tag:blogger.com,1999:blog-6331292467452860795.post3587894502674260190..comments2024-03-27T04:05:15.220-07:00Comments on The Sooty Empiric: Visualising PhilosophyLast Positivisthttp://www.blogger.com/profile/11677699402952932577noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6331292467452860795.post-69341419827936920252017-12-24T15:31:46.015-08:002017-12-24T15:31:46.015-08:00Thanks for this Liam. It's nice to see someone...Thanks for this Liam. It's nice to see someone else doing phenomenology of philosophy. I've just got two points to add. <br /><br />First, that this isn't quite a spontaneous image, but something like a way of becoming self-conscious of my own conscious reasoning processes, by way of reading a lot of Jean-Yves Girard's work on logical proof syntax and its inherent dynamics. Ludics is based on the idea that you can erase the formulas/subformulas from sequent calculus proof trees (producing labelled loci: 0, 0.1, 0.1.1, 0.1.2, 0.2, 1, 1.1., etc.), and treat them as interacting arguments by cutting them together (e.g., 0 ⊢ with ⊢ 0, and so on up the trees) leaving a contradiction at their root (i.e., an empty sequent [ ⊢ ]) and tracing the corresponding computational dynamics through cut-elimination. Turns out this weird dialogical game is Turing complete. <br /><br />This all sounds pretty abstract, but it's where the imagery of trees with interacting branches comes from. Perhaps most interestingly, because the formulas have been erased from the proofs, this means there can't be any leaves (e.g., A ⊢ A). What this means is that the only way a branch can end (the alternative being going on for ever) is with a symbol Girard calls the Daimon (✠), which is equivalent to something like 'I agree to disagree', which means its opponent wins. There are all sorts of other things that can happen, but it's from this winning/losing that Girard spins something like a bizarro version of game theory, out of which he can reconstruct linear logic (and thereby the classical and intuitionist logics you can simulate in it). In essence, instead of taking a proof system and trying to find a semantics that fits it, he tries to find the semantics *within* the syntax itself.<br /><br />It took me a long time to understand what was going on in ludics, but when I *got* it it gave me a new way of articulating the *geometry* of my dialogical intuitions. Girard then goes on to do transcendental syntax, which I'm still digesting, but it involves moving from proof trees to proof nets, hence the slightly gnomic concluding remarks. In short, I genuinely meant it when I said that I was sneaking in some philosophy of logic, and I would have snuck in more, but I had to delete two sections that got too technical for the flow of the piece :)<br /><br />Second, for me philosophy is a *very* social activity. It's just a social activity I've increasingly had to do on my own, or in venues like this, because one feature of not having a job is not having access to conversational arenas where you can *genuinely* do it, rather than simulating it in your own head. It's the sort of thing you don't quite appreciate till you leave graduate school, and you no longer have a cast of people you can just invite to have a casual conversation, access to resources that might help simulate this, or the funds to attend conferences that might make up for it. I also have a tendency to dump more information than people can process quickly (cf. this), and this puts more strain on the few people I can interact with than they should have to bear. In short, I live for the dialogical stimulation of philosophical socialising, but it's been thin on the ground for the last 5 years or so, outside of isolated events. JB was great for this, until it wasn't, alas.<br /><br />Long live the ocean of reason, and all who swim therein!deontologisticshttps://www.blogger.com/profile/16652214325422205917noreply@blogger.com