Here's a proposition (presented to me originally by Ben Hijink about a year ago) that some might argue challenges the limits of logical positivism:
Proposition One: We are all living in a computer simulation.
As a transhumanist, the idea of life in simulation is a familiar one. We could theoretically create intelligent life in a simulation (even if it's just a simulation of human cells), and control the universe of the simulated life as we wished. If we wanted, we could also guarantee that no experiment performed in the simulation ever gave the game away.
Star Trek: The Next Generation had an epidode entitled Elementary, My Dear Data that featured just this scenario. A computer simulation of Professor Moriarty becomes self-aware and eventually comes to learn that he is running in a simulation. Of course, Moriarty discovers his situation because the simulation isn't perfect (dang holodecks!).
Let's look at a refined version of the proposition:
Proposition Two: We are all living in a perfect computer simulation.
Here, perfection is in the sense that we can never find out that we are living in simulation on our own, and that the owners of the simulation will never reveal their secret. A logical positivist would say that this proposition is meaningless because no experiment the we ever perform will falsify, or confirm the proposition.
Yet, the creators of the simulation know that the proposition spoken by us is actually true because they built our universe. To the owners of the simulation, our proposition seems meaningful. You're probably beginning to see why people think this argument might have some relevance to the religious debate.
Can it be that logical positivism can claim that propositions are meaningLESS in sub-universes, but meaningFUL in enclosing universes?
Well, not exactly. While the creators of the simulation can say that Proposition Two is meaningful for the occupants of the simulation, they cannot say that Proposition Two is meaningful for themselves. The creators could themselves be living in perfect simulation!
The creators have built a mathematical system in which Proposition Two is meaningful, but outside of that system, the proposition remains meaningless.
Let's now return to Proposition One. Proposition One is very different than Proposition Two because it opens the possibility of transference of existence between simulation and the "real world."
Suppose we build our own simulated universe. In principle, we could see into the simulation we built, and we could give the occupants of that simulation a view of our world. For example, inside the simulation, the link to our universe might appear as a "magic" artifact. However, we can do better than this. We could create a portal into our universe. Upon passing through the portal, a simulant becomes wired into a robotic body, with the robotic sensors mapped to the simulant's senses.
Of course, we could also do the same in reverse, and transplant a person from our universe into the simulation. The idea of "uploading" people into computer systems is not implausible, and is frequently the topic of debate at transhumanist conferences. You just scan the person into digital form and simulate the action of their molecules.
We can now see that the premise of this scenario is that our intellect is independent of whether we are running on real atoms or on simulated ones. Our essence is information and computation, and the means of data processing is largely irrelevant. For the purposes of this debate, the barrier between the real world and the simulated world is not significantly different from a steel barrier between similar physical entities.
Clearly then, logical positivism must accept Proposition One as meaningful.
How does this affect the status of religious arguments under the principle of verifiability?
It doesn't. Proposition One is a purely scientific proposition. Propositions that explain UFO's in terms of alien spaceships are also scientific. Claims that bigfoot and the yeti are "missing links" in human evolution are scientific, too.
So, to the extent that a religious claim is a scientific, naturalistic claim, logical positivism is willing to accept it. This has always been the case.
However, most religions will never accept this. Their deities are beyond science and reason by definition. Such religious claims are meaningless because they insist that no experience can ever alter the probability of their being true. After all, who wants to worship the Klingons, even if their technology does look like magic to us?
Out of curiosity, is Proposition One metaphysical? Can a proposition be metaphysical and scientific at once?