Is the bootstrap paradox worse than Lewis admits? An argument I can’t find in the literature
I’ve been going down a rabbit hole on the bootstrap paradox and developed what feels like a stronger objection than the standard Horwich “inexplicability” critique. I want to know whether (a) this argument is already out there and I’ve missed it, and (b) whether it has obvious holes.
The standard debate: Lewis (1976) says closed causal loops are internally consistent, every event in the loop has a local cause, so there’s no logical contradiction. Horwich says loops require inexplicable coincidences. Smith replies that given the loop’s existence, nothing is left unexplained. The debate mostly stalls there.
The argument I’m not finding addressed: the problem isn’t internal consistency or explanation. It’s what I’m calling the initialization problem. Self-consistency is a property of the loop given its existence. It says nothing about whether the loop can be instantiated within a universe that already has an established causal history.
More precisely: take a universe U with a cosmological origin, governed by conservation laws, where causal processes are in principle traceable back through the prior history. Now suppose a bootstrap loop involves an object O whose worldline forms a closed curve in the spacetime manifold, topologically isolated from the prior causal history H(U, t1). No continuous worldline from within H(U, t1) leads to any stage of O. The total mass-energy configuration across temporal slices at t1 minus epsilon vs t1 plus epsilon is discontinuous in a way that the prior causal history cannot account for.
The loop is not merely unexplained. It’s uninitializable: there is no possible world that shares our universe’s causal structure and contains a genuine bootstrap loop, because inserting the loop requires matter and information to exist in the causal order with no causal ancestry within that order.
A strengthened version using what I’m calling the sui generis stipulation: suppose the loop-object is unique in category, meaning no manufacturing process exists or has ever existed that could produce it. Then not just the form but the matter itself has no causal history in U. This closes the escape route of saying “the atoms are old, only the arrangement loops.”
Two moves against standard responses:
Against Lewis’s infinite chain analogy: infinite chains don’t require any particular object to appear without a causal ancestor. Every slice of an infinite-chain universe is accountable by the preceding slice. A bootstrap universe has exactly one slice, the insertion point, where this fails. Lewis’s analogy operates at the cosmological level; the initialization problem is local.
Against the Boltzmann objection (if time is infinite, fluctuations make anything probable): a Boltzmann spectacle has a causal ancestor, namely the vacuum fluctuation itself. The bootstrap object has no causal ancestor at all. The distinction is topological, not probabilistic. Infinite time dissolves probabilistic barriers but it doesn’t dissolve topological ones.
My questions: Has this specific argument, focusing on causal graph disconnection rather than inexplicability, been made in the literature? I’ve found Lewis, Horwich, Smith, Wasserman, and Smeenk and Wuthrich but haven’t seen it stated this way. The obvious Lewisian response is that we’re begging the question by demanding linear causal ancestry. Our response is that we’re not demanding linear causation, we’re demanding causal connectedness: the loop’s causal subgraph G(L) is disconnected from G(H) at a location in the causal future of H(U, t1) where disconnection is physically prohibited. Does that work? And is there anything obvious we’re missing?