Is it possible to simulate a reality like ours using other logic than classical logic?

Question

Are there alternative logical systems that could serve as a foundation for simulating a reality similar to ours, given that non-classical logics such as paraconsistent logic, while applicable in specific domains or philosophical contexts, are typically avoided for simulating complex, dynamic systems due to their potential for generating inconsistencies? I believe that while other logical systems may have utility, they might only be capable of modelling simpler phenomena to maintain consistency, rather than replicating the complexity of our three-dimensional reality.

Imagine we're trying to use paraconsistent logic to simulate a video game world where certain objects can exist in contradictory states. For instance, consider a virtual object that is both solid and transparent at the same time. In paraconsistent logic, this kind of scenario might not lead to an outright contradiction, allowing for the coexistence of contradictory properties.

However, in a video game, this could lead to confusing and nonsensical interactions. Players might be able to walk through walls that are simultaneously solid and transparent, which would break the immersion and coherence of the game world.

In contrast, a logical system designed for simulating virtual environments, like a physics engine using classical logic augmented with specific rules for handling object properties, would likely produce a more intuitive and consistent simulation.

This example highlights how paraconsistent logic, while valuable in certain contexts, might not be the best choice for simulating dynamic systems with complex interactions, like a video game world. Different logical systems are tailored for different purposes, and choosing the right one depends on the nature of the simulation being attempted.

Answer 1

Just to expand a little on Conifold's comments. Logic is not reality, it is something we use to help us describe reality and form representations of it. Logic helps us to organise information and render it into a compact and computable form. We are able to work with several different logics, and you are obviously aware that there are non-classical logics.

Logic does not itself simulate reality: for that we need a computer. Though of course we may well make use of logic when building a computer and writing a computer program to perform a simulation. A simulated game world might feature interactions that we would find confusing and nonsensical, but that does not mean that the simulation itself is inconsistent. The confusion is ours. If we perform the same interaction in a simulation and get different results each time, we might wonder what is going on, and we might even give up in frustration, but it doesn't mean the computer is itself inconsistent. More likely, the programmer is using a pseudo-random number generator.

Classical logic has become the most commonly used logic because it ticks a lot of boxes for features such as simplicity and expressive power. As you say, other logics have their uses for different purposes, but creating simulations does not seem to be one of them.

Incidentally, solid and transparent are not opposites. Solid, as a state of matter, contrasts with liquid, gas, plasma, etc. Or solid may colloquially mean impenetrable, so it contrasts with penetrable. Transparent contrasts with opaque or translucent.

Answer 2

Let's raise to the top a claim that Bumble makes: Simulation is modeling using computation. Both mathematics and logic are forms of computation, and in computer science, we are interested not just in the formal systems that encode computation, but the physical processes that undergird computation (SEP). You ask:

Is it possible to simulate a reality like ours using other logic than classical logic?

So the question is not can logic and math be used to simulate the physical universe (they are routinely in dynamical simulation for engineering), but can it do so completely perhaps leading off to the question of whether or not we can fully simulate our own physical reality. This is known as the simulation hypothesis. From WP:

he simulation hypothesis, as formulated by Nick Bostrom, is part of a long tradition of skeptical scenarios. When it was presented by Bostrom as not merely a philosophical speculation but an empirical claim with quantifiable probabilities, the hypothesis received criticism from some physicists, such as Sabine Hossenfelder who called it pseudoscience and cosmologist George F. R. Ellis, who stated that "[the hypothesis] is totally impracticable from a technical viewpoint" and that "Late-night pub discussion is not a viable theory." Versions of the hypothesis have also been featured in science fiction, appearing as a central plot device in many stories and films, such as The Matrix.

The question isn't is there a "best" logic capable of simulating physical reality. There are classical and non-classical logics and mathematical theories such as differential geometry that can be used to simulate just about anything you can think of. I've yet to see an argument that something that we observe as a physical phenomenon can't be at least somewhat accurately simulated. Rather, it's that phenomenon themselves are stochastic. How do you model something that is random?

In computer science, pseudorandom number generators (PNRGs) are used all the time. But they are not random. Therefore, one cannot simulate random phenomena with PNRGs completely accurately. Often, in strong cryptographic systems, physical phenomena are used to produce physical randomness which is mathematically secure in the same way as a Vernam cipher (the non-CSPNRG sense).

How do you simulate the randomness in the universe besides using the randomness of the universe? Is it even a meaningful question? And what of particles who obey wave functions? How do you simulate Heisenberg's uncertainty principle? Ultimately it may not matter.

Coming back full loop to the nature of physical computation, there are limits to the physical computers we build. This means, we have to ask about the limits of a computer for simulating the universe as we understand it. For instance, it is not tractable to construct an actual Turing machine, because such an abstraction presumes an infinite tape for computation. There are space and time constraints in computation and those are studied in complexity theory. There are constraints on computation itself and those are studied in computability theory. And to simulate the universe would ultimately requires more resources than the universe itself has. Consider how complicated and how much physical mass and energy a quantum computer requires to model a handful of q-bits. So consider this argument.

Every simulated particle in the simulated universe (ignoring the fact they're more accurately described as point-like disturbances in a field) would need to correspond to at least one particle in the physical universe as part of the simulator. Then, additional particles are required to handle the act of transforming the state of those physical particles from a prior state to a new state for simulation (in CS, we call those states pre- and post-conditions in descriptions like Hoare logic). But we've already exhausted our particles in correspondence with the simulation. Thus the entire universe cannot be simulated a priori.

But maybe some some subspace of real space can be simulated. That is what a video game does. But the question of simulation our physical reality doesn't reduce to a question of which logic, but rather, what resources to construct the simulator.

Answer 3

Is it possible to simulate a reality like ours using other logic than classical logic?

If by "classical logic" you mean so-called mathematical logic, then it does not "simulate" reality. To begin with, it does not even include a formal model of the implication (or conditional).

That being said, it is precisely the job of logic to simulate not reality per se but the perceptible environment of the organism, and so, essentially, the world around us, although science considerably extended its scope.

Logic is a cognitive capacity which allows the brain to make sense of perception data and to produce something like a simulated world, which we consequently take to be the real world.

Are there alternative logical systems that could serve as a foundation for simulating a reality similar to ours

I wouldn't recommend any existing so-called "logical system". None is remotely close to the actual logic of the human mind (or brain).

If you want a system of formal logic which is correct, you'll have to design it from scratch, or perhaps from Aristotle's syllogistic.

a video game world where certain objects can exist in contradictory states. For instance, consider a virtual object that is both solid and transparent at the same time. (...) In paraconsistent logic, this kind of scenario might not lead to an outright contradiction, allowing for the coexistence of contradictory properties.

Transparent and solid are not contradictory.

If two qualities are contradictory, no thing can have them at the same time.