“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!

References for foundations of math!

If you are not interested in the foundations of mathematics (and of computer science, I think), then you may disregard this post. For those of you that are interested but are unsure where to start: I hope this will help you get started with the foundations movement at the turn of the twentieth-century!

  • From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (Jean van Heijenoort, editor)

This source book is definitely worth purchasing for your own library and use. It contains highly influential primary texts in logic by, among others, Cantor, Peano, Frege, Russell, Zermelo (yes, the one of ZF fame), von Neumann, Hilbert, Brouwer, and, of course, Gödel. It is sorely missing Tarski and Church and Marcus, but you can make up for that elsewhere. Frege’s Begriffsschrift alone justify purchasing this, as do Gödel’s papers.

  • The Search for Mathematical Roots, 1870-1940 (Ivor Grattan-Guinness, author)

Grattan-Guinness, sadly now deceased, was a highly regarded historian of mathematics (he also wrote a book on the history of calculus). This book offers a good sketch of the history of the foundations of mathematics movement. It is not exhaustive, but it covers a good enough selection to contextualize whatever else you go on to read.

A combination of those two should put you in a position to pursue whatever else you find interesting about the foundations of mathematics movement at the turn of the 20th century. I am, of course, happy to recommend further items. Just get in touch!