But what's outside the simulation could be quite different. And humans could always be mistaken about both what they think they observe, their observations themselves, and the conclusions they make from these.
At best its a matter of estimating probabilities (ie. educated guesses), and even there they're probabilities regarding appearances. It has been argued as far back as Kant (over two hundred years ago) that one can never get to the "thing-in-itself" that is behind those appearances.
There is not even a reason to believe that the "outer universe" has such things as space and time or information as we know it, and no way to know what a "computation" might comprise in such a situation.
Maybe the situation is not that pessimal, and an outer universe is much like ours, but to prefer that believe one would need evidence, of which we have none.
Consciousness -- as in the sheer fact of experience -- is itself the base "reality," out of which everything is made. If you examine everything you're calling "the universe," all you will ever discover is sights, sounds, thoughts about sights and sounds, belief (or certainty) that those sights and sounds are caused by something external, etc. What are all of those made of? Consciousness, of course.
In this reality, "brains" are the entities that consciousness has dreamed up to demonstrate correlations with conscious properties. In our reality, we therefore say that "the brain causes consciousness."
If you investigate your experience closely, you'll discover that the epiphanies "I exist," "I am conscious," "I am alive", "a world exists" all point to the same ineffable "miracle" of existence, the one "substance" of which all realities are made.
Upon hearing this, perhaps the mind thinks "just as there are realities that exist without time and space, why can't there be some without consciousness?" There's a very interesting answer to that question, but it won't come in the form of thoughts.
Of course, there's no reason to believe any of that. On the other hand, as the Buddha said, don't believe me....
I can make 2 + 2 = 5 in a simulation. That doesn't mean 2 + 2 = 5 outside of the simulation.
I'm not sure you can. Yes you can make a chest with 2 apples contain 5 apples if you put 2 more, but it's impossible (IMHO) to make it consistent. How many apples do you have if you place 2 chests besides 2 other chests and put 1 apple in each? What if you repeat the process 2 times and then another 2 times?
Also - when some things in physics aren't intuitive (QM for example, but even adding velocities in relativity) we don't think math is wrong - we think math doesn't apply in that way to this particular phenomena.
Taking it further, what if rules and logic, and by extension, math as we know it, is just a construct that is not applicable in the "real" universe. What if, in that "real" space, 7+7=5, or mathematical operations are not possible. What if causality and time dont exist?
And if sometimes its 5 - they will do what we did with relativity when it turned out velocities doesn't add up like they "should". We haven't changed addition - we changed the equations used in physics.
I guess you could hand-made an intelligent life that is designed never to discover the true math.
The act of putting things in boxes (after first perceiving and classifying them as discrete entities) and the abstract notion of addition are only as related as you need them to be for a given purpose.
Yes. That was my point. How would you change the abstract notion invented by creatures in your simulation if not by changing reality to shape their abstractions? And how do you change enough instances that their math develops in such way that 2+2=5?
I think our basic math (logic, set theory, integer math) with some exceptions (choice theorem) is the only useful consistent basic math there is.
I do not believe that to be true. While physics is heavily dependent on math, the reverse is not true.
> I can make 2 + 2 = 5 in a simulation.
No, I am fairly confident that you absolutely can not. You can make a simulation where putting 2 oranges in a box and adding two more oranges results in 5 oranges in the box (rather like putting together certain nucleons together into a nucleus results in a mass different than the sum of their individual masses). But in that simulation it would be a peculiar property of oranges, not a property of mathematics -- just as we don't claim addition is invalidated by the behavior of nucleon masses.