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Philosophers

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Frege's Puzzle
In his 1879 Begriffsschrift (or "Concept-Writing"), Gottlob Frege developed a propositional calculus to determine the truth values of propositions from their general form, not from any particular predicates (using specific words, names, properties, attributes, relations, etc.) The propositional calculus, a truth-functional analysis of statements as a whole, is widely considered to be the greatest advance in logic since Aristotle, whose logic of syllogisms was a predicate logic, where truths depend on the meaning of individual terms in the predicate (or the subject).

In Frege's 1892 Über Sinn und Bedeutung ("Sense and Reference"), he distinguished the reference (name, denotation, extension, signifier) from the sense (meaning, connotation, intension, significance). He called the reference "direct" and the sense "indirect." Frege was very clear about how the Bedeutung, literally the pointing out or indication of an object or concept, generates different ideas in the minds of different persons.

He says that all persons probably get a basic "sense" of a reference, from the common knowledge of things passed down through the generations, but that the particular ideas, or representations (Vorstellung) in each mind will be different, because everyone has had a different set of experiences, different memories. This agrees perfectly with our idea of the Experience Recorder and Reproducer (ERR). The "meanings" are dependent on what a given mind plays back when stimulated by a new experience. Frege said ideas could only be compared if they were present to the same consciousness, which is of course impossible.

What is sometimes called Frege's Puzzle is how two names for the same object can be distinct words (his example was the Morning Star and Evening Star) and yet in some respect be identical? His word was Gleichheit ("sameness"), mistranslated into English as identity.

Here begins a vast problematic in philosophy for the next 135 years
Frege speculated that two references to the same object could therefore be considered "identical" in that respect even if the "names" are distinct.

Frege was following Gottfried Leibniz, who said, "To suppose two things indiscernible is to suppose the same thing under two names." Here is how Frege described it...

Frege said he uses sameness in the sense of identity and understands "a=b" in the sense of "a is the same as b" or "a and b coincide." It was mistranslated in English as identity.
Sameness gives rise to challenging questions which are not altogether easy to answer. Is it a relation ? A relation between objects, or between names or signs of objects? In my Begriffsschrift I assumed the latter. The reasons which seem to favor this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori...

Now if we were to regard sameness as a relation between that which the names "a" and "b" refer to, it would seem that a = b could not differ from a = a (i.e., provided a = b is true).

Frege is saying that two names referring to the same thing can be in some respect "the same" because the thing they refer to is identical to itself. They are the same qua references
A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a = b seems to be that the signs or names "a" and "b" refer to the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only insofar as they named or designated something. It would be mediated by the connection of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign "a" is distinguished from the sign "b" only as object (here, by means of its shape), not as sign (i.e., not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true. A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated...

If we found "a = a" and "a = b" to have different cognitive values, the explanation is that for the purpose of knowledge, the sense of the sentence, viz., the thought expressed by it, is no less relevant than its referent, i.e., its truth value. If now a = b, then indeed the referent of "b" is the same as that of "a," and hence the truth value of "a = b" is the same as that of "a = a." In spite of this, the sense of "b" may differ from that of "a," and thereby the sense expressed in "a = b" differs from that of "a = a." In that case the two sentences do not have the same cognitive value.

Names and Reference

Frege's puzzle is clear, the names "a" and "b" refer to the same thing, but the names are only identical qua references to the object. They have different senses, or meanings.

Since Frege, generations of philosophers have puzzled over different names and/or descriptions referring to the same thing that may lead to logical contradictions when one term is substituted for the other in a logical statement. Frege's original example was the Morning Star and Evening Star (often called Hesperus and Phosphorus) as names that refer to the planet Venus. Do these names have differing cognitive value? Yes. Can they be defined qua references to uniquely pick out Venus. Yes. Is identity a relation? No. But the names are relations, words that are references to the objects. And words put us back into the ambiguous realm of language.

Over a hundred years of confusion in logic and language consisted of finding two expressions that can be claimed in some sense to be identical, but upon substitution in another statement, they do not preserve the truth value of the statement. Besides Frege, and a few examples from Bertrand Russell ("Scott" and "the author of Waverly." "bachelor" and "unmarried man"), Willard Van Orman Quine was the most prolific generator of paradoxes ("9" and "the number of planets," "Giorgione" and "Barbarelli," "Cicero" and "Tully," and others).

Just as information philosophy shows how to pick out information in an object or concept that constitutes the "peculiar qualifications" that individuate it, so we can pick out the information in two designating references that provide what Willard Van Orman Quine called "purely designative references." Where Quine picks out information that leads to contradictions and paradoxes (he calls this "referential opacity"), we can "qualify" the information needed to make the terms referentially transparent.

Quine's Paradoxes
Quine generated a number of apparently paradoxical cases where truth value is not preserved when "quantifying into a modal context." But these can all be understood as a failure of substitutivity of putatively identical entities. Information philosophy shows that two distinct expressions that are claimed to be identical are never identical in all respects. So a substitution of one expression for the other may not be identical in the relevant respect. Such a substitution can change the meaning, the intension of the expression.

Perhaps Quine's most famous paradox is his argument about the number of planets:

(1) 9 is necessarily greater than 7

for example, is equivalent to

'9 > 7' is analytic

and is therefore true (if we recognize the reducibility of mathematics to logic)...

Given, say that

(2) The number of planets is 9

we can substitute 'the number of planets' from the non-modal statement (2) for '9' in the modal statement (1) gives us the false modal statement

(3) The number of planets is necessarily greater than 7

But this is false, says Quine, since the statement

(2) The number of planets is 9

is true only because of circumstances outside of logic.

Ruth Barcan Marcus analyzed this problem in 1961, which she calls the "familiar example" :

(27) 9 eq the number of planets

is said to be a true identity for which substitution fails in

(28) ◻(9 > 7)

for it leads to the falsehood

(29) ◻(the number of planets > 7).

Since the argument holds (27) to be contingent (~ ◻(9 eq the number of planets)), 'eq' of (27) is the appropriate analogue of material equivalence and consequently the step from (28) to (29) is not valid for the reason that the substitution would have to be made in the scope of the square.

The failure of substitutivity can be understood by unpacking the use of "the number of planets." It is not a purely designative reference, as Quine calls it.

In (27), "the number of planets" is the empirical answer to the question "how many planets are there in the solar system?" It is not what Saul Kripke would call a "rigid designator" of the number 9. The intension of this expression, its reference, is the "extra-linguistic" fact about the current quantity of planets (which Quine appreciated).

The expression '9' is an unambiguous mathematical (logical) reference to the number 9. It refers to the number 9, which is its meaning (intension). Kripke mistakenly claims that '9' is a rigid desgnator of the number 9 "in all possible worlds." This is false. The mathematical concept of the number 9 is true in all possible worlds.

We can conclude that (27) is not a true identity, unless before "the number of planets" is quantified, it is qualified as "the number of planets qua its numerosity, as a pure number." Otherwise, the reference is "opaque," as Quine describes it. But this is a problem of his own making.

As Marcus says, when we recognize (27') as contingent, ~◻(9 eq the number of planets), it is not necessary that 9 is equal to the number of planets, its reference to the number 9 becomes opaque.

The substitution of a possible or contingent empirical fact that is not "true in all possible worlds" for a logical-mathematical concept that is necessarily true is what causes the substitution failure.

When all three statements are "in the scope of the square" (◻), when all have the same modality, we can "quantify into modal contexts," as Quine puts it. Both expressions,
'9' and 'the number of planets, qua its numerosity,' will be references to the same thing,
They will be identical in one respect, qua number. They will be "referentially transparent."

The New Theory of Reference

Frege's Puzzle motivated several philosophers to develop a new theory of how words refer to objects, especially in modal contexts. It gave rise to Saul Kripke's theories about "possible world semantics."

When in the 1940's, Ruth C. Barcan and Rudolf Carnap added modal operators to quantification theory, Quine strongly objected, developing his demonstrations that "quantifying into modal contexts" leads to "referential opacity" and logical nonsense like "the number of planets is necessarily greater than 7."

This was nothing but the fact first seen by Frege that different descriptions, different names that are "disguised descriptions," have different cognitive value, different "senses," that cannot be substituted for one another in any logical context, not just modal contexts, as Quine thought.

What we call a "concept" about a material object is some subset of the information in the object, accurate to the extent that the concept is isomorphic to that subset. By "picking out" different subsets, we can sort objects. We can compare objects, finding them similar qua one concept and different qua another concept. We can say that "a = b" qua color but not qua size.

Frege said that "the Morning Star = the Morning Star" is an identity and therefore tautological and tells us nothing. But "the Morning Star = the Evening Star" has cognitive value. In 1961, Ruth Barcan Marcus said it tells us something empirical about Venus in the morning and evening skies. She suggested less ambiguous, purely designative names would have no cognitive value beyond their reference to named objects.

Her work gave rise to the sophisticated modern idea of the "necessity of identity."

In modern times, Frege's insight has been defended with elaborate modal logical arguments, beginning with Barcan in 1947, using Leibniz's Law about identity and indiscernibility, that seem to suggest that for any a and b, if a = b (even contingently), then necessarily a = b.

∀x ∀y (x = y) ⊃ [◻(x = x) ⊃ ◻ (x = y)]

Frege in English and German
Because there are well-known difficulties with the English translation, we are preparing a bilingual version of the Frege original German and the popular translation by Max Black and Peter Geach. So far we provide the first few critical pages and important last paragraph.

Black's choice of English terms was complicated, because the German terms Sinn and Bedeutung are both frequently translated as "meaning." Black translated it as "reference." He could have chosen "denotation" following Bertrand Russell ("On Denoting") and John Stuart Mill, who very nicely distinguishes denotation from connotation (meaning). .

Our English title would then have been Meaning and Denotation, and would have very likely been much less confusing to modern readers. (Russell suggested this very translation in his 1905 On Denoting, p. 383)

The etymological base of bedeuten is to indicate, to point out (ostension is used by the logical philosophers). The root of denotation is to mark, to provide a sign for something. To designate is very close, and Frege uses the German equivalent bezeichnen and Bezeichnet (signified). But its use in recent philosophy is to name. The English denominate is literally to name, German benennen, but broadly to assign things to categories, which much of linguistic philosophy tries to do with set theory and logic.

To refer is etymologically to send back, to relate one thing to another. This is what a word or name bears to an object, so perhaps is what Frege then and Quine and Kripke recently are trying to explain.

Black provided a list of translations for several important terms we list here.

Anschauung - Experience
Art des Gegebenseins - Mode of presentation
[Gegebenseins is givenness, being given] Bedeutung - Reference [for the process]
              - Referent [for the object]
Black uses Referent for Bezeichnet (Signified)
Begriff - Concept or predicate
Begriffsausdruck - Predicate expression
Behauptungssatz - Declarative sentence
Bezeichnung - Designation
Eigenname - Proper name
Erkenntniswerth - Cognitive value
Gedanke - Thought, or Proposition
Gewöhnliche Bedeutung - Customary reference
Sinn - Sense
Satz - Sentence or clause
Unbestimmt andeutender Bestandtheil
      - Indefinite indicator or variable
Vorstellung - Conception [Idea, Representation?]
Warheitswerth - Truth value
Sense and Reference Über Sinn und Bedeutung
Translated by Max Black and Peter Geach
(1948) The philosophical review, 57(3), 209-230.

[Numerical footnotes are in the German original.
Alphabetic footnotes are from Black and Geach.
Pages 209-230 are the Philosophical Review.
Pages 25-50 the original Zeitschrift.]

 

25
209
Identity1 gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift A I assumed the latter.

The reasons which seem to favor this are the following: a=a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was of very great consequence to astronomy. Even today the identification of a small planet or a comet is not always a matter of course.

 

26
Now if we were to regard identity as a relation between that which the names "a" and "b" designate, it would seem that a=b could not differ from a=a (i.e., provided a=b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a=b seems to be that the signs or names "a" and "b" designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only insofar as they named or designated something. It would be mediated by the connection of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a=b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign "a" is distinguished from the sign "b" only as object (here, by means of its
210
shape), not as sign (i.e., not by the manner in which it designates something), the cognitive value of a=a becomes essentially equal to that of a=b, provided a=b is true. A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated. Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names ("Point of intersection of a and b," "Point of intersection of b and c") likewise indicate the mode of presentation; and hence the statement contains true knowledge.

 

It is natural, now, to think of there being connected with a sign (name, combination of words, letter), besides that to which the sign refers, which may be called the referent of the sign, also what I would like to call the sense of the sign, wherein the mode of presentation is contained.

 

27
In our example, accordingly, the referents of the expressions "the point of intersection of a and b" and "the point of intersection of b and c" would be the same, but not their senses. The referent of "evening star" would be the same as that of "morning star," but not the sense.

It is clear from the context that by "sign" and "name" I have here understood any designation representing a proper name, whose referent is thus a definite object (this word taken in the widest range), but no concept and no relation, which shall be discussed further in another article.B The designation of a single object can also consist of several words or other signs. For brevity, let every such designation be called a proper name.

 

The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs;2 but this serves to illuminate only a single aspect of
211
referent, supposing it to exist. Comprehensive knowledge of the would require us to be able to say immediately whether every given sense belongs to it. To such knowledge we never attain.

 

The regular connection between a sign, its sense, and its referent is of such a kind that to the sign there corresponds a definite sense and to that in turn a definite referent, while to a given referent (an object) there does not belong only a single sign. The same sense has different expressions in different languages or even in the same language. To be sure, exceptions to this regular behavior occur. To every expression belonging to a complete totality of signs, there should certainly correspond a definite sense; but natural languages often do

28
not satisfy this condition, and one must be content if the same word has the same sense in the same context. It may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense. But this is not to say that to the sense there also corresponds a referent. The words "the celestial body most distant from the earth" have a sense, but it is very doubtful if they also have a referent. The expression "the least rapidly convergent series" has a sense; but it is known to have no referent, since for every given convergent series, another convergent, but less rapidly convergent, series can be found. In grasping a sense, one is not certainly assured of a referent.

 

 

If words are used in the ordinary way, one intends to speak of their referents. It can also happen, however, that one wishes to talk about the words themselves or their sense. This happens, for instance, when the words of another are quoted. One's own words then first designate words of the other speaker, and only the latter have their usual referents. We then have signs of signs. In writing, the words are in this case enclosed in quotation marks. Accordingly, a word standing between quotation marks must not be taken as having its ordinary referent.

 

In order to speak of the sense of an expression "A" one may simply use the phrase "the sense of the expression 'A."' In reported speech one talks about the sense-e.g., of another person's remarks. It is quite clear that in this way of speaking words do not have their customary referents but designate what is usually their sense. In order to have a short expression, we will say: In reported speech, words are used indirectly or have their indirect referents.
212
We distinguish accordingly the customary from the indirect referent of a word; and its customary sense from its indirect sense. The indirect referent of a word is accordingly its customary sense. Such exceptions must always be borne in mind if the mode of connection between sign, sense, and referent in particular cases is to be correctly understood.

 

29
The referent and sense of a sign are to be distinguished from the associated conception. If the referent of a sign is an object perceivable by the senses, my conception of it is an internal image, 3 arising from memories of sense impressions which I have had and activities, both internal and external, which I have performed. Such a conception is often saturated with feeling; the clarity of its separate parts varies and oscillates. The same sense is not always connected, even in the same man, with the same conception. The conception is subjective: One man's conception is not that of another. There result, as a matter of course, a variety of differences in the conceptions associated with the same sense. A painter, a horseman, and a zoologist will probably connect different conceptions with the name "Bucephalus." This constitutes an essential distinction between the conception and the sign's sense, which may be the common property of many and therefore is not a part or a mode of the individual mind. For one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another.4 In the light of this, one need have no scruples in speaking simply of the sense, whereas in the case of a conception one must precisely indicate to whom it belongs and at what time. It might perhaps be said: Just as one man connects this conception and another that conception with the same word, so also one man can associate this sense and another that sense. But there still remains a difference in the mode of connection. They are not prevented from grasping the same sense; but they cannot have the same conception. Si duo idem faciunt, non est idem.

 

 

 

30
If two persons conceive the same, each still has his own conception. It is indeed sometimes possible to establish differences in the conceptions, or even in the sensations, of different men; but an exact comparison is not possible, because we cannot have both conceptions together in the same consciousness.

 


Let us return to our starting point!

If we found "a=a" and "a=b" to have different cognitive values, the explanation is that for the purpose of knowledge, the sense of the sentence, viz., the thought expressed by it, is no less relevant than its referent, i.e., its truth value. If now a=b, then indeed the referent of "b" is the same as that of "a," and hence the truth value of "a=b" is the same as that of "a=a." In spite of this, the sense of "b" may differ from that of "a," and thereby the sense expressed in "a=b" differs from that of "a=a." In that case the two sentences do not have the same cognitive value. If we understand by "judgment" the advance from the thought to its truth value, as in the above paper, we can also say that the judgments are different.


 

 

Footnotes
1 I use this word strictly and understand "a=b" to have the sense of "a is the same as b" or "a and b coincide." [Frege's actual word was Gleichheit, "sameness" and he says he uses it in the sense of Identität. But Black and Geach simply use Identity!]

, A The reference is to Frege's Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Halle, 1879).

B See his "Über Begriff und Gegenstand" in Vierteilahrsschrift fur wissenschaftliche Philosophie (XVI [i892], I92-205).

2 In the case of an actual proper name such as "Aristotle" opinions as to the sense may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. Anybody who does this will attach another sense to the sentence "Aristotle was born in Stagira" than will a man who takes as the sense of the name: the teacher of Alexander the Great who was born in Stagira. So long as the referent remains the same, such variations of sense may be tolerated, although they are to be avoided in the theoretical structure of a demonstrative science and ought not to occur in a complete language.

3 We can include with the conceptions the direct experiences in which senseimpressions and activities themselves take the place of the traces which they have left in the mind. The distinction is unimportant for our purpose, especially since memories of sense-impressions and activities always help to complete the conceptual image. One can also understand direct experience as including any object, in so far as it is sensibly perceptible or spatial.

4Hence it is inadvisable to use the word "conception" to designate something so basically different.

ZEITSCHRIFT FÜR PHILOSOPHIE UND PHILOSOPHISCHE KRITIK
Im Verein mit mehreren Gelehrten vormals
herausgegeben von
Dr. J. H. Fichte und Dr. H. Ulrici,
redigirt von Dr. Richard Falckenberg,
Professor der Philosophie in Erlangen.
Neue Folge Hundertster Band. Leipzig
Verlag von C.E.M. Pfeffer, 1892

25
Die Gleichheit 1 fordert das Nachdenken heraus durch Fragen, die sich daran knüpfen und nicht ganz leicht zu beantworten sind. Ist sie eine Beziehung? eine Beziehung zwischen Gegenständen? oder zwischen Namen oder Zeichen für Gegenstände? Das letzte hatte ich in meiner Begriffsschrift angenommen. Die Gründe, die dafür zu sprechen scheinen, sind folgende: a=a und a=b sind offenbar Sätze von verschiedenem Erkenntniswerte: a=a gilt a priori und ist nach Kant analytisch zu nennen, während Sätze von der Form a=b oft sehr wertvolle Erweiterungen unserer Erkenntnis enthalten und a priori nicht immer zu begründen sind. Die Entdeckung, daß nicht jeden Morgen eine neue Sonne aufgeht, sondern immer dieselbe, ist wohl eine der folgenreichsten in der Astronomie gewesen. Noch jetzt ist die Wiedererkennung eines kleinen Planeten oder eines Kometen nicht immer etwas Selbstverständliches.

26
Wenn wir nun in der Gleichheit eine Beziehung zwischen dem sehe wollten, was die Namen "a" und b" bedeuten, so schiene a=b von a=a nicht verschieden sein zu können, falls nämlich a=b wahr ist. Es wäre hiermit eine Beziehung eines Dinges zu sich selbst ausgedrückt, und zwar eine solche, in der jedes Ding mit sich selbst, aber kein Ding mit einem andern steht. Was man mit a=b sagen will, scheint zu sein, daß die Zeichen oder Namen "a" und "b" dasselbe bedeuten, und dann wäre eben von jenen Zeichen die Rede; es würde eine Beziehung zwischen ihnen behauptet. Aber diese Beziehung bestände zwischen den Namen oder Zeichen nur, insofern sie etwas benennen oder bezeichnen. Sie wäre eine vermittelte durch die Verknüpfung jedes der beiden Zeichen mit demselben Bezeichneten. Diese aber ist willkürlich. Man kann keinem verbieten, irgendeinen willkürlich hervorzubringenden Vorgang oder Gegenstand zum Zeichen für irgend etwas anzunehmen. Damit würde dann ein Satz a=b nicht mehr die Sache selbst sondern nur noch unsere Bezeichnungsweise betreffen; wir würden keine eigentliche Erkenntnis darin ausdrücken. Das wollen wir aber doch grade in vielen Fällen. Wenn sich das Zeichen "a" von dem Zeichen "b" nur als Gegenstand (hier durch die Gestalt) unterscheidet, nicht als Zeichen; das soll heißen: nicht in der Weise, wie es etwas bezeichnet: so würde der Erkenntniswerth von a=a wesentlich gleich dem von a=b sein, falls a=b wahr ist. Eine Verschiedenheit kann nur dadurch zustande kommen, daß der Unterschied des Zeichens einem Unterschiede in der Art des Gegebenseins des Bezeichneten entspricht. Es seien a, b, c die Geraden, welche die Ecken eines Dreiecks mit den Mitten der Gegenseiten verbinden. Der Schnittpunkt von a und b ist dann derselbe wie der Schnittpunkt von b und c. Wir haben also verschiedene Bezeichnungen für denselben Punkt, und diese Namen ("Schnittpunkt von a und b", "Schnittpunkt von b und c") deuten zugleich auf die Art des Gegebenseins, und daher ist in dem Satze eine wirkliche Erkenntnis enthalten.

Es liegt nun nähe, mit einem Zeichen (Namen, Wortverbindung, Schriftzeichen) 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.

27
Es würde danach in unserem Beispiele zwar die Bedeutung der Ausdrücke "der Schnittpunkt von a und b" und "der Schnittpunkt von b und c" dieselbe sein, aber nicht ihr Sinn. Es würde die Bedeutung von "Abendstern" und "Morgenstern" dieselbe sein, aber nicht der Sinn.

Aus dem Zusammenhange geht hervor, daß ich hier unter "Zeichen" und "Namen" irgendeine Bezeichnung verstanden habe, die einen Eigennamen vertritt, deren Bedeutung also ein bestimmter Gegenstand ist (dies Wort im weitesten Umfange genommen), aber kein Begriff und keine Beziehung, auf die in einem anderen Aufsatze näher eingegangen werden soll. Die Bezeichnung eines einzelnen Gegenstandes kann auch aus mehreren Worten oder sonstigen Zeichen bestehen. Der Kürze wegen mag jede solche Bezeichnung Eigenname genannt werden.

Der Sinn eines Eigennamens wird von jedem erfaßt, der die Sprache oder das Ganze von Bezeichnungen hinreichend kennt, der er angehört; Die Gleichheit 2 damit ist die Bedeutung aber, falls sie vorhanden ist, doch immer nur einseitig beleuchtet. Zu einer allseitigen Erkenntniß der Bedeutung würde gehören, daß wir von jedem gegebenen Sinne sogleich angeben könnten, ob er zu ihr gehöre. Dahin gelangen wir nie.

Die regelmäßige Verknüpfung zwischen dem Zeichen, dessen Sinn und dessen Bedeutung ist der Art, daß dem Zeichen ein bestimmter Sinn und diesem wieder eine bestimmte Bedeutung entspricht, während zu einer Bedeutung (einem Gegenstande) nicht nur ein Zeichen zugehört. Derselbe Sinn hat in verschiedenen Sprachen, ja auch in derselben verschiedene Ausdrücke. Freilich kommen Ausnahmen von diesem regelmäßigen Verhalten vor. Gewiß sollte in einem vollkommenen Ganzen von Zeichen jedem Ausdrucke ein bestimmter Sinn entsprechen; aber die Volkssprachen

28 erfüllen diese Forderung vielfach nicht, und man muß zufrieden sein, wenn nur in demselben Zusammenhange dasselbe Wort immer denselben Sinn hat. Vielleicht kann man zugeben, daß ein grammatisch richtig gebildeter Ausdruck, der für einen Eigennamen steht, immer einen Sinn habe. Aber ob dem Sinne nun auch eine Bedeutung entspreche, ist damit nicht gesagt. Die Worte "der von der Erde am weitesten entfernte Himmelskörper" haben einen Sinn; ob sie aber auch eine Bedeutung haben, ist sehr zweifelhaft. Der Ausdruck "die am wenigsten convergente Reihe" hat einen Sinn; aber man beweist, daß er keine Bedeutung hat, da man zu jeder convergenten Reihe eine weniger convergente, aber immer noch convergente finden kann. Dadurch also, daß man einen Sinn auffaßt, hat man noch nicht mit Sicherheit eine Bedeutung.

Wenn man in der gewöhnlichen Weise Worte gebraucht, so ist das, wovon man sprechen will, deren Bedeutung. Es kann aber auch vorkommen, daß man von den Worten selbst oder von ihrem Sinne reden will. Jenes geschieht z.B., wenn man die Worte eines Anderen in gerader Rede anfährt. Die eigenen Worte bedeuten dann zunächst die Worte des Andern, und erst diese haben die gewöhnliche Bedeutung. Wir haben dann Zeichen von Zeichen. In der Schrift schließt man in diesem Falle die Wortbilder in Anführungszeichen ein. Es darf also ein in Anführungszeichen stehendes Wortbild nicht in der gewörhnlichen Bedeutung genommen werden.

Wenn man von dem Sinne eines Ausdrucks ,A' reden will so kann man dies einfach durch die Wendung "der Sinn des Ausdrucks ,A'". In der ungeraden Rede spricht man von dem Sinne z. B. der Rede eines Andern. Es ist daraus klar, daß auch in dieser Redeweise die Worte nicht ihre gewöhnliche Bedeutung haben, sondern das bedeuten, was gewöhnlich ihr Sinn ist. Um einen kurzen Ausdruck zu haben, wollen wir sagen: die Wörter werden in der ungeraden Rede UNGERADE gebraucht, oder haben ihre UNGERADE Bedeutung. Wir unterscheiden dem nach die GEWÖHNLICHE Bedeutung eines Wortes von seiner UNGERADEN und seinen GEWÖHNLICHEN Sinn von seinem UNGERADEN Sinne. Die ungerade Bedeutung eines Wortes ist also sein gewöhnlicher Sinn. Solche Ausnahmen muß man immer im Auge behalten, wenn man die Verknörpfungsweise von Zeichen, Sinn und Bedeutung im einzelnen Falle richtig auffassen will.

29
Von der Bedeutung und dem Sinne eines Zeichens ist die mit ihm verknüpfte Vorstellung zu unterscheiden. Wenn die Bedeutung eines Zeichens ein sinnlich wahrnehmbarer Gegenstand ist, so ist meine Vorstellung davon ein aus Erinnerungen von Sinneseindrücken, die ich gehabt habe, und von Thätigkeiten, inneren sowohl wie äußern, die ich ausgeübt habe, entstandenes inneres Bild. 3 Dieses ist oft mit Gefühlen getränkt; die Deutlichkeit seiner einzelnen Theile ist verschieden und schwankend. Nicht immer ist, auch bei demselben Menschen, dieselbe Vorstellung mit demselben Sinne verbunden. Die Vorstellung ist subjectiv: die Vorstellung des Einen ist nicht die des Andern. Damit sind von selbst mannigfache Unterschiede der mit demselben Sinne verknüpften Vorstellungen gegeben. Ein Maler, ein Reiter, ein Zoologe werden wahrscheinlich sehr verschiedene Vorstellungen mit dem Namen "Bucephalus" verbinden. Die Vorstellung unterscheidet sich dadurch wesentlich von dem Sinne eines Zeichens, welcher gemeinsames Eigenthum von Vielen sein kann und also nicht Theil oder Modus der Einzelseele ist; denn man wird wohl nicht leugnen können, daß die Menschheit einen gemeinsamen Schatz von Gedanken hat, den sie von einem Geschlechte auf das andere überträgt. 4
Während es dem nach keinem Bedenken unterliegt, von dem Sinne schlecht weg zu sprechen, muß man bei der Vorstellung genau genommen hinzufügen, wem sie angehört und zu welcher Zeit. Man könnte vielleicht sagen: ebensogut, wie mit demselben Worte der Eine diese, der Andere jene Vorstellung verbindet, kann auch der Eine diesen, der Andere jenen Sinn damit verknüpfen. Doch besteht der Unterschied dann doch nur in der Weise dieser Verknüpfung. Das hindert nicht, daß beide denselben Sinn auffassen; aber dieselbe Vorstellung können sie nicht haben. SI DUO IDEM FACIUNT, NON EST IDEM.

30
Wenn zwei sich dasselbe vorstellen, so hat jeder doch seine eigene Vorstellung. Es ist zwar zuweilen möglich, Unterschiede der Vorstellungen, ja der Empfindungen verschiedener Menschen festzustellen; aber eine genaue Vergleichung ist nicht möglich, weil wir diese Vorstellungen nicht in demselben Bewußtsein zusammen haben können.


Kehren wir nun zu unserem Ausgangspunkte zurück!

Wenn wir den Erkenntniswert von "a=a" und "a=b" im Allgemeinen verschieden fanden, so erklärt sich das dadurch, daß für den Erkenntniswerth der Sinn des Satzes, nämlich der in ihm ausgedrückte Gedanke, nicht minder in Betracht kommt als seine Bedeutung, das ist sein Wahrheitswerth. Wenn nun a=b st, so ist zwar die Bedeutung von "b" dieselbe wie die von "a" und also auch der Wahrheitswerth von "a=b" derselbe wie von "a=a". Trotzdem kann der Sinn von "b" von dem Sinn von "a" verschieden sein, und mithin auch der in "a=b" ausgedrückte Gedanke verschieden von dem "a=a" ausgedrückten sein; dann haben beide Sätze auch nicht denselben Erkenntniswerth. Wenn wir wie oben, unter "Urtheil" verstehen den Fortschritt vom Gedanken zu dessen Wahrheitswerthe, so werden wir auch sagen, daß die Urtheile verschieden sind.


Fußnoten
1g Ich brauche dies Wort im Sinne von Identität und verstehe "a=b" in dem Sinne von "a ist dasselbe wie b" oder "a und b fallen zusammen."

2 Bei einem eigentlichen Eigennamen wie "Aristoteles" können freilich die Meinungen über den Sinn auseinander gehen. Man könnte z.B. als solchen annehmen: der Schüler Platos und Lehrer Alexanders des Großen. Wer dies thut, wird mit dem Satze "Aristoteles war aus Stagira gebürtig" einen anderen Sinn verbinden als einer, der als Sinn dieses Namens annähme: der aus Stagira gebürtige Lehrer Alexanders des Großen. Solange nur die Bedeutung dieselbe bleibt, lassen sich diese Schwankungen des Sinnes ertragen, wiewohl auch sie in dem Lehrgebäude einer beweisenden Wissenschaft zu vermeiden sind und in einer vollkommenen Sprache nicht vorkommen därften.

3 Wir können mit den Vorstellungen gleich die Anschauungen zusammennehmen, bei denen die Sinneseindrücke und die Thätigkeiten selbst an die Stelle der Spuren treten, die sie in der Seele zurückgelassen haben. Der Unterschied ist für unseren Zweck unerheblich, zumal wohl immer neben den Empfindungen und Thätigkeiten Erinnerungen von solchen das Anschauungsbild vollenden helfen. Man kann unter Anschauung aber auch einen Gegenstand verstehen, sofern er sinnlich wahrnehmbar oder räumlich ist.

4 Darum ist es unzweckmäßig, mit dem Worte "Vorstellung" so Grundverschiedenes zu bezeichnen.

References
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