Once again, Spellbound posts a jargon-filled cut-and-paste that he almost certainly doesn't understand, presumably because it sounds "deep" or something.
"It might be objected that the CTMU, being based by definition on the human cognitive syntax, already resides in each of our minds and thus represents no informational gain.
That would be a good objection. This 'CTMU' seems to just be an analogy with human natural language, attempting to turn linguistic principles like 'syntax' into metaphysical principles that supposedly tell us something about the fundamental nature of reality. One can (and should) ask what justifies that metaphysical leap.
But this syntax is not so easily formulated within itself, and equating metaphysical reality to it is neither obvious nor simple. As explained above, a net informational gain comes from freeing information once "locked up" (artificially isolated) within U*-pseudotautologies and the scientific and mathematical theories implicitly based on them.
That just piles incomprehensible jargon atop the original question. "(artificially isolated) within U*-pseudotautologies"? Perhaps Spellbound can explain to us what that means.
What's a 'tautology', Spellbound? What's a 'pseudotautology' and how is it different from a 'tautology'? What does it mean for information to be 'isolated within' a 'pseudotautology'? (Isolated how and from what?) What does it mean to say that isolation is 'artificial'?
Now that we have the essential picture
We do??
let's try for some detail. Let Ui, be that part of a generalized universe U* to which we refer as the physical universe, or the set of all things directly observable by Ui-observers. This is a recursive definition in which Ui is defined on Ui-observers and vice versa, and varies with choice of subscript.
Ok, that's sorta clear if we assume that when Langan says "the set of all things directly observable by Ui-observers" he's talking about Ui and not U* (what does 'generalized universe' mean?) and 'Ui-observers' means individual observers (human or otherwise).
But I'm not entirely comfortable with defining "the physical universe" in terms of observability.
Subscripts correspond to cognitive equivalency classes within U*, or sets of observers sharing the same information-transductive syntax.
"Information-transductive syntax"? Langan seems to be conceiving the epistemic conditions that determine observability in terms of his underlying linguistic analogy. In my opinion it probably makes more sense to look at whether and how the thing observed physically interacts with the observer, and to the observer's conceptual resources.
Ui consists of that part of U* specifically decidable to Ui-observers, and is mathematically equivalent to the cognitive class itself.
Langan has already said that Ui is what we call physical reality, right up above. Then he defined that in terms of observability. Now we are supposed to understand both in terms of decidability? Is it plausible to say that physicality is a matter of decidability? Isn't decidability something that applies to propositions about physical reality, not to physical reality itself? Decidability seems to be more applicable to identifying and naming what's observed, or deciding whether propositions that make reference to those things are true.
The assertion that the physical universe (or the universe of observables) is "mathematically equivalent to the cognitive class itself" seems to me to just be false. It isn't clear what "the cognitive class itself" means, but assuming that if refers to the class of propositions which can possess truth values, it would seem to consist of things like ideas, linguistic and mathematical expressions, not physical objects. It would also include imaginary, hypothetical and counterfactual propositions propositions which have no physical world reference at all.
Assume that the class Ui is human.
Why? Space aliens can't observe or things
or perform cognitive acts?
Aristotelian metaphysics is universal, containing in principle all Ui-relevant information (Ui-potential) U*.
Why name-drop Aristotle here? It's questionable how successful Aristotelian metaphysics is at being a general theory of being itself.
A theory of metaphysics M is an open inferential system
Aristotle never gave his metaphysics the deductive form of Euclid's geometry. So it must not be a theory of metaphysics as Langan defines it. It isn't really an 'inferential system'.
which, because necessarily universal, reduces to a Ui-recognizable tautology T on U* heritable in M via generalized rules of inference (where "generalized inference" is just logical substitution).
Since when does a theory of metaphysics have to reduce to a tautology? In formal logic, tautologies are expressions that remain true no matter what truth value assignments are given to their variables. Negating a tautology results in a self-contradiction. So I guess that it's tempting to try to use them as axioms in a metaphysical system. Some philosophers have thought of them as a-priori knowledge and have tried to construct entire philosophies around them. Logicism in the philosophy of mathematics holds that every true proposition of pure mathematics is a tautology.
But the classic difficulty with that is that a tautology is true by logical form alone. Since it doesn't exclude any logical possibilities, it is are said to be uninformative. If a tautology's truth is independent of what is true or false about the rest of the world, it doesn't provide us with any information about the world.
As specific information equates inductively to ancestral generalisms,
What does the phrase 'equate inductively' mean? What does it mean for 'specific information' to 'equate inductively' to 'ancestral generalisms', whatever they are?
and U* is both unique and Ui-indiscernible from T, the identification M = T = U* is practically unconditional.
This appears to be a simple assertion of Langan's grand conclusion. It still isn't clear why anyone should believe it.
What does 'Ui-indiscernable from T' mean? And how does one get from U* being 'Ui-indiscernable from T' (assuming just for the sake of argument that it is) to equating the universe U* with M and T (which presumably mean Langan's theory)? How does Ui-indiscernable turn into identity?
Langan now attempts to argue that there can only be one metaphysical theory (namely his own).
Now suppose that there exist two Ui-distinguishable true metaphysical theories M and M’; i.e., two Ui-distinguishable Ui-tautologies T and T’. These can only be Ui-distinguishable by virtue of a nonempty Ui-informationa1 disjunction
Penetrating the jargon, he just seems to be saying that if there are two different metaphysical theories, there has to be some difference between them. Ok, lets accept that.
This information d, being the distinction between two Ui-perceptible truths, exists in Ui and thus U*. But as it is disjoint information, one member of the pair (T, T’) does not contain it. So this member does not cover U*, is not a U* tautology, and thus is not a theory of metaphysics.
As far as I can see, he's just saying that two different metaphysical theories will say different things about reality and they can't both be right.
I don't think that's persuasive. For one thing, it's possible to imagine two theories that produce precisely the same propositions about the observable world, but advance them for very different reasons. They might imagine very different processes at work and posit very different unobservables. If they are mathematical, they may take very different mathematical form. (One is reminded of Schroedinger's wave mechanics and Heisenberg's matrix mechanics. I've heard that Feynman's sum-over-histories method produces the same results too.)
Even if we accept the questionable proposition that two different theories can't both be right, that doesn't exclude the possibility that they both are wrong.
And Langan produces his grand conclusion like a rabbit out of a hat:
So the assumption fails, and there can be only one correct theory of metaphysics at the tautological level. This, by definition, is the CTMU.
