If we assume logic is correct, does it imply that our consciousness processes real information?

Question

[major edits] Even if our consciousness is an illusion (even in the sense Denett suggests), the mere fact we see some information flowing across the universe means there is at least something that creates the illusion. That something is real - even though it might be only as real as a hallucintion (it exists). And if we can make our thought constructs, we can work with this information that makes what we are.

The obvious problem here is that if we think about our minds being simulated, we cannot see into the logic of the "real" world (world outside the Matrix). That's because in our world, we know that we can simulate only logical things (nothing illogical exists=is real) but we cannot know this is right from the "real" world.

But clearly the mere fact that we can think about this concept of the "real" world means something in our logic system.

So let's assume the logic we know indeed governs this universe. From this fact we know that our thought constructs (what we think consciousness is) are real (/hallucination-real).

And if our thought constructs are real, than cogito ergo sum is real - our simple logic "if something exists, than it exists" (Hilbertian axiom a→a).

Doesn't it prove that if our logic system is true, than we exist?

I understand this might be an awfully broad question, so I'll be grateful for any references.

Answer 1

Logical systems cannot define themselves, as Tarski and Gödel demonstrated. 'X=X', the classical law of identity, is actually a 0 information law as it is a tautology.

Are you embracing some notion of permanent existence? No single 'thing' has ever been observed to not decay, even protons and black holes disappear. Direct observation pushes one to accept, or at least infer, impermanence at every level. Observer dependence for accurate, though frame-dependent information leads to QM and the relational anatta that solves EPR (if we skip the preamble and head strait for https://arxiv.org/pdf/quant-ph/9609002.pdf, https://arxiv.org/pdf/quant-ph/0604064.pdf and https://ia800400.us.archive.org/4/items/NagarjunaTheFundamentalWisdomOfTheMiddleWay/Nagarjuna%20-%20The%20Fundamental%20Wisdom%20Of%20The%20Middle%20Way.pdf)

Logic (and mathematics) is a tool for inference, useful as direct observation is not possible for every thing. It can model experience accurately, subject to having been built as an accurate linguistic description of the system it seeks to model.

Answer 2

Does existence of logic imply something has to exist ?

We have to start from a reasonable view of what logic is: we may say that logic is the study of the properties of reasoning. Reasoning in turn is an activity of thought, in which conclusions are drawn inferentially from assumptions.

If so, logic is a human activity, and thus its "existence" presupposes the existence of the human mind and probably also the existence of human linguistic practices, like that of making arguments.

Answer 3

This sounds a lot like Cogito Ergo Sum, which you already mentioned. The thing is Cogito Ergo Sum is already supposed to prove your existence. It stands to reason that for a question to be asked (Do I exist) then there would have to be someone asking it. You can use this as evidence of the existence of a universe as well, as it it stands to reason something must exist, or there would be nothing to think the thoughts you have, or make the perceptions.

Answer 4

Doesn't it prove that [...] th[e]n we exist?

The big issue here is that you have not defined "we". If "you" refers just to your thoughts, then 'you' exists, sure. The question of whether it is an illusion is orthogonal to whether it exists. Most people use "you" to refer to more than your thoughts; presumably you also have a physical body and free agency and so on, and all those are not guaranteed to exist by merely the 'you think thus you exist' argument.

In short, you think, thus your thinking exists. Sure. Nothing more than that can be concluded from that pithy argument. There is no need to bring in the issue of "logic", and even more so it has absolutely nothing to do with the propositional tautology A⇒A.

By the way, it is always amusingly ridiculous to see people talk about 'simulation' type of hypotheses, because ultimately we should simply think about the entire reality. What's the point of saying that the rules governing the world we are in may not be the so-called 'true' rules just because our world is simulated? As you probably realize, the reality as a whole is governed by some rules whether or not we can figure them out. If we are in a simulation, that simulation is still part of the (larger) full reality, and hence unless there is good evidence of phenomena that are most easily explained as artifacts arising from a simulation, the simpler explanation that there is no simulation is simpler and therefore preferable.

Answer 5

"Doesn't it prove that if our logic system is true, then we exist?" Your question is quite broad, I will note some possible areas of exploration:

1. First, your notion of proof: Generally, we understand a notion of proof with respect to a logical system. Thus, you are presumably formulating this question with respect to a logical system, perhaps the "correct" logical system (if there is indeed one).
2. Given that there is a correct logical system, you claim that this logic system is "true". Two points. First, logical systems are not in general "true". "Truth" is not a property of formal systems. Logical systems can be "complete", "sound", "decidable", etc... but "True" is a bit harder. So what then is truth? This is a controversial question, so I delay answering it here.
3. We can say at least one thing about your logical system: since you appear to be able to formulate it ( you are asking a question about it in itself), your logical system must have the ability to self-reference! So it is quite powerful- perhaps powerful enough to generate paradox. If this is so, you can get your answer for free, but this may come at quite a high cost.