But in order to answer the claim that our senses merely “organize” things and don’t really say anything about reality, you answer: “Remarkably, this ‘game’ simply works. Again and again, the use of these ‘arbitrary’ rules leads us to theories and laws of nature that are confirmed in laboratory experiments.”
According to what you’re writing now, one could simply reject that claim and say that only our senses themselves—about which we indeed do not trust them regarding reality—show us the results/conclusions of those experiments.

But that too is a result obtained from the senses. How do you know it works? Because the senses tell you so. It really is remarkable that this happens, but Kant, for example, argued that there is no wonder here, because it follows from the structure of our cognition. I argue that there is no indication that there is a correspondence between our cognition and our thinking, and therefore his explanation is not plausible. The wonder remains in place. The explanation I propose is that this really does reflect reality, and that we have the ability to perceive it.

So if I understand correctly, there are 3 ways to deal with this problem:
1. To say that the fact that the senses reflect reality is simply an axiom.
2. To say that there is no correspondence between the senses and reality (is that what Kant says?), and everything we experience is a kind of separate reality that is explained by our cognition.
3. To assume that there is an intelligent factor that coordinated between our senses and reality (one of Leibniz’s proofs for the existence of God, if I’m not mistaken).
Did I understand correctly?

Because I’m watching a TED lecture now by a neuroscientist who talks about this, and he says that we’re basically hallucinating all the time and that there is no connection between what we experience and real reality (that’s what I meant in 2).

1. An axiom is not an explanation. The question is why accept it.
2. Kant says there is correspondence. The cognitive picture is a product of what exists in reality. But we interpret it in accordance with our a priori categories. The quality of that interpretation is a result of the action of the Holy One, blessed be He.

Scientists of that type say quite a lot of nonsense. In some cases they don’t really understand the philosophical meaning of what they are saying. Take such things with a grain of salt. We are not hallucinating in ordinary life (except perhaps at certain moments). That’s nonsense. We represent reality through the tools of cognition and in our own concepts.

So basically, if someone wants to assume that the match between his cognitive picture and reality is accurate, he has to assume the existence of something that coordinates between them (God)?

But then one could say that if you simply assume that someone coordinated between our cognition and reality, you could just as well assume that our cognition fits reality. Why prefer one assumption over the other?

This is the proof from epistemology that I presented both in Two Wagons and in other places as well (The First Existent). Though one should note that the main fit for our needs is not between the cognitive picture and what it reflects, but between the generalizations and processing that we do and reality. See there for details. I also answered your last question there. This is the root of the difference between a theological proof and a philosophical one. One indeed assumes that there is a fit, and the question is what that assumption is based on (or: how did it come about).

The senses do not reflect reality.
In reality there are electrons or fields or whatever it is; the senses don’t see them.

So the purpose of the argument is basically to show that anyone who relies on the fit between his cognition and reality is actually a “hidden believer”?

Exactly right.

Excellent. If we are in a state of doubt regarding the accuracy of our cognition, do we have any reason to prefer that it is accurate (and the existence of God) over it not being accurate? Other than the fact that otherwise the discussion gets stuck?

And if we assume, for example, that God exists (just so we can continue the discussion) without proofs, because such proofs can’t be brought before clarifying the nature of cognition—what is the difference between assuming that God exists without proofs and simply saying that our cognition is accurate without proofs?

Thank you.

There is definitely a difference. To say that our cognition is accurate without proofs is absurd. Because a system that is built just like that will not come out reliable. But assuming that God exists without proofs can be based on direct acquaintance (there is no obstacle to saying that He exists). I have discussed all this at length in The First Existent and in the notebooks. We’re repeating ourselves. I suggest stopping.

But direct acquaintance also relies on cognition being reliable.

No. It is not sensory cognition but intellectual cognition. Intuition. I have elaborated on this.
Trust in the senses is itself based on assumptions (that the senses are reliable). Therefore those assumptions cannot be grounded in the senses.

Yeah, but intuition too, or anything of that sort, ultimately assumes that cognition/senses/intuition is accurate.

And on what basis does he assume that? After all, that is absurd on its face!
I’m done. I won’t answer anymore.