
  63. 62.
    Keckermann [1], Index: “Accidens… numero unum de subiecto non migrat in subiectum… numero unum in subiectis numero diversis esse nequit…”Google Scholar
  64. 63.
    Ibid., Liber I, cap. 5 (p. 72): “Sic Logica quae fuit in Aristotele, non fuit idea vel species, sed Logica individua et singularis.” Keckermann adds: “Scholasticorum Canon huic pertinet: Accidentia numerantur ad numerum subiectorum.”Google Scholar
  65. 64.
    Descartes [1], §§ 51, 57. Gilson [3], p. 46, gives a list of passages where Descartes refers to “choses particulières et universelles”.Google Scholar
  66. 65.
    For example, Descartes [1], § 52 in fine, asserts that when we come across a property we may conclude that there is a substance having that property. This is not the ontological argument… but probably an obvious argument about properties understood as individual accidents. Ibid. n. 61, Descartes examines the distinction modale; he considers four cases of distinction: (i) between a mode and a substance, (ii) between two modes of the same substance, (iii) between a mode of a substance and another substance, (iv) between a mode of a substance and a mode of another substance. Obviously, this is conceived in terms of properties-of-a-given-individual.Google Scholar
  67. 66.
    Contrary to Scholz’s program, cf. Scholz [7], for example, p. 414.Google Scholar
  68. 67.
    Port-Royal [1], Première partie, Chapitre 2: “On ne sçauroit nier ce rapport du mode, qu’on ne detruise l’idée qu’on en avoit.”Google Scholar
  69. 68.
    Ibid., Chapitre 6.Google Scholar
  70. 69.
    Accidents “stick on” substances; substances are “under-propping” (Locke [1], II, 13, § 20).70. Locke [1], II, 23, § 4.Google Scholar
  71. 71.
    In the notice that our senses take of the constant vicissitude of things, we cannot but observe that several particulars, both qualities and substances, begin to exist“ (Locke [1], II, 26, § 1, italics ours).Google Scholar
  72. 72.
    This is further to be observed concerning substances, that they alone of all our several sorts of ideas have particular or proper names, whereby one only particular thing is signified. Because in simple ideas, modes, and relations, it seldom happens that men have occasion to mention often this or that particular when it is observed“ (Locke [1], III, 6, § 42).Google Scholar
  73. 73.
    On this account, if one should say, that the whiteness of this sheet is the whiteness of another sheet, every man perceives this to be absurd“ (Reid [1], p. 327, Essay V, Ch. 3).Google Scholar
  74. To this I answer, that the whiteness of this sheet is one thing, whiteness is another; the conceptions signified by these two forms of speech are as different as the expressions; the first signifies an individual quality really existing and is not a general conception, though it be an abstract one; the second signifies a general conception, which implies no existence, but may be predicated of every thing that is white, and in the same sense“ (ibid.).Google Scholar
  75. 74.
    In such terms Russell [1], § 10, describes a passage of Leibniz’s polemics with Clarke (in Leibniz [1], vol. VII, p. 400–401).Google Scholar
  76. 75.
    Car deux sujets differens, comme A et B, ne sauroient avoir precisement la même affection individuelle, un même accident individuel ne se pouvant point trouver en deux sujets, ny passer de sujet en sujet“ (Leibniz [1], loc. cit.).Google Scholar
  77. 76.
    The Concise Oxford Dictionary of Current English (1949), article “Siamese”.Google Scholar
  78. 77.
    Russell [1], § 10: “After he has seemed for a moment to realize that relation is something distinct from, and independent of, subject and accident, he thrusts aside the awkward discovery.” If Russell means universal relation (that R which applies between a and b as well as between c and d), then (1), it is not true to say that Leibniz rejects them, for he still assigns to them an objective ontological status in the mind (cf. note 83); (2), moreover, Russell’s statement would not fit with the Leibnizian text where individual relations are meant (cf. note 79). If Russell means individual relation (that Ra, b which is an individual instance of R applying between a and b), then the Leibnizian discovery is indeed so awkward that one wonders how Leibniz could do otherwise than to thrust it aside. But the second alternative seems improbable.Google Scholar
  79. 78.
    Itaque plena omnia relationum in mundo, nec res ulla nascitur, quin infinitae propemodum cum ea nascantur relationes“ (Keckermann [1], Lib. I, cap. XII = p. 115).Google Scholar
  80. 79.
    The fragment quoted by Russell [1], § 10, does not mention individual accidents but only accidents. It is obvious, however, from the immediately preceding context that Leibniz is simply abbreviating “accident” for “individual accident”. The fragment quoted by Russell is intended by Leibniz as an example of his previously formulated thesis about individual accidents (cf. our note 75).Google Scholar
  81. 80.
    Leibniz would say: Ra, b and Rc, a conviennent seulement (loc. cit., p. 401 above). For a modern approach to these “concrete” properties cf. Kling [1] and [2].Google Scholar
  82. 81.
    Cf. following note.Google Scholar
  83. 82.
    Leibniz says, in the English translation quoted by Russell: “You will not, I believe, admit an accident which is in two subjects at once. Thus, I hold, as regards relations, that paternity in David is one thing, and filiation in Solomon is another, but the relation common to both is a merely mental thing, of which the modifications of singulars are the foundation” (in Russell [1], Appendix, ad § 10).Google Scholar
  84. 83.
    Russell [1], § 10. The critical phrase “being in the mind” has primarily an objective sense in traditional philosophy. Leibniz himself would say, for example, that necessary truths are dans l’entendement (Leibniz [1], Vol. V, p. 76 ).Google Scholar
  85. 84.
    Dependent on Russell’s interpretation are Maritain [1] (n. 40, b), ScholzHasenjaeger [1], § 84. Bergmann [1] is perhaps the only adequate approach to Leibniz in the present questions; but still it would seem that even Prof. Bergmann does not point to the ultimate source of Leibniz’s difficulty with relations, i.e., the awkwardness of individual instances of relations. Leibniz’s difficulty was to find a model — a sound model — for hoc aequale, not for aequale (to take Paulus Venetus’ example of a relation and its individual instance, cf. note 57).Google Scholar
  86. 85.
    In particular Russell [1], § 4.Google Scholar
  87. 86.
    In such a context it is meaningless to speak of properties “migrating” from one subject to another (cf. note 75) and in fact Russell does not consider this aspect of Leibniz’s ontology (for example, Russell [1], § 67, where the text quoted in our note 75 is paraphrased but the phrase on migration of properties is curiously dropped).Google Scholar
  88. 87.
    Russell [1], § 23.Google Scholar
  89. 88.
    For instance Trendelenburg [1], pp. 14–15.Google Scholar
  90. 89.
    Wo ein Urteil im eigentlichen Sinne vorliegt, so daß es die Sache aussagt, wie sie wird, ist das Subject die erzeugende Substanz (a$aia). Die ausgesagten Begriffe (xaTnyoeovµsva im eigentlichen Sinne) setzen das Subject voraus, und, inwiefern sie nicht Substanzen sind, sind sie, real gefaßt, in der Substanz avußeßp o’Ta“ (Trendelenburg [1], p. 210).Google Scholar
  91. The “authenticity” of a “judgment” is determined by Aristotle’s ruling on correct predication (Analytica Posteriora I, 22; cf. Trendelenburg’s text referred to in the preceding note).Google Scholar
  92. 90.
    The clandestine introduction of concepts under the heading of “predicate” is clear, for example, in the following text: “Hiernach erscheinen die Kategorien als die allgemeinen Begriffe, unter welche die Prädikate des einfachen Satzes fallen… Die Kategorien sind die allgemeinsten Prädikaten” (Trendelenburg [1], p. 20). One may compare this use of “Fallen unter” with Frege’s. This is an occasion to appreciate the importance of Frege’s stressing the necessity of distinguishing names and designata. In the text quoted in note 89 we had already seen the expression “ausgesagten Begriffe”; the same phrase occurs in p. 19 of Trendelenburg [1]. The “judgment” is analysed into subject—predicate, but “predicate” ambiguously covers linguistic as well as non-linguistic entities (i.e. universals, concepts).Google Scholar
  93. 91.
    Cf. for instance the description of categories as die allgemeinen Begriffe in the text quoted in the preceding note.Google Scholar
  94. 92.
    Therefore, in the polemic between Trendelenburg and Bonitz about the significance of the categories, it appears how ambiguous the very formulation of the problem is.Google Scholar
  95. 93.
    For the opposition “formal” and “real”, cf. Trendelenburg [1], p. 18, below.Google Scholar
  96. 94.
    How essential predication is to be understood, remains obscure in the “parallelism” version of the ontological square. Trendelenburg [1], p. 16, mentions this kind of predication without, however, saying whether or how it fits with the correspondence between substance—accident and subject—predicate. In the text quoted in note 89, there is only a negative reference.Google Scholar
  97. 95.
    This is an old and fundamental approach to universals.Google Scholar
  98. 96.
    A typical Aristotelian scholar of the 16th century would teach that the division of entities into singulars and universals is a “divisio subiecti in accidentia, nam cuilibet rei sive enti accidit ratio universalis et singularis; ut enim superius diximus, res ipsa neque per se universalis est, neque singularis, sed potius illud ei convenit per abstractionem intellectus, hoc vero per condiciones particulares” (Gasconius [1], II, 67a, below). Kant teaches that in concepts there is a Materie and a Form. The former is the Gegenstand (here, obviously, as in Gasconius: Gegenstand = res, indifferent or neutral with respect to universality and singularity; not Gegenstand = existing individual given, for instance, in the Anschauung); the latter is the Allgemeinheit. Now, universality is always made by us, jederzeit gemacht (Kant [2], §§ 2, 4, 5).Google Scholar
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    As Kant puts it: “er [i.e., the distinction singular—universal] keinen Unterschied in der Beschaffenheit der Dinge, sondern nur des Gebrauchs der Begriffe, ob sie im allgemeinen oder aufs einzelne angewandt werden, anzeigt” (Kant [4], Erst. Abschn., C, fourth note).Google Scholar
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    Eisler [1], “Akzidenzen”.Google Scholar
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    Cf. text quoted in note 96.Google Scholar
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    Heidegger also seems to support the “parallelism” version described in the present ` section (cf. Heidegger [1], p. 28). A recent version is the following: “Aristotle’s position in logic, that every proposition is reducible to subject—predicate form, is paralleled by his metaphysical doctrine that the world consists of substances with attributes” (Körner [1], p. 21).Google Scholar
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    Husserl [1], 1, §§ 31, 34, 39. As for the other dimension cf. Husserl [1], I. Untersuchung, § 15, where universality is described in the following terms: “Fähigkeit, auf eine Vielheit von Gegenständen prädikativ bezogen zu werden”.Google Scholar
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    Husserl [2], Erster Artikel.Google Scholar
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    Bergmann, J. [1], § 5, 2 and 3.Google Scholar
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    Cf. Section 5.32.Google Scholar
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    Elias [1], p. 153; Simplicius [1], p. 54, lines 15–20.Google Scholar
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    Husserl [1], I, 41.Google Scholar
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    Carnap [1], p. 216 (or Linsky [1], p. 222). Cf. Carnap [7], p. 20, and also Simpson [1], pp. 272, 277, 291, 295–6.Google Scholar
  110. 108.
    Reichenbach [1], p. 53 and [2], pp. 27–28 suggests that “property” has to be understood in two senses. One of them involves the so-called “specific properties” of an entity; a specific property of x is for instance the individual motion of x and it is only of this specific property that we may predicate the (higher property?) of being slow. Unfortunately, Reichenbach does not develop this question systematically. Let us only observe that “specific properties” are, in classical terms, individual accidents.Google Scholar
  111. 109.
    Ingarden [1] p. 73: “Indessen führt bekanntlich anderseits gerade die Annahme von Eigenschaften der Eigenschaften zu einer Antinomie. Zugleich müßte man zugeben daß es in dem Seinsbereiche eines Gegenstandes etwas gibt (nämlich die Eigenschaften der Eigenschaften), das zugleich außerhalb dieses Bereiches liegt. Denn indem die Eigenschaft das dem Gegenstande in einer Hinsicht Zukommende ist, kommt sie ihm mit allem und jedem, was in ihr selbst ”ent-halten“ ist, zu. Somit muß sie mit allem und jedem in ihr Unterscheidbaren in den Seinsbereich des betreffenden Gegenstandes fallen. Wenn dagegen das der Eigenschaft Zukommende dem entsprechenden Gegenstande nicht zukommt, so liegen, wie es scheint, mindestens die vermeintlichen Eigenschaften der Eigenschaft außerhalb des Seinsbereiches des betreffenden Gegenstandes.”Google Scholar
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    Schütz [1] article “accidens”. This impressive thesis of classical ontology underlies the paradox discussed by Ingarden [1].Google Scholar
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    F. Kaufmann [1] (pp. 18–19) and [2].Google Scholar
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    F. Kaufmann [I] ibid.: “Wie steht es aber demgegenüber mit der Behauptung, daß eine bestimmte Eigenschaft E1 (z.B., eine bestimmte Farbe) eine bestimmte ”Eigenschaft“ E2 (z.B. eine bestimmte Helligkeit) habe? Da zeigt es sich, das eine Eigenschaft (Farbe) E1 als bestimmt überhaupt nur dann gelten kann, wenn feststeht, ob sie die ”Eigenschaft“ E2 (bestimmte Helligkeit) besitzt oder nicht.” The situation described by this text may be expressed by the following schema: In fact, F. Kaufmann seems to have in mind that rationalis is not a property of a determined animal (homo) for it is only due to rationalis that one may speak at all of a “determined” animal. Thereby F. Kaufmann apparently assumes that to speak of a property of an object a implies that a is “already” a sufficiently determined entity, regardless of its having or not having the property in question (ibid.). Actually his rejection of properties of properties seems also to involve the pointing out of an ambiguity in “property” rather than to reject as absolutely meaningless the locution “properties of property” (ibid.). F. Kaufmann denounces the meaninglessness of this phrase in the famous (Fregean) example of existence as property of properties (ibid.). He says, that it is unsinnig to assign a spatio-temporal property (i.e., “to have three individuals in such a place and such a time”) to a property which is not a spatio-temporal entity. It is curious that F. Kaufmann has not discussed examples of a more properly mathematical nature (for instance, to be local as a property of properties of functions). In any case, it should be observed that F. Kaufmann’s pretended “Ausschaltung” of the infinite from mathematics (cf. the title of F. Kaufmann [I]) largely depends on these ontological subtleties; for instance, he partially eliminates the possibility of speaking of sets of sets by referring to his doctrine on properties of properties (cf. F. Kaufmann [1], p. 98–99).Google Scholar
  115. 113.
    Bolzano [1] (§ 178) discusses sentences of the form “A, als ein C, ist B”, i.e., the so-called “reduplicative” sentences. For instance, “Cajus, als Musiker, ist unübertrefflich” is interpreted by Bolzano as meaning that “die Beschaffenheit C des A hat die Beschaffenheit B”. But this would not be readily admitted by Frege as an example of properties of properties; for the same reasons Frege would be suspicious of the examples of “types” and “orders” given by Crahay [Il, P. 48.Google Scholar
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    Cf. for example Scholz [7]: “… über der eigenschaftstheoretischen Ontologie des Aristoteles eine unanfechtbare eigenschaftstheoretische Logik zu konstruieren…” (p. 414).Google Scholar
  117. 115.
    BG., p. 17.Google Scholar
  118. 116.
    Cf. Chapter 10.Google Scholar
  119. 117.
  120. 118.
    GED., pp. 67–68: Vorstellungen are not selbständig; they require a subject, a Träger; moreover, “Jede Vorstellung hat nur einen Träger”, which corresponds to the Leibnizian (traditional) axiom that an accident cannot inhere in more than one subject.Google Scholar
  121. 119.
    Trendelenburg [1], which is a possible philosophical source of Frege (cf. BG, Vorwort). The Selbständigkeit of individual substances is determined in a double way: negatively or logically as that which is not a predicate, and “really” (real) as that which is not in (does not inhere in) another entity (p. 21, note 2; also pp. 53–54).Google Scholar
  122. 120.
    GRL, §§ 21–25, cf. Section 10.11; GRG II, p. 125; GED p. 61, cf. Chapter 2, note 82. It is not clear to me whether in this late text Frege perhaps is aware of the equivocal use of “Eigenschaft”. Grossmann [1], IV, does not seem to consider the possibility of an “ambiguity” in the term “Eigenschaft”. Cf. also Chapter 2, note 65.Google Scholar
  123. 121.
    Cf. 10.11.Google Scholar
  124. 122.
    Cf. note 41.Google Scholar
  125. 123.
    Cf. Chapter 2, in particular Section 2.24.Google Scholar
  126. 124.
    Cf. Section 2.62.Google Scholar
  127. 125.
    Cf. Section 4.2.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1967

Authors and Affiliations

  • Ignacio Angelelli
    • 1
  1. 1.University of TexasUSA

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