Comparing Frege and Russell

KENT BACH

Frege's and Russell's views are obviously different, but because of certain superficial similarities in how they handle certain famous puzzles about proper names, they are often assimilated. Where proper names are concerned, both Frege and Russell are often described together as "descriptivists." But their views are fundamentally different. To see that, let's look at the puzzle of names without bearers, as it arises in the context of Mill's purely referential theory of proper names, aka the 'Fido'-Fido theory.

According to Mill, "a proper name is but an unmeaning mark which we connect in our minds with the idea of the object, in order that whenever the mark meets our eyes or occurs to our thoughts, we may think of that individual object" (1872, 22). The function of proper names, Mill thought, is not to convey general information but rather "to enable individuals to be made the subject of discourse;" names are "attached to the objects themselves, and are not dependent on … any attribute of the object" (1872, 20). As a result, our use of names in communication can accommodate such pervasive facts as that a person, place, or thing can change over time, that one's conception of something can change over time, that we can be mistaken in our conceptions of it, and that different people's conceptions of the same thing can differ. All this is possible if using a name in thinking of or referring to an object is not a matter of representing it as having certain properties but, as Russell said, "merely to indicate what we are speaking about; [the name] is no part of the fact asserted … : it is merely part of the symbolism by which we express our thought" (1919, 175).

An obvious problem with this simple view is that if the role of names were simply to refer to their bearers, names without bearers would be meaningless. Yet names without bearers seem perfectly meaningful and sentences in which they occur seem to express propositions. Otherwise, how could a sentence like 'Santa Claus does not exist' be not only meaningful but true? Descriptivism about proper names avoids this problem, as well as Frege's two famous puzzles (about the informativeness of identity statements and about failure of substitution in indirect quotation and attitude reports). Descriptivism is often referred to as the "Frege-Russell view."1 However, their views were quite different. I'll call Frege's view "sense" descriptivism and Russell's view "abbreviational" descriptivism. Let's take up Russell's view first, although it came second.

Russell's view concerned "ordinary" proper names, like 'Bill Clinton' and 'Santa Claus.' He contrasted these with "logically proper" names, i.e. the individual constants of formal logic, which he regarded as Millian. For reasons connected with his doctrine of acquaintance, he thought that the only logically proper names of ordinary language, English in particular, are the demonstratives 'this' and 'that,' as used to refer to one's current sense data, and the pronoun 'I' (1917, 216). He held that ordinary proper names are really "abbreviated" or "disguised" definite descriptions. Definite descriptions in turn, according to Russell's famous Theory of Descriptions, function not as referring expressions but as quantificational phrases. We should not be misled by Russell's characterization of them "denoting phrases," because for Russell denotation is a semantically inert property. That is, the proposition expressed by a sentence in which a description occurs is the same whether the description has a denotation or not. So its denotation does not enter into that proposition.2 As Russell explains,

The actual object (if any) which is the denotation is not … a constituent of propositions in which descriptions occur;3 and this is the reason why, in order to understand such propositions, we need acquaintance with the constituents of the description, but do not need acquaintance with its denotation.4 (1917, 222)

Thus, for any sentence containing a definite description, grammatical form is misleading as to logical form. For example, 'The inventor of silly putty got rich' is of subject-predicate form grammatically but not logically-it is not really about the inventor of silly putty. According to Russell's famous theory of descriptions, a simple subject-predicate sentence of the form 'The F is G' does not express a singular proposition, of the subject-predicate form 'a is G,' but a general, existential proposition, what might be called a "uniqueness proposition." The quantificational structure of such a proposition is revealed only after the definite description is "broken up," to yield (in modern notation) the form '(Ex)((y)(Fy _ y=x) & Gx),' in which the description, not being a semantic unit, does not even appear.5 Accordingly for Russell, if a proper name is a disguised description, e.g., if 'George Kistiakowski' is short for 'the inventor of silly putty,' the bearer of the name does not enter into the proposition expressed by a sentence in which the name occurs. This is not because the name has a sense (in Frege's sense of 'sense') but because it abbreviates a definite description.

Russell's view is clear from what he says about the name 'Bismarck.' In his view, "the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description" (1917, 208). Russell makes allowances for the fact that the requisite description

will vary for different people, or for the same person at different times (the description in our minds will probably be some more or less vague mass of historical knowledge far more, in most cases, than is required to identify him), … but so long as the object to which the name applies remains constant, the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears. (1917, 208-9)

For purposes of illustration, he uses the description 'the first Chancellor of the German Empire.' Russell first considers the situation of Bismarck himself, who "might have used the name directly to designate [himself] … to ma[k]e a judgment about himself," with himself as a constituent (209). "Here the proper name has the direct use which it always wishes to have, as simply standing for a certain object, and not for a description of the object." But our situation, in referring to Bismarck, is different from his:

when we make a statement about something known only by description, we often intend to make our statement, not in the form involving the description, but about the actual thing described. That is, when we say anything about Bismarck, we should like, if we could, to make the judgment which Bismarck alone can make, namely, the judgment of which he himself is a constituent. [But] in this we are necessarily defeated. …What enables us to communicate in spite of the varying descriptions we employ is that we know there is a true proposition concerning the actual Bismarck and that, however we may vary the description (as long as the description is correct), the proposition described is still the same. This proposition, which is described and is known to be true, is what interests us; but we are not acquainted with the proposition itself, and do not know it, though we know it is true. (1917, 210-11)

The proposition that "interests us" is a singular proposition, but we cannot actually think it-we can know it only by description, that is, by entertaining a general (uniqueness) proposition which is, if true, made true by a fact involving Bismarck. But this general proposition does not itself involve Bismarck, and would be thinkable even if Bismarck never existed.

Frege is a descriptivist of a different sort than Russell. He claims not that proper names are disguised descriptions but that they have senses as well as references. The sense of a name is both the mode of presentation and the determinant of its referent (it also functions for Frege as the "indirect" (as opposed to "customary") reference when the name is embedded in a context of indirect quotation or propositional attitude ascription). Frege agrees with Russell, and with Mill for that matter, that words are ordinarily used to talk about things, not ideas: "If words are used in the ordinary way, what one intends to speak of is their reference" (1892, 58). Even so, in so using them we must associate reference-determining properties with our words. Moreover, insofar as our words also express our thoughts, they must correspond to constituents of those thoughts. Thus, for Frege, the semantic and the cognitive significance of expressions are intimately related. Indeed, because an expression can have a sense without having a reference, Frege holds that the constituents of thoughts are senses, not references.

Frege does not hold that every proper name is equivalent to some definite description but rather that expressions of both kinds are of the same semantic genus, which he calls "Eigennamen" (literally translated as 'proper names' but better paraphrased as 'singular terms'). Unlike Russell, he does not assimilate definite descriptions to quantificational phrases but treats them, like proper names (properly so-called), as semantic units capable of having individuals as semantic values, determined by their senses. The sense of such an expression plays the semantic role of imposing a condition that an individual must satisfy in order to be the referent. A proper name, like a definite description, contributes its sense to that of a sentence in which it occurs regardless of which individual actually is its referent and even if it has no referent at all. This is because the condition imposed by sense, the determinant of reference, is independent of that which it determines. For example, Frege says, "the thought remains the same whether 'Odysseus' has reference or not" (1892, 63). The same object can be presented in different ways, under different modes of presentation, but it is not essential to any mode of presentation that it actually present anything at all.

Frege's conception of sense does not entail that every proper name has the sense of some definite description, or that the sense of every proper name is an individual concept expressible by some definite description. His conception of sense leaves open the possibility of non-descriptive senses, such as percepts. If one thinks of an object by means of a percept, as one does when visually attending to it, this is not equivalent to thinking of it under a description of the form 'the thing that looks thus-and-so.' One might verbally express a thought about an object one is looking at by saying something of the form, 'the thing that looks thus-and-so is …,' but, as Frege says about indexical thoughts, "the mere wording ... does not suffice for the expression of the thought" (1918, 24). He does not explicitly make the analogous point in regard to proper names, but nowhere does he explicitly assert that each proper name is equivalent to some definite description, and his overall theory of sense and reference does not require this equivalence.

Russell's conception of presentation is quite different from what Frege means by 'presentation' (in 'mode of presentation'). For Russell, any object that can be presented at all cannot be presented in different ways. Russell's restrictive notion of acquaintance is a "direct cognitive relation" and, indeed, is "simply the converse of the relation of object and subject which constitutes presentation" (1917, 202). Notoriously, Russell disqualifies public objects as objects of acquaintance, but this is the price he is willing to pay to avoid the problem of names without bearers as well as Frege's puzzles (about identity statements and about indirect quotation and attitude reports). He avoids having to appeal to senses to solve them. The notion of sense, as the determinant of reference, has no place in Russell's theory of language or thought. Constituents of propositions are individuals (particulars and universals), and the Principle of Acquaintance requires that "every proposition which we can understand must be composed wholly of constituents with which we are acquainted" (1917, 211). For Frege modes of presentation are the constituents of thoughts, and the objects which modes of presentation present are not. Because the relation between subject to object is mediated by a sense, this relation is indirect, unlike Russellian acquaintance.6 So the difference between Frege's two-tiered and Russell's one-tiered semantics is reflected in their different epistemological views on presentation. They are, in their respective ways, descriptivists about singular thought as well as about proper names.

Russell held that ordinary proper names are abbreviated definite descriptions, but he denied that definite descriptions (or expressions of any other sort) have two levels of semantic significance. This was the central point of "On Denoting" (1905). For Russell, what distinguishes both definite descriptions and ordinary proper names from genuine, "logically" proper names, like the individual constants of logic, is not that they do have senses but that they do not have references (they do have denotations, but these are not their semantic values). For Frege there are two levels of semantic significance, sense and reference, and sense is primary. Despite their differences, neither Frege's sense-descriptivism nor Russell's abbreviational descriptivism is susceptible, as Mill's view is, to the problem of names without bearers. On both views, a proper name can play its (primary) semantic role whether or not it belongs to anything. But this is so for different reasons. For Russell, the reason is the semantic inertness of denotation; for Frege it is the independence of sense from reference.

References

Frege, Gottlob. 1892. "On Sense and Reference." Reprinted in P. Geach and M. Black, eds., Translations from the Philosophical Writings of Gottlob Frege. Oxford: Blackwell, 1960.

Frege, Gottlob. 1918. "The Thought: A Logical Inquiry." Reprinted in P. Strawson, ed., Philosophical Logic. Oxford: Oxford University Press, 1967.

Kripke, Saul. 1980. Naming and Necessity. Cambridge, Mass.: Harvard University Press.

Mill, J. S. 1872. A System of Logic, definitive 8th edition. 1949 reprint, London: Longmans, Green and Company.

Neale, Stephen. 1993. "Term Limits." Philosophical Perspectives 7:89-123.

Russell, Bertrand. 1905. "On Denoting." Reprinted in R. C. Marsh, ed., Logic and Knowledge. London: George Allen and Unwin, 1956.

Russell, Bertrand. 1917. "Knowledge by Acquaintance and Knowledge by Description." In Mysticism and Logic, paperback edition. Garden City, NY: Doubleday, 1957.

Russell, Bertrand. 1919. Introduction to Mathematical Philosophy. London: George Allen and Unwin.

Notes

1. For example, in Naming and Necessity Kripke uses this phrase for a single view and only once, in a footnote (1980, 27n), does he acknowledge the difference between Frege's and Russell's views.

2. I am using the term 'proposition,' here and throughout, with no commitment as to the nature of propositions or even as to their ineliminability. Accordingly, phrases like 'express a proposition,' 'enter into a proposition,' and 'singular/general proposition' should be understood in as theoretically neutral a way as possible (except when views are being attributed, e.g., to Russell).

3. It might be noted here that the phrase, 'propositions in which descriptions occur,' like 'the proposition in which the name appears' (1917, 208), typifies Russell's tendency toward a kind of use-mention conflation, since it is not symbols but the items symbolized that enter into propositions.

4. Moreover,

The denotation [of the description] is not a constituent of the proposition, except in the case of proper names, i.e. of words which do not assign a property to an object, but merely and solely name it. And I should hold further that, in this sense, there are only two words which are strictly proper names of particulars, namely "I" and "this." (1917, 216)

In a footnote here, Russell adds the afterthought, "I should now exclude 'I' from proper names in the strict sense, and retain only 'this'."

5. Thus Russell often calls definite descriptions "incomplete symbols," which "disappear upon logical analysis." A contemporary Russellian, Stephen Neale, sharpens Russell's distinction between terms (logically proper names and variables) and incomplete symbols (quantificational phrases) in "Term Limits" (1993). For the sake of perspicuity, he recommends the use of restricted quantifier notation, whereby a description sentence may be represented by the form, '[the x: Fx]Gx.' This notation has the benefit of assimilating the form of sentences containing descriptions to that of quantificational sentences in general, both standard ('[some x: Fx]Gx,' '[every x: Fx]Gx') and nonstandard ('[most x: Fx]Gx,' '[few x: Fx]Gx').

6. Even so, it is not indirect in the sense of being mediated by a direct cognitive relation: one does not have to think of a sense (mode of presentation) in order to think of that which it presents. Moreover, the sense-mediated relation of subject to object is not indirect in the way that for Russell knowledge by description is indirect. Knowledge of something by description always involves a direct cognitive relation to other items, namely objects of acquaintance, which can be sense-data and unanalyzable universals. When we know something by description, "we know that there is one object, and no more, having a certain property" (1917, 207). This is an entirely different relation from Frege's sense-mediated relation of subject to object, whereby one is presented with an object by way of grasping a sense.