I'm not exactly sure what you mean by "binary logic," but there is the Church-Turing-Deutsch principle which states that a "universal computer" (essentially a working quantum computer) can simulate all physical processes. But I suspect it's not a "proof" that would satisfy skeptics.
It's a Strong Church-Turing so you're correct that sceptics just say they don't believe this.
Actually it's not uncommon for AI "sceptics" (the sort of people who write these articles not just people who suspect we'll have another AI Winter) to just not accept Church-Turing at all, or to insist upon squinting at it in a peculiar way that renders it tautological.
I'm consistently disappointed that people who feel they're quite sure general AI isn't possible mostly have bad intuitions about Computer Science. Twice so far I've been recommended books by sceptics "which will show you why you're wrong" and been disappointed with the poor quality of argument deployed which sometimes is little more than a show of incredulity or a resort to mysterious dualism.
A more robust attempt at this sort of argument was put up by Stevan Harnad, who taught an undergraduate class I sat in on many years ago now (one of the privileges of a post-graduate is that they're entitled to attend relevant undergraduate lectures and so I did). Harnad thinks† you need to build a robot because the intelligence will need some means to experience the universe for itself. But Harnad doesn't disbelieve that general AI is in principle possible, he just thinks our present methods can't get there.
† In general with people who've made a career of such thing they are very careful with words, and so I have doubtless mis-characterized (or even misunderstood) the details and you should blame me for that not Stevan.
https://en.wikipedia.org/wiki/Church%E2%80%93Turing%E2%80%93...