The Liar Paradox: A Reading Guide

If you’re reading this, you likely stumbled on my YouTube video about the Liar Paradox. This is a guide for further reading and self-study, since a YouTube video really doesn’t allow you to go into much detail.

This guide, along with quite a bit of my writing, is free. You can subscribe below, and you can also choose to become a paying subscriber. That helps me make content on Substack and YouTube, plus you get access to everything.

Some Prefatory Remarks

I received my PhD from the University of Connecticut. UConn is famous (perhaps infamous) for being friendly to non-classical logic, especially when you’re talking about paradoxes. My dissertation committee was Keith Simmons, Stewart Shapiro, Michael Lynch, and Magdalena Kaufmann. Keith and Stewart are some of the most classical-friendly philosophers at UConn, but even they have some complicated views of the paradoxes. My dissertation was not about paradoxes, but I did defend a degree theory of truth. That’s a very non-standard view.

I was also a research assistant for Jc Beall, previously at UConn but now at Notre Dame. This further colors my view of the paradoxes.

All of this is to say that I have a slant when it comes to paradoxes.

Introductory Reading

If you’re looking for well-written and fairly accessible introductions to the general topic, then you should read a selection of articles from the Stanford Encyclopedia of Philosophy.

To start, Liar Paradox by Jc Beall, Michael Glanzberg, and David Ripley.

I studied (and co-authored) with Jc while getting my PhD, and David was also a professor at UConn at the time (he taught me substructural logic). Jc favors a structural, dialethic approach to the Liar; David is interested in some very complicated substructural logics in relation to the paradoxes; Glanzberg is more classical in orientation. It is a healthy balance of approaches. (If you don’t know what these terms mean, don’t worry — you’ll learn the terminology as you read.)

Second, Dialetheism by Graham Priest. Priest is one of the most prominent modern dialetheists along with Jc, and his book In Contradiction is a staple in the literature. But In Contradiction is not a beginner-friendly book, so if you want to learn about dialetheism this article will serve you well.

Third, Classical Logic by Stewart Shapiro and Teresa Kouri Kissel. Stewart was one of my dissertation advisors, and Teresa was his student at Ohio State. This is a great introduction to classical logic – by far the dominant logical approach – that is also fair-minded about competitors.

After that, you probably need to learn some formal logic. I like Logic: The Basics (2nd Edition) by Jc Beall and Shay Allen Logan. LTB is a good introduction as the mathematics is not particularly involved (it is very basic set theory), plus you get an introduction to classical logic, K3 (a gappy approach), LP (a glutty approach), and FDE (a gappy and glutty approach).

Paradoxes by R.M. Sainsbury is also a nice read about paradoxes. It is very accessible, as it is written for the level of an undergraduate who is just learning about these things. Tim Maudlin’s Truth and Paradox is highly recommended, but I have two caveats: I haven’t read it (I’m going on secondhand knowledge here) and it seems to be aimed at a slightly more advanced audience.

If you’ve read a selection of these books, then you’re ready to go into more advanced reading.

Advanced Logic

Logic: The Basics is a good introductory text, but it lives up to its title; you will only get the basics. Eventually, to grapple with the Liar and other paradoxes, you will want to learn more about logic.

Enderton’s A Mathematical Introduction to Logic is very good as a next step. You will learn more about proofs by induction, some slightly more advanced set theory, and so on. This was a foundational text for me going beyond the basics of logic. This book is also strictly classical, but it will give you a foundation.

When you want to explore non-classical logic in more detail, there are two books to read.

An Introduction to Non-Classical Logic by Graham Priest is the definitive introduction. The proof system, based on trees, is straightforward. The advantage of Priest’s book is that it is quite comprehensive, which gives you a nice view of the many varities of non-classical logic.

An Introduction to Substructural Logics by Greg Restall is the best textbook on substructural logic. However, it must come with a warning. This is an incredibly difficult textbook, and unless you are very interested in the topic it will prove hard-going (and will likely prove hard-going regardless). I would only recommend this book if you are sincerely interested in advanced study of very niche logics.

Philosophy of Logic

You might think it is weird that I’ve talked about logics in the plural. In order to make sense of this, and the general approach to logic by contemporary philosophers, check out these books.

Philosophical Logic by John Burgess, who helpfully explains why philosophers care about these formal models. He discusses major topics such as conditionals and the variety of logics on offer.

Logical Pluralism by Jc Beall and Greg Restall is a modern classic. Beall and Restall believe there is no one ‘true’ logic; instead, there are many correct logics depending on the relevant definition of validity (or more accurately, cases). It’s a slim volume that initiated an entire literature. It is not strictly about paradoxes, but it would provide you with a framework for thinking about logic like a contemporary analytic, Anglophone philosopher.

Many Approaches to Paradoxes

There are too many approaches to paradoxes in general, and the Liar in particular, to enumerate here. There are also too many papers for me to direct you toward, and what you read is going to depend on what you think is interesting.

Eventually, if there is enough interest, I’ll identify key papers about common approaches to paradoxes: gappy solutions, glutty solutions, Tarskian solutions, and so on. Let me know if you’d actually use that.

For a survey, written at a very advanced level, you could try selections from Beall’s Revenge of the Liar. Unfortunately, it is $80 new. However, you’ll find many discussions of ‘revenge’ phenomena written by leading philosophers in the field. It will introduce you to some other paradoxes (like Curry’s Paradox), approaches to the Liar we didn’t cover in the video (like Burge’s and Simmons’ contextualism), and some radical approaches by people like Kevin Scharp. If you can find a used copy, it is worth a read. The same could be said for Liars and Heaps, though that goes beyond semantic paradoxes (and includes the Sorites).

Once you’ve read enough to start pursuing individual approaches, your best bet is to go to PhilPapers and start searching. There you find papers like Tarski’s work on hierarchy, Kripke’s ‘Outline of a theory of truth’, Priest’s other work on consistency and inconsistency, the revision theory of Gupta and others, and so on. There are currently over 2,000 papers indexed on PhilPapers about the Liar; each has a bibliography you can explore as well.

Happy researching.