Can humans symbolically manipulate X that describes themselves?

Consider the following premise:

Any statement regarding the physical world can be proven within the system of X (assume X to be something like Quantum Field Theory) by humans. One may argue that this should be impossible given Godel's incompleteness theorem. However, to counter one argues that X is a fundamentally a mathematically inconsistent theory. Now, since the space of what constituents of humans are describable by X.

Is it an impossibility that humans can symbolically manipulate X that seemingly describe themselves as well? Assuming it is a sensible view what is this view known as? (feel free to include relevant read ups)

• This question is based on a misunderstanding of Godel's theorem. Godel's incompleteness theorem is not a general theorem about self representation or symbolic manipulation of a system that describes itself. It makes a very specific mathematical statement about a very specific kind of mathematical system. Commented Dec 23, 2022 at 5:56

It is perfectly possible to have a formal theory that completely and consistently specifies what happens in a universe. For example, the rules of Conway's game of life completely and consistently specify the state of every cell at every point in the future, given the state of all the cells in the present. To find the future state of Conway's game of life, based on the present state, is simply a matter of rote calculation. Godel's incompleteness theorem does not apply.

• Yes but can you have systems within Conway's game of life which describe Conway's game of life? Commented Dec 23, 2022 at 5:52
• @MoreAnonymous Yes. You can build a Turing machine within Conway's game of life, and that Turing machine can itself be running a simulation of Conway's game of life. Commented Dec 23, 2022 at 5:57
• Ah thanks :) I really got to study Godel's incompleteness theorem Commented Dec 23, 2022 at 6:03

No.

You cannot have a perfect model of a house inside that house.

Its because that model must have a model in it ad infinitum. You can never reach infinity so you can never have that.

There is a story by I think Asimov in which someone make a super computer that predicts economic behaviour of all humans therefore can predict very well future stocks prices, real estate prices etc.

The thing is, as it starts using that information to invest and make profit for its owner it has to start predicting its own self which change its behavior which make it predict which make it change behavior and so on, the machine halts.

If you manipulate what describes you then you are changed, you have a new defintion now. X means something else now. So you have to change X again. And so on. You cannot win this game.