The passage below provides fairly strong evidence that Frege held something like a theory of direct reference. He is discussing Schroeder's version of set theory, and as usual when he comes to the work of other mathematicians and logicians, finds much there that is wrong. He objects in particular to Schroeder's conflation of two ideas which, according to Frege, are entirely distinct. There is the idea of a set as simply being the elements of which it is a set, as when we identify the set of dishes with those dishes. In this case, there can be no 'empty' set. For the set is its elements: if there are no elements, there is no set. 'If we burn down all the trees of a wood, we thereby burn down the wood'. Then there is the idea of a set as determined by the properties that its elements must have, in order to be in the set. Under this conception, there can be an empty set, and it is this conception only that allows us to express thoughts in general by stating relations between classes, and only so do we get a logic
Underlying this confusion, argues Frege, is the failure to distinguish whether a proper name designates or names something, from whether a concept takes objects under itself. For the relation of a proper name to the object it designates is direct, and a proper name that designates nothing is 'illegitimate'. But a word like 'planet' has no such direct relation at all to the Earth at all, but only to a concept that the Earth falls under. Thus its relation to the Earth is only an indirect one, by way of the concept, and the judgment that anything falls under this concept is not in any way part of our knowledge of what the word 'planet' means. (Whereas by implication, the knowledge that something is the reference of 'Earth', is part of our knowledge of what the proper name 'Earth' means).
This innovation is a significant point in the history of connotation and denotation. As Russell remarks here, we should not confound the relation of Socrates to the set of Greeks, with the relation of the set of Greeks to the set of men, or the relation between Socrates and men considered collectively, with the relation between Socrates and the class-concept man. The traditional system of logic distinguishes the connotation from the denotation of names. The connotation is a sort of primary or semantic meaning, which the name (i.e. both the proper and the common name) possesses in the absence of anything that falls under the name. The denotation is simply whatever falls under the name. Proper names are 'proper' in that only one object is denoted by them, common names are 'common' in that more than one object is denoted by them. In both cases, the primary meaning of a name, its connotation, is part of its semantics, and not any of the objects it denotes. Frege's innovation is the idea that, in the case of the proper name, its connotation or primary meaning is the object itself. This is a departure for logic, and leads to all the good things, if they are good things, that set theory has brought us. The passage below makes that point both clearly and forcefully.
Unlike many other exhibits in the Logic Museum, this is not a parallel text, as I am still unable to locate the original German, and provide a new translation. So, unfortunately, I had to use the Geach and Black translation. The translation of this passage is itself a very good argument against the strange decision by the editors of the third edition of Translations from the Philosophical writings of Gottlob Frege to translate nearly all occurrences of Frege's term 'Bedeutung' by the English word 'meaning', which had before been translated by the word 'reference'. This would have been just about acceptable had the word 'meaning' only been used to translate 'Bedeutung', but this little word crops up all over the place in English, and one is always left wondering which German word it is the translation of. (German editions of Frege are reasonably easy to come by for most of his work, but this one I have not been able to find).
For example, when Frege says 'a proper name without any meaning', it is probably 'Bedeutung' that is being translated. But when he says
'Round square', on the other hand is not an empty name, but a name of an empty concept, and thus one not devoid of meaning ...
we are left in doubt. More recent translations get over this problem by avoiding the translation altogether and rendering the word as 'Bedeutung'.
See the new Logic Museum site for a parallel German English version.
From Frege, G. (1895) "A critical elucidation of some points in E. Schroeder"s Vorlesungen Ueber Die Algebra der Logik", Archiv fur systematische Philosophie 1895, pp 433-456, transl. Geach, in Geach & Black 86-106 .
Only because classes are determined [453] by the properties that individuals in them are to have, and because we use phrases like this: 'the class of objects that are b: only so does it become possible to express thoughts in general by stating relations between classes; only so do we get a logic. The complete difference, and indeed incompatibility, between this conception of classes and the one first mentioned is, of course, concealed at first. Thus there arises a cruder conception of classes and extensions, side by side with a subtler one, the only one that can be used in logic; and the incompatibility of the two becomes noticeable only incidentally, by means of contradictions. It is understandable that this happens most obviously where there is no class in the 'domain-calculus' sense - when we have empty concepts. Somebody might have the idea of rejecting such concepts as illegitimate; but this would involve excluding from logic wide and particularly fruitful domains. Herr Schroeder is quite right in not wanting to do this and in stressing the importance of introducing the 'identical' zero (p. 189) - though the recognition of empty concepts need not be made exactly in this form. If we admit a sentence 'there is a --', we may not exclude a sentence 'there is no --'; for unless the negation of a sentence has a sense, the sentence itself is without sense.
We must here keep well apart two wholly different cases that are easily confused, because we speak of existence in both cases. In one case the question is whether a proper name designates, names, something; in the other, whether a concept takes objects under itself. If we use the words 'there is a --' we have the latter case. Now a proper name that designates nothing has no logical justification, since in logic we are concerned with truth in the strictest sense of the word; it may on the other hand still be used in fiction and fable* [cf. my paper Ueber Sinn und Bedeutung, Zeitschrift fuer Phil. und phil. Kritik, vol. 100]. For concepts that do not comprehend anything under them it is quite different; they are entirely legitimate. The author [Schroeder] confuses these two cases when he calls 'Nothing' and 'round square' alike senseless, nonsensical, or meaningless names. His 'Nothing' is in many cases, e.g. in the sentences 'Nothing is black' and 'Nothing is not black' (p. 238), a proper name without any meaning, and hence logically illegitimate 'Round square', on the other hand is not an empty name, but a name of an empty concept, and thus one not devoid of meaning, in sentences like 'there is no round square' or 'the Moon is not a round square'. The word 'common name' is confusing here, for it makes it look as though the common name stood under the same, or much the same relation to the objects that fall under the concept as the proper name does to a single object. Nothing could be more false! In this case it must, of course, appear as though a common name that belongs to an empty concept were as illegitimate as a proper name that designates nothing. The word 'planet' has no direct relation at all to the Earth, but only to a concept that the Earth, among other things, falls under [my emphasis]; thus its relation to the Earth is only an indirect one, by way of the concept; and the recognition of this relation of falling under requires a judgment that is not in the least already given along with our knowledge of what the word 'planet' means. If I utter a sentence with the grammatical subject 'all men', I do not wish to say something about some Central African chief wholly unknown to me. It is thus utterly false that I am in any way designating [my emphasis] this chief when I use the word 'man', or that this chief belongs in any way to what the word 'man' means. It is likewise equally false that in such a sentence many judgments are put together by means of the common name, as Herr Schroeder thinks (p. 69). In order that a word like 'man' or 'planet' should have logical justification, it is necessary only that there should answer to it a sharply delimited concept; whether the concept comprehends something under itself is not here relevant.
It is easily seen how the use of the word 'common name' hangs together with the conception that the class or extension consists or is compounded of single things. In both cases the emphasis is laid on the things and the concept is overlooked. Now we do admittedly also get in Schroeder's work passages like this: 'In this [455] way we show that for us what characterises a concept ... is just that a definite group of traits, distinguishable from all others ... are associated and invariable correlated with its name' (pp. 89-90). But this is only another sign of the pervasive inconsistency that the author has not noticed and has thus not been able to escape*. [It would take us too far here to explain more precisely the nature of the concept. I therefore refer to my address Function und Begriff, Pohle, Jena 1891; to my paper Ueber Begriff und Gegenstand ...]
Someone may get the impression from my procedure that in the battle between the extensionalist and intensionalist logicians I take the side of the latter. I do, in fact, maintain that the concept is logically prior to its extension; and I regard as futile the attempt to take the extension of a concept as a class, and make it rest, not on the concept, but on single things. That way we get a domain calculus, not a logic. All the same, in many respects my position may be closer to the author than to those who could in contrast to him be termed intensionalist logicians.
In conclusion, we may sum up the results of this discussion:
1. The domain-calculus, in which the fundamental relation is that of part to whole, must be wholly separated from logic. For logic Euler's diagrams are only a lame analogy.
2. The extension of a concept does not consist of objects falling under the concept,in the way, e.g., that a wood consists of trees; it attaches to the concept and to this alone. The concept thus takes logical precedence of its extension.
3. We must keep separate from one another(a) the relation of an object(an individual) tothe extension [456] of a concept when it falls under the concept (the subter relation);4. By means of a definition we can neither create an object with any properties we like, nor magically confer any properties we like on an empty name or symbol.
(b) the relation between the extension of one concept and that of another when the first concept is subordinate to the second (the sub relation).
5. The questions whether a proper name means something, and whether a concept comprehends something under itself, must be kept separate. Proper names without any meaning are illegitimate in science; empty concepts cannot be banished.
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