Recent News

Proof Terms are fun

2 September 2016

Today, between marking assignments and working through a paper on proof theory for counterfactuals, I’ve been playing around with proof terms. They’re a bucketload of fun. The derivation below generates a proof term for the sequent \(\forall xyz(Rxy\land Ryz\supset Rxz),\forall xy(Rxy\supset Ryx),\forall x\exists y Rxy \succ \forall x Rxx\). The playing around is experimenting with different ways to encode the quantifier steps in proof terms. I think I’m getting somewhere with this.

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Talking to Jc Beall during his recent visit to Australia, I got thinking about first degree entailment again.

Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions”. First Degree Entailment (fde) is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts (and there seems to be no very good reason to prefer gaps over gluts or gluts over gaps if you’re happy with fde), then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How is the fde theory any different from the theory with gaps alone?

I think I have a clear answer to this puzzle—an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone. But to explain the answer and show how it works, I need to spell things out in more detail. If you want to see how this answer goes, read on.

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For the first time in my home owning career, the picket fence outside my home sports a how-to-vote sign.

This is a change for me. I’m a member of no political party, and I’ve never encouraged my neighbours to vote in any particular way. For almost all of my life, I’ve lived in safe Labor seats, from growing up in working class Brisbane to living in the inner north of Melbourne, my members of Federal Parliament have all been members of the ALP in safe seats. (Only short sojourns in Toowong and Marsfield found me in conservative territory.) My vote in my electorate hasn’t made a difference over the years.

More importantly, I think that there is much more to politics than voting. It’s one thing to distribute a few votes once every few years in to record your voice about how we are governed. There are plenty of other, more effective ways to take part in our common life, both locally, and globally. Broader political action can take many different forms, beyond party politics. Different forms of political action include investigating and exposing injustice or corruption, campaigning for change, making proposals for different ways to do things, protesting, raising awareness, building alternative communities and political structures and resisting injustice—through to covert and overt struggle and revolution. Politics is a complicated business with many different strands.

So, given all of that, why do I have a campaign poster on my fence?

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A few weeks ago, Richard Marshall interviewed me for 3am Magazine’s series of interviews with philosophers. If you’re interested in my work on logical pluralism, proof theory and things like that, this interview might be a good place to start. I hope you like it. If you’ve got any questions, please let me know.

Prompted by a colleague and friend (thanks Ruth!), I’ve been asking students who took my upper level logic subjects last year what they learned about how to learn logic. This is helpful for me—I get a better understanding of how students are learning. It’s hopefully helpful for them, too, to reflect more explicitly on how they learn. But most of all, I hope that their reflections will help students who come after them.

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Recent Writing

  • Review of Advances in Proof-Theoretic Semantics edited by Thomas Piecha and Peter Schroeder-Heister, Notre Dame Philosophical Reviews (2016) Abstract
  • “Fixed Point Models for Theories of Properties and Classes,” article under submission. Abstract  pdf
  • “On Priest on Nonmonotonic and Inductive Logic,” Thought, 5:2 (2016) 119–124 Abstract  pdf
  • “Three Cultures—or: what place for logic in the humanities?” unpublished essay. Abstract  pdf
  • “Generality and Existence I: Quantification and Free Logic,” article in progress. Abstract  pdf

Recent & Upcoming Presentations

Recent & Upcoming Classes


I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.



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