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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. .
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