FREGE ON TRUTH
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.
|
Frege on Truth
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.
TRUTH "When entering
upon the study
of a science, we need to
have some idea,
if only a provisional one,
of its nature.
We want to have in sight
a goal to strive
towards; we want some point
to aim at that
will guide our steps in
the right direction.
The word `true' can be
used to indicate such
a goal for logic, just
as can `good' for
ethics and `beautiful'
for aesthetics. Of
course all the sciences
have truth as their
goal, but logic is concerned
with the predicate
`true' in a quite special
way, namely in
a way analogous to that
in which physics
has to do with the predicates
`heavy' and
`warm' or chemistry with
the predicates `acid'
and `alkaline'. There is,
however, the difference
that these sciences have
to take into account
other properties besides
these we have mentioned,
and that there is no one
property by which
their nature is so completely
characterized
as logic is by the word
`true'. (...)
Now it would be futile
to employ a definition
in order to make it clearer
what is to be
understood by `true'. If,
for example, we
wished to say `an idea
is true if it agrees
with reality' nothing would
have been achieved,
since in order to apply
this definition we
should have to decide whether
some idea or
other did agree with reality.
Thus we should
have to presuppose the
very thing that is
being defined. The same
would hold of any
definition of the form
`A is true if and
only if it has such-and-such
properties or
stands in such-and-such
a relation to such-and-such
a thing'. In each case
in hand it would always
come back to the question
whether it is true
that A has suchand-such
properties, or stands
in such-and-such a relation
to such-and-such
a thing. Truth is obviously
something so
primitive and simple that
it is not possible
to reduce it to anything
still simpler. Consequently
we have no alternative
but to bring out the
peculiarity of our predicate
by comparing
it with others. What, in
the first place,
distinguishes it from all
other predicates
is that predicating it
is always included
in predicating anything
whatever."
From: Gottlob Frege - Logic
(1897) - in:
Posthumous Writings - Edited
by Hans Hermes,
Friedrich Kambartel, Friedrich
Kaulbach -
Chicago, The University
of Chicago Press
1979 pp. 128-129.
7. What true is, I hold
to be indefinable.
8. The expression in language
for a thought
is a sentence. We also
speak in an extended
sense of the truth of a
sentence.
12. Logic only becomes
possible with the
conviction that there is
a difference between
truth and untruth.
13. We justify a judgement
either by going
back to truths that have
been recognized
already or without having
recourse to other
judgements. Only the first
case, inference,
is the concern of Logic.
14. The theory of concepts
and of judgement
is only preparatory to
the theory of inference.
15. The task of logic is
to set up laws according
to which a judgement is
justified by others,
irrespective of whether
these are themselves
true.
16. Following the laws
of logic can guarantee
the truth of a judgement
only insofar as
our original grounds for
making it, reside
in judgements that are
true.
17. No psychological investigation
can justify
the laws of logic."
From: Gottlob Frege - [17
Key sentences on
Logic] (1906 or earlier)
- in: Posthumous
Writings - Edited by Hans
Hermes, Friedrich
Kambartel, Friedrich Kaulbach
- Chicago,
The University of Chicago
Press 1979 pp.
174-17
|