“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!

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