Alan uses the word "demonstrably" in a strange way. For him, it seems to mean "I think it, therefore it is real". This seems different from its normal usage, whereby I demonstrate something to the satisfaction of others. For example, if I say that there is demonstrably a new star in Cassiopeia, that requires further demonstration, and in fact, agreement by others, based on their own observations. They won't just take my word for it, and if they can't find it, my claim fails. It's not demonstrably anything.