In early February I'll be at the University of Connecticut, where I plan to finally give Nathan Kellen the relevanceless motivation for relevance logics that I’ve promised him for years. While I’m at it I’ll also try to convince Jc Beall that the arguments he’s given in his recent papers should really lead him to a stronger logic than FDE.
Later In February, I’ll be giving a talk at the University of Melbourne. If all goes according to plan, that talk will be about why, despite the fact that quantification in relevance logics is similar to quantification in intuitionistic logic, the whole “translate into a model logic and use local quantifiers” bit doesn’t work in the relevant setting. But I haven’t worked out the details there yet, so who knows. Maybe I’ll end up talking about something else altogether.
Other than that, if you want to hang out and are in the Twin Cities area, come to a FIG meeting!
Who I Am as a Researcher:
I'm a logician. That means that I build formal models of language, study the mathematical features of these formal models, and (try to) shed light on philosophical questions while doing so. The logics I study are mostly relevant logics. So I guess that means I'm a relevance logician. Having said that, I need to address something: there is a stereotype of the relevance logician that one may encounter in philosophical communities. This stereotyped curmudgeon bangs their fist on tables and grumbles/hollers/otherwise-antagonistically says things like "silly classical/intuitionistic logicians! Only relevance logics are real logics." I am not that person. I think we can use relevance logics to do interesting things and to build models that capture things that are otherwise hard to capture. I think the same is true of classical logics and intuitionistic logics.
All of that to say that I hope you want to chat about my research! If you do, have a look at my recent thoughts. Also, fair warning: if you ask me about what I’m working on, I'll probably as you about what you’re working on.
What I actually DO:
In logic we study what follows from what. But here’s something funny: this might follow from that relative to one background theory but not relative to a different background theory. Logicians tend to get around this by saying that what we’re really interested in is what follows from what no matter what — that is, regardless of which background theory we use.
The most obvious way to cash this out is by say that this follows logically from that just when this follows from that relative to every background theory. The problem I have with this story is that it leaves the background theories too far in the background. That is, the story treats background theories like all they do is give us local rules for how to use the “this follows from that” construction. That’s ok as a first gloss, but I think we can do better.
In my research, I let background theories play in the front yard with all the rest of the logical children. The way I do this is fairly straightforward: rather than treating “this follows from that relative to background theory b” as telling us something about a special sense of “follows from” that relates this and that, I instead treat it as telling us that the ordinary (logical) sense of “follows from” relates this and the closure of that under b. In short, I expand the stock of things logic is concerned with relations among — we need to be concerned not just with the “this’s” and the “that’s”, but also the “that closed under b’s” as well. This requires extending our semantics and rethinking a lot of things. Surprisingly, the logic that results is relevant.
I’m still working out the details of how quantification plays with all this. And my longterm goal is to see what impact this has on our metamathematical theories. So there’s no shortage of work to be done. But it’s a fairly fun sort of work, so if you want to take some of the load, let me know and I’ll point you in the direction of things that need doing. ;)