The idea that we are living in a simulation, or even that we are ourselves simulations (known as the “Simulation Hypothesis”) has hit the mainstream consciousness, with people like Elon Musk endorsing the idea. Though similar arguments are old, the modern version is driven by the apparently looming advances in technical ability. For instance, Nick Bostrom frames his argument as a trilemma:
But all such arguments are necessarily flawed: they are necessarily self-undermining, because any argument that purports to show that we are living in a simulation must undermine itself by removing the premises on which that argument must lie. Our very logic is unreliable if we are merely simulations.
To see this, consider a computer program performing bitwise math, calculating the sum 2+2. This procedures is broken into multiple operation and performed over multiple cycles. A programmer could step through each operation, and the last one, change the answer to read 5 instead of 4. To the program, nothing would seem amiss: its only perception of time is the ticking of the cycles, and it could only spot a flub with another logical process that could be similarly thwarted by a programmer.
Likewise, any logical argument we can produce could be mislead if we are living in a simulation. No conclusion is reliable, because the simulators could simply intervene to change our conclusions in ways that are necessarily imperceptible to us. So the conclusion that we are in a simulation is necessarily unreliable.
Therefore, no argument can reliable show that we are living in a simulation.
Now, we can’t reliable conclude that we aren’t in a simulation either, granted. But that is the nature of deeply skeptical arguments: you can’t really proceed beyond them, because the tools of argumentation are themselves stripped away. The truth or falsity of living in a simulation is an unanswerable question, by its nature.