Verify Solipsism using Statistics
Ha! Ha!! Ah-luv-it. Me-thinks that's a new and original one!
More seriously, I'll address your question:
What does professional philosophy say about the persuasiveness of solipsism?
By looking at it from a history-of-philosophy angle. But I am not a historian, still less a philosophy-historian.
Nowadays we have a newtool which can help such 'research'...
chatGPT
So I asked chatGPT where it starts.
And apart from an indirect reference to Parmenides the main founder of this "philosophical school" seems to be Descartes.
Aha! So now we are getting warmer.
And what do we find of Descartes+Solipsism?
IEP says this:
Solipsism is implicit in many philosophies of knowledge and mind since Descartes and any theory of knowledge that adopts the Cartesian egocentric approach as its basic frame of reference is inherently solipsistic.
There we have it — Descartes!
IEP continues:
Solipsism merits close examination because it is based upon three widely entertained philosophical presuppositions, which are themselves of fundamental and wide-ranging importance. These are: (a) What I know most certainly are the contents of my own mind—my thoughts, experiences, affective states, and so forth.; (b) There is no conceptual or logically necessary link between the mental and the physical. For example, there is no necessary link between the occurrence of certain conscious experiences or mental states and the “possession” and behavioral dispositions of a body of a particular kind; and (c) The experiences of a given person are necessarily private to that person.
These presuppositions are of unmistakable Cartesian origin, and are widely accepted by philosophers and non-philosophers alike. In tackling the problem of solipsism, one immediately grapples with fundamental issues in the philosophy of mind. However spurious the problem of solipsism per se may strike one, these latter issues are unquestionably important. Indeed, one of the merits of the entire enterprise is the extent that it reveals a direct connection between apparently unexceptionable and certainly widely-held common sense beliefs and the acceptance of solipsistic conclusions. If this connection exists and we wish to avoid those solipsistic conclusions, we shall have no option but to revise, or at least to critically review, the beliefs from which they derive logical sustenance.
In introducing “methodic doubt” into philosophy, René Descartes created the backdrop against which solipsism subsequently developed and was made to seem, if not plausible, at least irrefutable.