I was recently given the opportunity to give a lecture on Frege’s logicism and related topics for our Logic III course (cross-listed as an undergraduate and a graduate course). That class had gotten up to the point of looking at second-order Peano Arithmetic, which is a natural jumping off point for looking at the logic of Frege’s logicism, Frege’s theorem, and Scottish neo-logicism. Topics, which some readers may recall, I’m am writing about in my dissertation. So basically, I got to spend 75min talking about the background to my own research.

I won’t say much about the content of that lecture here (but if you’re interested in those sorts of things see this recent post of mine, or the SEP articles on Frege’s Theorem and (neo)-Logicism). Rather I’m just going to make a few observations about my experience teaching that session.

To start at the beginning, preparing for the lecture was both useful for me, as well as enjoyable. The former because I hadn’t gone back and looked at the details of the proof(s) of Frege’s Theorem for a while, despite invoking those proofs from time to time. The latter because, well, I still enjoy my dissertation research, which is to say that 3-years-ago me did a good job choosing a dissertation topic.

Then, also in preparation, but much more so delivering the lecture, I realized just how well I know that stuff. I had lots of notes which I referred to for structure, and, more importantly, the correct forms of the definitions and axioms*, but I was able to fill in a lot of historical and technical detail pretty much off the cuff. This is as it should be – I wrote my first paper on Frege’s philosophy of mathematics about 10 years ago (!). I found however, that the extent of my knowledge and my confidence in that knowledge were much more apparent to me in a teaching context.

Giving this lecture also reinforced something else for me: the knowledge I’ve gained for the purpose of my dissertation is really (*really*) narrow and arcane. This is not to say that I’ve haven’t gained a broad and useful knowledge base studying philosophy, just that the minutiae of logicism and neo-logicism aren’t widely known or widely applicable. I’m also not claiming that this is a problem unique to me (it certainly isn’t), or that it should be surprising to anyone (it shouldn’t), but *teaching* it brought that out much more for me.

**Frege’s versions of the axioms of arithmetic use a predecessor, rather than successor function, and need to be relativised to the natural numbers, the definition for which requires the weak ancestral. None of that is particularly standard vis a vis philosophical discussions of arithmetic in general.*

*Logic, Philosophy, Philosophy of Math, Teaching, Teaching as a Grad Student*

Posted on April 26, 2017byAaron Thomas-Bolduc0