About PLM Reviews

Who am I?

I'm a doctoral researcher at the University of Vienna working on the Philosophy of Mathematics and Philosophy of Logic, though I have wider interests across the whole of philosophy, especially in metaphysics, epistemology and philosophy of science.

My research is focused on logic and axiom selection. With respect to the former, I argue for a kind of logical pluralism based on a pluralist conception of truth. Concerning the latter, I'm pursuing several lines of inquiry. First, I'd like to give a nominalist account of axiom selection. Second, I'd like to argue that if mathematical Platonists (and other sorts of realists) want to think of axioms as descriptively correct laws/generalisations of mathematical reality (alternatively, as a "strong" foundation for mathematics), then this will lead to a number of undesirable outcomes. Everyone, so I argue, should think about axiom selection very pragmatically.

If there's an overriding theme that connects these two projects, it's that logic and axiom selection should be approached pragmatically, not metaphysically. To put a name on things, one might call my views "qazi-Carnapian".

What is this blog?

This blog aims to publish short, informal reviews of published academic papers on the philosophy of logic and mathematics. Occasionally, I might branch out and write something different. For instance: longer reviews of books, reviews of papers in other areas of philosophy, informal notes on my own work in progress, technical introductions or more general commentary posts. Perhaps, if this blog gains some momentum, I might even indulge in an interview or two. That notwithstanding, the focus will definitely be on short, informal paper reviews in PLM.

I will try and favour newer work over older, well-known papers. Hopefully, this will keep things fresh and interesting for potential readers! Finally, I'm aiming for a degree of diversity across the authors I read, both in terms of things like gender identity but also national origin. Sadly, pressing diversity issues within my sub-field mean that full parity will likely be unattainable.

If you know of a (published) paper that you would like to see reviewed, you are invited to email me at gareth.pearce@univie.ac.at. Self-recommendations are welcomed, especially if you'd be willing to discuss your paper with me or would like to write a short rejoinder to my review.

Who is this blog for?

First of all, for myself. There are hundreds of philosophy blogs available, many by more well-known and established philosophers than myself. I am not anticipating more than a handful of readers for each review (though would be delighted to be proven wrong!) and as such would be foolish to start doing this for anyone other than myself. I enjoy writing, I enjoy reading papers on PLM and this blog provides a pleasant outlet for both.

Secondly, the blog is for the authors that I review. Most comments one receives on one's papers are either in very formal settings such as journal reviews and responses or in perhaps overly brief settings like conferences. Both of these have their value, but I suspect that it is a nice middle ground to have one's work reviewed in an extended but still friendly and informal setting.

Lastly, this blog is for anyone interested in philosophy of logic, philosophy of mathematics or wider theoretical-analytic philosophy. I hope that this will be true irrespective of prior knowledge. My aim is to write accessibly and informally, though still to hit the important philosophical points. As such, I hope that this blog has something for everyone!

I welcome comments and replies, either of a critical or clarificatory nature.

New reviews are advertised over Twitter so follow me @GarethRPearce for updates

Comments

Post a Comment

Popular posts from this blog

Luca Incurvati's "How to be a Minimalist about Sets"

Image
  Introduction This was an interesting paper by Luca Incurvati and I enjoyed reading it quite a bit. We read this paper as part of our weekly philosophy of maths reading group at the University of Vienna. My thanks, in alphabetical order, to Julie Lauvsland, Benjamin Marschall and Simon Weisgerber. In particular, thanks to Julie for suggesting the paper. This is, though, the first paper I've reviewed where I've generally disagreed with the author. It's not that I necessarily disagree with all the conclusions, but I think there responses that Incurvati doesn't consider and alternative arguments that are important. I'm also unconvinced by Incurvati's positive proposal. Now one quasi-objection I have is that the paper takes place from a Platonist/realist perspective. I think that's wrong from the start and is bound to lead to confusion when we worry about which axioms or claims about sets are really  correct and why. I think we should choose our concept of &quo
Read more

Jared Warren's "Infinite Reasoning"

Image
Introduction This was an exciting paper to read, as it was the first as part of a new reading group on the Philosophy of Maths at the University of Vienna. My thanks to Benjamin Marschall both for organising the group and suggesting the paper. I look forward to reviewing many of the papers that we'll read in this group. Present this week, in alphabetical order, was Julie Lauvsland, Benjamin Marschall, myself and Georg Schiemer. In the paper, Warren advances the claim that it is possible for us to reason infinitely. What does this mean? A working definition is that inferences are a kind of mental or cognitive act connecting a series of premises to a conclusion. Oxford's dictionary of philosophy says something similar stating: "Any process of drawing a conclusion from a set of premises may be called a process of reasoning." An inference might be a good (valid) inference or it might be a bad (invalid) one. Typically, though, inferences are finite in the sense that one i
Read more

David Lewis's Philosophy of Maths (Preview of my SSHAP talk)

Image
Introduction Around 18 months ago my supervisor, Georg Schiemer, and I were catching up about the state of my work whilst taking a short walk through Vienna. Towards the end of this walk, Georg asked me if I was planning on submitting to a conference he was organising: the annual meeting of the Society for the Study of the History of Analytic Philosophy (SSHAP). I said about it but, now that he mentioned it, I did have a short little paper I was meaning to write on the history of Mathematical Formalism, why it fell out of fashion and why I thought David Lewis would have made a good Formalist. Georg liked the idea and so I wrote it. The paper was only ever supposed to be a bit of fun; more catharsis than serious scholarship as I think most of the serious points regarding Gödel's Incompleteness Theorems and Formalism were already well known by philosophers of maths. Alan Weir, for instance, has clarified most of this in several places. Nevertheless, the David Lewis connections were (
Read more