Abstract
The relations which Frege would have called Grundsteine of his system (GRG I, p. 3) are examined. Why should such relations be called logical rather than, for instance, ontological (3.1)? “Subject—predicate” in Frege has a different meaning from that of traditional logic (3.3); traditional philosophy has taken into account facts covered by Frege’s UF and UO (3.4). But the most interesting point is what we call hierarchy of predicates, about which our contemporary (Fregean) philosophy of logic has not yet provided a clear statement; traditional logic, to the contrary, was somehow “suffocated” by such a hierarchy of predicates (3.5). Some aspects of the relations between Husserl and Frege are next considered. Husserl’s Philosophie der Arithmetik was still pre-Fregean in matters of predication-theory (3.62), whereas Frege’s review of Husserl’s book was still pre-Aristotelian, since Frege did not realize that there was a hierarchy of predicates behind Husserl’s “psychologism” (3.63).
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References
The falling of an individual under a concept (UZBG, p. 3).
Bartlett [1], p. 58.
For the following remarks, cf. 7.54.
Frege speaks of die logischen Beziehungen in UZBG, p. 4.
Cf. note 1.
We shall abbreviate this by “UO”.
For instance, pp. 3, 5, 8, 9.
Ibid., p. 3.
Ibid., p. 8.
Cf. note 1.
(concepts), UZBG, p. 3.
UZBG, p. 2.
UZBG, GRG II, §§ 162–164.
Cf. GRL, § 9; tyrannicides are said to be parts of murder as a whole, and Frege comments: “Hier hat man die logische Unterordnung.”
GRL, § 47. The example is “alle Wallfische sind Säugethiere”.
GRG I (p. 24 note) confirms this.
GRL, § 53.
GRL, § 70.
BGGE, p. 194.
For example (apart from BGGE, p. 194), WIF, p. 665; HUSS, p. 326. As an example of not distinguishing predication and identity, let us consider the following text (the author would assume that “W. Scott” is predicated about the author of Waverley): “Cum vero in definitione audis, ”de pluribus“ [the author means his definition of nomen universale = quod praedicatur de pluribus],nomine ”Plurium“ intellige plura secundum idem nomen. Nam ut nomen aliquod dicatur commune non satis est si praedicetur de iis, quae dicuntur plura secundum aliud nomen, sic nomina singularia, communia esse iudicabuntur. Platonis siquidem nomen una sola ratione acceptum, praedicatur de pluribus attributis Platonis, ut pote de hoc Aristonis filio, de hoc Philosopho, de hoc Aristotelis praeceptore. Nomen etiam Conimbricae praedicatur de pluribus attributis Conimbricae, ut de urbe prope Mondam sita, de hac bonarum artium cultrice ...” (Fonseca [1], Lib. Primus, Cap. XXVI).
Bartlett [1], p. 58.
BGGE, p. 201; cf. UGG1, p. 373.
GRG I, p. 240.
GRG I, § 34.
KSCH, p. 442.
UBR, p. 9; UGG2(III), p. 427 note. In the “inedita” we have “Subordination” for “Unterordnung”.
This is an interpretation which seems correct, although the difficulties implied by the ontological square should be considered. It would be enough to recall Frege’s philosophy of number: numbers concern concepts because they say how many individuals fall under each concept.
Cf., for instance, GRL, § 54.
Cf. Section 6.71.
GRL associates Begriff and mögliches Prädikat (§ 66 note), or just Prädikat (§ 77). This Kantian terminology also occurs in GRG II (§ 56). In BGGE “predicate” or “predicative” are used to characterize unsaturatedness which indicates the extreme importance those terms have in Frege’s system (BGGE, p. 197, note). WIF mentions in several places subjects of predication (for example, p. 658). The following text (from a later paper) shows how Frege understands the relation subject-predicate in a sentence: “Nehmen wir den Satz ‘Zwei ist eine Primzahl’. Wir unterscheiden hier sprachlich ein Subjekt “Zwei” und einen prädikativen Bestandteil ”ist eine Primzahl”” (UGGI, p. 371).
For example SUB, p. 35 (first line).
For example UGG2(I), p. 305, bottom; BGGE, p. 193, note.
Cf. 6.7.
Cf. Section 6.8.
In “Blut ist rot” the subject is “Blut”, Sigwart [1], I, p. 117. In “l’homme est un animal”, “l’homme” is the subject, “animal” the predicate, Gardeil [1], p. 51, 90. Cf. also Quine [1], § 14 and § 23. Also Geach [2].
BGGE, p. 198.
Schröder’s curious idea (certainly not only his) was that “einige Menschen” denotes a class, but a class consisting of an undetermined number of individuals (KSCH, p. 435, 441 note).
Cf. Geach [2]. Aristotle views “every” as giving to the sentence a universal character (Aristotle [1], Perihermeneias, 7, 17b, 12 ).
Indefinita est quae habet subiectum universale sine ulla nota, ut homo est iustus“ (Pacius [2], cap. 5, n. 6). Frege has been interested in the vestiges.of ”propositiones indefinitae“, such as ”das Pferd ist ein vierbeiniges Thier“ (UWB, BGGE, p. 196). He interprets this as a universal affirmative sentence. Leaving aside whether this interpretation is absolutely valid, let us only refer for this use of the definite article as a universal quantifier, to Sigwart [1] (p. 117) and Reichenbach [2] (p. 25).
Cf. Chapter 6.
GRL, p. 57.
This will be confirmed by the inedita (letter to Husserl, Oct. 30, 1906).
Petrus Hispanus [1] (2.09) defines: “Individuum est quod de uno solo praedicatur, ut Socrates et Plato”, where one would think rather of individual concepts or idées individuelles (Port-Royal [1], I, Ch. VI) than of individuals proper. Incidentally, Carnap’s proposal of speaking of individual concepts (Carnap [1], § 9, p. 41 top) is indeed quite in agreement with the traditional approach. Perhaps Kant’s term “Anschauung” reflects the traditional ambiguity of “individuum”: (1) without intuitions, concepts are empty, where “intuition” means existent individual, (2) the intuitions “apply” to only one object, while concepts apply to many objects, where “intuition” means individual concept (cf. Eisler [1], “Anschauung”). Frege noticed, in GRL, § 12, an ambiguity in Kant’s “Anschauung”, which seems to be related to this one. An extensive discussion is to be found in Caietanus [2], p. 62f.
Ultimate subject.
Praedicatio enim est quiddam quod completur per actionem intellectus componentis et dividentis, habens fundamentum in re ipsa unitatem eorum quorum unum de altero dicitur“ (Aquinas [3], Chap. III). Cf. Ioannes a Sto Thoma [1], p. 470a, top. Frege, on the contrary, says: ”Bemerkt sei hierzu noch, daß das gesperrt gedruckte ist sowie sind als bloße Copula aufzufassen ist, ohne irgend einen besonderen Inhalt, dass also damit keine Identität gemeint ist“ (KSCH, p. 442).
Cf. Chapter 1.
This is actually Porphyry’s evasive procedure, to consider only the “substantial” tree, cf. Section 1.41.
As for the species infima the natural question is why there should be at all such a limit in approaching individuals through Unterordnung structures. The answer seems to depend on the notion of matter; male and female do not make a new species because they are properties deriving from matter (Aristotle [2], I, 9).
Porphyry [1], (Isagoge),pp. 6, 12–13.
Now it is clear that if the predications terminate in both the upward and the downward direction (by “upward” I mean the ascent to the more universal, by “downward” the descent to the more particular), the middle terms cannot be infinite in number“ (Aristotle [3.1], Anal. Post., A20).
Aristotle says that a predicate (5tp.oi a thing (Aristotle [1], 2b, 31). Some humanist commentators have translated this Greek word by declarare (Pacius [1], Gruchius [1]).
Aristotle [2], B2, 996b, 15f.
This concept is important in Frege’s foundation of arithmetic.
Aristotle [3], An. Post., B, 10, 94a, 11.
Aristotle [2], A, 17, 1022a, 8–10.
Locke [1], III, 6, § 2; also § 5.
Aquinas [1], 1048. Cf. Porphyry [1], for the notion of differentia.
Martinus de Dacia [1], n. 34; Husserl [5], § 90.
Duns Scotus on Boethius: “Secundo modo accipit Boethius, distinguendo rem contra modum rei, sicut loquitur libro de Trinitate. ”Patet“, inquit, ”quae sit differentia praedicationum, quia aliae quidem rem mostrant, aliae quidem quasi circumstantiam rei; quia istae praedicantur sic quod secundum se rem aliquam mostrant. Illae vero ut non esse, sed potius extrinsecus aliquid apponunt“. Vult ergo distinguere rem contra circumstantiam; et sic, secundum eum, sola tria genera (substantia, qualitas et quantitas) rem mostrant; alia vero rei circumstantias.” (In Fernandez-Garcia [1], distinctio ens-res.)
A Renaissance author (Eust. a Sto. Paulo) shows how the passage from “accident” to “mode” was accomplished: “Quarta conclusio. Essentia accidentis modus quidam est substantiae; omne enim accidens substantiam aliqua ratione modificat” (in Gilson [3], p. 104, “essence”).
Port-Royal [1], I, Ch. 2.
Kant [4], 2. Abs., p. 242. Vaihinger [l] (I, p. 264) clearly explains how reine Anschauung is introduced in the sophisticated traditional theory of predication. Locke [1] (II, 31, § 6) had already made it clear that nothing “flows” from the (nominal) essence. Kant nevertheless has to explain the fact of synthetical a priori knowledge.
Cf. Kauffmann [1], p. 335. Of course, this is but an example of “negative theology”.
P. 76 bottom.
Carnap [1], § 27. Cf. also Anscombe-Geach [1], p. 34; Quine [3], p. 155. An interesting comparison of both approaches (i.e., with and without hierarchy of predicates) is in Springer [1].
Husserl [4]. For Frege-Husserl in general, cf. Fr llesdal [1].
HUSS.
Husserl [4], pp. 11, 91, 92.
Frege in GRL, § 24, Husserl in [4], p. 11.
Javellus [1] (f. 164) reduces number to a particular category of being (quantitas).
Husserl [4], Chapter IV in fine.
Frege mentions only once, briefly and incidentally, Husserl’s view of the universality of number (HUSS, p. 315).
Which Frege thus easily accuses of psychologism (not using this term). But if Husserl employs a “psychological” terminology, this is motivated by his program of ensuring and respecting the “transcendental” (in the scholastic sense) nature of number and other formal ontological categories (cf. Husserl [4], pp. 86, 91). As we shall see shortly (Section 3.63), Husserl’s program plus his traditional approach to the hierarchy of predicates determined that apparent psychologism. (For Frege and psychologism, see Papst [1].)
Multitude, plurality.
Husserl [4], p. 8.
For the use of this adjective “concrete”, see Husserl [4], pp. 10, 67, 89, 185 (bottom), etc.
See below.
The example is given in Husserl [4], p. 79; it is also mentioned by Frege in HUSS, pp. 322–323.
For example Husserl [4], pp. 87, 88, 164, etc.
Ibid., pp. 87, 185.
Die Zahl ist die allgemeine Vielheitsform unter welcher der Inbegriff der Gegenstände a, b, c fällt“ (Husserl [4], p. 185). If ”allgemeine Vielheitsform“ = ”abstracte Vielheit“, we may conclude that {der Mond, die Röte, Napoleon} falls under {Etwas, Etwas, Etwas}. But there is a more explicit text: ”Zwei Äpfel, zwei Menschen, ein Apfel und ein Mensch, u.s.w. sind sämmtlich zwei, weil sie concrete Inbegriffe repräsentieren, welche durch das Zählungsverfahren gerade unter die abstracte Mengenform: Eins und Eins, fallen und unter keine andere“ (Husserl [4], p. 162).
Unless it is explicitly agreed that the concept of Vielheit is itself a Vielheit, as the concept of entity is an entity. But for Husserl the concept Vielheit is higher than the abstracte Vielheiten; see below.
Husserl [4], pp. 90, 158.
Cf. the next note. Also, Husserl [4], p. 9.
Bei dem Namen Anzahl compliciert sich die Sache noch dadurch, daß er nicht bloß als allgemeiner Name für irgend welche concrete Mengen, sondern auch als allgemeiner Name für jede unter den Begriff der Anzahl fallenden besonderen Zahlen: Zwei, Drei, Vier… dient“ (Husserl [4], p. 154).
In this text I assume that “allgemeiner Name für irgend welche concrete Mengen [zu sein]” means that these Mengen fall under the concept denoted by that general name. There is justification for this in Husserl himself, some pages previous: “Jeder abstracte Name wird in einer zweifachen Bedeutung gebraucht; das eine Mal dient er als Name für den abstracten Begriff als solchen, das andere Mal als Name für irgend eine unter diesen Begriff fallenden Gegenstand” (Husserl [4], p. 151).
The fact that both concrete Vielheiten and abstracte Vielheiten (i.e. numbers) fall under the Anzahlbegriff had already been suggested by Husserl at the beginning of the book: “Der Anzahlbegriff umfaßt also, obschon erst auf dem Wege über die Umfänge seiner Speciesbegriffe, der Zahlen Zwei, Drei, Vier,... dieselben concreten Phänomene wie der Begriff der Vielheit” (Husserl [4], p. 9). Cf. also the example given by Husserl on page 189.
Cf. Husserl’s text quoted at the end of the preceding note; also Husserl [4], p. 89.
HUSS, p. 313.
HUSS, p. 313.
HUSS, p. 324.
HUSS, p. 326. As if “man” were a name of Hans as “Hans” is. Cf. Husserl’s semantics of general terms (at the time of Husserl [4]) in note 85 above. Cf. also Section 2. 62.
HUSS, p. 327.
Cf. Chapter 10.
HUSS, p. 326.
With respect to five concrete stones or five concrete syllogistic modes.
Husserl [4], p. 181.
Ibid., p. 180.
Ibid. But of course this is trivially rejected; an apostle is not twelve (p. 181, below).
Ibid., p. 164.
Eine leichte Unterscheidung wird zeigen, daß in gewissem Sinne beide Parteien Recht haben. Rechnen wir zum Inhalte einer Vorstellung nur Theilvorstellungen im eigentlichen und strengen Sinne (“innere Merkmale” nannten sie manche Logiker) und betrachten demgemäß Vorstellungen nur dann als vergleichbar, wenn sie gemeinsame Theilinhalte dieser Art besitzen, dann giebt es unendlich viele disparate und unvergleichbare Vorstellungen, und es ist klar, daß dann die Zählung Vergleichbarkeit (in dieser Bedeutung) nicht verlangt, da vielmehr ganz disparate Dinge zusammengezählt werden können. Meine Seele und ein Dreieck sind zwei, obgleich sie keinerlei gemeinsame innere Merkmale besitzen. Rechnen wir jedoch zum Inhalte einer Vorstellung auch alle ihr zukommenden negativen und relativen Bestimmungen (die “äußeren Merkmale”), dann giebt es überhaupt keine unvergleichbaren Vorstellungen; denn es giebt keine, die nicht mindestens als unter den Begriff Etwas fallende, gleichartig sind. Und gerade diese Subsumption unter den Begriff Etwas müssen wir (nach unserer Theorie) hinsichtlich eines jeden der zu zählenden Gegenstände vollziehen, um die Zahl zu erfassen. Insofern ist also richtig, daß die zu zählenden Dinge unter einen gemeinsamen Gattungsbegriff (dies Wort freilich im äußerlichsten Sinne genommen) gebracht werden müssen“ (Husserl [4], p. 158).
Man kann in jedem Falle die gezählten Objecte durch gemeinsame Merkmale (seien es innere oder relative) so genau determinieren, daß der entstehende Gattungsbegriff nur auf die hic et nunc gezählten Objecte päßt und auf keine anderen“ (Husserl [4], pp. 187–188). In the following text we notice some irony with respect to considering as concepts predicates which normally would not be so regarded: ”Urtheilen wir z.B.: der Wagen des Kaisers wird von vier Pferden gezogen, dann würde der Begriff Pferd dieser Anforderung nicht genügen, denn es giebt auch sonst noch Pferde. Anders wenn wir den Begriff “Pferd, das den Wagen des Kaisers zieht”, wählen, insbesondere wenn wir Ort, Raum, Datum und Tageszeit zu notiren nicht vergessen; dieser Begriff päßt nur auf die vier hier concret gegebenen und gezählten Pferde“ (Husserl [4], p. 188).
Die vollste Bestätigung für unsere Auffassung bietet wieder die innere Erfahrung. Fragen wir, worin die Verbindung bestehe, wenn wir z.B. eine Mehrheit so disparater Dinge wie die Röte, Napoleon und der Mond denken, so erhalten wir die Antwort, sie bestehe bloß darin, daß wir diese Inhalte zusammen denken, in einem Akte denken“ (Husserl [4], p. 79).
HUSS, p. 322–323.
Husserl [4], p. 184.
Signoriello [1].
I think that such is the correct interpretation of the following text: “Aber nehmen wir selbst an, es wäre immer so, wie man behauptet, wir colligierten und zählten stets nur Objecte, sofern sie unter einen gemeinsamen Begriff fallen, dann geht aus unserer Betrachtung klar hervor, daß die Zahl in keiner Weise als Bestimmung dieses Begriffes angesehen werden kann” (Husserl [4], p. 185). Perhaps because of this (typically traditional) difficulty of viewing higher predicates (i.e., there are already “higher” predicates: animal with respect to man!), Husserl finally arrives at the following formulation: “Nur indirect kann man allenfalls sagen, der Begriff hat die Eigenschaft, daß seinem Umfange die Zahl vier zukommt” (Husserl [4], p. 189).
Cf. Section 5.32.
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Angelelli, I. (1967). The So-Called Logical Relations. In: Studies on Gottlob Frege and Traditional Philosophy. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3175-1_4
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