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On Sense and Reference
(Excerpt)
Gottlob Frege
1892
Equality
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
Begriffsschriftz
I
assumed the latter. The reasons which
seem to favour 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 labelled
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
one of the most fertile astronomical discoveries.
Even
today the identification of a
small planet or a comet is not always a matter of
course. Now if we were
to regard
equality as a relation between that which the
names
'a'
and '6' 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 'by 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 in so far as they
named or
designated something. It would
be mediated by the connexion 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
'6'
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.
Let
a,
6,
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
by,
'point
of
intersection
of
b
and
c
’)
likewise
indicate
the
mode
of
presentation;
and
hence
the
statement
contains actual
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 reference of the sign, also what
I should like to call the
sense
of the sign, wherein
the mode of presentation is contained. In our
example, accordingly, the reference 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 reference
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, which thus has as its reference a
definite object (this word taken in the
widest range), but not a concept or a
relation, which shall be discussed further in
another article. 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;
but this serves to illuminate only a single
aspect of the reference, supposing it
to have one. Comprehensive knowledge of the
reference would
require us to be able
to say immediately whether any given sense belongs
to it. To such knowledge
we never
attain.
The regular
connexion between a sign, its sense, and its
reference is of such a kind that to the
sign there corresponds a definite sense
and to that in turn a definite reference, while to
a given
reference
(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 behaviour
occur. To every expression belonging to a complete
totality of signs, there should
certainly correspond a definite sense;
but natural languages often do 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 reference. The
words 'the
celestial body most distant
from the Earth' have a sense, but it is very
doubtful if they also have a
reference.
The expression 'the least rapidly convergent
series' has a sense; but it is known to have no
reference, 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 reference.
If
words are used in the ordinary way, what one
intends to speak of is their reference. 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
reference. 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 reference.
In order to speak of the
sense of an expression 'A' one may simply use the
phrase 'the sense of
the expression
is quite clear that in this way of
speaking words do not have their customary
reference 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
reference. We
distinguish accordingly the
customary
from the
indirect
reference of a word; and its
customary
sense from its
indirect
sense. The indirect
reference of a word is accordingly its
customary sense. Such exceptions must always be
borne in
mind
if
the
mode
of
connexion
between
sign,
sense,
and
reference
in
particular
cases
is
to
be
correctly understood.
The
reference
and
sense
of
a
sign
are
to
be
distinguished
from
the
associated
idea.
If
the
reference
of a sign is an object perceivable by the senses,
my idea of it is an internal image, arising
from memories of sense impressions
which I have had and acts, both internal and
external, which I
have performed. Such
an idea 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 idea.
The idea is subjective: one
man's idea is not that of another. There result,
as a matter of course, a
variety of
differences in the ideas associated with the same
sense. A painter, a horseman, and a
zoologist
will
probably
connect
different
ideas
with
the
name
'Bucephalus'.
This
constitutes
an
essential distinction between the idea
and the sign's sense, which may be the common
property of
many and therefore is not a
part of 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.
In
the light of this, one need have no scruples in
speaking simply of
the
sense, whereas in the
case
of an
idea
one
must,
strictly
speaking,
add
to
whom
it
belongs
and at
what
time.
It
might
perhaps
be said: Just as one man connects this idea, and
another that idea, 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 connexion.
They are not prevented from grasping the same
sense; but they cannot have
the same
idea. Si
duo idem faciunt, non est
idem.
If two persons picture the same
thing, each still has
his own idea. It
is indeed sometimes possible to establish
differences in the ideas, or even in the
sensations, of different men; but an
exact comparison is not possible, because we
cannot have both
ideas together in the
same consciousness.
The
reference of a proper name is the object itself
which we designate by its means; the idea,
which we have in that case, is wholly
subjective; in between lies the sense, which is
indeed no
longer subjective like the
idea, but is yet not the object itself. The
following analogy will perhaps
clarify
these relationships. Somebody observes the Moon
through a telescope. I compare the Moon
itself to the reference; it is the
object of the observation, mediated by the real
image projected by the
object glass in
the interior of the telescope, and by the retinal
image of the observer. The former I
compare to the sense, the latter is
like the idea or experience. The optical image in
the telescope is
indeed
one-
sided
and
dependent
upon
the
standpoint
of
observation;
but
it
is
still
objective,
inasmuch as it
can be used by several observers. At any rate it
could be arranged for several to use it
simultaneously. But each one would have
his own retinal Image. On account of the diverse
shapes of
the
observers'
eyes,
even
a
geometrical
congruence
could
hardly
be
achieved,
and
an
actual
coincidence
would
be
out
of
the
question.
This
analogy
might
be
developed
still
further,
by
assuming A's retinal image made visible
to B; or A might also see his own retinal image in
a mirror.
In this way we might perhaps
show how an idea can itself be taken as an object,
but as such is not for
the observer
what it directly is for the person having the
idea. But to pursue this would take us too
far afield.
We
can
now
recognize
three
levels
of
difference
between
words,
expressions,
or
whole
sentences. The difference may concern
at most the ideas, or the sense but not the
reference, or,
finally, the reference
as well. With respect to the first level, it is to
be noted that, on account of the
uncertain connexion of ideas with
words, a difference may hold for one person, which
another does
not find. The difference
between a translation and the original text should
properly not overstep the
first
level.
To
the
possible differences
here
belong
also
the
colouring
and
shading which
poetic