Editing Strange loop (section)

== Downward causality ==
Hofstadter thinks that minds appear to determine the world by way of "downward [[causality]]", which refers to effects being viewed in terms of their underlying causes. Hofstadter says this happens in the proof of [[Kurt Gödel|Gödel]]'s [[Gödel's incompleteness theorems|incompleteness theorem]]:
<blockquote>Merely from knowing the formula's meaning, one can infer its truth or falsity without any effort to derive it in the old-fashioned way, which requires one to trudge methodically "upwards" from the axioms. This is not just peculiar; it is astonishing. Normally, one cannot merely look at what a mathematical conjecture ''says'' and simply appeal to the content of that statement on its own to deduce whether the statement is true or false. (pp. 169–170)</blockquote>
Hofstadter claims a similar "flipping around of causality" appears to happen in minds possessing [[self-consciousness]];  the mind perceives itself as the cause of certain feelings. 

The parallels between downward causality in formal systems and downward causality in brains are explored by [[Theodor Nenu]] in 2022,<ref>{{Cite journal |last=Nenu |first=Theodor |date=2022 |title=Douglas Hofstadter's Gödelian Philosophy of Mind |url=https://philpapers.org/rec/NENDHG |journal=Journal of Artificial Intelligence and Consciousness|volume=9 |issue=2 |pages=241–266 |doi=10.1142/S2705078522500011 }}</ref> together with other aspects of Hofstadter's metaphysics of mind. Nenu also questions the correctness of the above quote by focusing on the sentence which "says about itself" that it is provable (also known as a Henkin-sentence, named after logician [[Leon Henkin]]). It turns out that under suitable [[Metamathematics|meta-mathematical]] choices (where the [[Hilbert-Bernays provability conditions]] do not obtain), one can construct formally undecidable (or even formally refutable) Henkin-sentences for the arithmetical system under investigation. This system might very well be Hofstadter's [[Typographical Number Theory]] used in ''Gödel, Escher, Bach'' or the more familiar [[Peano Arithmetic]] or some other sufficiently rich formal arithmetic. Thus, there are examples of sentences "which say about themselves that they are provable", but they don't exhibit the sort of downward causal powers described in the displayed quote.