Abstract
Before his paper ‘Sinn and Bedeutung’, Frege had described his own semantics as if it were dyadic (names-content, meaning), but he actually viewed names as having a double semantical dimension (2.1).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BG, §§ 2, 3 passim.
BG, § 8. Except when other references are given, Frege’s texts mentioned in this section belong to BG, § 8.
This is the Latin translation of Aristotle’s definition of onoma at the beginning of Perihermeneias. Cf. LNE, p. 73.
BG, pp. IV and 3.
Cf.: “der Name B hat also in diesem Falle denselben Inhalt wie der Name A”.
Cf. GRL, § 51 (quoted in note 177), or HUSS, p. 326, where Frege criticizes Husserl because he suggests that “man” is a name of Hans just as “Hans” is.
The metalinguistic approach to identity is emphasized by Frege’s stressing that signs are sometimes names standing for things or designata and sometimes standing for themselves. But this reference to “suppositio materialis” is not completed by the deeper distinction between the symbol and its concrete occurrences or tokens. “Suppositio materialis” had been defined with reference to this further distinction: “significatio termini in propositione... pro seipso solummodo aut sibi consimili” (Paulus Venetus [2], f. 16a). “Gleichgestaltigkeit” of signs will be discussed by Frege in later works: GRG II, § 99; hints of this are already in UFT, p. 98 top, SUB, p. 26, middle.
Frege misses this fundamental point in at least three formulations of his analysis of statements of identity in BG; in the definition proposed before the objection, in the discussion of the geometrical example and in the final definition of the sign of identity.
Cf. in particular: “… die verschiedenen Namen für denselben Inhalt nicht immer bloß eine gleichgiltige Formsache sind, sondern… sie das Wesen der Sache selbst betreffen, wenn sie mit verschiedenen Bestimmungsweisen zusammenhängen.”
For example SUB, and BGGE, p. 198.
GRL, p. 76.
GRL, p. 78.
In GRL, § 67, Frege opposes: “to introduce an object” and “to assert something about an object”, “... ein Urteil, das von dem Gegenstande handelt, aber führt ihn nun auch nicht mehr ein…”. The expression “die Weise wie ein Gegenstand eingeführt ist” appears not only in the text of § 67 but also in the title of this paragraph in the analysis of contents of GRL. Not only is the expression “way in which an object is introduced” misleading (because what is primarily “introduced” is a new sign), but also the expression “definition of an object” (used by Frege in § 67). The latter should not be confounded with “definition of an object from a concept” (cf. Section 2.9) and it should be replaced by “introduction of a new name”.
This is expressed in GRL, § 67, but already in BG p. 56 it was a clearly formulated view.
This sort of superlative “denominatio extrinseca” enjoys in Frege’s doctrine the same right to be a property of an object as the essential predicates do (cf. Section 3.5). In fact Frege uses this kind of property in order to have a substitute of existential propositions for individuals; it is not possible to say “there is Julius Caesar” but it is possible to say, instead, “there is an x called Julius Caesar” (cf. BGGE, p. 200).
Porphyry [1], p. 12, 1. 19 and p. 13, 1. 1, says that both the proprium and the inseparable accident may be disregarded in our approach to the thing; i.e., Porphyry implies that the thing may be given under other aspects.
UFT, p. 101.
Only with such qualifications would I agree with Papst [1], p. 8.
In the present section all references (unless otherwise stated) are to SUB, p. 25–26.
GRL, §§ 29 and 49, respectively.
Frege prefers to use the term “figure” (Figur) when the meaning should not be taken into account. Cf. UFT, p. 97, GRG II, p. 107; the situation is clearly described in KSCH, p. 449, where a figure is said to be able to acquire the property of serving as a sign.
To use an expression of Quine [3], p. 22; but then cf. ibid., p. 9.
(i) “Eine Verschiedenheit kann nur dadurch zu Stande kommen, daß der Unterschied des Zeichens einem Unterschiede in der Art des Gegebenseins des Bezeichneten entspricht.” (ii) “Wir haben also verschiedene Bezeichnungen für denselben Punkt, und diese Namen […] deuten zugleich auf die Art des Gegebenseins, und daher ist in dem Satze eine wirkliche Erkenntnis enthalten.” (iii) “Es liegt nun nahe, mit einem Zeichen […] außer dem Bezeichneten, was die Bedeutung des Zeichens heißen möge, noch das verbunden zu denken, was ich den Sinn des Zeichens nennen möchte, worin die Art des Gegebenseins enthalten ist”. Senses as “sides” (Seiten) of a thing is an image appearing in SUB, p. 27 and FUB, p. 5. In the latter, the variety of names of a thing is viewed again as grounded on that plurality of “sides”. The same in GED.
These well-known terminological distinctions are to be found in SUB, p. 26–27, 31.
Aristotle [4], 190b, 24. Two examples to be compared with Frege’s analysis of identity: “‘To be capable of health’ and ‘to be capable of illness’ are not the same, for if they were there would be no difference between being ill and being well. Yet the subject both of health and of sickness […] is one and the same” (Aristotle [4.1], 201a, 34b, 3). “This is an identical substratum (whether a point or a stone or something else of this kind), but it has different attributes — as the sophists assume that Coriscus’ being in the Lyceum is a different thing from Coriscus’ being in the marketplace” (ibid., 219b, 18–22). There is also the famous distinction between the road from Thebes to Athens and the road from Athens to Thebes (Aristotle [4], 202b, 12). As for Frege, WIF, pp. 658, 660 may be compared with the Aristotelian or traditional approach.
Brentano [1], § 18: “der Name gibt etwas kund”.
Ibid.: “der Name etwas bedeutet, auf einen Begriff hinweist”.
Ibid.: “der Name hat eine Beziehung zum Gegenstand, der möglicherweise der Vorstellung entspricht. In diesem Sinne sagen wir, der Name nennt den Gegenstand”.
Ibid.: “So daß jede [Vorstellung] nur einer gewissen Seite oder einem gewissen Teil eines Dinges entspricht”.
SUB, p. 27, GED, p. 66.
SUB, ibid.
SUB, p. 28.
SUB, p. 27.
It should be observed that in SUB, p. 27 Frege is careful to exclude from perfect languages some defects which are typical of natural languages, but he does not explicitly reject the possibility that a sense be given under different names (under… different senses). In fact Frege has thought it convenient rather to disregard such different ways of a sense’s being given. This is apparent in his reference to propositions being given under many sentences (BGGE, p. 196 note). For proper names the following later text is interesting: “Ob ich das Wort ‘Pferd’ oder ‘Ross’ oder ‘Gaul’ oder ‘Märe’ gebrauche, macht keinen Unter- schied im Gedanken” (GED, p. 63 below). To some extent this is just common sense; nevertheless in the case of Frege there are other implications (cf. 2.26).
SUB, p. 26 below, and 31.
Carnap [1] § 29: “It is more difficult to see clearly what constitutes the ordinary sense in Frege’s method. As mentioned before this is due to the lack of precise explanation and especially of a statement as to the condition of identity of sense.” Cf. also Church [1], note 15.
Scholz [5], 1, B, but cf. Scholz-Hasenjaeger [1], § 50, 2.5. In the former, the least difference in the sign implies a difference of senses. In the latter, definiendum and definiens, usually different signs, are allowed to be gleichsinnig.
I would make a similar objection to the interpretation proposed by Wienpahl [1].
“Note Church’s ambiguous use of ‘meaning’. On the one hand he speaks of denotation as one aspect of meaning and of sense as another kind of meaning. Either we have two kinds of meaning or only one kind with two aspects” (R. M. Martin [1], p. 609, the last italics ours). Such familiar “aspects” of things are all which is involved in Frege’s Sinn.
According to Frege’s dyadic semantics of his earlier works (cf. 2.1), names have a content.
SUB, p. 27 twice identifies Bedeutung and Gegenstand; cf. also p. 30. On the other hand, the Sinn is said not to be the Gegenstand selbst (p. 30).
Cf. Section 10.11.
Cf. Section 1.46, note 118.
SUB, p. 28.
BGGE, pp. 195, 198, 203.
SUB, p. 27.
For the question dealt with in the present section, cf. Jackson [1]; an interesting discussion is in Caton [1].
Cf. Bartlett [1], p. 58.
Church [1], note 32, rejects unsaturatedness but keeps sense-reference. Cf. also Church [2].
Cf. Angelelli [2], Buridan [1], p. 49, Bodemann [1], p. 113.
A weaker formulation appears’in fine of Gedankengefüge.
In comparison with such basic objections, any confusion of use and mention, inherent in the famous Leibnizian principle appears as secondary.
GRL, § 65; FUB, p. 2–5; GRG II, p. 71; SCHUB, p. 10.
In particular FUB, pp. 2–5.
GRG 1, p. IX and FUB, pp. 2–5 are careful to explain that the senses may be different.
Incidentally, a further inconsistency in GRL § 65 is that Frege’s reduction of equality to identity does not seem to respect the meaning of “Eigenschaft” as individual accident, which prevails in some fragments of GRL. Frege says in GRL, § 65 that instead of asserting that two surfaces are equal as to their color, one should say that the color of the two surfaces is the same. But of course it cannot be the same (except specifically) if “color of a surface” means an individual accident inhering in that surface, as is the case for GRL, §§ 21–25 (cf. our 10.11, 1.45 and 1.46).
GRG II, p. 111.
Aristotle [5], pp. 179a, 36. The quoted Greek formula belongs to Aristotle [4], P, 3, 202b, 15. My interpretation of these texts is also intended as a correction of Bochenski [3], 11.46 and [4] ibid.
Cf. HUSS, p. 319–320 and Bartlett [1], p. 59.
“… gemeint ist die Wahrheit, deren Erkenntnis der Wissenschaft als Ziel gesetzt ist” (GED, p. 59). This was written in 1918, but it is in accord with SUB, p. 32–33.
Bartlett [1], p. 59 and HUSS, p. 320.
Pp. 264–5.
SUB, p. 28: “In der ungeraden Rede spricht man von dem Sinne, z.B. der Rede eines Andern.”
SUB, p. 32: “Wir fragen nun nach Sinn and Bedeutung eines ganzen Behauptungssatzes.”
“Ein solcher [Behauptungs]satz enthält einen Gedanken” (SUB, p. 32). Frege explains that by “Gedanke” he means the objective content of a sentence which may be the common property of several thinkers (ibid.).
“Ist dieser Gedanke nun als dessen [of the sentence] Sinn oder als dessen Bedeutung anzusehen?” (ibid.)
In BG (p. 4) Frege mentions the possibility of making of assertion “the only predicate” of his symbolic language. But this is, in my view, a rather ironical way of assigning some function to the term “predicate” (the couple of terms “subject-predicate” having been eliminated in favor of function-argument, cf. Section 6.1). In FUB, p. 22, note, Frege stresses the peculiarity of the assertion sign which is reiterated in GRG I (§ 26). Frege rejects the unqualified making of the adjective “true” a predicate of propositions or sentences (SUB, pp. 34–35; cf. Bartlett [1], p. 18). The most interesting presentation of this point is to be found in GED, where Frege discusses whether truth is a property, in a way quite similar to GRL’s discussion of whether number is a property. In GED (p. 61) as in GRL Frege uses “Eigenschaft” in the sense of individual accident (cf. our 1.46). He assumes that it is meaningful to talk about sinnlich wahrnehmbare Eigenschaft, while the normal use of “Eigenschaft” excludes this (properties are abstract entities). Now, even if we provisionally call truth a property, Frege shows that it is quite a peculiar one: (1) to every property of a thing truth is associated as a property of the proposition which assigns that property to the thing, (2) “p” has the same content as “p is true” (though - as Frege remarks - they do make a difference for a researcher who has painfully arrived at the second) (GED, p. 61).
A particular sub-class of conceptual content (cf. 2.11) is propositional content (beurteilbarer Inhalt). Propositional content should be understood as that which counts for deduction, and in this sense the fact that a sentence is given in the active or passive voice does not affect its propositional content (BG, p. 3). The distinction of apodictic and assertoric sentences is rejected on the same grounds (BG, pp. 4–5). The same applies for such “rhetorical” particles as “aber” (BG, p. 13). Nevertheless, it is not clear how far this elimination of elements irrelevant to “deduction” extends. The notion of beurteilbarer Inhalt belongs only to the earlier works of Frege; it is afterwards replaced by the well known distinction of Gedanke and truth-value. In GRG I (p. X) and BGGE (p. 198) Frege says that the propositional content included both the Gedanke and the truth-value.
GED, pp. 59–60.
SUB, p. 32 f.
FUB, pp. 13 and 16. Frege says “ebenso”. Compare the “ebensogut” in SUB, p. 32, line 10 from the bottom.
Cf. Section 2.26.
FUB, p. 14.
SUB, p. 32f.
SUB, p. 32.
At the time of SUB the most that can be attained from Frege as to the nature of Gedanke is his footnote to SUB, p. 32 (cf. note 80). But the borderline between objectivity and subjectivity is not clear in Frege. Why are the Färbung or Beleuchtung of propositions mere subjective elements? Only because they do not concern the logician? (cf. BGGE, p. 196, note; SUB, p. 45). In a later period, Frege suggests a definition of Gedanken (in a letter to Husserl, 1906, published recently by Bartlett [1], p. 19). But the criterion set forth therein does not seem to help in deciding whether interchanging non-logical constants (such as “the Morning Star” and “the Evening Star”) preserves the same Gedanke.
BGGE, p. 196, note.
Cf. note 104.
The Leibnizian principle is actually Frege’s source of inspiration, SUB, p. 35.
SUB, p. 32, lines 4–9 from the bottom. Actually Frege gives “, p ’ r.
Ibid., lines 1–3 from the bottom.
SUB, p. 33, lines 10–13.
Ibid., lines 15–18.
Ibid., below.
SUB, p. 32 below, and 33.
Odyssey, Invocation.
“Mit der Frage nach der Wahrheit würden wir den Kunstgenuß verlassen and uns einer wissenschaftlichen Betrachtung zuwenden” (SUB, p. 33). Rivetti Barbó [1] views Frege’s semantics in SUB as tacitly related to the principle of contextual meaning of GRL; “Odysseus” has no Bedeutung because its context is not true (§ 6). But I think that there was no such principle in Frege’s semantics (cf. 2.7) and that “Odysseus” non supponit or has no Bedeutung because neither it nor the Odyssey as a whole have any importance (Bedeutung) for Frege (qua philosopher of mathematics), cf. 2.26.
SUB, p. 33, lines 8–9: “für den Sinn eines Satzes kann ja nur der Sinn, nicht die Bedeutung dieses Theiles [Frege means a part of the sentence] in Betracht kommen”. Cf. Carnap [1], 28.7, and Stegmüller [1], p. 135.
SUB, p. 34.
Cf. 2.62.
As Frege himself suggests (SUB, p. 34, line 16).
SUB, p. 34, last line of the first passage.
SUB, p. 35, last line of the first passage.
SUB, p. 32, note.
Cf. Section 2.24.
“Wenn nur der Wahrheitswert eines Satzes dessen Bedeutung ist, so haben einerseits alle wahren Sätze dieselbe Bedeutung, andrerseits alle falschen. Wir sehen daraus, dass in der Bedeutung des Satzes alles Einzelne verwischt ist (SUB, p. 35).
“Es kann uns also niemals auf die Bedeutung eines Satzes allein ankommen…” (ibid.).
SUB, pp. 35–36.
SUB, p. 36.
UGG2 (II), pp. 377 f.; 400; 402.
SUB, pp. 36, 39, 42–46, 49.
The indetermination is implicit in the following example: “Wenn sich die Sonne im Wendekreise des Krebses befindet, haben wir auf der nördlichen Erdhälfte den längsten Tag” (SUB, pp. 43–44). Frege understands such a sentence as a formal implication (the “quantifier” applies to the time variable). In formal implications, only the whole has a sense, i.e., expresses a proposition (WIF, p. 659).
SUB, p. 44, line 10.
This interpretation could be supported by BGGE, p. 205, where Frege says that a Gedanke must have at least one unsaturated element in order that its parts can be put together. The same interpretation is likewise favored by considering that pseudo-sentences become sentences as soon as a proper name, for example, is put in the “empty” place (SUB, p. 44).
SUB, p. 27.
UGG2(II), p. 379; cf. also pp. 400, 402. Frege says that in “If a2 = 1, then a4 = 1”, the fragment “a2 = 1” is not the name of a concept until “a” is replaced by a proper variable sign.
SUB, p. 39.
This ambiguity seems to be present in Frege’s analysis of relative subordinate sentences.
SUB, p. 39.
Against, for example, Aristotle [1], 13b, 16. For Frege’s approach, cf. also GRG I, p. XXI.
SUB, p. 27–28, 41.
SUB, p. 40.
GRG I, § 28. Already in UFT (p. 101) there is an indication of the necessity of ensuring reference for the signs being used. The requirement of scharfe Begrenzung of functions is closely connected with this; a function which is not defined for some arguments implies that some well formed sentences will be neither true nor false, a new menace to the tertium non datur (GRG II, § 56).
SUB, p. 41.
KSCH, p. 447. Scheineigenname is for instance “nothing”; “nihil”, as Paulus Venetus, for example taught, should be expanded into “nulla res” (P. Venetus [2], f. 2a).
SUB, p. 28.
SUB, p. 36, middle.
SUB, p. 28, lines 12–10 from the bottom.
SUB, p. 39 (middle), also pp. 37 (line 5, “also”), 46, 48. Cf. for both part (a) and (b), SUB, p. 37, bottom and p. 38, top.
Cf. Carnap [1], § 30.
SUB, p. 37, top.
Cf. SUB, p. 28.
Cf. Carnap [1], § 30: “Frege’s special form of the method of the name relation involves additional complications. Starting with any ordinary name, it leads to an infinite number of entities…”
Carnap [1], ibid., and Stegmüller [1], p. 149.
GRL, p. X; p. 37 note.
Cf. Chapter 1, note 118; also: GRL, p. 37 note, SUB, p. 29, GED.
GRL, p. 37, note.
For example, GRL, p. X.
For example, SUB, p. 31.
For instance, the Färbungen and Beleuchtungen which natural or poetical language adds to the sense and reference of words (SUB, pp. 31, 45). Frege realizes that he is condemning as subjective, things which are not interesting for him as a logician; he curiously admits some “accessibility to many thinkers” for Vorstellungen (“eine Verwandtschaft des Menschlichen Vorstellens”, SUB, p. 31). Other texts where Vorstellung is considered are: GRG I, p. XVIII; UTG, p. 160; HUSS; GED, p. 66. In the last mentioned text there is an interesting description of Vorstellung.
For example, SUB, p. 32, note. Cf. note 150. LNE, p. 74.
This is a key concept in Frege’s foundations of arithmetic; zero will be the class of concepts equiextensional with not being self-identical. To the extent that this concept is sharply defined (i.e., for every object it may be decided whether or not it falls under that concept), it is logically legitimate (GRL, § 74). I take it to be obvious that Frege regards the concept not being self-identical as objective.
For references, see the next note.
HUSS, pp. 317–318: objectivity as Öffentlichkeit; HUSS, pp. 331–332: objectivity as von unserm Denken ganz unabhängig. In GRG I, p. XVII the sense of being independent of us predominates; on p. XVIII the sense accessible to all prevails. Predication (Fallen unter) in HUSS, p. 317 is described as something independent of us; but is this univocally meant both for the falling of the Moon under being a satellite and for the falling of x x under number zero? Gedanke (i.e., proposition) is defined in terms of weak objectivity (SUB, p. 32, note) but also as something previous to me (GED, pp. 69 note, 77), which suggests the stronger sense of being independent of me. By asking further who is the “me” or the “us” we would be compelled to discuss transcendental subjectivity; this is not departing too much from Frege but rather understanding or clarifying him as suggested in our section 10.13.
GRG II, p. 86: Wirklich is what acts upon the senses (“auf die Sinne wirkt”, GRG I, p. XVIII). Since GRL Frege stresses that there is a domain of unwirkliche but still objective entities. His supreme category is das Denkbare (which for him coincides with das Zählbare, GRL, § 14). Das Denkbare was in Lotze [1], p. 17 the only supreme concept, and in the second scholastics it was called a super-transcendental (Fonseca [1], lib. primus, cap. 28).
A probable source is Eucken [1] (p. 209), where Herbart’s distinction Vorstellung—Begriff is mentioned. Eucken’s book is quoted by Frege in GRL, p. 43.
This is the English translation (in Aristotle [3.1]) of the Greek expression raOi vara zijç yvxfiç. The text in question is Aristotle [1], 16a, 3–8, i.e., the opening lines of Perihermeneias. For Theophrastus, cf. Bocherìski [2], p. 39.
Ammonius [2], p. 17 and Stephanus Alexandrinus [1], p. 4.
This would be the opinion of Ammonius [2], and not that assigned to him by Mates [1], p. 12.
Aquinas [4] has the four Aristotelian terms in the following version: scripturae, voces, intellectus conceptiones,res. The intellectus conceptiones are the locus of universals and this is enough to suggest that they are (also) objectively meant. In Caietanus [1] (p. 19) the objective interpretation is definitely supported: “Nomen autem cum sit nota earum quae sunt objective in anima passionum”.
Aquinas [5] draws a parallelism between the divine Trinity and human intellectual operations: “Quia semper cum actu intelligitur aliquid, verbum formatur”. Human verbum is tanquam speculum in quo res cernitur. It has nothing to do with the quidditas which is grasped through it; the verbum is a concrete (accidental) reality, in continuo fieri.
Suarez [1], II, sect. I, 1.
For example, Gredt [1], note 7.
Eisler [2] (article “Vorstellung”) paraphrases our Suarezian text in the following terms: “Die Scholastiker unterscheiden ”formale“ Vorstellung (Vorstellungsakt) und ”objektive“ Vorstellung (Vorstellungsinhalt)”.
Cf. Gredt [1], note 7.
GRL, p. 37, note.
Suarez [1], VI, sect. 2, 1.
Ibid., pp. 3, 9.
Descartes [1], § 59. That the risk of ambiguity transmitted to modern philosophy was indeed great, may be seen in Pacius’ presentation of the Aristotelian semantics: “. Nominibus non significari immediate res ipsas, sed per animi conceptionem. Quodlibet enim nomen significat aliquem mentis conceptum, consequenter significat rem, quae per eum conceptum repraesentatur, ut imago in speculo” (Pacius [3], pp. 60–61).
“The meaning of words being only the ideas they are made to stand for by him that uses them…” (Locke [1], III, Ch. 4, § 6).
“Je vois Monsieur que Vous entendez souvent par idée la realité objective de l’idée ou la qualité qu’elle represente” (Leibniz [1], V, p. 212).
For example, GRG I, p. XVIII. For Russell, cf. Simpson [1], pp. 111–112.
Cf. Section 2.51.
For the latter, cf. Eisler [1], article “Objektiv”.
Cf. for instance De Wulf [1], III, p. 223.
The tendency to see “to be in the mind” as subjectivism is clear, for instance, in Goodstein [1], p. 4. Cf. also Russell’s suggestion that Leibniz had made of relations subjective entities (Chapter 1, note 83). This tendency is also discernable in Frege, who reads “in the mind” as meaning either “in my mind” or “in your mind” (GRG I, p. 2), but who also is incapable of reading that expression as referring to a transcendental subjectivity (which he, paradoxically and perhaps unconsciously, is compelled to introduce, cf. Section 10.13).
It would be necessary to apply the same qualifications to many statements of “platonism”, especially in the field of mathematical foundational research (for example: Scholz-Hasenjaeger [1], § 1; Bernays [2]; Bourbaki [1], p. 88, etc.). (For the particular case of H. Scholz, I owe this remark to Prof. I. M. Bochenski). That those qualifications are “pertinent”, is indicated by Cantor’s distinction of an inmanente or intrasubjektive Realität vs. a transsubjektive Realität (Cantor [1], p. 181); where is Cantor’s “paradise”? In terms of traditional philosophy, this would make a difference in one’s calling him “platonist”.
Cf. Section 10.13. For platonism, cf. also Mortan [1] and Egidi [1], p. 26.
Cf. Section 2.11 (and notes 5 and 6), 6.3 in fine.
UWB, p. 50. Frege accuses natural language of not being eindeutig: “Von vielen Beispielen mag nur eine durchgehende Erscheinung hier erwähnt werden: dasselbe Wort dient zur Bezeichnung eines Begriffes und eines einzelnen unter diesen fallenden Gegenstandes. Überhaupt ist kein Unterschied zwischen Begriff und Einzelnem ausgeprägt. ”Das Pferd“ kann ein Einzelwesen, es kann auch die Art bezeichnen, wie in dem Satze: ”das Pferd ist ein pflanzenfressendes Thier“. ”Pferd“ kann endlich einen Begriff bedeuten wie in dem Satze: ”dies ist ein Pferd.“ Is it possible to conjecture that Frege has here, already, his later explicitly formulated requirement that concepts be designata of unsaturated expressions? Unsaturatedness would thus not be a mere reaction to Kerry (as we would like to think) but an original insight (cf. Chapter 6). In the last sentence the name of the concept would be ”… ist ein Pferd“.
In GRL Frege states three fundamental principles of research, one of them being “der Unterschied zwischen Begriff und Gegenstand ist im Auge zu behalten” (p. X). The following text shows his requirement of a parallel distinction between names of concepts and objects: “Zunächst ist es unpassend, ein allgemeines Begriffswort Namen eines Dinges zu nennen. Dadurch entsteht der Schein als ob die Zahl Eigenschaft eines Dinges wäre. Ein allgemeines Begriffswort bezeichnet eben einen Begriff. Nur mit dem bestimmten Artikel oder einem Demonstrativpronomen gilt es als Eigenname eines Dinges, hört aber damit auf, als Begriffswort zu gelten. Der Name eines Dinges ist ein Eigenname”.(GRL, § 51). But it is not necessary to see, already, Ungesättigtheit in this text. The sharp distinction between concepts and objects is sufficiently supported by what we call “the good” criterion (Section 6.43), which is stated by Frege precisely in the same § 51 of GRL: “Bei einem Begriffe fragt es sich immer, ob etwas und was unter ihn falle. Bei einem Eigennamen sind solche Fragen sinnlos ”
GRG I, pp. X, XIV, XXIV; GRG II, p. 154 bottom; UBR, p. 9; in the latter text natural language is once again accused: “Doch ist in der Sprache die Schärfe des Unterschiedes etwas verwischt, indem ursprüngliche Eigennamen (z.B. ”Mond“) Begriffswörter und ursprüngliche Begriffswörter (z.B. ”Gott“) Eigennamen werden können.”
Cf. Section 6.7.
The traditional passage from homo to humanitas — from f(x) to Ax(fx) — is not allowed by Frege.
Once Frege views the concept as the sachliches Subject of statements of number, i.e., once he sees a concept like to be a Jupiter’s moon as the subject of the property of having four members (GRL § 57), he is necessarily led to protest against any lack of sharpness in the separation of individuals and universals. Thus, he blames natural language for blurring the true nature of statements of number insofar as it does not show that concepts — not individuals — are the real subjects (GRL, § 52).
Cf. Section 6.43.
Cf. Section 6.72.
The “modus intelligendi”, cf. Section 6.75.
Cf. Section 4.4.
GRG II, § 151. Just before the modern decline of logic and semantics, Fonseca included in his Dialectica a thorough discussion on names (Fonseca [1], Lib. 1) wherein the chapter ‘De nomine communi et singulari’ is worth mentioning for our present purposes. Our author defines: Nomen {commune seu universale: eadem ratione de pluribus praedicari. Singulare seu discretum seu Individuum: non praedicatur de pluribus. For comparisons with Fregean terminology, the following remark of Fonseca is interesting: “nomina quidem communia vocari apud Grammaticos appellativa, singularia vero, propria.” Fonseca counts definite descriptions (existence and uniqueness) as proper names. See Section 2.9.
BG, p. 15.
Cf. note 176.
Cf. note 177.
BGGE — a paper where SUB is announced as a forthcoming publication (pp. 195, 198, 203) — defines concept as Bedeutung eines grammatischen Prädikats (p. 193, note). Commenting on the example “dieses Blatt ist grün”, Frege says: “Wir sagen dann, daß etwas unter einen Begriff falle, und das grammatische Prädikat bedeutet dabei diesen Begriff. Also diese Worte [i.e., ”nichts anderes als Venus“] bedeuten einen Begriff…” (BGGE, p. 194). Cf. also pp. 198, 201 (last line of the first passage). FUB is also written under the semantics of SUB (p. 14, note). Frege analyses the sentence “Caesar eroberte Gallien” into two parts: “Caesar” and “eroberte Gallien”. The latter is said to have a function as its reference (FUB, p. 17). It is obvious that Frege would not use the term “Bedeutung” unless he expected the reader to take that term with all its implications within the theory. of sense and reference. Other texts where Frege speaks of the Bedeutung of predicate-terms are HUSS, p. 326 below, UGG I, p. 298. Frege does not seem to speak of the sense of predicate-terms; a rare reference would be the following: “… der Fehler liegt […] in der Hilbertschen Definition, die der grammatischen Prädikate ”ist ein Punkt“ weder einen Sinn noch eine Bedeutung verleiht” (UGG2(I), p. 305). The inedita will show that Husserl at the end of the century did already know what we are now painfully inferring: the reference of a predicate term is a con- cept (or relation). As for the sense, we (including Husserl) are not further instructed by Frege; but we may trivially say that the sense is that way in which the concept is given. For this question see also Dummett [2] and [3] and Marschall [1] and [2].
Mill [1], I, 2, § 5: “The word ‘white’ denotes all white things, as snow, paper, the foam of the sea, etc., and implies, or, in the language of the schoolmen, connotes the attribute whiteness”. Cf. 3.62, note 85.
Aristotle [2], Z, 6, 1031b, 23–25.
“Dieser unglückliche Ausdruck ‘Gemeinname’ […] Dieser sogenannte Gemeinname — besser Begriffswort genannt — hat unmittelbar nichts mit den Gegenständen zu thun, sondern bedeutet einen Begriff, und unter diesen Begriff fallen vielleicht Gegenstände; er kann aber auch leer sein, ohne daß der Begriffswort darum weniger bedeutete” (HUSS, p. 326). Cf. UGG2(I), p. 308.
“Wenn wir Hans einen Mensch nennen, so sagen wir damit, Hans falle unter den Begriff Mensch” (HUSS, p. 326).
Cf. text quoted in note 193; also: “Das Wort ‘Planet’ bezieht sich gar nicht unmittelbar auf die Erde, sondern auf einen Begriffe… So ist die Beziehung zur Erde nur eine durch den Begriff vermittelte” (KSCH, p. 454).
Cf. GRG I, § 26. (Of course we are here using “Andeuten” in a manner which is not actually Frege’s.)
Cf. Section 6.7; also Bartlett [1], pp. 58–59. GRG II, p. 254 also stresses that classes are not unsaturated or predicative.
Cf. Chapter 5.
Cf. KSCH, and Section 8.3. Frege suggests that classes have their “Bestand” in the marks of concepts.
In the same paper, where the text quoted in the preceding note 193 is found, Frege says that in a statement of number (which is actually a statement about a concept) “… direkt weder ein Begriffsumfang noch ein Inbegriff bezeichnet ist, sondern nur ein Begriff” (HUSS, p. 322). This would cut any semantic relation between the predicate-term and the class.
Cf. Section 2.26.
As is shown by the texts published by Bartlett [1] (pp. 58–59), it is clear that Frege has in mind an “identification” of equiextensional concepts, in the sense that they “behave” in an equivalent way in many contexts. Cf. also HUSS, p. 320, above.
HUSS, p. 319–320; Bartlett [1], p. 59. It is indeed inconsistent that Frege, who has the typical intensionalist insight into concepts as sets of marks (cf. Chapter 5), agressively rejects Husserl’s proposal of an identity criterion for concepts, according to which two concepts are identical if their marks are the same (HUSS, ibid.). But one should not insist on comparing Frege with extensionalist or intensionalist philosophers of the 19th century; Frege’s class is “almost” an intension (cf. 8.3), very far removed from the intuitive or traditional notion of class (in spite of Frege’s will to preserve the latter in his system). We may say that for Frege a class of stones is a class (now in the intuitive sense) of intensions (cf. ibid.). On the other hand, he knows that even if he says that he supports “extensionalists”, unsaturatedness will ultimately prevent him from falling into the position erroneously attributed to him by Carnap [1], § 29. Against such a background, one should not pay too much attention to Frege’s statements about his own attitude with regard to the polemics intensionalismextensionalism in KSCH (p. 456).
xarì yderiva (Aristotle [2], I, 2).
Cf. Tricot in Aristotle [2.1], I, p. 179, note 4.
emo ovOeiv â,14Rotç (Aristotle [2], r, 2, 1003b, 23.
GRL, p. X.
GRL, p. X, §§ 60, 62 and 106. Schweitzer in Scholz [5], p. 99 (note 11), views a Fregean phrase in GRG II, § 97 (p. 105, line 6) as a reiteration of the semantical principle of GRL, but the context clearly indicates that this is not Frege’s intention.
Rivetti Barbé [1] (p. 2) includes many references. Cf. Wittgenstein [2] (p. 24); Quine [3] (p. 39); Geach [2] (p. XI and pp. 25–26); Stegmüller [1] (p. 311); Patzig [1] (p. 139 note). There is some paradox in the fact that in Brentano and his school the idea of Synsemantika was indeed a systematically and consciously adopted principle, but has not become proportionally famous. Brentano develops the idea of syncategorematic terms beyond the traditional limits (cf. Brentano [4], II, pp. 214–215; 228–229: “Doch ist es fraglich ob nicht auch Hauptwörter and Adjective manchmal mitbedeutend seien”) and Marty makes of that a fundamental notion (cf. Marty [2], p. 47, note). Earlier, the problem of syncategorematica was discussed in a most technical and subtle way, cf. Paulus Venetus [2].
GRL, p. X.
GRL, § 106.
GRL, § 60. Actually, the context to be considered begins in § 58; cf. in particular the footnote on page 69.
UGG2(I), pp. 307–308; UGGI, pp. 319–320, p. 322; UBR, p. 13. Cf. also GRG II, § 66 and p. 255; SUB, p. 41.
GRL, § 60.
GRL, p. 67.
Cf. 10.2, at the beginning.
Cf. LNE, p. 74, bottom.
GRL, p. 71, line 8 from the bottom.
GRL, p. 72 top.
GRL, § 61.
GRL, p. 72 note 1, and also GRL, § 63.
GRL, § 62.
Cf. GRL, p. 3, note. For the term “explication”, see for instance Carnap [1], p. 8.
“außer von Kant noch wenig in dieser Richtung geleistet ist” (COH, p. 324).
BG, § 8.
Because they enlarge our knowledge, BG, p. 15.
BG, p. 56.
In the Vorwort of BG Frege seems interested only in Leibniz.
In BG, p. III: the question whether a sentence may be proved rein logisch depends on the innern Wesen des betrachteten Satzes.
GRL, § 3. Synthetic propositions are characterized by their being restricted to a besonderes Wissensgebiet.
Against the foregoing argument it might be observed that in GRL, § 8 (in fine) Frege says that there is a sense in which even Miinchhausen’s tales are empirical or a posteriori. This text of GRL could be interpreted as saying that Miinchhausen’s tales are not rein a priori (in Kantian terms, cf. Kant [3], Einleitung, I, in fine), i.e., that they include a posteriori concepts. This would enable us to retain “content” in Frege’s formulation of his criterion. Frege would mean that he does not take into account whether some concepts making up a proposition are of empirical origin.
Reines Denken is that whose laws the Begri f fsschrift is supposed to express (cf. the title of BG).
GRL, §§ 17, 87, 88.
BG, p. 55; cf. also GRL, § 17 (p. 24).
GRL, § 88. Rieffert [1] (p. 123) confirms Frege’s view.
Carnap [1], p. 222. Cf. GRL, § 17, and especially the note on p. 24.
White [1], p. 273, bottom.
GRL, §§ 90, 91. Also of course BG, Vorwort.
Frege thinks he has established the plausibility of his Verbesserung of Kant’s views. Unfortunately, he expresses this by saying that arithmetic is analytic (GRL, § 109). The reason for doing symbolic logic (the Begrifsschrift of BG, GRG I and GRG II) was to confirm this view (GRL, § 91).
BG, p. 15, GRL, § 67, UFT, p. 98; for a later period: UBR, p. 13; UGGI, p. 320.
Bartlett [1], pp. 55–56. The letter is dated 1902.
GRG I, p. XIV, p. 3 (line 15); GRG II, §§ 56, 62; GED, p. 60 (middle).
GRL, § 51, § 67, p. 87, p. 89 bottom; UFT, p. 103. Genii [2] (p. IX, 103) suggests that the lack of the article in Latin means that we should not look for a theory of definite descriptions in mediaeval writers. But one of the normal ways of “determining” an individual in traditional logic has been precisely the consideration of existence plus uniqueness; cf., for instance, the following text: “Individuum quadruplex est. Determinatum, ut Socrates. Signatum, ut hic homo. Vagum, ut quidam homo. Ex hypothesi, ut Antonii filius supposito quod Antonius habeat unicum filium” (Gasconius [1], II, 37 v). In Frege, the problem of descriptions and the definite article is so interwoven with the paradoxes of unsaturatedness, that it is better discussed together with Ungesättigtheit (Chapter 6).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1967 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Angelelli, I. (1967). Semantics. In: Studies on Gottlob Frege and Traditional Philosophy. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3175-1_3
Download citation
DOI: https://doi.org/10.1007/978-94-017-3175-1_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8326-5
Online ISBN: 978-94-017-3175-1
eBook Packages: Springer Book Archive