A demonstration that φ is not in n-PROVABILITY_T for sufficiently large n and sufficiently powerful T shows that no comprehensible proof of φ exists, even if a proof exists in principle.
The branch of logic that studies how proofs work and what makes an argument logically valid.
n-PROVABILITY_T(Proof theory and computational complexity; the problem is in NP)
The decision problem asking, given a formula φ in the language of theory T and a natural number n, whether there exists a valid T-derivation of length at most n constituting a valid proof of φ.
φ (phi)(IIT framework)
A measure corresponding to the quantity or degree of consciousness a system possesses according to Integrated Information Theory.
1 On the significance of \(\textbf{P} \neq \textbf{NP}\)? The appreciation of complexity theory outside of theoretical computer science is largely due to the notoriety of open questions such as 1–4. \) – has attracted the greatest attention. e. the Millennium Problems (Cook 2006). g. (Sipser 1992), (Fortnow 2009), and (Fortnow 2013). \) will prove to have far reaching practical and theoretical consequences outside of computer science. Perhaps the most significant of these revolves around the pos