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Physicist John Wheeler proposed a model of the universe based on "It from Bit" asserting that the world is fundamentally information.

I've been told both that Wheeler's It from Bit is compatible with inconsistency (for example, the bits in "It from Bit" could be arranged in inconsistent ways and thus inconsistent realities would exist)

Or, for example, in this article (https://www.utpjournals.press/doi/pdf/10.3138/uram.20.1.61) which is related to Wheeler's concepts of "It from Bit"/"Participatory Universe"/"Pregeometry and Law without Law" it is said that universes with different logics could exist (in section 6.3.2.2).

Also, Wheeler's ideas (specially Participatory Unuiverse) is related to Strong Anthropic Universes, which is related with the idea of a multiverse with multiple universes governed by even different logics (for example, in John's Barrow book "The Constants of Nature" in chapter 13, he talks about a hypothetical multiverse composed of universes governed by other logics. Specifically, he talks about different approaches that physicists take when studying the multiverse, and he mentions a radical approach where even logic could change from one universe to another)

Also, since Wheeler's models are based on the concept that reality is information, since we can imagine and simulate (at least partially) inconsistent worlds in our brains and computers (which are basically patterns of circuits/neurons and informational processes) wouldn't that mean that information could also create an inconsistent world in Wheeler's models?

But I've also been told the contrary. For example, I was reading an article "The Tao of It From Bit" (https://arxiv.org/pdf/1311.0765.pdf) where this was said:

Just because we don’t have access to reality, but only to the bits, it doesn’t mean that there is no reality. Which possibility is simpler: (1) that the yes/no bits are consistent with one another, that the probabilities are correlated, and that’s all, or (2) that at any moment there is at least one possible reality, which ensure the consistency and the correlations?

For me, possibility (2) would mean that in an infinitely "ocean" of inconsistent realities there would be at least one consistent reality. I thought this meant that in Wheeler's model there would be a vast multiverse of inconsistent realities

But I contacted the author and he told me that this did not mean what I thought. He said...

In (2) I don't say " inconsistent realities would exist": The difference between (1) and (2) in my essay is that (1) just requires the propositions to be consistent with one another, as well as their consequences. (2) requires a mathematical structure to make this happen. Both (1) and (2) are consistent, but (2) is "more consistent", because (2) requires a mathematical model to exist which gives the same answer to those questions

So, what is happening here? Who is right? Did Wheeler tolerate inconsistent realities in his models or not? Does anyone know how did Wheeler treat/consider inconsistencies? Did he say that they did not exist or did he accepted them?

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"(1) just requires the propositions to be consistent with one another, as well as their consequences. (2) requires a mathematical structure to make this happen". By the completeness theorem, a consistent theory has a model, so there is no difference between these statements. Wheeler, like Tegmark, confuses physical existence with mathematical representation, so the question is basically moot.

– Conifold – 2019-06-11T00:42:29.033Certainly bait for philosophers of information :) You're right that Wheeler has an unusual (bizarre?) metaphysical view, and this complicates matters. His participatory universe is not quite the same as the anthropic cosmology of Barrow and Tipler, according to which the universe becomes self aware. Wheeler's participatory cosmology says that the subject-observer can actually create reality by querying. His 'It from Bit' is about asking binary yes-no questions using scientific apparatus. As Conifold says, there's a basic metaphysical disagreement about the nature of information to deal with. – Bruce Long – 2019-06-11T11:07:25.433

@Conifold Keep in mind that this "difference" was not made by Wheeler but by the author of the arxiv article I posted in my question... Also, from what I know Wheeler did not support the idea that mathematical representation=physical existence, again, is the author from that article who, basing his work in "It from Bit" concept, makes such claims. – inuflatze – 2019-06-14T16:02:18.340

@Conifold Anyways what I was asking was if there was some "evidence" that would indicate that Wheeler did propose that inconsistencies and inconsistent worlds could exist: He collaborated with Bohr in many occasions and he admired his work. Wheeler proposed the "it from bit" idea basing on Weizsäcker's ur-theory (which can reproduce Bohr's atomic model, which is inconsistent-paraconsistent) and also, he based his "It from Bit" idea on Bohr's complementarity principle (which has been interpreted as a paraconsistent principle by many authors). – inuflatze – 2019-06-14T16:02:28.910

@Conifold That's why I think that Wheeler would propose that inconsistent/paraconsistent worlds would exist, but I would need confirmation from someone who knows all of this better – inuflatze – 2019-06-14T16:02:34.090

1Confusing inconsistency of models (i.e. of descriptions) with that of the world itself is exactly what I was talking about. Neither inconsistencies in Bohr's model of atom, nor complementarity, are properties of the world, they are properties of our descriptions of it. If one wishes to talk about "inconsistent existence" they would have to explain what this means, and pointing to inconsistent models does nothing in that direction. Unless one simply means projecting inconsistent descriptions unto what they describe. But if one does that they "exist" trivially, you do not need Wheeler's say-so. – Conifold – 2019-06-14T21:48:47.623

@Conifold But in Wheeler's models one does not say "x exists", period (as Tegmark would say). Wheeler uses a pre-geometric model (en.wikipedia.org/wiki/Pregeometry_(physics)) where some kind of informational process (through entropy, quantum entanglement...etc) would produce the laws of physics (bits of information would describe an entire universe. This would be analogous to having a simulation of an entire universe: a program describes entirely a universe). This informational process could in principle create all kinds of possible laws and spaces... – inuflatze – 2019-06-14T23:00:00.900

@Conifold but since we can have informational processes representing inconsistent/paraconsistent models (for example, we can imagine, at least partially, how would Bohr's atom behave, and that thought would be nothing more than informational processes caused by our neurons), then, shouldn't it be the same for Wheeler's models? Couldn't we have a "pattern" of bits representing an inconsistent world (just as we can have a computer simulating or a brain thinking about an inconsistent world)? And if yes, then wouldn't that mean that inconsistent worlds could exist in Wheeler's models? – inuflatze – 2019-06-14T23:00:08.787

If Wheeler himself does not use "exist" then the question what "inconsistency exists" means is for

you, since you are using it. As I mentioned above, on the obvious interpretation the answer is a trivial yes: we can have a pattern of bits "representing" anything. You will not make it any less trivial by using the word "exists", or even by having Wheeler himself use it. – Conifold – 2019-06-15T00:14:35.947@Conifold I don't know what you mean with "If Wheeler does not use "exist"...". Maybe you misunderstood me. I meant that he does not just assume the existence of a universe without "justifying" it (for example, Tegmark assumes the existence of mathematical structures, but does not explain how do they come to exist. For him they just simply exist. But Wheeler proposed a mechanism where universes are created through informational processes) – inuflatze – 2019-06-15T09:04:04.083

The problem with both Tegmark and Wheeler is not that they do or do not explain coming into existence, but that they trivialize existence by equating it to a representation. Wheeler's "mechanism of creation" is just a play of words that amounts to just that. – Conifold – 2019-06-16T09:20:21.993

@Conifold oh, I thought you said that Wheeler, as Tegmark,said that only mathematical structures are real (Wheeler considers more than only mathematical structures). In that case yes. But then, and this is what I was originally asking, didn't Wheeler consider every bit-representation as a reality? Didn't he consider inconsistent information/representations of inconsistent things as realities? Didn't he consider that inconsistent realities would exist? In that case, do you know of any "evidence" (e.g a quote) where Wheeler considered that inconsistent information corresponded to real universes? – inuflatze – 2019-06-16T11:33:41.730