pete wolfendale on X: "For anyone who wants to know why I want to burn down ...

[OP]

For anyone who wants to know why I want to burn down Oxford style analytic philosophy and then salt the Earth, here's a thread for you. It covers: vagueness, time/space, coalgebraic modal logic, thermodynamics, Leibniz’s God, David Lewis, quantum mechanics, and God *as* dice.

[1]

Someone on the other site asked me why I hate Timothy Williamson, and this was my response, suitably compressed for changes in char limit.

[2]

I hate epistemicism about vaguenss with a burning passion, because it’s the one solution to the problem of vagueness that says “Nuh uh!”. I’m all for dissolving false problems, but it doesn’t even rise to the level of an actual dissolution, because that would require an analysis.

[3]

I also hate possible world semantics, the continued dominance of set-theoretic model theory, and the uncritical slippage between said model theory and metaphysics qua first philosophy that plagues analytic philosophy, and TW is the living avatar of their paradigmatic unity.

[4]

It’s worth noting that I think all these things are connected insofar as empirical vagueness is at root an essentially temporal phenomenon. You can see this if you look at choice of thermodynamic macrostates as a lattice of predicates on the microstates (via Stone duality).

[5]

The supervaluationist idea that there are multiple precisifications of the same vague predicate is manifest directly in the physics of entropy: in the arbitrary (or non-deterministic) choice of micro/macro mapping (or equivalently, the alphabet in Shannon information).

[6]

Another way to get an intuition for this is to read Lawvere’s analysis of the Banach-Tarski paradox, where he motivates his account of cohesive structure in statistical terms. The right way to read this is that a real sphere can have different energy states/temperatures.

[7]

A material sphere has an actual dynamic threshold at which its spatial structure will begin to decay and then blast apart. The point-set sphere is one that has always already exploded, and this is why you can reassemble the bits into two separate copies.

[8]

If you want to then connect this back to the problems with analytic natural semantics and its corresponding confusion between metaphysical speculation and finding the most convenient set-theoretically tractable truth-makers you can find, it’s all about coalgebra.

[9]

Kripke frames have long been understood to be a form of F-coalgebra, and this fact was used to provide a full generalisation of modal logic via Stone duality, treating the space of points as a space of states and grasping modal operators via functors on this space.

[10]

This is a true successor theory to Kripke's because it not only unifies non-standard modal logics, van Bentham’s theorem, the modal-mu calculus, and the dynamic logics that overlap analytic epistemology and computer science, but break the stranglehold of ‘worlds’ as states.

[11]

Universal coalgebra unifies discrete state transition systems like automata and continuous dynamic systems at the intersection of analysis and physics. In each case it gives us a generative account of the dynamics, distinguishing the flow from the output behaviours.

[12]

This just is Deleuze’s notion of the virtual. Instead of treating time as a dimension along which state varies (chronos), you see it as the dynamic interface where the past state determines future state (aion). This is mathematically and metaphysically compositional.

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This is vastly superior to PWS, which makes a big deal of being syntactically compositional, but is in truth semantically holistic. The whole possibility space of the entire world is individuated in two ways, one spatial and syntactic and the other temporal and semantic.

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A world considered as a complete and consistent set of propositions about its current state is syntactic/spatial. It is an illegitimate overgeneralisation of a way of recording present state in certain very well behaved discrete systems with point like states.

[15]

A world considered as a complete and consistent historical trajectory over such states is semantic qua final-coalgebra of some functor over the syntactic state space (the micro/macrostate division or the Shannon alphabet of the signal channel through which you observe the world).

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This means the world trajectories are the set of behaviours of the world considered as an open system with a single causal input from the outside, and the task of understanding the world is compressing the observational state space into the hidden state of the signal generator.

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What this does is to give a maximally coarse-grained and non-compositional reading of computational/causal non-determinism. Everything is packed into the RNG signal travelling through the open port at the beginning of time, from the place where God plays with his dice.

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This is Leibniz’s universe, and he saw it more clearly than Williamson or Lewis. Completeness, consistency, and the Leibniz laws governing identity imply that you can to determine which world you are in from the full state description of any one (untyped) thing within it.

[19]

The choice of actual world is given by God’s benevolence. He loads the dice in favour of the most information that can be squeezed into a causally complete+consistent world, which is essentially a version of the Neoplatonists’ conception of beauty as harmony taken from Augustine.

[20]

It’s worth noting the relation to thermodynamics. It fixes the microstates to the point that they are not just perfectly observable but without any sort of randomness. Brownian motion gets deterministically smoothed out even as it is rendered in non-explanatory Humean terms.

[21]

Lewis fixes the microstates (in a ridiculous way: cf. Ladyman & Ross) and thereby makes quantification over macrostates maximally vague. The predicate lattice deals in complete branches of worldlines rooted in the present, over bisimulations quantified by proximity of worlds.

[22]

There are many sins here, but the original one is treating observation as if it can be in principle perfect and stretches down all the way to the microstates themselves. No vagueness of microstates means no hidden state, which means observation is not itself causal interaction.

[23]

Quantum mechanics was always embarrassing for Lewis, insofar as he had to make clear his possible worlds are not Everettian ones. But I think this is more or less false given that his counterpart relation is bisimulation between branching behaviours with the coalgebra forgotten.

[24]

If you want possible worlds qua total world states and total world behaviours, your choice is either an open system with an RNG channel that chooses the world (God is Dice), or a closed system that is epistemically fucked (neither causation nor observation make any sense).

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The alternative is coalgebra qua compositional semantics of the non-deterministic behaviour of coupled open systems. This means accepting vagueness into your heart as a real, thermodynamic feature of the world whose logical correlate is suspending indiscernibility of identicals.

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And this is why Gareth Evans smug one page paper refuting the possibility of vague objects is the perfect encapsulation of everything bad in (Oxford style) analytic philosophy, as it deploys the indiscernibility of identicals without even fucking listing it as a premise.

[27]

TW is simply the living avatar of Oxford philosophy on Earth, and its peculiar ignorance of anything outside Boolean logic/set theory. It’s my ambition to one day drop a mathematical proof on Oxford from orbit so weighty it finally obliterates all traces of the cursed paradigm.

[28]

P.S. I should note that Lewis’s own triviality result regarding embedding conditional probabilities into Boolean algebra should be commended for tracing the problem with causality and non-determinism from the other side of the Stone duality. Would that he’d seen the full story.

[29]