Affirming The Consequent
Argument From Complexity
Argument By Prestigious Jargon
Argument From Outdated Information
Argument From Personal Astonishment
Take your pick... as we fall prey to Argument From Authority because it's Penrose, a man who knows mathematical physics but not necessarily neuroscience, making the argument.
For me, neither a physicist nor a neuroscientist, complex adaptive systems theories seem more than adequate to explain us without having to invoke spooky physics. Each little addition to our overall intelligence creates a more and more complex system that develops and adapts and, as in our case, might eventually begin to notice itself and have its thoughts (which we just call 'cognition' in animals) then turn to considering itself. Ergo... consciousness. Penrose seems to need a still more 'mystical' answer (and not just on this subject...) and, without quite going so far as to invoke a deity, chooses the most mysterious and currently least-understood science to hang his god hat on.