Question

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) 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. 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. a) The notion you're referring to, where a system describes itself and encounters limitations or paradoxes due to self-reference, aligns with the ideas surrounding self-referential paradoxes and Gödel's incompleteness theorem.

b) Your description shares similarities with the concept of reflexive systems or self-referential paradoxes, where a system refers to itself, leading to logical challenges and potentially infinite regress.

c) This viewpoint resonates with the idea of internal consistency within limitations. When a system tries to encapsulate or describe itself entirely, it often faces contradictions or limitations due to self-reference.

d) The situation you've outlined reflects the idea of an infinite loop of self-description. When a system attempts to describe itself, it triggers an infinite loop of self-modification due to the changes induced by self-reference.

Answer 1

The debate touches on whether a theoretical system can consistently and completely describe the physical world, including humans, which is complicated by Gödel's incompleteness theorem and paradoxes of self-reference. This touches on philosophical principles evident in Wittgenstein's context-dependent meaning of language and Kant's categories of human experience. Limits of descriptive theories are also seen in superstring theory and the concept of alternate universes.

Step-by-step explanation:

The discussion centers around the notion that a theoretical system, such as Quantum Field Theory (denoted as 'X'), might be able to completely and consistently describe the physical world, including humans. Considering Gödel's incompleteness theorem, which asserts that certain truths in a mathematical system cannot be proven within that system, it's contentious to claim that X can prove any physical statement. This becomes even more complex when the system tries to describe or manipulate itself, leading to paradoxes of self-reference.

Ludwig Wittgenstein's later work, Philosophical Investigations, illustrates that language and its meaning are context-dependent, challenging the idea of a system possessing internal continuity irrespective of context. Furthermore, concepts rooted in human experience, such as causation and identity, are articulated outside of empirical derivation, pointing out limits to what theories can encompass, as suggested by Kant's categories of thought. Such self-referential challenges are also encapsulated in the concept of causal closure and determinism, where everything, including human behavior, is determined by unbreakable natural laws and past events. Despite these philosophical considerations, advanced theories like superstring theory and the contemplation of alternate universes suggest the existence of realms beyond empirical verification or self-consistent fields, reminding us of the limits of any theory's descriptiveness.