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\documentclass[a4paper,10pt,twoside]{article}
\usepackage{a4wide,amssymb,begriff}
\title{Begriffsschrift examples}
\author{Josh Parsons}
\parindent0pt
\setlength{\BGthickness}{1pt}
\begin{document}
\maketitle
if p then q:
$$\BGassert\BGconditional{p}{q}$$
and with a content stroke instead of assertion:
$$f\BGbracket{\BGcontent\BGconditional{p}{q}}$$
from Frege's correspondence with Russell (a version of basic law V):
$$
\BGassert (\acute{\epsilon}f(\epsilon) = \acute{\alpha}g(\alpha)) =
\BGquant{\mathfrak{a}}
\BGbracket{\BGconditional{
\BGnot\BGconditional{
\BGnot\mathfrak{a}=\acute{\alpha}g(\alpha)
}{
\mathfrak{a}=\acute{\epsilon}f(\epsilon)
}
}
{f(\mathfrak{a}) = g(\mathfrak{a})}}
$$
\setlength{\BGlinewidth}{2.6in}
from Russell's correspondence with Frege:
$$
\BGstem{T=\acute{\beta}\acute{\gamma}}
\BGnot\BGquant{\varphi}
\BGconditional
{\BGterm{\gamma = \acute{\alpha}\acute{\epsilon}\varphi(\alpha,\epsilon)}}
{\BGconditional
{\BGterm{\beta = \acute{\alpha}\acute{\epsilon}\varphi(\alpha,\epsilon)}}
{\BGterm{\varphi(\beta,\gamma)}}
}
$$
the Geach-Kaplan sentence (thanks to Marcus Rossberg):
$$
\BGnot \BGquant{\mathfrak{F}}%
\BGconditional{
\BGquant{\mathfrak{c}}\BGquant{\mathfrak{d}}
\BGconditional{
\BGnot
\BGconditional{
\BGterm{A(\mathfrak{c},\mathfrak{d})}
}{
\BGnot \BGterm{\mathfrak{F}(\mathfrak{c})}}
}{
\BGnot \BGconditional{
\BGterm{\mathfrak{F}(\mathfrak{d})}
}{
\BGterm{\mathfrak{c}=\mathfrak{d}}
}
}
}{
\BGconditional{
\BGnot\BGquant{\mathfrak{b}}\BGnot\BGterm{\mathfrak{F}(\mathfrak{b})}
}{
\BGterm{f \BGbracket{\BGquant{\mathfrak{a}} \BGconditional{
\mathfrak{F}(\mathfrak{a})
}{
C(\mathfrak{a})
}}}
}
}
$$
That's all folks
\end{document}
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