You didn't answer my question. You stated that he would alway paint the same picture for a given title.
You did not state that he could not paint the same picture for two given titles. This would be necessary information if we are to say that the art critic can go back from painting to title. Is this now part of the argument?
Then I will introduce another concept to satisfy you: our art critic and muse are both normalised in the sense that if we allowed a set of titles to describe the same artwork we could simply create a new titling system where a single title could describe the set - this would be the
normal form of the title.
Anything I wish? It is your argument, you should state whether this is consistent with what you mean. You introduce the concept of paint being thrown at the canvas and you have defined three players muse, artist and art critic. Which one throws the paint at the canvas?
UGH - why are you persisting with asking about an inconsequential detail? I am telling you to invent any persona you like: it is a generalised scenario, not a specific one. The point here is that we have created a new piece of art in a way we think cannot be produced by the artist because of the restrictions we have placed on him. The question is then simple: is this piece of art part of our gallery?
That is just another way of saying the same thing. If it does not resonate then it does not convey the information.
Correction: it does not resonate the information to
you.
That's just equivalent to saying, "If I bury my head in the sand I don't need to listen to what you are presenting to me therefore I can say it is invalid."
And incidentally "how it feels to eat a peach" consists of more than just the emotional information, you are just taking "feel" in the wrong sense.
So what other information would you like to introduce which is unrepresentable?
If I had never eaten a peach I would never know what it is like to eat a peach if I just relied on the mathematical model.
You argument was about representations - not subjective realisations.
So again: is there anything that cannot be represented about the nature of eating a peach with respect to any given human in a formal system?
This is not a question asking you if you have a concept of eating a peach or not - just whether or not you recognise the description as relating the physical causalities involved. (Assuming you accept that you are a being that cannot escape the physical).
So either "how it feels to eat a peach" is not information (why not?)
In your case, from your argument, it would not be information because you require that you have an experience of the existential quality being described. As such it may as well be in Chinese for all that the symbols matter in conveying anything. If you are able to think in the abstract however then why single out the experience of 'eating a peach' as significant? Surely you could point to something trivially expressible in mathematics which would equally be unable to convey information about your experience of it? Say, the effect of a single photon on your retina?
You can reject the notion of reality being representable if you wish but then I would like to be informed in advance so I know that there is no possible way for me to persuade you of anything: since I am somewhat limited in this physical reality to being only able to demonstrate anything to your system by means of representations.
or there is always at least one piece of information about the physical system that the mathematical model cannot convey.
That is incompleteness of the uninteresting kind: you are asserting that some more powerful system of representation exists.
If you want to have a bash at demonstrating have at it.
That is not logic. You claim that there does not exist any x such that x is not describable. Yet when I ask you to demonstrate the truth of your claim you respond by asking me to demonstrate the falsity of your claim. That is not how it works, you made the claim, you demonstrate it is true.
*Sigh* This isn't empirical hour; this is metalogical hour.
Either way you're the one asserting that indescribable things exist. I am not claiming they do not - I am claiming that attempting to show they do will lead you to a fatal paradox. Hence I am asking you to attempt it in order that you may demonstrate this to yourself. It is from the paradox we conclude that indescribable things cannot exist - or rather we conclude that if it exists it can be described.
Semantic dodge - I use it myself sometimes. So for example when somebody told me that you cannot represent a non-computable number using natural numbers I said - yes I can, look:
Thus I refute Turing. But it is as nonsensical as saying that applying the label "undefinable" is somehow defining the undefinable.
No - it's paradoxical - not nonsensical. It is a perfectly sensible statement. This is the whole damn point.
First define supernatural.
I'm using your definition remember?
If you define supernatural in terms of natural, then also define natural.
I already have: that's where you introduced supernatural remember?
Your claim is that the supernatural cannot be represented naturally. Your claim: demonstrate it is so.
I would be fascinated to hear a definition of natural that excludes something that has a mathematical isomorphism.
That would be trivially uninteresting: I would simply create a system that lacks the ability to express all the things natural numbers can.
There's nothing fascinating in pointing out that a system of logic less powerful than a number theory cannot describe things number theory can.
