# “Principia” Notation in LaTeX

I recently had occasion to use the Peirce arrow, NOR (↓), in LaTeX! But I wanted to use Peirce’s notation from 1902. This takes the form of the symbol for strict implication, ⥽, turned 270 degrees so that the arrow’s head faces down, like so: ⥿. I was helped in typesetting this by Richard Zach’s helpful post. I have worked on Principia quite a bit, and I have needed to make ad hoc commands to rotate letters and other symbols to match the logical symbols used there. So I thought to share my work in case it saves others some time! I will update this as I devise further ad hoc commands.

All this requires is the package graphicx. With it, you can then use the command \text{\rotatebox[origin=c]{[DEGREES]}{[TEXT]}}. The reason for the \text{…} on the outside is to avoid conflicts in math mode and similar environments.

With that ado, here is LaTeX code I use for:

• \Runi for the universal set, V (an upside-down Lambda):
\newcommand{\Runi}{\text{\rotatebox[origin=c]{180}{$\Lambda$}}}
• \Dom for the domain, D’, of a relation:
\newcommand{\Dom}{$\text{D}$}
• \CDom for the converse domain of a relation (a ‘D’ rotated 180 degrees):
\newcommand{\CDom}{\text{\rotatebox[origin=c]{180}{$\text{D}$​}}}
• \Parrow for the Peirce arrow NOR in Peirce’s 1902 notation (⥿):
\newcommand{\Parrow}{\text{\rotatebox[origin=c]{270}{$\strictif$}}}

No doubt there will be more to come!