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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
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+\documentclass[12pt]{article}
+\usepackage[bguq]{frege}
+\usepackage{amsmath}
+
+%% For condensed itemize:
+\newcommand{\squishlist}{
+ \begin{list}{$\bullet$}{
+ \setlength{\itemsep}{0pt}
+ \setlength{\parsep}{0pt}
+ \setlength{\topsep}{0pt}
+ \setlength{\partopsep}{0pt}
+ \setlength{\leftmargin}{1em}
+ \setlength{\labelwidth}{1em}
+ \setlength{\parskip}{0pt}
+ \setlength{\partopsep}{0pt}
+ \setlength{\rightmargin}{0pt}
+ \setlength{\labelsep}{0.5em}}}
+\newcommand{\squishlistend}{\end{list}}
+
+\title{frege.sty \\ A \LaTeXe Package for Typesetting Begriffsschrift}
+\author{Quirin Pamp \\ \texttt{Quirin.Pamp.2009@my.bristol.ac.uk}}
+
+\begin{document}
+\maketitle
+\section{Background}
+\subsection{Motivation for this Package}
+ I recently decided to read Frege's \emph{Begriffsschrift} from 1879 and found that
+ the only copy I could find online was a rather poor quality scan of the original.
+ Since the copyright on german publications expires some 70 or so years after the
+ death of their author, I had the bright idea to combine reading the paper with
+ the making of an electronic copy. This required the typesetting of begriffsschrift.
+ A quick search on the internet assured me that there was a LaTeX package for just
+ this purpose, and off I went. However I quickly noticed that it would be very
+ difficult to achieve a typesetting I deemed sufficiently close to the original
+ using only the package \emph{begriff} by Josh Parsons. Despite the fact that I
+ have never written a LaTeX package before, a quick look at the source file (only
+ some 300 or so lines with plenty of comments) along with some head scratching
+ convinced me to embark on this further project.
+
+ With the help of the begriff package and the good people on Stack-Exchange, I
+ eventually produced a package that was able to do everything that the original
+ begriff package can, albeit with a few changes I consider an improvement. Further
+ versions largely reflect additional features I added as I continue to type up
+ Frege's original paper, as well as bug fixes and input by members of the LaTeX
+ community. Once I am done I will add the tex file for Fege's paper as the
+ definitive example for the usage of this package.
+
+\subsection{The \emph{begriff} Package}
+ This package is based on begriff.sty released under the GNU General Public
+ License.
+ Copyright (C) 2003 by Josh Parsons (josh@coombs.anu.edu.au) with changes made in
+ October 2004 by Richard Heck (heck@fas.harvard.edu) and minor changes by Josh
+ Parsons to fix a problem with linespacing made in May 2005.
+
+ While I could not have done so without the aforementioned work, I have reworked the
+ package from the ground up, to the point where some of the underlying approaches
+ have changed. On the downside this means there is no simple way of converting
+ anything typeset using begriff.sty to use this package instead. I felt this was
+ necessary to achieve an end result I was happy with.
+
+\subsection{The \emph{bguq} Package}
+ Since version 1.3 I added the option to use the bguq character for all
+ quantifiers. This character is provided by the bguq package by J.J. Green.
+
+\section{Version History}
+\subsection{Changes as Compared to begriff.sty}
+ \squishlist
+ \item correct (closer to the original typesetting) relative lengths of the
+ content stroke with respect to other strokes attached to it;
+ \item content strokes point at the middle of the following symbols, rather
+ than the bottom;
+ \item greater width for the assertion stroke as compared to the content stroke;
+ \item a more intuitive structure for the conditional (arguments are now given in
+ the same order as they appear on the left of a completed formula);
+ \item the command for the conditional with empty arguments now results in a
+ vertical line (conditional stroke) on it's own the other strokes are added as
+ the arguments;
+ \item the linewidth is properly accounted for so that things remain properly
+ centered when scaled;
+ \squishlistend
+
+\subsection{Changes in Version 1.1}
+ \squishlist
+ \item added an optional scale factor to all basic strokes;
+ \item simplified the code for Fbracket in terms of that for Fbox;
+ \item rearranged the code in the style file in a more logical way;
+ \squishlistend
+
+\subsection{Changes in Version 1.2}
+ \squishlist
+ \item added a new command ``Fargument'' for typesetting arguments;
+ \item added a new command ``Fstrut'' to be used in conjunction with Fargument;
+ \item changed Fbaselength to be equal to the full length of a basic stroke (20pt);
+ \item fixed a bug where the scale factor introduced in version 1.1 does not reset
+ after all uses;
+ \squishlistend
+
+\subsection{Changes in Version 1.3}
+ \squishlist
+ \item made the ``():'' used in the Fargument command introduced in version 1.2
+ user defined so as to make the option properly optional;
+ \item added a strut to Fargument so as to produce visually correct centering;
+ \item added optional shorthands for all commands for a better flow of usage;
+ \item added the option ``bguq'' to the package which uses the bguq font by J.J.
+ Green for all quantifiers;
+ \squishlistend
+
+\subsection{Changes and Features yet to come}
+ \squishlist
+ \item a way to display nested arguments;
+ \item the fregean conjunction (it exists);
+ \item a vertical shorthand stroke such as used by Frege for typesetting arguments
+ in his original paper;
+ \item scaling symbols automatically with changes in font size;
+ \item scaling of the bguq character with changes in Flinewidth;
+ \squishlistend
+
+\section{Features and Usage}
+\subsection{Commands}
+\subsubsection{Basic Commands}
+ The following is a list of the basic commands provided by this package along with
+ accompanying output and the optional shorthand for the command.
+ \begin{flalign*}
+ &\mbox{Command:} & &\mbox{Output:} & &\mbox{Shorthand:}\\
+ &\mbox{\textbackslash Fcontent[1]} & &\Fcontent
+ & &\mbox{\textbackslash F[1]}\\
+ &\mbox{\textbackslash Fncontent[1]} & &\Fncontent
+ & &\mbox{\textbackslash Fn[1]}\\
+ &\mbox{\textbackslash Fnncontent[1]} & &\Fnncontent
+ & &\mbox{\textbackslash Fnn[1]}\\
+ &\mbox{\textbackslash Facontent[1]} & &\Facontent
+ & &\mbox{\textbackslash Fa[1]}\\
+ &\mbox{\textbackslash Fancontent[1]} & &\Fancontent
+ & &\mbox{\textbackslash Fan[1]}\\
+ &\mbox{\textbackslash Fanncontent[1]} & &\Fanncontent
+ & &\mbox{\textbackslash Fann[1]}\\
+ &\mbox{\textbackslash Fquant[1]\{a\}} & &\Fquant{a}
+ & &\mbox{\textbackslash Fq[1]}\\
+ &\mbox{\textbackslash Fnquant[1]\{a\}} & &\Fnquant{a}
+ & &\mbox{\textbackslash Fnq[1]\{a\}}\\
+ &\mbox{\textbackslash Fnnquant[1]\{a\}} & &\Fnnquant{a}
+ & &\mbox{\textbackslash Fnnq[1]\{a\}}\\
+ &\mbox{\textbackslash Fquantn[1]\{a\}} & &\Fquantn{a}
+ & &\mbox{\textbackslash Fqn[1]\{a\}}\\
+ &\mbox{\textbackslash Fquantnn[1]\{a\}} & &\Fquantnn{a}
+ & &\mbox{\textbackslash Fqnn[1]\{a\}}\\
+ &\mbox{\textbackslash Fnquantn[1]\{a\}} & &\Fnquantn{a}
+ & &\mbox{\textbackslash Fnqn[1]\{a\}}\\
+ &\mbox{\textbackslash Fnquantnn[1]\{a\}} & &\Fnquantnn{a}
+ & &\mbox{\textbackslash Fnqnn[1]\{a\}}\\
+ &\mbox{\textbackslash Fnnquantn[1]\{a\}} & &\Fnnquantn{a}
+ & &\mbox{\textbackslash Fnnqn[1]\{a\}}\\
+ &\mbox{\textbackslash Fnnquantnn[1]\{a\}} & &\Fnnquantnn{a}
+ & &\mbox{\textbackslash Fnnqnn[1]\{a\}}\\
+ &\mbox{\textbackslash Faquant[1]\{a\}} & &\Faquant{a}
+ & &\mbox{\textbackslash Faq[1]\{a\}}\\
+ &\mbox{\textbackslash Fanquant[1]\{a\}} & &\Fanquant{a}
+ & &\mbox{\textbackslash Fanq[1]\{a\}}\\
+ &\mbox{\textbackslash Fannquant[1]\{a\}} & &\Fannquant{a}
+ & &\mbox{\textbackslash Fannq[1]\{a\}}\\
+ &\mbox{\textbackslash Faquantn[1]\{a\}} & &\Faquantn{a}
+ & &\mbox{\textbackslash Faqn[1]\{a\}}\\
+ &\mbox{\textbackslash Faquantnn[1]\{a\}} & &\Faquantnn{a}
+ & &\mbox{\textbackslash Faqnn[1]\{a\}}\\
+ &\mbox{\textbackslash Fanquantn[1]\{a\}} & &\Fanquantn{a}
+ & &\mbox{\textbackslash Fanqn[1]\{a\}}\\
+ &\mbox{\textbackslash Fanquantnn[1]\{a\}} & &\Fanquantnn{a}
+ & &\mbox{\textbackslash Fanqnn[1]\{a\}}\\
+ &\mbox{\textbackslash Fannquantn[1]\{a\}} & &\Fannquantn{a}
+ & &\mbox{\textbackslash Fannqn[1]\{a\}}\\
+ &\mbox{\textbackslash Fannquantnn[1]\{a\}} & &\Fannquantnn{a}
+ & &\mbox{\textbackslash Fannqnn[1]\{a\}}\\
+ \end{flalign*}
+ This may seem like a daunting list, but there is an exceedingly simple way to think
+ about it. In a sense there are only two commands \textbackslash Fcontent[1] and
+ \textbackslash Fquant[1]\{\}. These two commands can be augmented with a
+ combination of as and ns so as to add assertion and negation strokes respectively.
+ Any stroke that is asserted (has a fat vertical line at the start) starts with
+ `\textbackslash Fa'. This may be followed by either one or two or no `n' to add one
+ or two or no negation strokes (the small vertical lines below the content
+ stroke). Next comes the name of the main command, either `quant' or `content'.
+ Finally the quantifiers may be followed by either one or two `n' to add one or two
+ negation strokes to the content stroke after the quantifier's depression.
+
+ Consider also that many of these commands are only really present for completeness
+ sake. It is difficult to imagine a situation where a twice negated quantifier with
+ twice negated content would ever be needed.
+
+ Since version 1.1 all basic strokes also have an optional scaling factor. A command
+ followed by [.5], for example would produce a stroke exactly half the default
+ length while [2] produces a stroke twice the default length. (The default length
+ is given by \textbackslash Fbaselength which is set to 20pt. Scaling allows for
+ greater control in the total length of formula as well as for a shorter syntax.
+ (We can replace expressions like \textbackslash Facontent \textbackslash Fcontent
+ with \textbackslash Facontent[2].) Care must be taken not to set a length that is
+ shorter than what is needed to fit all the parts of some basic stroke. This will
+ lead to negative lengths and hence unpredictable output.
+
+ All quantifiers also have a mandatory argument that specifies the variable
+ associated with the quantifier. (Mandatory arguments are contained in a set of
+ curly brackets \{ and \}). This argument should be a single small letter and
+ will be typeset above the semi circular depression in the assertion stroke in
+ mathfrak font which is provided by tha amssymb package. This font can be used in
+ maths mode by using the command `\textbackslash mathfrak\{\}'. Note that all the
+ commands provided by this package may be used in both math and text mode. (Though
+ math mode usually results in better formatting.)
+
+ Finally one may combine the above commands in arbitrary combinations which will
+ result in gapless longer strokes. (Eg.: $\Faquant[0.6]{a}\Fnquantn[1.4]{b}A$)
+ which may be roughly translated into english as ``for all $\mathfrak{a}$ there
+ exists a $\mathfrak{b}$ such that $A$''. (The commands I used for this expression
+ are \$\textbackslash Faquant\{a\}\textbackslash Fnquantn\{b\}A\$).
+
+\subsubsection{Conditional}
+ The conditional is the most important command in this package since it gives
+ Frege's Begriffsschrift it's two dimensional structure.\\
+ The syntax for the Fconditional command is as follows:
+
+ \textbackslash Fconditional[\textless option\textgreater]
+ \{\textless consequent\textgreater\}\{\textless antecedent\textgreater\}\\
+ The shorthand version (since version 1.3) is given by ``\textbackslash Fcdt''.
+
+ The arguments may in principle be anything, but you will only get a begriffschrift
+ formula if the arguments are themselves given by appropriate commands from the list
+ of basic commands given earlier. As an example, an asserted conjunction between $A$
+ and $B$ would be given as follows:
+
+ \$\textbackslash Fconditional[\textbackslash Fancontent]\{\textbackslash Fncontent
+ A\}\{\textbackslash Fcontent B\}\$ \\
+ and produce the following output:
+ \begin{align*}
+ \Fbox{\Fconditional[\Fancontent]{\Fncontent A}{\Fcontent B}}
+ \end{align*}
+ In addition Fconditional may be nested as it's own argument to arbitrary depth.
+ Nesting in the option is not recommended. \\
+ A conditional with nested consequent may be given as follows:
+
+ \$\textbackslash Fconditional[\textbackslash Facontent]\{\textbackslash
+ Fcontent\textbackslash Fconditional\{\textbackslash Fcontent A\}\{\textbackslash
+ Fcontent B\}\}\{\textbackslash Fcontent\textbackslash Fcontent C\}\$\\
+ and produces the following output:
+ \begin{align*}
+ \Fbox{\Fconditional[\Facontent]{\Fcontent\Fconditional{\Fcontent A}
+ {\Fcontent B}}{\Fcontent[2] C}}
+ \end{align*}
+ A conditional with nested antecedent may be given as follows:
+
+ \$\textbackslash Fconditional[\textbackslash Facontent]\{\textbackslash Fcontent
+ \textbackslash Fcontent A\}\{\textbackslash Fcontent\textbackslash Fconditional
+ \{\textbackslash Fcontent B\}\{\textbackslash Fcontent C\}\}\$\\
+ and produces the following output:
+ \begin{align*}
+ \Fbox{\Fconditional[\Facontent]{\Fcontent[2] A}{\Fcontent\Fconditional%
+ {\Fcontent B}{\Fcontent C}}}
+ \end{align*}
+ Each section of a content stroke may thus be replaced with any of the strokes given
+ by the list of basic commands. Note that it is up to the user to place the
+ appropriate number of strokes in each argument to ensure that the content strokes
+ all line up on the right hand side.
+
+\subsubsection{Brackets and Boxes}
+ There are two more commands to be considered:
+
+ \textbackslash Fbox\{\textless complex expression\textgreater\}\\
+ The shorthand version (since version 1.3) is given by \textbackslash Fb\{\}
+
+ \textbackslash Fbracket\{\textless complex expression\textgreater\}\\
+ The shorthand version (since version 1.3) is given by \textbackslash Fbb\{\}
+
+ Both Fbox and Fbracket take what I have called a `complex expression' for their
+ argument. A `complex expression' is any formula in begriffsschrift that has at
+ least one conditional in it. It is generally a good idea to put all complex
+ expressions into either a Fbox or a Fbracket. It is never necessary to place a
+ complex expressions into both an Fbox and an Fbracket since an Fbox simply is a
+ Fbracket without the actual brackets. Fbracket exists only for convenience with
+ the same effect being achieved by \textbackslash left(\textbackslash Fbox\{\}
+ \textbackslash right).
+
+ The reason why the Fbox is a good idea, is that the baseline is very near the top of
+ a complex expression of Begriffsschrift, which can make for some odd formatting
+ effects. In addition to placing the baseline at the middle of a complex expression
+ an Fbox ensures the expression is treated by LaTeX as a single object and given
+ enough space.
+
+ Finally a complex expression may not format correctly in some environments (like
+ the align* environment for example) unless it is placed in an Fbox. In short,
+ always use an Fbox (or Fbracket).
+
+\subsubsection{Arguments and Struts}
+ Since version 1.2 two commands have been added that allow for the typesetting of
+ arguments. The syntax for the argument command is as follows:
+
+ \textbackslash Fargument[\textless premise 0\textgreater]\{\textless premise
+ 1\textgreater\}\{\textless premise 2\textgreater\}\{\textless conclusion
+ \textgreater\}\\
+ The shorthand version (since version 1.3) is given by \textbackslash Farg
+
+ In the following esample the optional argument for premise 0 (an absent premise
+ takes the value `$(X):$' the premises are the two formulas above the therfore line
+ and the conclusion is the formula below the therefore line. The Begriffschrift
+ expressions in the arguments of the Fargument command do not need to be placed in
+ an Fbox, since the Fargument command works by boxing it's arguments allready.
+ \begin{align*}
+ \Fargument[(X):]
+ {\Fconditional[\Facontent]
+ {\Fcontent[2] A}
+ {\Fcontent\Fconditional{\Fcontent B}{\Fcontent C}}}
+ {\Fstrut[2]\Facontent C}
+ {\Fstrut[2]\Facontent A}
+ \end{align*}
+ where $X=\Facontent B$; (this is typeset seperately from the Fargument command);
+
+ The three begriffsschrift formulas above are in fact aligned leftbound. To make
+ them appear rightbound no matter what the relative lengths of $A$, $B$, and $C$,
+ the command ``Fstrut'' has been used in front of $\Facontent C$ and $\Facontent A$.
+ The command ``\textbackslash Fstrut[1]'' works exactly like an invisible content
+ stroke, that is it inserts space of length Fbaselength. Like all basic strokes it
+ can be scaled via an optional scale factor. Since version 1.3 it may be called by
+ the optional shorthand ``\textbackslash Fs''
+
+\subsection{Lengths}
+ In theory all the dimensions in this package can be changed with the command
+ \textbackslash setlength\{\textless name of length\textgreater\}\{\textless new
+ value\textgreater\}, though I have not done a great deal of testing and recommend
+ sticking to the default values. The following then is a table of all lengths: \\
+ \begin{tabular}{|l|l|l|}
+ \hline
+ name & default value & description \\
+ \hline
+ \textbackslash Fbaselength & 20pt & the length of the basic strokes \\
+ \textbackslash Flinewidth & 0.5pt & the line width \\
+ \textbackslash Fspace & 2pt & seperation between lines and text/formula \\
+ \textbackslash Fassertwidth & 3\textbackslash Flinewidth & width of assert
+ stroke \\
+ \textbackslash Fraiseheight & 1ex-\textbackslash Flinewidth & height of content
+ lines above baseline \\
+ \textbackslash Fnegsep & 3\textbackslash Flinewidth & seperation between a
+ double negation \\
+ \textbackslash Fnegshort & 2\textbackslash Flinewidth & space between negation
+ stroke and baseline \\
+ \textbackslash Fquantwidth & 6pt & width of the semi-circular quantifier
+ depression \\
+ \hline
+ \end{tabular}
+ the height of the conditional stroke is determined by the size of the contents of
+ the conditionals argument, as well as the baselineskip of the surrounding text. It
+ cannot be changed manually.
+
+\subsection{The \emph{bguq} Option}
+ Since version 1.3 this package may be called with the option ``bguq'' as follows: \\
+ \textbackslash usepackage[bguq]\{frege\}\\
+ If the option is enabled all quantifiers will be typeset using the bguq font
+ provided by the bguq package by J.J. Green. (This document is typeset using the
+ option). This means that the bguq package must be installed if the option is
+ enabled. (It can be found on ctan).
+
+ Warning: At present the bguq character scales with font size while the rest of the
+ symbols provided by this package do not. Also the bguq character does not respond
+ to a change in Flinewidth.
+
+\subsection{Final Example}
+ The Geach-Kaplan sentance (with thanks to Marcus Rossberg):
+ \begin{align*}
+ \Fbox%
+ {%
+ \Fconditional[{\Facontent[.2]\Fnquant{F}\Fcontent[.2]}]%
+ {%
+ \Fcontent%
+ \Fconditional%
+ {%
+ \Fcontent[3]%
+ \Fbox%
+ {%
+ f\Fbracket%
+ {%
+ \Fconditional[\Faquant{a}]%
+ {\Fcontent C\mathfrak{(a)}}%
+ {\Fcontent \mathfrak{F(a)}}%
+ }%
+ }%
+ }%
+ {\Fcontent\Fnquantn{b}\Fcontent\mathfrak{F(b)}}%
+ }%
+ {%
+ \Fcontent[0.4]%
+ \Fquant[0.6]{c}%
+ \Fquant[0.6]{d}%
+ \Fcontent[0.4]%
+ \Fconditional%
+ {%
+ \Fncontent%
+ \Fconditional{\Fcontent\mathfrak{c=d}}{\Fcontent\mathfrak{F(d)}}%
+ }%
+ {%
+ \Fncontent%
+ \Fconditional{\Fncontent\mathfrak{F(c)}}{\Fcontent A\mathfrak{(c,d)}}%
+ }%
+ }%
+ }%
+ \end{align*}
+ And that is all. \\
+ For comments, suggestions, identified errors, email me at \\
+ \textless Q.Pamp.2009@my.bristol.ac.uk\textgreater.
+\end{document}
+
+\section{GNU General Public License}
+ This package and all accompanying documentation is released under the GNU General
+ Public License. It is free software; you can redistribute it and/or modify it under
+ the terms of the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful, but WITHOUT ANY
+ WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+ PARTICULAR PURPOSE. See the GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License along with this
+ program; if not, write to the Free Software Foundation, Inc., 59 Temple Place -
+ Suite 330, Boston, MA 02111, USA. (Or just search for it online.)