This quote is one of the earliest one’s I could find where Eric introduces oracles:
I believe Eric admits mutual information can be created during the process we call evolution. But he also believes that his theoretical math arguments must apply to any natural biological process. He claims these arguments show mutual information cannot be generated by any process which is Turing computable (ie any algorithmic or stochastic process). Hence some super-Turing machine processes must be involved. These are called ‘oracles’.
Turing himself invented the term ‘oracle’ to help him “explore the mathematics of the uncomputable”. See this article in SEP for details of why he did so.
I have seen posts in the forum claiming that oracles are logically impossible. But this is not true. Oracles are logically possible. They can be implemented by supertasks or by encoding information in real numbers, for example.
However, logical possibility does not imply that oracles are physically possible, if physically possible refers to something implementable under the physics of our universe. Whether oracles are physically possible remains an open possibility. One approach would involve “Malament-Hogarth spacetime, which is physically possible in the sense of constituting a solution to Einstein’s field equations for General Relativity.” But whether our spacetime has even local regions of Malament-Hogarth spacetime is unknown.
See this link plato.stanford.edu/entries/computation-physicalsystems/#Hyp for more details on physical computation, supertasks, and Malament-Hogarth spacetime.
Sorry for the incomplete link, but as a new user I can only have two links per message. So you have to add https:// to front of above to get link. Or go to Stanford Encyclopedia of Philosophy and search for Physical Computation. The subtopic is Hypercomputation.