I've set it out multiple times, and you disagree with it each time. Your turn. Set it out for us, and how it goes astray. — Banno

That's right, each time I offer terms of interpretation, you assert that they are erroneous, and you reject them. Then you provide none of your own, simply insisting that your conclusion is valid and my interpretation is erroneous. So, I suggest that we proceed from clearly defined interpretive terms, whether they are produced by you or I does not matter to me, so long as we craft acceptable definitions.

Ok, then can you at least explain why Fitch and others think it a paradox? Why is it worthy of it's own article, in the Stanford Encyclopaedia, in Wikipedia, in Oxford Academic, and so on. What is it that the folk who wrote this stuff think is happening? — Banno

It seems to me like the paradox appears to these philosophers because they are making the mistake of assuming that the model modal says something about the real independent metaphysical world, when it does not. The separation between the "modal actual world", and the "independent metaphysical world" makes the semantics of terms like "know" and "true" extremely difficult and ambiguous.

So, to sort out the apparent paradox requires that we clearly define such terms, and adhere strictly to the definitions. I will make a proposal for definitions here, but you are free to reject them and offer your own. The point is to have rigorous terms of interpretation. Remember, from the SEP article on possible worlds, there is no extensionality inherent within the modal model, true extensionality is provided only by the interpretive terms. This makes interpretation extremely important, and produces the possibility of significant flexibility, if the interpretive terms are confusing or ambiguous.

Here are my proposals. "True" signifies a judgement which is made concerning a proposition. It is a very specific type of judgement which is incompatible with the judgement of "false", the opposing judgement of the very same type. To "know" a proposition means that a judgement of this type has been made, the proposition has been judged as either true or false. Note, that for the sake of the modal model we must allow for both judgements, "p is true", "p is false", to adequately represent the possibility of knowing p.

Lets now consider the meaning of the follow two propositions:
1. If p then p is possible.
2. If p is known then it is possible to know p.
The first implies that if p is true (has been so judged), then it is possible that p is true (has been judged that way). The second implies that if p has been judged as either true or false, then it is possible that p has been judged as true or false.

Due to the likelihood that you will not agree, and would prefer to use your own definitions, I will not proceed further with the analysis at this time. If you agree to the definitions, then we can continue, if not, then you can produce alternative definitions for these terms, and we can proceed from those definitions.

In the end, the question becomes a cry for god — Christoffer

This has not been my experience. I recognize that reality may consist of planes that I am unable to detect, but I believe they would be as "natural" as what I am able to experience.

I am having some trouble following the logic of your reasoning, which appears to be this:

1. Human senses are limited.
2. There may exist parts of reality humans cannot detect.
3. It must be god.

1. Human senses are limited.
2. There may exist parts of reality humans cannot detect.
3. It must be god. — Questioner

First two correct, but not the third. What I meant is that the act of asking the question in the way the OP does, is a form of cry out for God. It’s a cry out for a meaning beyond the reality we have. My argument is that this kind of question is a form of circular reasoning in which the usage of the fact we face a hard limit to know the unknown conditions beyond our bubble of reality, becomes the reason to question if “this is all there is”. The question rather expose the intention underneath to be about the fantasy of something beyond our reality, rather than engaging with the possible scientific reasoning about what would likely exist outside our reality.

And with the example of the holographic theory, the problem we run into if we entertain the question scientifically is that the conditions of our reality makes it impossible to comprehend any other reality and likely impossible for that reality to comprehend our own.

Reality is not the same as our bubble of the universe, it is the definition of the parameters that allows this universe to exist. If those parameters change or are different, it not only changes the resulting universe, but also perception itself, leading to a hard limit for which there is no comprehension of the other.

So, I’m not talking about “God”, but that the way the question is asked reveals an underlying fantasy of a state of reality beyond our own, that would somehow be accessible by us. Because if we can imagine it, it is in a way accessible to us. My answer to that is that it isn’t. The question itself becomes nonsensical as the answer is that we cannot access it, not even through imagination based on our best scientific theories. It is fundamentally inaccessible. Imagination of it relates more to our religious beliefs of a realm beyond our own, a heaven and a God etc. so the discussion often just takes the form of a religious one, rather than a scientific one. Metaphysics leading to a craving for heaven and God, rather than reasoning about the physical properties of a reality outside our own.

so the discussion often just takes the form of a religious one, rather than a scientific one. Metaphysics leading to a craving for heaven and God, rather than reasoning about the physical properties of a reality outside our own. — Christoffer

I understand better now, thank you for explaining.

However, as I mentioned, this is not the path that this takes me on. And I don't think I am alone in viewing the possibility in purely scientific terms.

And I don't think I am alone in viewing the possibility in purely scientific terms. — Questioner

As do I, but we still run into the hard problem, that our imagination of another reality is dependent on the physical properties of our own, thus making our imagination unable to comprehend any of it. We can try and theorize it, but it will mostly boil down to extrapolations of how it relates to our reality, rather than form an actual understanding of the other reality.

@Banno
So, are we ready to proceed, or are you back to ignoring me?

Here are my proposals. "True" signifies a judgement which is made concerning a proposition. It is a very specific type of judgement which is incompatible with the judgement of "false", the opposing judgement of the very same type. To "know" a proposition means that a judgement of this type has been made, the proposition has been judged as either true or false. Note, that for the sake of the modal model we must allow for both judgements, "p is true", "p is false", to adequately represent the possibility of knowing p. — Metaphysician Undercover

You are conflating the epistemic notion of ‘judging’ with the metaphysical or semantic notion of truth. Truth doesn’t require anyone to make a judgment; it exists independently of whether anyone knows or judges it.

It is not that the act of judging that is "incompatible", but that the semantic structure does not allow something to be both or neither true and false. Hence we can construct non-classical logics. You are mistakenly making the epistemic act do the logical work.

Your definition collapses knowledge into the merely epistemic act of judgment. Knowledge is not reducible to judging; one could judge falsely or incompletely. Your definition might lead to our knowing this that are not true.

Modal semantics works with truth conditions of propositions across possible worlds, not with human acts of judging. There’s no need to posit ‘both judgments’ to represent epistemic possibility; you only need to track where the proposition is true or false.

The first implies that if p is true (has been so judged), then it is possible that p is true (has been judged that way). — Metaphysician Undercover

Nuh. It just says that if p is true then it's possible that p is true. Again, the alternative would be that only impossible things are true.

2. If p is known then it is possible to know p.
...The second implies that if p has been judged as either true or false, then it is possible that p has been judged as true or false. — Metaphysician Undercover

Nuh. It just says that it is not possible to know stuff that is impossible to know...

Can we get on to Fitch now?

Can we get on to Fitch now? — Banno

Sure, you reject my definitions, as I knew you would. So, what does "know" mean to you in this context, and what does "true" mean in this context? Then we can look at interpreting Fitch's argument under these conditions.

You are perhaps intent on using "first lets define our terms" in order to avoid setting out the argument.

Lets' use the definition of knowledge in the SEP article...

Lets' use the definition of knowledge in the SEP article... — Banno

I don't see a definition of "knowledge" there. It says "The operative concept of 'knowability' remains elusive...". That's the problem I mentioned, why the appearance of paradox is created, there's too much ambiguity in key terms like "know" and "true".

So, I'll tell you again. Approaching with clear definitions for these terms, and adhering to them will resolve any apparent paradoxes. I proposed definitions already, which would dissolve the appearance of a paradox. You did not accept them. Now it's time for you to propose some definitions.

I will not proceed without definitions, because my thesis is that it is a lack of definition which is the problem. Therefore we need definitions to try my thesis. If every time that we try a set of definitions, the paradox disappears, this is good evidence for my thesis.

I don't see a definition of "knowledge" there. — Metaphysician Undercover

Yes, indeed. I wonder why.

I will not proceed without definitions — Metaphysician Undercover

You are perhaps intent on using "first lets define our terms" in order to avoid setting out the argument. — Banno

SEP didn't need a definition, but you do. No doubt that's because your explanation will be so much more nuanced...