No logical positivists to be found. Such a lonely world. =(

How does the model allow for dark matter? Gotta know what it is to model it.

I see little connection between the historical tradition of logical positivism and what you call the "simulated universe theory". Logical positivism also has been called logical empiricism. It is concerned with clarifying the language of science while also assuming science to be grounded in experience for the meaningfulness of its claims; whether experience be understood in phenomenalist terms (e.g. sense data) or physicalist terms (e.g. intersubjectively and operationally defined physical magnitudes). This essential reference to experience goes missing in the the idea that our universe could be identified with the representational content of a simulation being run on some super-computer. The experiences logical positivists were talking about were experiences had (or performed) within the empirical universe, not representational states ascribed to it from without, as it were.

Yes, the phenomenological experiences you are talking about are simply put emergent properties of such a system. I think this concept get's confused a lot with what people take a 'real' or 'apparent'.

I think the connection is that the logical empiricism advocated by Russell and Ayer saw all ordinary things as logical constructions (out of sense data).

I think the connection is that the logical empiricism advocated by Russell and Ayer saw all ordinary things as logical constructions (out of sense data). — The Great Whatever

Although he was an empiricist and a phenomenalist, I would hesitate to rank Russell as a logical empiricist himself. It's true that his work on logic and meaning served as a foundation for logical empiricism, but so were the works of Frege and Peano. Whatever the case may be, consider Question's reply immediately above yours. He takes experiences -- i.e. phenomena -- to be emergent properties of some computer simulation (according to the "simulated universe theory"). This idea clashes with the logical empiricist idea that, as you say, the world itself is a logical construction from our phenomena. I think logical empiricists such as Carnap or Hempel would balk at the idea that our experiences are epiphenomena, or emergent properties, arising from of an unknowable underlying reality, which can't itself possibly be constructed on the basis of such experience. That is also something that Kant would reject as unintelligible -- a rejection which logical positivists rightfully inherited from Kant.

On edit: I think the idea of "experience" (or consciousness, or qualia) being some kind of emergent property from underlying physical processes -- an idea popular among some theoretical physicists and 'transhumanist computer-simulationalists', as I would dub them -- may stem from a vehicle/content confusion regarding mental representations. This is a confusion that is promoted by representationalism in the philosophy of mind, and effectively countered by newer externalist or embodied paradigms. Those newer paradigms (newer in analytic philosophy, anyway!) rightfully displace the theoretical concern from inert material representations (which are individuated in accordance with their intrinsic structures) to representational acts, conceived as situated actualisations of animal powers.

There really is no other way around it considering/taking into account Godel's Incompleteness Theorem, in regards to emergent properties from sound logical truths. There is nothing logically wrong with supposing that epiphenomena can arise from the totality of facts or the logical space that the universe is. However, I'm hinging this on unproven facts yet to be demonstrated by science. Specifically, the feasibility to human esk AI on computational machines.

But then again, counter Penrose and the quantum weirdness inherent in his propositions about the workings of the mind, if the human mind can be simulated via logical machines (emphasis being on the fact that there are no ground to doubt that conditional), then everything else follows.

I don't understand what argument you are trying to make, or what it is I have written that you may be disagreeing with (if anything). There is no mention of "Gödel's incompleteness theorem" (which one?) in you OP and I am unsure how you wish to connect this idea with the cogency of the "simulated universe theory", or its relevance to the thinking of logical positivists.

Sorry, if I wasn't clear.

Basically my point is that if the logical positivists have a contention with things such a 'qualia' or the subjectiveness of phenomenological experiences, then one can assert that some emergent properties of complex systems (such as the brain) are independent of logically derived outcomes, say some computer churning away. In essence, every logical positivist has to deal with Godel's Incompleteness Theorem, and it is my opinion that Godel's Incompleteness theorem can be referenced in apparent emergent properties that cannot be described within a complex system itself as the human brain with such things such a qualia...

Did I make more sense there?

The set of all things (the universe) can be understood as the sum total of necessary mathematical truths and physical laws at play. — Question

Even if that were true, why would anyone want to equate the universe to the sum total of "necessary mathematical truths and physical laws at play"?

I find it odd having finally dismissed the notion of a proof of God's existence that anybody should be replacing it with an argument towards proving the existence of a computer so utterly beyond our comprehension in terms of calculation speed, parallel processing, and complexity as to create a simulation of a Universe which includes life forms with sufficient (artifificial?) intelligence to posit that they might after all be simulations. After all if there is such a computer doesn't that rather beg the question of who built it and wouldn't that builder be God in all but name? Unless of course the builder is also a simulation within an even bigger and yet more complex computer in which case we seem to be on to a very familiar rocky road to infinite regression awfully familiar to those of us whose primary interest is the philosophy of religion! Scream when you want to get off the ride!

Because given our current understanding of the universe hinges on the logic of science, which then exclusively relies on mathematics and physical laws to describe how it functions.

Because given our current understanding of the universe hinges on the logic of science, which then exclusively relies on mathematics and physical laws to describe how it functions. — Question

Except that it doesn't. Even the most arrogant scientist would not pretend that science gives us a complete understanding of the totality of the Universe. The very existence of theoretical physics (or made up stuff which plugs the gaps as I prefer to call it) is testament to that. And life of even the least complex kind simply blows away any notion that the Universe is describable purely in terms of mathematics and physical laws.

A Universe governed entirely by physical laws is simply an ideal abstraction. An extremely useful one, no doubt, but an abstraction nonetheless for it takes no account whatsoever of acts of will by which those laws can be subverted or outright broken.

But it would be making a possible (but not the only possible) map the territory.