Abstract
In the present chapter those elements of the philosophical tradition which may be said to involve a structure of levels are examined (7.1). The analysis begins with some miscellaneous remarks about several doctrines which seem to be of this kind (7.2–7.4). As for second intentions (the most suitable theme for comparison with Frege’s and contemporary logic’s levels), little research has been done which could serve as a starting point. After examining three important cases (Aquinas, Scotus, Ockham 7 51–7.53), I propose some general considerations about the usual manner of presenting second intentions in traditional textbooks (7.54). Although Nizolius’ contribution to second intentions seems to be unimportant, he is the only (known) “extensionalist” thinker of the philosophical tradition, and to this extent it was necessary to inquire whether he had classes of classes (7.55). In modern philosophy, second intentions and predicates of predicates no longer attract the attention of philosophers (7.56). Finally, Brentano’s views (7.57) are examined and the chapter is completed by a brief reference to Platonism and levels (7.58).
Hier kommt meine Unterscheidung von Begriffen erster und zweiter Stufe in Betracht — ich sage “meine”, weil mir nicht bekannt ist, daß sie vor mir in hinreichender Schärfe gemacht ist. (Frege, UBR, p. 23)
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References
Cf. Section 6.8.
Ibid.
Cf. Fitch [1].
Cf. Beth [1], p. 498, and Fraenkel-Bar-Hillel [1], p. 168 n. 3.
Another example of pseudo-levels: “quality of quality” in Trendelenburg [1], pp. 225–226.
Keckermann [1], Liber 1, cap. XX, in fine
Keckermann’s treatises on logic are to a great extent ontology, insofar as they follow the contents of the Organon Cf. Chapter 1, notes 62 and 63.
Un accident peut être le sujet d’un autre accident“, will say later Descartes, quoted in Gilson [3], p. 4.
Cf. Section 6.8.
GRG II, p. 253; UFT, p. 100.
This is confirmed by Sluga [1], pp. 198–199. But Frege’s version of self-predication proposed therein is unintelligible, because it depends on unsaturatedness and on what a class really is.
Cf. for instance Kent Sprague [1], pp. 26–28, Moravcsik [1].
This is apparent in Bochenski [1].
Prior [2], p. 286 points out that Buridan erroneously deals with a true case of self-predication as if it were to be solved by mere semantic means.
Objicies secundo: si universale genus esset horum universalium colligeretur aperte, non esse quinque universalia, consequens absurdum videtur, ergo et antecedens. Maior probatur hoc modo: genus est species universalis, igitur genus et species erunt unicum universale. Dicendum est, speciem non praedicari de genere, ea ratione qua species est: haec enim propositio falsa est, secunda notio generis est species universalis, hoc est denominatur a secunda notione speciei: siquidem potest praedicari de pluribus differentibus numero in eo quod quid. Neque hoc est aliquod inconveniens: nam quemadmodum homo, et albedo sunt duae species, quarum una albedo videlicet denominat hominem, ita etiam secunda notio generis et speciei sunt duae species, quarum altera, hoc est secunda notio speciei denominat secundam notionem generis hac denomination, quod sit species. Neque hoc solum fieri poterit, sed etiam ut, aliqua notio seipsam denominet: quemadmodum universalitas denominat seipsam universalem, atque secunda notio speciei seipsam speciem denominat, ex accidenti tarnen. Nam cum proprium sit secundaenotionis speciei rem illam afficere, quae de pluribus differenti-bus numero praedicari potest in eo quod quid, atque contingat ipsammet notionem de pluribus secundis notionibus in quaestione quid est praedicari, ideo seipsam denominat speciem. Eodem modo de universalitate, et aliquibus aliis secundis notionibus loquendum est. Hine ortum habuit illud, quod de Dialectica dicitur, nimirum ipsam non solum deseruire aliis scientiis, sed etiam sibi: reflectuntur enim secundae notiones interdum in seipsas,atque ita praecepta quibus aliae scientiae utuntur, in Logica ipsa exerceri possunt“ (Gasconius [1], f. 13, italics ours). It is interesting to observe how cumbersome the Aristotelian predication theory was for dealing with these subtle phenomena of higher predicates. Higher predicates are submitted to the preliminary remark that they do not belong tochwr(133) the set of marks (of essences). They are in a sense equated with accidental properties of individuals,which is true because neither white nor universal belong to the set of marks of the concept man Unfortunately, this seems to be all that Aristotelian logic can say about higher predicates: they apply to other predicates, they apply even to themselveschwr(133) ex accidenti tarnen
Cf. Fitch [1].
Gilson [2], p. 53 note.
L’infinité n’est de la raison d’aucun attribut comme tel. Si elle l’était, elle serait incluse dans la définition de chacun d’eux et il n’y aurait alors de sagesse ou de bonté qu’infinies, ce qui est manifestement faux.“ (Gilson [2], p. 248). We find here a variant of the argument mentioned in Section 5. 42.
“... l’infinité n’est à proprement parler un attribut de Dieu, mais le mode propre de l’essence divine” (ibid.)
chwr(133) et non intrare quidditatem rei sed ipsam circumstare.“ In such terms a later scotist, Mastrius de Meldula, describes the ”modus intrinsecus“ (quoted by Alcorta [1], p. 160).
Pp. 205–241.
Pp. 242–244, 244–252, 252–261, respectively.
A relation “entre la raison et l’objet de son acte comparatif” (p. 211). Of course, “intentio” had also, perhaps primarily, a subjective sense, but this is not the point of the discussions on second intentions in traditional philosophy.
l’objet de l’acte raisonnable“ (pp. 221–223).
P. 221, note.
Ibid
P. 241.
Ioannes a Sto. Thoma [1], p. 292 (I owe this reference to Prof. A. Moreno). For Duns Scotus’ school, cf: “secunda intentio [potest] cognosci ab intellectu et in quantum obiectum cognitum [est...] prima intentio” (Sarnanus, quoted by Swiezawski [1], p. 211, note 3). The same idea in Piaget.
Texts quoted and the author’s own conclusion (p. 227) confirm that a processus in infinitum is allowed. The so-to-speak “constructive” character of these predicates of predicates is clear in Ioannes a Sto Thoma’s text referred to in the preceding note.
Quoted from Sarnanus, in Swiezawski [1], p. 247, note.
Pp. 232, 234, 239 (note 2), 240. At the same time, the author mentions the Avicennian doctrine of the triplex respectas without discussing its intimate relation to higher predicates (pp. 244–252), in the sense in which, I think, that should be done (cf. our Chapter 5). Moreover, it is regrettable that the author has not discussed such important questions as self-predication or quantification of higher predicates. Nevertheless, Swiezawski [1] is not only a remarkable contribution, but it is worth noting that it is a work done with acquaintance with modern logic, an exception indeed in the early thirties.
P. 216.
P. 217.
La difficulté, pensons nous, serait sans issue, si l’intentio n’était qu’une forme inerte et bien decoupée, colleé comme une étiquette a la natura cui attribuitur“ (p. 217, above).
Pp. 176–179.
Baudry [1] “intentio”, shows that intentions should be understood as acts of the mind, and he quotes: “tam intentiones primae quam secundae sunt vere entia realia quia sunt vere qualitates existentes subjective in intellectu”. Cf. also De Wulf [1], §§ 380, 472.
Pp. 176–179.
Cf. also Baudry [1], “impositio”. But certainly second intentions and names of names are closely related.
De Wulf [1], § 380.
Aquinas [3], Chapter 3.
Animal“ is opposed to ”animalitas“ because ”animal“ signifies the same thing per modum totius,not per modum partis as does the abstract term ”animalitas“. Frege says that ”the concept F“ is only a part of the grammatical predicate, i.e., of the name of the concept in question (BGGE, p. 197). ”Animal“ is unsaturated, as ”... is an animal“ in Frege’s system; it involves, though implicite et indistincte, totum quod in individuo est Would Frege have admitted that ”the concept F“ is a name of a concept per modum partis?
The eleventh category is meticulously described in, for instance, Gasconius [1].
Authors presenting schema (4) are Caietanus [2], pp. 18–19; Eust. a Sto-Paulo, quoted by Gilson [3], p. 107; Signoriello [1], “intentio”; Fonseca [1], lib. primus, cap. 32; Ioannes a Sto. Thoma [1], p. 291, bottom; and of course many others. Recently, cf. Gardeil [1], p. 52.
Cf. Angelelli [1].
chwr(133) supra quod nullum est genuschwr(133)“ (Nizolius [1], Lib. II, cap. IX).
Cf. the index of Nizolius [1]: “Intentiones primae et secundae in philosophiam introductae fuerunt propter ignorationem sermonum propriorum et figuratorum”, which is precisely Nixolius’ point in semantics.
Pereira Gomez [1], p. 17.
Port-Royal [1], Premier Discours
“Que si ces mots sont tiréz de quelque manière dont on conçoit les choses, on les appelle secondes intentions” (Port-Royal [1], Part. I, Ch. II). To be a subject and to be a predicate are examples of second intentions (ibid.)
Kant [3], pp. 280–281 speaks of “die logischen Functionen des Subjekts und Praedikats” (cf. preceding note). A rare reference is given in Spinoza [1], II, prop. 40, schol. 1. Kauppi [1], p. 48 suggests that Leibniz’s abstracta abstractorum are in the line of “logical types”, but the fact that Leibniz expresses them by means of adverbs (Couturat [1], (pp. 437–38) casts some doubt on this interpretation; adverbs in higher predication mean accidents rather than predicates (cf. Section 1.45, in particular note 108).
Brentano [2], Chapter V, § 8 (p. 113).
This is an important change in Brentano’s thought; cf. Stegmüller [2], p. 16, note and p. 63, note.
Brentano [4], II, pp. 214–215; 231, passim
Daß man für jeden Satz, der etwas von dem Erwähnten zum Subjekt oder Prädikat zu haben scheint, einen äquivalenten bilden kann, bei welchem Subjekt und Prädikat durch Reales ersetzt sind“ (Brentano [4], ”Von den wahren und fiktiven Objekten“, p. 163).
Brentano [1], p. 40.
Wir können oft von solchen, was wir denkend zum Gegenstand haben, nichts prädizieren, weil er gar nicht ist und weil nur, was ist in recto mit etwas identifiziert werden kann. Gleichwohl haben wir es zum Objekt und nichts hindert, daß wir unser Denken seinem Gegenstande nach beschreiben“ (Brentano [1], p. 43).
The expressions “ein den allgemeinen Begriff von etwas Denkender” or “ein etwas universell Denkender” are echte Namen “Aber die darin verwendeten Worte ”Begriff“, ”Gattung“, ”Spezies“ sind es nicht, sie fungieren nur synsemantisch” (Brentano [1], p. 43).
I am grateful to Prof. F. Mayer-Hillebrand for generous information about Brentano. On the basis of such information we may confirm that Brentano was not especially concerned with second intentions (in the sense of predicates of predicates, i.e., in the objective sense of “intentio”). A rare reference is to be found in Brentano [1], p. 57. Second intentions are absorbed by contextual meaning.
Cf. Section 6.8.
Cf. Clauberg’s phrase quoted in Chapter 1, note 13. Cf. Bochenski [1], p. 179, or Aquinas [1], n. 574 and 1308, where we see how there is a parallelism between logic and metaphysics consisting in the fact that the former deals with ens rationis,while the second deals with “real” being.
Cf. Section 7.54.
As perhaps Brentano would say ([4], II, p. 275). Cf. also De Muralt [1], who refers to Husserl’s platonism. But Husserl was rid of traditional predication theory (cf. in particular the text referred to in Chapter 5 note 39), and to this extent he was not obliged to drive away second intentions from his ontology in the sense of opening a Clauberg’s abyss between them and real things.
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Angelelli, I. (1967). The Idea of Levels (Stufen) in the Philosophical Tradition. In: Studies on Gottlob Frege and Traditional Philosophy. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3175-1_8
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