Frege’s treatment of propositional names initially seems to be a pleasing and

concise little theory. At first glance it appears capable of answering any questions

we might entertain about the meanings of propositional signs by dividing meaning

into two clear categories. Frege solves the problem that arises when two

synonymous names for an object are unable to act as perfect substitutes. His

solution is simple: while propositional names for the same object do indeed have

the same designation (Bedeutung), each name brings to mind a different set of

mental impressions (a sense, or Sinn,) which are particular to that name itself.

Thus, while a single referent (Bedeutung) may have multiple signs, each sign has

a unique sense. [S&B, 153]


The dichotomy between sense and reference is initially so clear and forward that

one almost begins to believe that Frege has solved the entire philosophical problem

of linguistic expressions in the space of a few paragraphs. While ‘George Walker

Bush’ clearly has the same Bedeutung as ‘the current president of the United

States,’ the two names each specify a different sense, so it is unnecessary to ask

whether ‘George Walker Bush is the current president of the United States’ is

identical to the proposition ‘George Walker Bush is George Walker Bush.’

Furthermore, Frege’s theory seems to solve the problem of empty names – those

propositional signs which clearly alert the human mind to a certain sense, but have

no referent within the scope of reality. It is easy at first to be content passing off

names like ‘Pegasus’ as carrying a very apparent sense, and simply denying that

they designate anything at all.

This dismissive view raises a problem, though. If two propositions such as

‘Pegasus is a winged horse’ and ‘Pegasus does not exist’ are taken together, a

contradiction arises. Clearly if there is no Pegasus in all of reality, then there is no

meaning to ‘Pegasus is a winged horse.’ Even though ‘Pegasus’ has a sense, the

term designates nothing that is, in fact, a horse with wings. It is obvious that it

cannot be just the sense of ‘Pegasus’ that is a winged horse. How can one

therefore meaningfully talk about Pegasus? If ‘Pegasus’ is universally understood

then there must be some artifice which allows the name to convey information.

Frege makes some attempts at answering the question posed by empty names,

but none of his conjectures lead to a solution which is in accordance with the rest

of the theory. He abandons his earlier convention Sinn/Bedeutung but falls short

when he tries to justify the fact that empty names are intelligible to the human

mind. A sign expresses both sense and reference in order to convey meaning. If a

sign had a referent but no sense, then it would designate an object that no one

could know anything about. Conversely if a sign had sense but no referent than

would it not convey as its meaning a lot of intellectual stimuli that do not amount to

anything? “Without a Bedeutung, we could indeed have a thought, but only a

mythological or literary thought…Without a sense, we would have no thought, and

hence also nothing that we could recognize as true.” [LJ, 320] Certainly there are

names that have a Sinn but no Bedeutung. ‘The highest number’ and ‘the smallest

fraction’ are both examples. However, Frege insists that propositions such as

these cannot meaningfully be used outside of certain contexts. Because ‘The

highest number’ has no Bedeutung, a proposition such as ‘The highest number is

higher than thirty-five’ cannot be deemed either true or false in Frege’s system.

Frege is concerned with the idea that in order for a sentence or proposition of

subject-predicate nature to have truth or falsity there must be a Bedeutung for

each proper name to designate. “Why must anything have a Bedeutung?” he asks

rhetorically. The reply in Sinn und Bedeutung is that “when we say ‘the Moon’, we

do not intend to speak of our idea of the Moon, nor are we satisfied with the sense

alone, but we presuppose a Bedeutung.” [S&B, 156] This indicates that in any

assertion made about the Moon or any object, the speaker’s idea of that object is

not in question, but rather the object itself; the specific designation of the name.

While this may seem initially obvious, Frege is correct in stating that it is

necessary for one to realize that it is of very little use to speak of ideas of objects.

Since these differ from speaker to speaker, this would make it impossible to speak

about anything at all. It is important that names designate objects that exist

independently of the speaker’s mind. Proceeding from this point, Frege explains

that the truth value of a sentence containing a proper name is hinged on that

name’s Bedeutung. If anything true is to be asserted, it must be in concordance

with truths about the actual object named in a sentence and not merely the

speaker’s ideas about them.

This raises the question of what is required in order for a name or sign to

actually refer to an object. Since it is evidently a strain on the theory to say that

some terms merely have sense but no Bedeutung, and yet somehow meaningful

sentences which make use of such terms can be constructed, a method for

reconciling empty or fictional names must be developed. By Frege’s own

admittance a Bedeutung is understood to be a definite object “taken in the widest

sense.” [S&B, 153] His first example is a geometrical point on the side of a

triangle. Because a point in mathematics is not tangible (and by definition does not

have any dimensions,) Frege admits that the designation of a name need not be a

physical object. ‘Justice’, ‘love’, ‘peace’, ‘point’, ‘line’, and ‘circle’ each have not

only a sense that the human mind can grasp, but also refer to entities that are

indisputably real. However, the problem of ‘Pegasus’ and other such names still

persists. For it seems that names such as these make false claims about reality in

general. Even if one maintains that ‘Pegasus’ refers to something, that something

is not a winged horse. There are measurably zero winged horses.

The footnote on page 157 of Sinn und Bedeutung sums up Frege’s view: “It would

be desirable to have a special term for signs intended to have only sense.”

Unfortunately, Frege is not content to provide his readers with such a term.

Instead, he hopes that his readers will be content believing that empty names must

be dismissed as mere aesthetic details with no real meaning. For instance, since it

is questionable that an Odysseus ever existed, it is not possible use ‘Odysseus’ as

the subject of a sentence that is capable of signifying anything true or false.

‘Odysseus’ can only be taken with in the context of fiction. “In hearing an epic

poem…we are interested only in the sense of the sentences and the images and

feelings thereby aroused. The question of truth would cause us to abandon

aesthetic delight for an attitude of scientific investigation.” [S&B, 157] Frege

clearly intends that empty names and sentences containing empty names are to

be excluded from the realm of possible true statements. This however is where he

goes too far. If empty names have no Bedeutung, (designate nothing whatsoever)

then by his earlier assertion we cannot say anything universal about them. “When

we say ‘the Moon’, we do not intend to speak of our idea of the Moon, nor are we

satisfied with the sense alone, but we presuppose a Bedeutung.” [S&B, 156] If the

names ‘Pegasus’ and ‘Odysseus’ do not refer to anything then only their senses

can be known. However, as Frege says, the sense is not enough, and anyone

who uses either of these names must only be speaking of his or her own ideas

associated with them. This would lead to the unreasonable claim that no one who

speaks about ‘Odysseus’ or ‘Pegasus’ is really speaking about some definite

thing, but rather is speaking about subjective ideas supported only by a sense

which seems equally unjustified. Clearly, to have a sense, there must be an

element of universality.

Fortunately, solving the problem of empty names in Frege’s theory of sense and

reference does not require too much bending of the rules he sets forth. It is self

evident that there is difference between the object described by an empty name

and that described by a “meaningful” name. ‘Odysseus’ is inherently different from

‘George Walker Bush’ in that the object named by the former cannot and never

was perceived by the human senses, while the object named by the latter can be

and is. Regardless of this difference, both names point to characteristics and

qualities that exist independently of mere idea. Both an empty name and a

meaningful name point to a sense. Frege has already conceded this point. Let it

be proposed that by having a sense, a name implies that if there were to exist a

referent to which that sense applied, then the name also designates that object. To

illustrate what is meant here, consider: one day a winged horse appears in the

world. It is not just any winged horse – it is a winged horse for which there is

substantial proof that it sprang from the blood of Medusa, and was ridden by

Bellerophon and Perseus. Given this information, would it not be immediately

apparent that this winged horse, a real, breathing, corporeal entity correlates

directly with the sense given by the name ‘Pegasus’ and therefore must be

‘Pegasus’? ‘Pegasus’ has an indirect, but nevertheless implied Bedeutung to

which it refers, and though we may have no perception of the referent, it does not

exist outside to scope of reality. This is reflected in the usage of empty names.

When someone uses ‘Pegasus’ or ‘Odysseus’, he does not intend an overly

complex proposition along the lines of ‘[this entity as it appears to the human mind

as well as the characteristics associated with it through what has been said about

it]’ he intends the meaning of that name as it would occur in reality.

The only difference between empty names and names for existing objects is that

there is less evidence for the referents of the former type. If there were a winged

horse of which everything true of Pegasus were true of it, and it existed on an

island that no man had ever visited, so that its existence was unknown to

humankind, would not ‘Pegasus’ still seem to be an empty name having some sort

of sense but no attainable referent? While the physical existence of such a horse

would evoke changes in the truth about the world in general, the use of the name

‘Pegasus’ as a merely linguistic expression and the sense it conveys would not be

altered. The physical existence of a Bedeutung is of such little consequence to a

proposition that it will never affect how a sign is used, what sense that sign has, or

how meaningful a sentence employing such a proposition is. Because of this it is

possible to say that a Bedeutung always exists, whether it is direct or implicit, and

in both cases is capable of acting as the referent of a name. Linguistic meaning is

left unscathed. Because the names of all types have referents, all names can be

used to make a claim on propositional truth or falsehood.

The same can be applied to names for certain referents that once existed

physically but do not anymore. ‘Socrates’ has a sense that is very apparent. The

sign also has a referent. At one time, this referent was physical, but since it has

been close to 2400 years since Socrates drank hemlock, the designation of the

name ‘Socrates’ is now implicit. Simply because there is not a Socrates who is

perceivable to the senses is not a reason that the meaning of ‘Socrates’ or its use

in true or false statements has been altered. Whether Socrates exists directly

(physically) or implicitly is the result of the passage of time. Time can change the

perceivable world, but it cannot change meaning. Meaning, as Frege asserts on

the first page of Uber Sinn und Bedeutung proceeds from sign to sense to referent

– not from referent backward.

This manner of reasoning can be applied to all signs. Even self defeating

propositions, like ‘The largest number’ must be taken to have an implicit

Bedeutung, because they convey a sense and can be used in claims regarding

trueness or falsehood. Consider the proposition ‘The largest number is greater

than thirty-five.’ The subject of this proposition is ‘The largest number.’ The sense

universally agreed on for ‘The largest number’ is something along the lines of “that

x such that x is a number and there is no number greater than x.” or “that x such

that x is a number and the arithmetic difference between x and any other number

is always positive.” Even though ‘The largest number’ has no direct Bedeutung (as

even a basic knowledge of mathematics makes apparent,) it can be used in

sentences that are true or false. Given ‘There is a number x which is equal to

thirty-six and which is greater than thirty-five.’ ‘The largest number is that number

x such that x is greater than all other numbers.’ ‘The largest number is greater than

thirty-five.’ Each of these propositions can be shown to be logically true based on

their sense. In the first, the referents of the constituent propositions are direct, and

in the second two the referents are implicit. Either a direct or an implicit

Bedeutung is sufficient for meaning to exist. The senses of each proposition are

completely unaffected. It follows perfectly that a truth value can be given by such

propositions. While Frege thought it necessary to restrict his theory of sense and

reference to perceivable reality, here it has been shown that it can adequately be

used to describe the extent of what can be thought.














Sources:
[S&B]
Uber Sinn und Bedeutung (On Sense and Reference) by Gottlob Frege, (translated by Max Black) First published in Zeitschrift fur Philsopohie und philosophische Kritik, 1892

[LJ]
Letter to Jourdain, Jan 1914, Gottlob Frege


(c)2005 Franklin T. Rea, Dartmouth College, Hanover NH

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