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The Traditional Lack of Distinction between UF and UO

  • Ignacio Angelelli
Chapter

Abstract

The present chapter is devoted to a consideration of Frege’s (or modern logic’s) accusation that traditional logic has not distinguished das Fallen eines Einzelnen unter einem Begriff from Unterordnung of concepts. After formulating the problem (4.1), the previous exposition of the traditional predication theory is completed (4.2). I next try to show that traditional predication theory cannot be viewed as a less fortunate presentation of the Fregean approach, as if it belonged to the same line of development. Indeed traditional predication theory is of another kind (4.3). The most important systematic reason responsible for this is next examined (4.4). Finally, some examples are given in which the distinction UF and UO is shown to be intrinsically required by the very traditional doctrines (and not only by our retrospective projections) (4.5). A brief remark on unit-classes in traditional philosophy is added (4.6).

Keywords

Predication Theory Modern Logic Traditional Logic Ontological Dimension Analytic Judgment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    UZBG; GRL, § 53; BGGE, p. 194 note; GRG I, p. 2; HUSS, p. 313. KSCH is written especially to show “die Notwendigkeit einer Unterscheidung […] die vielen Logikern unbekannt zu sein scheint” (p. 433; cf. also pp. 440, 441, 442 note, 455–456).Google Scholar
  2. 2.
    Whitehead and Russell [1], I, p. 342.Google Scholar
  3. 3.
    Scholz [2], p. 121, where, nevertheless, one finds the error of holding that traditional logic considered predication as part—whole; since Metaphysics A, 26 there is such a notion as totant universale.Google Scholar
  4. 4.
    UZBG and KSCH.Google Scholar
  5. 5.
    Or IF, cf. Section 3.2.Google Scholar
  6. 6.
    Cf. Chapter 7.Google Scholar
  7. 7.
  8. 8.
  9. 9.
    Cf. Section 3.3, note 35.Google Scholar
  10. 10.
    GRL, § 53.Google Scholar
  11. 11.
    GRL, p. 5 note.Google Scholar
  12. 12.
    Cf. note 1 here.Google Scholar
  13. 13.
    For example, Cornford [1], p. 256: “Plato nowhere implies that E…] the Form Man partakes of the Form Animal, in the same way as this man partakes of the Form Man. He uses the same word with his usual disregard for precise terminology, and he nowhere gives an explicit account of either relation. It seems obvious, however, that he cannot have regarded the two relations as the same.” One might also point to Ockham’s distinction of e and ⊂ (cf. Baudry [1], pp. 104, 107 ).Google Scholar
  14. 14.
    The present section continues Section 1.2.Google Scholar
  15. 15.
    Cf. Section 1.2.Google Scholar
  16. 16.
    Denominata dicuntur quae ab aliquo ita sumunt appellationem ut terminatione differant; veluti a grammatica, grammaticus. Quod si terminatione non differant, ut a grammatica arte mulier dicitur grammatica, homonymia est, non denominatio“ (Pacius [2], cap. 2).Google Scholar
  17. 17.
    For instance, if ciQs-t l (virtue) actually inheres in a man, we shall say that this man is arovddtoç (upright) (Aristotle [1], 10b, 5–9).Google Scholar
  18. 18.
    Aristotle [1], 10a, 27–10b, 11. Because it has a quality, a substance will be called by some name related to that quality.Google Scholar
  19. 19.
    Aristotle [1], 3a, 4–6.Google Scholar
  20. 20.
    Cf., nevertheless, 9a, 30–35, where substances are said to receive (to have) whiteness (Aevxózns). 11a, 31–32 would suggest that a substance “has” a singular accident because of the expression “ad xdO’ éxaoza”,but the context beginning in 11a, 20 is not clear as to whether that means individuals or subordinated species.Google Scholar
  21. 21.
    b, 2–10. Also 11b, 10–12 (to be completed by 6b, 10–15).Google Scholar
  22. 22.
    To be said of a subject.Google Scholar
  23. 23.
    For “de subiecto dici” as meaning essential predication, cf. note 31 here. For the new sense of that expression, the following references may be given: Aristotle [2], A, 9, 990b, 29–31 (cf. Aristotle [5], Top.,121, a, 11); Aristotle [4], A, 2, 185a, 31–32; A, 3, 186a, 34; A, 4, 188a, 8; A, 7, 190a, 35–36. Aristotle [2], B, 5, 100lb, 31–32; F, 4, 1007a, 35; LI,8, 1017b, 13–14; Z, 3, 1029a, 7; Z, 13, 1038b, 15. Aristotle [3], A, 22, 83a, 26; ibid. 83a, 31; 83b, 20–21 (Anal. Post.).Google Scholar
  24. It is perfectly clear that “de subiecto dici” apart from Categoriae covers accident-substance predication, and this is enough to justify one’s speaking of a “change” in the terminology of predication theory. Another question is whether the new sense of “de subiecto dici” excludes essential predication,i.e., whether it excludes the sense of that expression in Categoriae. To answer this question we must consider both the original texts and the critics.Google Scholar
  25. The two passages from Metaph. Z openly exclude ousia from things being said de subiecto,but 1038b 15 also excludes ousia from the domain of universals (katholou),which would still allow for the possibility of having substantiae secundae being said de subiecto. Nevertheless, this is an exception in our series of texts; Z, 3 and several other passages exclude ousia from being said de subiecto without further remarks as to whether this concerns singular or universal substance.Google Scholar
  26. On the other hand, Bonitz’s Index does not enlighten us on this point. Bonitz [1] (p. 798, b, 50–55) states that a genus (an essential predicate) may be said de subiecto although not being in subiecto,but this is supported only by reference to Topica 127, b, 1–3, which is a passage written in Categoriae’s terminology. (This is obvious, for the text asserts that if something is in-a-subject,it will not be predicated de subiecto about the subject in which it inheres.)Google Scholar
  27. A recent study on the two ontological dimensions, Chung-Hwan-Chen [1], affirms that the “new” sense of “kath’hupokeimenou legesthai” also involves essential predicates (secondary substances) being said de subiecto. But unfortunately the texts referred to (p. 157, note) do not state explicitly that man is said de subiecto of Callias (to take an example), but only affirm that “everything else” is said de subiecto of substances.Google Scholar
  28. On these grounds, I believe it is correct to say that “perhaps” the new sense of “de subiecto dici” excludes essential predication. (It is not clear why Sim- plicius [1], p. 54, 7f. does not pay more attention to the terminological change.)Google Scholar
  29. 24.
    If we look for KU (cf. D8 in the present section) in Categoriae,we find a variant of K (cf. Section 4.21, D7) such that the restriction of only predicating the name is not apparent (particularly in 12a, 12b). We may perhaps view 3a, 3–6 (where it is said that all the other things are predicated of substances) in the same sense, if we follow Chung-Hwan-Chen [1] (p. 153 note 3). This author considers that passage as abandoning the severe restrictive rules at the beginning of Categoriae which forbid that the logos of accidents be predicated of the substances. But that passage has been perhaps magnified by Chung-Hwan-Chen, because he has not included paronymous predication among the possibilities allowed by the severe rules at the beginning (he only mentions homonymous and synonymous predication). Thanks to paronymous names, it is possible to extend the possibilities of K very far, and if one adds names built “in some other way”, then “all other things” will be predicable of substances. Of course, the passage in question should say in addition “the names,not the logoi”,in order to be orthodox with respect to the severe rules.Google Scholar
  30. 25.
    Cf. note 23.Google Scholar
  31. 26.
    Aristotle [2], B, 995b, 35; Z, 3, 1029a, 23; Q, 7, 1049a, 27–40; A, 9, 992b, 1–3. The second text maintains that ousia is predicated of matter; the third that eidos is said of matter. Accordingly, hupokeimenon now is not only the individual Coriscus or Callias, but also matter. (Aristotle [2], Z, 13, 1038b, 5). Aquinas [1], 1288–9 (commenting on Metaphysics Z, 3) calls praedicatio denominativa this predication of substance about matter. Concerning matter — or materia prima — it should be observed that this is perhaps a notion more accessible today,considering the increasing interest in logic and ontology, than in the past. Aquinas [1] (1287, also 1308) distinguishes two approaches to matter, one per viam motus,the other per viam praedicationis; the latter, because of being proper to logic, is more adequate for Metaphysics. It is this second approach which today “makes sense” as soon as a hierarchy of predicates (and in particular essence) is introduced.Google Scholar
  32. 27.
    Aristotle [2], A, 6, 1015b, 32–35 opposes Coriscus to his two predicates: man and musical.Google Scholar
  33. 28.
    Cf. note 21.Google Scholar
  34. 29.
    Aristotle [3], A, 22 (Anal. Post.).Google Scholar
  35. 30.
    KS should be distinguished from accidental predication. The latter is to predicate an accident of a substance, which is not KS as defined in the text quoted in the preceding note. The Greek commentators have used a more expressive designation for KS (which had also the advantage of avoiding confusions with accidental predication): predication nao cktiacv (against nature) (Philoponus [1], 235; Alexander [1], 371, 8–13 ).Google Scholar
  36. 31.
    Simplicius [1], p. 52, identifies KU (cf. Section 1.2) with essential predication. I assume in the diagram that KU’ is directed to universal as well as to individual substances; cf. for instance Ross’ commentary in Aristotle [3] (p. 579, in the middle), where accidental attributes are said to apply to elements of the essence of an individual subject. Cf. also Aristotle [2], A, 6, 1015b, 28. I assume that KS comes both from individual and universal substances, although I cannot offer textual support for this. For ( K) cf. Section 4. 21.Google Scholar
  37. 32.
    For example, White [1].Google Scholar
  38. 33.
    Cf. note 16. “Praedicatio denominativa” became synonymous with “accidental predication” (cf. Ioannes a Sto. Thoma [1], p. 476). For a further extension of that term, cf. below, remark 2 to Burgersdicius’ text. “Denomination from” is the Lockian translation of the previous “denominatio ab” (Locke [1], II, 7, § 22 in fine; II, 25, § 2). In Husserl [1], VI, § 7, one finds an almost literal reproduction of the description of denomination in Categoriae: the name “red” is imposed on an object because of a Rotmoment appearing in that object. Formerly, denomination was subject to subtle distinctions, one of which is the philosophically important “denominatio extrinseca”.Google Scholar
  39. 34.
    Reid [1], Analysis of Aristotle’s Logic,ch. II.Google Scholar
  40. 35.
    Burgersdicius [1], Lib. 1, cap. XIX, theorema 1 (pp. 59–60).Google Scholar
  41. 36.
    Cf. note 33.Google Scholar
  42. 37.
    Neither does he [Aristotle] mean that the nine kinds of accidental things may not be predicated concerning substances […]. Isidore, Alcuin and other wise men tell us that all the remaining categories are predicated of primary substances“ (John of Salisbury [1], III, 3 = p. 160).Google Scholar
  43. 38.
    Aquinas [1], n. 1576, makes an interesting contribution to the present question. The author holds that essential predicates may be viewed as being predicated de subjecto only from the logician’s point of view, not from the point of view of the philosophus primus; by means of this distinction Categoriae and Metaphysics are conciliated. But we should observe that this is possible because the dimension singular-universal (the logician’s concern) is actually underestimated; it is “our” intervention in things (cf. Section 1. 44 ).Google Scholar
  44. 39.
    Cf. Section 2.25 in fine.Google Scholar
  45. 40.
    Cf. Section 1.2.Google Scholar
  46. 41.
    Gredt [1], n. 139.Google Scholar
  47. 42.
    Caietanus [2], p. 63, shows that even individual accidents, for example this white,have been considered as predicable of their substances: “…individuis accidentium tantum, quae praedicantur de subiectis suis denominative, ut cum dicitur: ‘Sortes est hoc album’.” (This is Averroes’ view, reported by Caietanus.)Google Scholar
  48. 43.
    Or KUI, cf. note 24. (The text of Categoriae is that of Aristotle [1].) “In demselben Sinne, wie von dem einzelnen Menschen das Prädikat sprachkundig ausgesagt wird, kann es auch von dem Menschen überhaupt ausgesagt werden” (Trendelenburg [1], p. 59).Google Scholar
  49. 44.
    An example of how seriously the tradition has assumed the possibility of universal accidents inhering in substances is given by Boethius: “Probatur quoque particulare album in subjecto esse hoc modo, nam color quod genus est albi vel cujusdam albi in corpore est, et est in subjecto. Quare cujus genus in subjecto est, ipsum quoque in subjecto est” (Boethius [1], p. 172, A-B).Google Scholar
  50. 45.
    Aristotle [2], A, 9, 991a, 29–32 (also: M, 5, 1079b, 32–35 ).Google Scholar
  51. 46.
    Ross’ analysis of the text: “Not only will the species be the pattern of the individuals, but the genus will be the pattern of its species, so that the same thing will be pattern and copy” (in Aristotle [2], I, p. 188).Google Scholar
  52. 47.
    Aristotle [3], Anal. Priora,I, 27; Analyt. Post., I,19–23.Google Scholar
  53. 48.
    Ibid. Anal. Priora, I, 27.Google Scholar
  54. 49.
    Cf. Section 4.1 in fine.Google Scholar
  55. 50.
    Aristotle [5], Topica,Z, 6, 144a, 32–33.Google Scholar
  56. 51.
    Ibid.,144b, 4–5.Google Scholar
  57. 52.
    For example Aristotle [2], B, 3, 998b, 22–27. Cf. Tricot in Aristotle [2.1], I, p. 140 and 141. Aquinas [1], n. 433.Google Scholar
  58. 53.
    Consider the Oxford translation: “Moreover, the differentiae will be all either species or individuals, if they are animals; for every animal is either a species or an individual” (Aristotle [3.1], 144b).Google Scholar
  59. If the species is predicated of the differentia, then Sil’Aov özc I7 8caSopà liv6pmicoç laxly,which Pacius translates in the following way: “manifestum est, differentiam esse hominem” (Pacius [1], p. 716). The Oxford translation seems to surround this text with some ambiguity: “the differentia is clearly the human race” (Aristotle [3.1], ibid.).Google Scholar
  60. 54.
    Aristotle [6], P, 133 (On Ideas).Google Scholar
  61. 55.
    Aristotle [2], A, 6, 1015b, 28.Google Scholar
  62. 56.
    Ibid.,22, 1022b, 25.Google Scholar
  63. 57.
    Porphyry [1], p. 13.Google Scholar
  64. 58.
    Ibid.,p. 5, 1.7.Google Scholar
  65. 59.
    A second-scholastics commentary:Google Scholar
  66. Cum enim perpetuo superiora de inferioribus praedicentur, species quidem de individuis praedicabitur; genus autem de specie et individuis; genus vero supremum de genere vel generibus (si in ea recta serie plura sint genera et species subalternae) atque etiam de specie, et individuis praedicatur. Genus namque supremum de omnibus generibus, speciebus et individuis dicitur. Genus autem quod collocatur ante speciem infimam, de omnibus speciebus infimis sub se contentis et individuis effertur. Species infima tantummodo praedicatur de omnibus individuis; at vero individuum de uno solo particulari“ (Gasconius [1], II, 28a ).Google Scholar
  67. Ex fis quae dicta sunt colligo duo. Alterum est, quod genus de speciebus sub se contentis et individuis illarum specierum dicitur, species tantummodo de individuis, differentia vero, proprium et accidens de specie cuius sunt talia et de individuis sub ilia specie contentis praedicantur. Alterum est […] Species namque est essentia individuorum, quae sub ea in categoria continentur. Genus autem, et differentia de speciebus et de individuis earum specierum essentialiter praedicantur“ (ibid., I, 2b - 3a ).Google Scholar
  68. Pacius’ presentation of the same subject-matter:Google Scholar
  69. Secundo, cum ait genus quidem’, tradit primam regulam: Superiora inferioribus attribuuntur, non contra superioribus inferiora. Intellige superiora et inferiora in eadem Categoria. Tertio cum ait Oportet enim’ datam regulam ex eo confirmat, quod vel attribuuntur aequalia aequalibus, vel maiora minoribus, non minora maioribus in singulis [enim?] Categoriis“ (Pacius [3], in the commentary on Isagoge).Google Scholar
  70. In the 17th century:Google Scholar
  71. Quum in inferiori sit superius, E...] est in individuo species, genus infimum, subalterna, summum, in specie genera, in genere infimo et subalterno superiora, in inferioribus omnibus summum“ (Baumgarten [1], § 153). ”Determinationes generis summi sunt in inferioribus eius E...] i.e. generibus subalternis, infimo, speciebus et individuis; determinationes generis subalterni sunt in inferioribus eius generibus, speciebus, et individuis; determinationes generis infimi sunt in speciebus et individuis; determinationes speciei sunt in individuis […] i.e. determinationes superioris sunt in eius inferiori, seu positivae fuerint seu negative […1 Haec propositio dicitur dictum de O[mni] et N[ullo]“ (Ibid., § 154, italics of the author).Google Scholar
  72. Reid’s exposition:Google Scholar
  73. Every genus, and every species of things may be either the subject or the predicate of a proposition, nay of innumerable propositions; for every attribute common to the genus or species may be affirmed of it; and the genus may be affirmed of every species, and both genus and species of every individual to which it extends“ (Reid [1], Essay V, ch. 1, 7).Google Scholar
  74. It should be observed that Reid had, shortly before, stated the possibility of attributes of attributes in a sense “corresponding” to our contemporary use of this expression. I say only “corresponding” because Reid’s attributes of attributes are Reichenbach’s individual accidents (cf. Chapter 1, note 108) rather than predicates of predicates. Nevertheless, it is clear that Reid’s insight into attributes of attributes conflicts with his Aristotelian view of animal as an attribute of the attribute man (cf. Section 5.32).Google Scholar
  75. 60.
    Porphyry [1], p. 13, 1. 20.Google Scholar
  76. 61.
    Aristotle [2], I, 9, 1058b, 10–13; A, 9, 1018a, 1.Google Scholar
  77. Convenit enim idem esse album et nigrum. Sed diversimode. Quia si illud quod dicitur album et nigrum sit aliquod universale, simul est album et nigrum quantum ad diversos. Sicut simul verum est dicere quod homo est albus propter Socratem et niger propter Platonem. Si vero fuerit aliquid singularium, non erit simul album et nigrum“ (Aquinas [1], n. 2138 ).Google Scholar
  78. Substantiae vero secundae, id est genera et species, substant solis accidentibus. Et hoc etiam non habent nisi ratione primarum. Homo enim est albus in quantum hic homo est albus“ (Ibid., n. 1274 ).Google Scholar
  79. Accidens commune inest magis individuis, quam universalibus. Teste Aristot. 9 Met. cap. 9, ubi ait: homo est albus, quia Callias est albus, i.e. albedo speciei inest propter individua; huius rei ratio est, quia communia non fluunt ab essentia subiecti, sed ab existentia potins, quae est singularium“ (Keckermann [1], Liber I, cap. XXI).Google Scholar
  80. 62.
    Quia vero huiusmodi praedicata per accidens prius praedicantur de singularibus, et per posterius de universalibus, cum tarnen e converso sit de praedicatis per se…“ (Aquinas [1], n. 845).Google Scholar
  81. 63.
    Gasconius [1], after having explained the Porphyrian doctrine that a genus is predicated both of the subordinate species and of the individuals, considers the question whether “genus respectu solius speciei genus sit, an vero respectu quoque individuorum, ita ut haec oratio Socrates est animal’ sit praedicatio generis, non minus quam haec homo est animal”’ (II, 20b). It should be observed that the distinction praedicatio per se praedicatio per accidens (notes 61 and 62) is not sufficient to qualify the two statements “Socrates est animal” and “homo est animal”, because both are essential predications. Thus, a further distinction is required, namely, the genus belongs per se primo to the species, and per se non primo to the individual. Still, our author thinks that some opponent would reply that even under such a qualification it happens that a genus has duo correlata,which absurdissimum est. The answer consists in simply repeating the distinction already made: “genus enim non habet duo correlata ad quae ex aequo ordinem dicat” (ibid.).Google Scholar
  82. Also: “Aliter enim individuum aliter species ponitur sub genere” (Caietanus [2], p. 35).Google Scholar
  83. 64.
    Signoriello [1], p. 250.Google Scholar
  84. 65.
    How the above mentioned qualifications may disappoint anyone hoping to find there an equivalent of OF—UO distinctions is shown by the following text: “Accidens vero ante praedicatur de individuis et postea de speciebus. Nam si quis dicat, homo sedet, quod est accidens separabile, cum quicumque singulum hominem, id est individuum, sedere viderit, tune id et de specie praedicat, ut dicat: quoniam Cicero sedet, Cicero autem homo est, homo sedet” (Boethius [2], p. 103).Google Scholar
  85. Certainly, this may be “arranged” by writing “(Ex) x is a man and x is sitting down”. This procedure is adopted for instance by A. Church (in Runes [1], “supposition”). But, did Boethius think in that way? Such an interpretation would appear as false if applied to traditional texts which depend on the pred- ication theory presented by Aquinas (cf. the text quoted in the next note).Google Scholar
  86. 66.
    Est autem considerandum quod de universali aliquid enunciatur quattuor modis.Google Scholar
  87. A) Nam universale potest uno modo considerari quasi separatum a singularibus, sive per se subsistens, ut Plato posuit, sive secundum sententiam Aristotelis, secundum esse quod habet in intellectu. Et sic potest ei aliquid attribui dupliciter. Quandoque enim attribuitur ei sic considerato aliquid, quod pertinet ad solam considerationem intellectus, ut si dicatur quod homo est praedicabile de multis,sive universale, sive species. Huiusmodi enim intentiones format intellectus attribuens eas naturae intellectae, secundum quod comparat ipsam ad res, quae sunt extra animamGoogle Scholar
  88. Quandoque vero attribuitur aliquid universali sic considerato, quod scilicet apprehenditur ab intellectu ut unum, tamen id quod attribuitur ei non pertinet ad actum intellectus, sed ad esse, quod habet natura apprehensa in rebus, quae sunt extra animam, puta si dicatur quod homo est dignissima creaturarum. Hoc enim convenit naturae humanae etiam secundum quod est in singularibus. Nam quilibet homo singularis dignior est omnibus creaturis irrationalibus; sed tarnen omnes homines singulares non stint unus homo extra animam, sed solum in acceptione intellectus; et per hunc modum attribuitur ei praedicatum, scilicet ut uni rei.Google Scholar
  89. B) Alio autem modo attribuitur universali, prout est in singularibus, et hoc dupliciter.Google Scholar
  90. Quandoque quidem ratione ipsius naturae universalis, puta cum attribuitur ei aliquid quod ad essentiam eius pertinet, vel quod consequitur principia essentialia; ut cum dicitur homo est animal,vel homo est risibilis. Quandoque autem attribuitur ei aliquid ratione singularis in quo invenitur, puta cum attribuitur ei aliquid quod pertinet ad actionem individui; ut cum dicitur homo ambulat.Google Scholar
  91. Singulari autem attribuitur aliquid tripliciter: uno modo, secundum quod cadit in apprehensione, ut cum dicitur Socrates est singulare,vel praedicabile de uno solo. Quandoque autem, ratione naturae communis; ut cum dicitur Socrates est animal. Quandoque autem, ratione sui ipsius, ut cum dicitur, Socrates ambulat. De singulari autem quamvis aliquid diversa ratione praedicetur, ut supra dictum est, tarnen totum refertur ad singularitatem ipsius, quia etiam natura universalis in ipso singulari individuatur; ut ideo nihil refert quantum ad naturam singularitatis, utrum aliquid praedicetur de eo ratione universalis naturae, ut cum dicitur Socrates est homo,vel conveniat ei ratione singularitatis“ (Aquinas [4], In Per.,n. 126f.).Google Scholar
  92. The content of this important text of predication theory may be summarized by means of the schema placed on p. 132.Google Scholar
  93. The last passage of the quoted text indicates that cases 3 and 2a, for instance, may be different, as far as the universal “concerned” in each of them is either a universal “proper” or a universal which is “individuated”.Google Scholar
  94. I have not found a clear enough interpretation of case 2 (an interpretation in Fregean terms). Is to be the dignissima creatura a mark of the concept man, or is it a property of the concept man? It cannot be the former, because it would follow that Socrates is the dignissima among creatures; nor can it be the latter, for this would be outside of the author’s intention.Google Scholar
  95. Case 3 should not be misunderstood, as if the statement “homo est animal” implied that individual men exist (cf. Aquinas [3], cap. 4: “Omnis autem essentia vel quiditas potest intelligi sine hoc quod aliquid intelligatur de esse suo; possum enim intelligere quid est homo vel fenix et tarnen ignorare an esse habeat in rerum natura”). The universal in case 3 is considered qua being capable of existing extra animam.Google Scholar
  96. Case la involves a reference to second intentions and the phrase “cadit in apprehensione” does not have any unusual meaning in this context. (I am grateful to Prof. M. D. Philippe for valuable remarks on this point.) Nevertheless, I have preferred not to attempt a precise formulation of this case.Google Scholar
  97. The point I wish to stress here is that such sentences as “homo ambulat” are not adequately interpreted by writing, “there is an x such that it is a man and it walks”. “Homo ambulat” involves a true predication about a universal (universal-in-the-thing).Google Scholar
  98. Frege’s distinction of Merkmal-Eigenschaft (cf. Chapter 5) is a most remarkable clarification of case 3 (and case 1), but his “logical” relations (UF, UO, IF…) are not sufficient to absorb cases 2, 4, and the nuance between 2a and 3a.Google Scholar
  99. 67.
    Cf. Section 3.5.Google Scholar
  100. 68.
    Genus about species, differentia about species, accident about substance, are praedicatio directa; species about genus, etc. is praedicatio indirecta. Also aGoogle Scholar
  101. superior (concept) about an inferior is praedicatio ordinata; otherwise: praedicatio inordinata (Signoriello [1], “praedicatio”).Google Scholar
  102. 69.
    This problem appears with second intentions (cf. Chapter 7). A very rare modern account is to be found in wiezawski [1]; a thorough discussion in Sanchez Sedeíïo [1]. The problem for tradition was how to insert higher predication in the Aristotelian system.Google Scholar
  103. 70.
    The Greek Antisthenes is a well known instance. Subsequently, predications or propositions where the subject has “no relation” with the predicate were called disparatae. These, together with propositiones identicae (tautological, a = a) were considered as useless for science; only an intermediate kind (nec disparatae nec identicae) appeared as having a cognitive value (Gasconius [1], II, 13b-14a). Cf. Bochenski [1], 29.02, and, of course, Frege’s SUB.Google Scholar
  104. 71.
    Aristotle [2], Z, 6. In Greek terms, the question is whether ëxaarov is Tatdv as its Tò Ti 9jv eivac. For the translation, we follow Ross, ibid.Google Scholar
  105. 72.
    This is an opportunity to consider one aspect of Frege’s requirement of a sharp distinction between individuals and predicates, namely his stressing that there are no “intermediate” entities between an object and a concept. In our case, anthropos must be either a particular or a universal man: tertium non datur. Both in traditional and modern logic one finds several vague entities between individuals and predicates; in traditional logic the individuum vagum,in Russell the “denoting” expressions. Caietanus [2] contains an interesting discussion on Individuum vagum (aliquis homo, aliquis bos, et huiusmodi) and individuum signatum (hic homo, hic bos,etc.; Sortes,etc.). Cf. also Geach [2]. Frege rejected such “vague individuals”:Google Scholar
  106. Das Wort Wallfisch’ benennt aber kein Einzelwesen. Wenn man erwidert, allerdings sei nicht von einem einzelnen, bestimmten Gegenstande die Rede, wohl aber von einem unbestimmten, so meine ich, daß “unbestimmter Gegenstand” nur ein andrer Ausdruck für “Begriff” ist, und zwar ein schlechter, widerspruchsvoller“ (GRL, p. 60).Google Scholar
  107. Frege reacted against Schröder’s assumption that “some men” is the name of an (indeterminate) class (cf. KSCH, p. 441 note).Google Scholar
  108. Frege’s reasons for rejecting “variable” signs are similar to those against “indeterminate objects” (cf. for instance, JOURD, p. 238).Google Scholar
  109. 73.
    Alexander [1], p. 479.Google Scholar
  110. 74.
    Asclepius [1], p. 391.Google Scholar
  111. 75.
    Averroes [1], vol. VIII. The Latin text of Averroes asks: “utrum ista substantia, quae est quidditas, et substantia singularis, sive individuum substantiae, sint idem”. In other words: whether individual and universal substances are identical. Averroes’ answer is affirmative: “Socrates enim nihil aliud est quam animalitas et rationalitas, quae sunt quidditates eius.” Once Averroes has said that Socrates is nothing else than his essence, he also gives the converse, namely, that Socrates’ essence (i.e. animalitas plus rationalitas) is nothing else than Socrates..., which of course is wrong, and Averroes must add, “and Plato”. “Nec animalitas et rationalitas sunt quidditates nisi Socratis et Platonis.”Google Scholar
  112. 76.
    Albertus Magnus [1], lib. VII, tract. II, cap. III (pp. 434–435). “Et ideo praedicatum de subjecto aliquando secundum quidditatem idem est subjecto, et aliquando non est idem cum ipso.”Google Scholar
  113. 77.
    Ibid.:“Ideo non est verum dicere de illis, quod idem sit quid esse ipsorum et id subjectum de quo praedicantur”.Google Scholar
  114. 78.
    Ross in Aristotle [2], II, p. 175f.Google Scholar
  115. 79.
    Aquinas [1], n. 1356–1380.Google Scholar
  116. 80.
    Suarez [1], 34, sect. 3, 18.Google Scholar
  117. 81.
    Javellus [2], f. 320: “res autem cuius est quidditas, ut Socrates et homo”.Google Scholar
  118. 82.
    Fonseca [2], tomus III, p. 231–239.Google Scholar
  119. 83.
    There is first an “explanatio” of the chapter 6 of Book Z, with the Greek text. This occupies almost 7 pages. Afterwards there is a systematic quaestio: “Num quod quid est sit idem cum eo, cuius est?”Google Scholar
  120. 84.
    Schwegler [1], p. 68: “Ist das Einzelding identisch mit seinem begrifflichen Wesen (seinem ti en einai)? Ja — wie im Verlaufe bewiesen wird”. Cf. also: “Aus der eben nachgewiesenen Identität des ti en einai mit den daseienden Einzeldingen…” (p. 71).Google Scholar
  121. Bonitz [2], p. 318: “His igitur ex causis idem per se sunt substantiae singulares earumque ta ti en einai”.Google Scholar
  122. 85.
  123. 86.
  124. 87.
    Port-Royal [1], I, Ch. II. An 18th-century Latin translation reads: “et tunc essentiale attributum, quod ipsissima res est” (Port-Royal [2], p. 12). Joffre [1], an “ars syllogistica” written more geometrico,includes the following ontological proposition: “… nam homo et humanitas […] sunt unum et idem…” (Lib. I, cap. 1, artic. 1, definitio VII). Also: “Nota attributum distingui a modo: quod attributum sit ita rei essentiale, ut sine illo res nec esse nec concipi possit” (ibid., art. 2, defin. II).Google Scholar
  125. 88.
    GRG II, § 151 (the title, in the analysis of contents).Google Scholar
  126. 89.
    Frege would say “Grundverschiedenheit” (GRG I, p. 37, passim),which does not necessarily imply unsaturatedness in the Fregean form. Here one might say that Frege is a platonist; Chapter 6 of Metaphysics Z is directed precisely against Plato (cf. Tricot in Aristotle [2.1], I, p. 378, note 1).Google Scholar
  127. 90.
    For example, Albertus Magnus [1]: “… quia hoc quidem erat quid esse quod constituit rem in eo quod est, oportet unum esse cum re, hoc est, non separatum ab ipsa” (lib. VII, tract. II, cap. III = p. 436; italics ours).Google Scholar
  128. 91.
    GED, p. 64.Google Scholar
  129. 92.
    Aristotle [2], Z, 1, 1028b, 4.Google Scholar
  130. 93.
    Ibid.,3, 1028b 33.Google Scholar
  131. 94.
    Cf. Ross in Aristotle [2], ad Z, 1. Aristotle [3.1] ad 83b. Zeller as quoted by Owens [1], p. 13. Tricot in Aristotle [2.1], I, p. 22. But especially Book Z itself (Metaph.) should be considered; and Owens [1], p. 242.Google Scholar
  132. 95.
    For “res”, cf. Chapter 1, note 96 and this chapter note 81; for “Ding”, cf. Section 4.54; for “Gegenstand” cf. Chapter 1, note 96; for “chose”, Section 4.41 in fine.Google Scholar
  133. 96.
    Utraque forma est idem secundum speciem“ (Aquinas [1], n. 1435). Cf. Tricot in Aristotle [2.1], I, p. 381, note 1.Google Scholar
  134. 97.
    Cf. Chapter 3, note 65.Google Scholar
  135. 98.
    Spinoza [1], I, prop. 5; also, Locke [1], III, 6, § 8.Google Scholar
  136. 99.
    Si Socrates est idem cum sua quiditate, ergo est idem cum animali rationali. Sed animal rationale est duo, ergo Socrates est duo […] Item si homo est sua quiditas, ergo est incorruptibilis, quia rerum quiditates sunt incorruptibiles, cum sint universales et ut sic abstrahant ab hic et nunc“ (Javellus [2], f. 320). •Google Scholar
  137. 100.
    Accidents inhere in universal substances as well as in individual ones (cf. SectionGoogle Scholar
  138. 1.
    ; this chapter, notes 44 and 61). And of course animal is predicated both of man and Socrates.Google Scholar
  139. 101.
    It is quite clear that once a universal has the power of sub-stare,it becomes the subject of the properties of the individual, in particular of those properties which depend on essence (cf. Aquinas’ text quoted in note 66). Springer [1] has clearly detected these peculiarities in predication theory deriving from metaphysics (pp. 21, 22 etc.). How else could the predication theory of a logical textbook be which, like Mercier [1], makes essence = res,and takes essence to be the subject (of inherence) of accidents (p. 77, note)? If white inheres in man as well as in Socrates,we shall say “man is white” as well as “Socrates is white”.Google Scholar
  140. 102.
    In Aristotle [1], Perihermeneias 10, 19b, 5: errrcv cívOgwrcoç,“homo est”. Cf. Bochenski [1], 29.01.Google Scholar
  141. 103.
    Brentano [1], § 27 (p. 101). Brentano intends to show that propositions are not necessarily zweigliedrig,i.e., they do not always contain a subject and a predicate.Google Scholar
  142. 104.
    Wenn er aber mit Recht sagt, ein Lebewesen, ein Mensch, ein Mann sei,so muß das Ding, wovon diese Aussagen richtig sind, natürlich ein vollkommen bestimmtes Individuum sein“ (Brentano [1], § 17, p. 41).Google Scholar
  143. 105.
    Das universell und individuell (oder besser weniger universell) bezieht sich also nur auf das Vorstellen“ (Brentano [1], p. 50). ”Kein Gegenstand wird also mit allen seinen individuellen Merkmalen, sondern in einer gewissen (größeren oder geringeren) Allgemeinheit vorgestellt“ (ibid.,p. 43).Google Scholar
  144. If we compare these texts with that quoted in the preceding note, we have: things in themselves are individuals, universality—singularity is an irrelevant dimension due to our dealing with things. In Hillebrand [1] there is a disagreement with Sigwart about existential propositions. Sigwart demands a sharper distinction between a “content” and the “instances” (particulars) of that content (p. 36). But Hillebrand does not care about this; within a single page he uses the expressions “einen Thaler”, “Thaler”, “der Thaler”, “der Thaler selbst”, and all these variants are different names for (the)… Gegenstand (which he opposes to the subjective vorgestellte Thaler). In Kastil [1], as well as in Brentano’s works, the variable “A” appears many times in order to facilitate the discussion. But shall we introduce concept-words or proper names into that empty place? Or rather: is this very question meaningful at all (for Brentano)?Google Scholar
  145. 106.
    Cf. Chapter 5.Google Scholar
  146. 107.
    Chapter 1, notes 96 and 97.Google Scholar
  147. 108.
    Section 4.42, in particular note 94.Google Scholar
  148. 109.
    For Brentano’s sympathetic approach to Hume’s notion of existence, cf. Brentano [3]. Also Marty [1], pp. 189, 200. All this indicates that we are faced with another theory,and not with a mere obscure version of the same theory, as Scholz’s evaluation of Brentano’s doctrines suggests: “Nach Brentano ist das ”ist“ in ”homo est“ nicht als Prädikat aufzufassen — darin stimmen wir mit ihm überein — sondern als Anerkennung der eingliedrigen Urteilsmaterie ”Mensch“ (Was ist das?) (Scholz [2], p. 116). Scholz [2] translates the propositions de secundo adiacente by ”(Ex). x ist ein Mensch“, which would be accepted as correct by traditional philosophers as far as ”aliquis homo est“ and ”homo est“ are equivalent, i.e. quodammodo eamden vim habent (Aquinas [4], n. 210). But the point of traditional predication theory is that homo is as good a subject of being or running as is Socrates. For Brentano, concepts or universals are fictions; nevertheless, his predication theory regards them as subjects (of predication) of theirGoogle Scholar
  149. own marks: “Wir machen den Menschen, den Wasserstoff usw. zum Subjekt von Aussagen”, Brentano [1], § 17 = p. 44.Google Scholar
  150. 110.
    So that of substance, we have no idea of what it is, but only a confused, obscure one of what it does“ (Locke [1], II, 13, § 19).Google Scholar
  151. 111.
    All our affirmations then are only in concrete, which is the affirming, not one abstract idea to be another, but one abstract idea to be joined to another“ (Locke [1], III, 8, § 1). The context supports my interpretation.Google Scholar
  152. 112.
    Mill [1], 1, 8, § 2.Google Scholar
  153. 113.
  154. 114.
  155. 115.
    Heidegger [1], pp. 119f.Google Scholar
  156. 116.
    This is suggested by Heidegger’s remark concerning two different formulations of the principle of contradiction in Kant’s works, one of them deals with Ding, das worauf der Subjektbegriff bezogen ist,the other concerns the Subjektbegriff selbst. Now, Heidegger says that “beide Fassungen unterscheiden sich nicht wesentlich” (ibid.,p. 134).Google Scholar
  157. 117.
    Cf. Kneale [1], p. 318.Google Scholar
  158. 118.
    Aristotle (2), A, 26, 1023b, 26–32.Google Scholar
  159. 119.
    Cf. Section 4.313.Google Scholar
  160. 120.
    Aristotle [5], Topica, 0,5, 126a, 27.Google Scholar
  161. 121.
    Cf. Chapter 3, note 45.Google Scholar
  162. 122.
    To Câiov 6vi nìr é la4’et “UP âvDec/mg) (Asclepius [1], p. 383, 1.27).Google Scholar
  163. 123.
    Constat quidem genus continere sub se turn species cum differentias sibi subjectas, saltem potestate: hoc enim videtur pertinere ad rationem totius potentialis seu universalis, alioquin non potest intelligi quomodo aptum sit de illis praedicari“ (Eust. a Sto. Paulo, Summa Philos.,quoted by Gilson [3], p. 134).Google Scholar
  164. 124.
    Vaihinger [I], I, pp. 253f.Google Scholar
  165. 125.
    Cf. Aaron [1], pp. 60, 65.Google Scholar
  166. 126.
    Jedes Ding der Wirklichkeit ist so beschaffen, daß ihm jede beliebige Bestimmung (gemäß dem Satze vom ausgeschlossenen Dritten) entweder zukommt oder nicht zukommt, indes etwa jeder Begriffsgegenstand, z.B., “das” Dreieck, unendlich viele Bestimmungen (wie Gleichseitigkeit, Rechtwinkligkeit) weder an sich hat noch nicht an sich hat (daher insofern dem Satze vom ausgeschlossenen Dritten nicht untersteht)“ (Meinong [1], p. 16).Google Scholar
  167. 127.
    Fries [1], p. X contains a very interesting discussion. Cf. also Bolzano [1], § 45.Google Scholar
  168. 128.
    Non multa, non unum“ (Henry of Ghent, quoted by De Wulf [2], p. 207, note 2).Google Scholar
  169. 129.
    Ioannes a Sto. Thoma [1], p. 315: “Dicimus enim, quod natura secundum se neque est una nec plures, nec est alba nec est non alba […] Nec tarnen inde inferas verificari dual contradictorias de natura secundum se; hoc enim numquam est possibile, sed semper altera est vera, altera falsa”.Google Scholar
  170. 130.
    Kant [3], p. 141.Google Scholar
  171. 131.
    “Der Mißverstand kommt bloß daher, daß man ein Prädicat eines Dinges zuvörderst von dem Begriff desselben absondert und nachher sein Gegentheil mit diesem Prädicate verknüpft, welches niemals einen Widerspruch mit dem Subjecte, sondern nur mit dessen Prädicate, welches mit jenem synthetisch verbunden worden, abgiebt, und zwar nur dann, wenn das erste und zweite Prädicat zu gleicher Zeit gesetzt werden” (ibid.).Google Scholar
  172. 132.
    In Categoriae’s terminology “Ding” must mean deutera ousia. In the “bad” formulation “Ding” means prate ousia.Google Scholar
  173. 133.
    But Frege would not say that man is predicated (UF) of c’Callias.Google Scholar
  174. 134.
    Porphyry [1], p. 7, bottom.Google Scholar
  175. 135.
    Cf. Gilson [3], p. 456, passim.Google Scholar
  176. 136.
    Heimsoeth [1], p. 263; Kneale [1], p. 324.Google Scholar
  177. 137.
    praedicatum continetur in subjecto[…] Superiores gradus includuntur cum suis proprietatibus […] in Petro“ (Goudin [1], p. 168).Google Scholar
  178. 138.
    xsam a’x c a. Cf. also Scholz [2], p. 151.Google Scholar
  179. 139.
    P. 40, especially note 21.Google Scholar
  180. 140.
    P. Hispanus [1], 2.09.Google Scholar
  181. 141.
    Theorema 8, Propositio 17.Google Scholar
  182. Propositio singularis est universalis, seu species propositionis universalis. Demonstratio. Ex demonstratis illa propositio est universalis, cujus subjectum sumitur pro tota sua extensione. Atqui, subjectum propositionis singularis sumitur pro tota sua extensione: illius enim subjectum est unum individuum, quod non aliam habet extensionem, quam ipsum; et consequenter, non potest sumi, nisi secundum totam suam extensionem. Ergo propositio singularis est universalis. Quod erat probandum“ (Joffre [1], p. 68).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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