In my browsing of Amazon, I came across something kind of exciting. There are two new collections of Quine’s work coming, edited by Dagfinn Follesdal and Douglas Quine. They are Confessions of a Confirmed Extensionalist and Other Essays and Quine in Dialogue. The former appears to be split between previously uncollected essays, previously unpublished essays, and more recent essays. The latter appears to consist of a lot of lighter pieces, reviews, and interviews. Amazon doesn’t seem to have the tables of contents available yet, but they are available at the publisher’s page, here and here. Both look promising for those that are interested in Quine. I’m curious to read Quine’s review of Lakatos in the latter volume. It could be wildly disappointing, but it would be nice to see Quine’s reaction a philosophy of math that is so at odds with his own. [Edit: In the comments, Douglas Quine points out that more detailed information for the new volumes, as well as information on other centennial events, are up on the W.V. Quine website.]

The other Quinean thing is a question. Is there anywhere in Quine’s writings where he discusses the role of statistics and probability in modern science? It seemed like there could be something there that could be used as the beginning of an objection to Quine’s fairly tidy picture of scientific inquiry. (This thought is sort of half-baked at this point.) Over the holidays I couldn’t think of anywhere Quine talked about how it fit into his epistemological views. It seemed odd that Quine didn’t ever discuss it, given the importance of statistics in science, so I’m fairly sure I’m forgetting or overlooking something. There might be something in From Stimulus to Science or Pursuit of Truth, but I won’t have access to those for a few days yet. [Edit: In the comments Greg points out that Sober presented a sketch of a criticism along the lines above in his paper “Quine’s Two Dogmas,” available for download on his papers page.]

Does anyone know of any proof systems in which some but not all contents have negations? I’m looking for examples for a developing project.

I’m trying to work out some thoughts on the topic of semantic self-sufficiency. My jumping off point for this is the exchange between McGee, Martin and Gupta on the Revision Theory of Truth. My post was too long, even with part of it incomplete, so I’m going to post part of it, mostly expository, today. The rest I hope to finish up tomorrow. I’m also fairly unread in the literature on this topic. I know Tarski was doubtful about self-sufficiency and Fitch thought Tarski was overly doubtful. Are there any particular contemporary discussions of these issues that come highly recommended? Read the rest of this entry »

I wanted to avoid having another post that was primarily a link, but I seem to be having some difficulty of getting a post together lately. In any case, there is a review of Gillian Russell’s Truth in Virtue of Meaning up at NDPR. The review seems to be fairly detailed, so I’ll let it stand on its own.

Today I submitted the last paper I needed to finish in order to fulfill my course requirements at Pitt. Now I get to concentrate on finishing up some side projects and working on my nascent prospectus. Yay!

An end of term reflection will likely follow in the next week or so.

This term I’ve spent some time studying nonmonotonic logics. This lead me to look at David Makinson’s work. Makinson has done a lot of work in this area and he has a nice selection of articles available on his website. One unexpected find on his page was a paper called “Completeness Theorems, Representation Theorems: What’s the Difference?” A while back I had posted a question about representation theorems. In the comments, Greg Restall answered in detail. Makinson’s paper elaborates this some. He says that representation theorems are a generalization of completeness theorems, although I don’t remember why they were billed as such. There are several papers on nonmonotonic logic available there. “Bridges between classical and nonmonotonic logic” is a short paper demystifying some of the main ideas behind non-monotonic logic. The paper “How to go nonmonotonic” is a handbook article that goes into more detail and develops the nonmonotonic ideas more. Makinson has a new book on nonmonotonic logic, but it looked like most of the content, minus exercises, is already available in the handbook article online.

There is now a multimedia section up on Brandom’s website. It includes the videos of the Locke lectures with commentary as given in Prague as well as the Woodbridge lectures as given at Pitt. I think one of the videos of the latter features a mildly hard to follow muddle of a question by me. If you are in to that stuff, it is well worth checking out.

The deadline for the Pitt-CMU conference [edit: has been extended to 12/15. Please submit!]

I just found out that Yiannis Moschovakis’s Elementary Induction on Abstract Structures was released as a cheap Dover paperback over the summer. It was previously only available in the horrendously expensive yellow hardback series by… North-Holland, according to Amazon. The secondary literature on the revision theory of truth has recently nudged me into looking at this book, and it is nice to know that it is available at a grad-student-friendly price. Philosophical content to follow soon.

I just finished reading Badesa’s Birth of Model Theory. It places Löwenheim’s proof of his major result in its historical setting and defends what is, according to the author, a new interpretation of it. This book was interesting on a few levels. First, it placed Löwenheim in the algebraic tradition of logic. Part of what this involved was spending a chapter elaborating the logical and methodological views of major figures in that tradition, Boole, Schröder, and Peirce. Badesa says that this tradition in logic hasn’t received much attention from philosophers and historians. There is a book, From Peirce to Skolem, that investigates it more and that I want to read. I don’t have much to say about the views of each of those logicians, but it does seem like there is something distinctive about the algebraic tradition in logic. I don’t have a pithy way of putting it though, which kind of bugs me. Looking at Dunn’s book on the technical details of the topic confirms it. From Badesa, it seems that none of the early algebraic logicians saw a distinction between syntax and semantics, i.e. between a formal language and its interpretation, nor much of a need for one. Not seeing the distinction was apparently the norm and it was really with Löwenheim’s proof that the distinction came to the forefront in logic. A large part of the book is attempting to make Löwenheim’s proof clearer by trying to separate the syntactic and semantic elements of the proof.

The second interesting thing is how much better modern notation is than what Löwenheim and his contemporaries were using. I’m biased of course, but they wrote ax,y for what we’d write A(x,y). That isn’t terrible, but for various reasons sometimes the subscripts on the ‘a’ would have superscripts and such. That quickly becomes horrendous.

The third interesting thing is it made clear how murky some of the key ideas of modern logic were in the early part of the 20th century. Richard Zach gave a talk at CMU recently about how work on the decision problem cleared up (or possibly helped isolate, I’m not sure where the discussion ended up on that) several key semantic concepts. Löwenheim apparently focused on the first-order fragment of logic as important. As mentioned, his work made important the distinction between syntax and semantics. Badesa made some further claims about how Löwenheim gave the first proof that involved explicit recursion, or some such. I was a little less clear on that, although it seems rather important. Seeing Gödel’s remarks, quoted near the end of the book in footnotes, on the importance of Skolem’s work following Löwenheim’s was especially interesting. Badesa’s conclusion was that one of Gödel’s big contributions to logic was bringing extreme clarity to the notions involved in the completeness proof of his dissertation.

I’m not sure the book as a whole is worth reading though. I hadn’t read Löwenheim’s original paper or any of the commentaries on it, which a lot of the book was directed against. The first two chapters were really interesting and there are sections of the later chapters that are good in isolation, mainly where Badesa is commenting on sundry interesting features of the proof or his reconstruction. These are usually set off in separate numbered sections. I expect the book is much more engaging if you are familiar with the commentaries on Löwenheim’s paper or are working in the history of logic. That said, there are parts of it that are quite neat. Jeremy Avigad has a review on his website that sums things up pretty well also.

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Shawn Standefer, recent Ph.D. in philosophy from Pitt. (More about me)

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