<s>
Begriffsschrift	B-Application
(	O
German	O
for	O
,	O
roughly	O
,	O
"	O
concept-writing	O
"	O
)	O
is	O
a	O
book	O
on	O
logic	O
by	O
Gottlob	O
Frege	O
,	O
published	O
in	O
1879	O
,	O
and	O
the	O
formal	O
system	O
set	O
out	O
in	O
that	O
book	O
.	O
</s>
<s>
Begriffsschrift	B-Application
is	O
usually	O
translated	O
as	O
concept	O
writing	O
or	O
concept	O
notation	O
;	O
the	O
full	O
title	O
of	O
the	O
book	O
identifies	O
it	O
as	O
"	O
a	O
formula	O
language	O
,	O
modeled	O
on	O
that	O
of	O
arithmetic	O
,	O
for	O
pure	O
thought.	O
"	O
</s>
<s>
In	O
the	O
first	O
chapter	O
,	O
Frege	O
defines	O
basic	O
ideas	O
and	O
notation	O
,	O
like	O
proposition	O
(	O
"	O
judgement	O
"	O
)	O
,	O
the	O
universal	O
quantifier	O
(	O
"	O
the	O
generality	O
"	O
)	O
,	O
the	O
conditional	O
,	O
negation	O
and	O
the	O
"	O
sign	O
for	O
identity	O
of	O
content	O
"	O
(	O
which	O
he	O
used	O
to	O
indicate	O
both	O
material	O
equivalence	O
and	O
identity	O
proper	O
)	O
;	O
in	O
the	O
second	O
chapter	O
he	O
declares	O
nine	O
formalized	O
propositions	O
as	O
axioms	B-Algorithm
.	O
</s>
<s>
Frege	O
declared	O
nine	O
of	O
his	O
propositions	O
to	O
be	O
axioms	B-Algorithm
,	O
and	O
justified	O
them	O
by	O
arguing	O
informally	O
that	O
,	O
given	O
their	O
intended	O
meanings	O
,	O
they	O
express	O
self-evident	O
truths	O
.	O
</s>
<s>
Re-expressed	O
in	O
contemporary	O
notation	O
,	O
these	O
axioms	B-Algorithm
are	O
:	O
</s>
<s>
The	O
rule	B-Algorithm
of	I-Algorithm
generalization	I-Algorithm
allows	O
us	O
to	O
infer	O
from	O
if	O
x	O
does	O
not	O
occur	O
in	O
P	O
;	O
</s>
<s>
For	O
a	O
careful	O
recent	O
study	O
of	O
how	O
the	O
Begriffsschrift	B-Application
was	O
reviewed	O
in	O
the	O
German	O
mathematical	O
literature	O
,	O
see	O
Vilko	O
(	O
1998	O
)	O
.	O
</s>
<s>
All	O
work	O
in	O
formal	O
logic	O
subsequent	O
to	O
the	O
Begriffsschrift	B-Application
is	O
indebted	O
to	O
it	O
,	O
because	O
its	O
second-order	O
logic	O
was	O
the	O
first	O
formal	O
logic	O
capable	O
of	O
representing	O
a	O
fair	O
bit	O
of	O
mathematics	O
and	O
natural	O
language	O
.	O
</s>
<s>
Frege	O
used	O
these	O
symbols	O
in	O
the	O
Begriffsschrift	B-Application
in	O
the	O
unified	O
form	O
├─	O
for	O
declaring	O
that	O
a	O
proposition	O
is	O
true	O
.	O
</s>
<s>
In	O
"	O
Begriffsschrift	B-Application
"	O
the	O
"	O
Definitionsdoppelstrich	O
"	O
(	O
i.e.	O
</s>
<s>
In	O
the	O
Tractatus	O
Logico	O
Philosophicus	O
,	O
Ludwig	O
Wittgenstein	O
pays	O
homage	O
to	O
Frege	O
by	O
employing	O
the	O
term	O
Begriffsschrift	B-Application
as	O
a	O
synonym	O
for	O
logical	O
formalism	O
.	O
</s>
<s>
In	O
particular	O
,	O
he	O
rejects	O
the	O
"	O
Begriffsschrift	B-Application
"	O
view	O
that	O
the	O
identity	O
predicate	O
expresses	O
a	O
relationship	O
between	O
names	O
,	O
in	O
favor	O
of	O
the	O
conclusion	O
that	O
it	O
expresses	O
a	O
relationship	O
between	O
the	O
objects	O
that	O
are	O
denoted	O
by	O
those	O
names	O
.	O
</s>
<s>
Begriffsschrift	B-Application
:	O
eine	O
der	O
arithmetischen	O
nachgebildete	O
Formelsprache	O
des	O
reinen	O
Denkens	O
.	O
</s>
<s>
Beaney	O
,	O
Michael	O
,	O
1997	O
,	O
"	O
Begriffsschrift	B-Application
:	O
Selections	O
(	O
Preface	O
and	O
Part	O
I	O
)	O
"	O
in	O
The	O
Frege	O
Reader	O
.	O
</s>
