Back in September 2006, Scott Aaronson wrote a famous blog post giving 10
- Reasons to believe that N!=NP. In March 2014, he wrote a more ambitious post about
The scientific case for N!=NP. He claims: "This post supersedes my 2006 post on the same topic, which I hereby retire." His post seems to be strongly influenced by previous intellectual exchanges with a convinced Bayesian "climate change" critic. The central Bayesian argument from the post left me with a feeling similar to the following quote from the post (replace "probability" with "science"):
John Oliver’s deadpan response was classic: "I’m ... not sure that’s how probability works..."
As a reaction, some computer scientists sympathetic to Scott wrote serious posts about
Why do we think N NE NP? They actually started by asking themselves: "Why do scientists believe any particular theory?" and listed the following actual reasons: "(1) By doing Popperian experiments- experiments that really can fail. (2) Great Explanatory power. (3) (Kuhn-light) It fits into the paradigm that scientists already have."
Other computer scientists more explicitly raised questions "with regard to the main technical argument in a recent post by Scott" by asking
- Could we have felt evidence for SDP!=P? My impression is that the main technical argument failed to convince them, but their high esteem for Scott prevents them from being blunt about this.
My question is the following: The post from 2014 tries to construct a single Bayesian argument with a single "Bayesian probability" for P!=NP. All the other posts work with multiple independent reasons, and make no attempt at all to unify this into a single Bayesian probability argument. Is subsuming multiple independent reasons into a single Bayesian judgment really in agreement with the scientific method? What does epistemology says about this? (There are statements which are either true or false, but I'm not sure whether this implies that I should only assign a single Bayesian probability to such a statement quantifying how sure I am that it's true.)
Edit Note that my confusion is not caused by using Bayesian probabilities in general, but by the procedure to subsume many different Bayesian probabilies for different facts into a single Bayesian probability for a "stronger" fact. So I'm OK that we can postulate Bayesian probabilities for facts like that N=NP would be very surprising, or that N!=NP explains many observed facts, or that P!=NP is extremely useful. But I'm confused how it should be possible to subsume these into a single Bayesian probability for a "stronger" fact like that P!=NP is true.