Liron comments on Call for new SIAI Visiting Fellows, on a rolling basis - Less Wrong
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That's what I would expect most mathematical-existence types to think. It's true, but it's also the wrong thought.
Wei, do you see it now that I've pointed it out? Or does anyone else see it? As problems in philosophy go, it seems like a reasonable practice exercise to see it once I've pointed to it but before I've explained it.
Is this it:
In logic, any time you have a set of axioms from which it is impossible to derive a contradiction, a model exists about which all the axioms are true. Here, "X exists" means that you can prove, by construction, that an existentially quantified proposition about some model X is true in models of set theory. So all consistent models are defined into "existence".
A causal process is an unfolded computation. Parts of its structure have relationships that are logically constrained, if not fully determined, by other parts. But like any computation, you can put an infinite variety of inputs on the tape of the Causality Turing machine's tape, and you'll get a different causal process. Here, "X exists" means that X is a part of the same causal process that you are a part of. So you have to entangle with your surroundings in order to judge what "exists".