Visualising Philosophy

Recently Peter Wolfendale wrote up a very frank and honest discussion of his time in and out and on the edge of academia, and the relationship between this and his type II bipolar disorder. It's a long essay - insightful, but heavy stuff, so give it a read when you feel in a place to read about depression and its effects on a philosopher's life. (It will perhaps pair well with this interview with Carrie Jenkins.)

While it's not really the focus of the essay, I was really struck by PW's description of how he thinks about philosophical problems:

Here’s how I think about a philosophical problem. It is a branching tree of paths, splitting off into alternative solutions, each with their own forking reasons, each caught in dialectical interaction with its opponents. You choose a path that seems right, and if you’re lucky you outlast the alternatives, chasing them into dead ends of bare assertion or loops that beg the question (either is a pyrrhic victory). However, these looping paths are tricky structures. They don’t always lead back to the alternative solution you’re disputing, but to other branches of the wider philosophical tree. This is the interesting thing about infinite trees, they’re self-similar in a sprawling fractalline fashion. This means that what you originally think is a well defined local problem can force you to see it as a branch of a bigger tree, if you want to continue arguing against an opponent whose premises reach deeper into the problem space. The tree analogy is at risk of bursting here, so let me make an explicitly formal modification: the structures we’re talking about are in some sense like proof nets, but they’re more like (infinite) directed graphs. The directional asymmetry between question and answer remains significant, and we always have to start somewhere, at what looks like the root of a tree.

I found this to be a really striking and evocative metaphor. One gets a real sense of a lot of how PW is thinking about doing philosophy. First, one gets a sense that the ideas being interacted with come with independent structure -- one starts from somewhere in the network of paths, and follows where they lead. This, I take it, means that PW experiences philosophical ideas as having a kind of inner structure that he must respond to. Second, one gets both a sense of competitiveness and a sense of playfulness, the imagery seems to be a kind of homely one of children chasing each other round a large garden, or something of this sort -- among these paths a competitive game is being played, wherein one gains victory by successfully getting one's adversaries to admit defeat at the end of a chase because they chose a bad path (where the path is bad because of features of the path rather than the one who chose it). This, I take it, mirrors PW's experience of debate among philosophers and philosophies.

But, third, one gets a sense of exploration, one is only learning where the paths lead as one chases one's opponents around. This, I take it, tells us what PW takes to be gained by the game in the previous; it's not just frivolous one upmanship or the like, we are actually learning through doing. And, fourth, the game may go on forever -- the tree is infinite and so you will never reach the end of all paths. In the other direction, while one picks what looks like the root to start from, I take it the qualification is exactly to indicate that one may well be able to turn back and try to follow the paths up to their source... and maybe it is infinite in that direction too...

Here is a sense of philosophy as an unending quest to explore a vast garden through our mutual competitive play.

It is also totally different from how I would describe my own phenomenology of doing philosophy. For one thing, I don't really encounter ideas as pre-structured. In fact when I reflected on this I realised that I have a somewhat dualistic picture of doing philosophy. There is, it seems to me, the activity of having ideas. And then there is the idea of me producing philosophy. I suspect this reflects poor self-esteem in some sense, but it doesn't really seem to me like the things that inspire me and make me able to work, and the things that I qua philosopher produce, are all that similar in type. Instead, it feels to me like there is a vast unstructured I-know-not-what that I may sometimes interact with through various interlocutors and texts and films and walks in the rain and the like, and through making myself receptive to this I am thereby provided with the means to engage in the workman like day to day activity that I engage in. What I produce will be small and structured, but that is a symptom of its artifice and artificer, not reflective of its ultimate source. I also feel I have somewhat different relationship to philosophy as a social activity; there's something frenetic, if not frantic, about philosophy as PW experiences it. (He writes about this aspect at length and movingly in the blog post above; you really should check it out!) Whereas for me philosophy is something that is done socially, but as a calm and calming and collaborative activity.

Following PW's lead and making my phenomenology of philosophy into something visualisable (and somewhat inspired by my advisor) I wrote a haiku:
Ocean of reason
laps gently against the bay;
castles in wet sand.
Have a Merry Christmas, and see yinz in the new year!


  1. Thanks for this Liam. It's nice to see someone else doing phenomenology of philosophy. I've just got two points to add.

    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.

    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.

    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 :)

    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.

    Long live the ocean of reason, and all who swim therein!


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