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    Category: Logic

    • Aristotle’s definition of the syllogism — a dialogical interpretation

      By Catarina Dutilh Novaes (Cross-posted at M-Phi) (I am currently finishing a paper on the definition of the syllogism according to Aristotle, Ockham, and Buridan. I post below the section where I present a dialogical interpretation of Aristotle's definition.) Aristotle’s definition of ‘syllogismos’ in Prior Analytics (APri)  24b18-22 is among one of the most commented-upon passages of the Aristotelian…

    • Review of Williamson’s Tetralogue

      By Catarina Dutilh Novaes (Cross-posted at M-Phi) I've been asked to write a review of Williamson's brand new book Tetralogue for the Times Higher Education. Here is what I've come up with so far. Comments are very welcome, as I still have some time before submitting the final version. (For more background on the book, here is a short video where…

    • In memoriam: Ivor Grattan-Guinness

      The great historian of logic and mathematics Ivor Grattan-Guinness passed away about a month ago, aged 73. I only heard it yesterday, when Stephen Read posted a link to the Guardian obituary on Facebook. From the obituary:  He rescued the moribund journal Annals of Science, founded the journal History and Philosophy of Logic, and was on the board of Historia Mathematica from…

    • The upside down world paradox

      By Catarina Dutilh Novaes (Cross-posted at M-Phi) As most kids (I suspect), my daughters sometimes play ‘upside down world’, especially when I ask them something to which they should say ‘yes’, but instead they say ‘no’ and immediately regret it: ‘Upside down world!’ The upside down world game basically functions as a truth-value flipping operator: if…

    • Review of T. Parsons’ Articulating Medieval Logic

      By Catarina Dutilh Novaes (Cross-posted at M-Phi) I was asked to write a review of Terry Parsons' Articulating Medieval Logic for the Australasian Journal of Philosophy. This is what I've come up with so far. Comments welcome! ===================================  Scholars working on (Latin) medieval logic can be viewed as populating a spectrum. At one extremity are…

    • What’s the big deal with consistency?

      (Cross-posted at M-Phi) It is no news to anyone that the concept of consistency is a hotly debated topic in philosophy of logic and epistemology (as well as elsewhere). Indeed, a number of philosophers throughout history have defended the view that consistency, in particular in the form of the principle of non-contradiction (PNC), is the…

    • Did Russell’s Paradox entail that set theory is incomplete (if axiomatized)?

      Tonight I was fondly recalling Michael Hand and Jonathan Kvanvig's old paper on Tennant's solution to Fitch's Paradox (it's a beautiful read) and a weird thought occured to me. Hand and Kvanvig argue that Tennant's solution would be analogous to a set theorist responding to Russell's Paradox by proposing naive set theory with Frege's comprehension…

    • Preferential logics, supraclassicality, and human reasoning

      (Cross-posted at M-Phi)   Some time ago, I wrote a blog post defending the idea that a particular family of non-monotonic logics, called preferential logics, offered the resources to explain a number of empirical findings about human reasoning, as experimentally established. (To be clear: I am here adopting a purely descriptive perspective and leaving thorny…

    • Williamson on David Lewis

      This summer I'm trying to get a little bit up to speed on modality issues by doing an independent study with some students.* I've started looking ahead to Williamson's recent magnum opus and this little bit of the preface weirded me out: Since cosmological theories in physics are naturally understood as embodying no restriction of…

    • “Mathematicians are supposed to prove things *in* arithmetic, not *about* arithmetic!”

      Hitler does not like Gödel's theorem one bit. Perhaps surprisingly, he displays a sophisticated understanding of the implications and presuppositions of the theorem. (In other words, there's some very solid philosophy of logic in the background — I think I could teach a whole course only on the material presupposed here.) (Courtesy of Diego Tajer,…