FREGE ON EXISTENCE
FRIEDRICH LUDWIG GOTTLOB FREGE
Frege on Existence
Friedrich Ludwig Gottlob Frege Gottlob Frege
Logician Germany
1848-1925
Frege was the father of modern mathematical
logic.
In 1879 he published Concept-notation,
a work
that included a formal language which
was able
to express generality through the
quantifier-variable
notation. This work also
set forth
a version of second order quantificational
logic
whcih he used to develop a logical
definition
for the ancestral of a relation.
He was
incredibly influential on the later
works
of Wittgenstein, Russell, George Boole,
and Ernst
Schroeder.
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Frege distinguishes between
the following
meaning.; of 'is':
(1) the 'is' of identity
(e. g., Phosphorus
is Hesperus; a=b),
(2) the 'is' of predication,
i. e., the copula
(e. g., 'Plato is blond';
P(a)),
(3) the 'is' of existence,
(i) expressed by means
of the existential
quantifier and the symbol
for identity (e.
g., 'God is'; ($x) (g=x)),
or
(ii) expressed by means
of the existential
quantifier and the symbol
for predication
(e. g., 'There are human
beings'/'There is
at least one human being';
($x) H (x)),
and
(4) the 'is' of class-inclusion,
i. e., generic
implication (e. g., 'A
horse is a four-legged
animal''; (x) (P(x) É Q(x)))."
From: Leila Haaparanta
- Frege's doctrine
of Being - Helsinki, Acta
Philosophica Fennica,
vol. 39, 1985 pp. 13-14.
EXISTENCE
"If you want to assign
a content to
the verb `to be', so that
the sentence `A
is' is not pleonastic and
self-evident, you
will have to allow circumstances
which the
negation of `A is' is possible;
that is to
say, that there are subjects
of which being
must be denied. But in
that case the concept
`being' will no longer
be suitable for providing
a general explanation of
`there are' under
which `there are B's' means
the same as `something
that has being falls under
the concept B';
for if we apply this explanation
to `There
are subjects of which being
must be denied',
then we get `Something
that has being falls
under the concept of not-being'
or `Something
that has being is not'.
There is no way of
getting over this once
a content of some
kind-it doesn't matter
what it is-is agreed
to the concept of being.
If the explanation
of `there are Bs' as meaning
the same as
`Something that has being
is B' is to work,
we just have to understand
by being something
that goes entirely without
saying. For this
reason the contradiction
still remains if
we say `A exists' means
`The idea of the
A has been caused by something
affecting
the ego'.
(...) We can say that the
meanings of the
word `exist' in the sentences
`Leo Sachse
exists' and `Some men exist'
display no more
difference than does the
meanings of `is
a German' in the sentences
`Leo Sachse is
a German' and `Some men
are Germans'. But
then the sentence `Some
men exist' or `Something
existing is a man' only
means the same as
`There are men' if the
concept `existing
thing' is superordinate
to the concept man.
So if such forms of expression
are to have
the same meaning in general,
the concept
`existing thing' must be
superordinate to
every concept. This is
only possible if the
word `exist' means something
that goes entirely
without saying, and if
therefore nothing
at all is predicated in
the sentence `Leo
Sachse exists', and if
in the sentence `Some
men exist' the content
of what is predicated
does not lie in the word
`exist'. The existence
expressed by `there is'
is not contained
in the word `exist' but
in the form of the
particular judgement. `Some
men are Germans'
is just as good an existential
judgement
as `Some men exist'. But
once the word `exist'
is given a content, which
is predicated of
an individual thing, this
content can be
made into the characteristic
mark of a concept-a
concept under which there
falls the individual
thing of which existence
is being predicated.
E. g. if one divides everything
into two
classes
1. What is in my mind,
ideas, feelings etc.
and
2. What is outside myself,
and says of the
latter that it exists,
then one can construe
existence as a characteristic
mark of the
concept `centaur', although
there are no
centaurs. I would not acknowledge
anything
as a centaur that was not
outside my mind;
this means that I shall
not call mere ideas
or feelings centaurs. The
existence expressed
by `there is' cannot be
a characteristic
mark of a concept whose
property it is, just
because it is a property
of it. In the sentence
`There are men' we seem
to be speaking of
individuals that fall under
the concept `man',
whereas it is only the
concept `man' we are
talking about. The content
of the word `exist'
cannot well be taken as
the characteristic
mark of a concept, because
`exists', as it
is used in the sentence
`Men exist', has
no content. We can see
from all this how
easily we can be led by
language to see 'things
in the wrong perspective,
and what value
it must therefore have
for philosophy to
free ourselves from the
dominion of language.
If one makes the attempt
to construct a system
of signs on quite other
foundations and `with
quite other means, as I
have tried to do
in creating my concept-script,
,we shall
have, so to speak, our
very noses rubbed
into the false analogies
in language."
From: Gottlob Frege - Dialogue
with Punjer
on Existence (written before
1884) - in:
Posthumous Writings - Edited
by Hans Hermes,
Friedrich Kambartel, Friedrich
Kaulbach -
Chicago, The University
of Chicago Press
1979 pp. 65-67.
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