Dear Brian D. Josephson,
I read your essay and the accompanying comments here. Good that you question a lot which is held to be true at the present by many scientists.
According to Yardley's Circular Theory, I just want to annotate that the American poet T.S. Eliot seemed to have expressed the circular movements of the analytic (and emotional) mind in his poem "little gidding" by writing
"We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time."
In my own essay here, I trace back all formal systems (including antivalent logics) to a circle, the latter being the beginning of mathematics and logics as we know it. Of course, I use the circle merely as a metaphor, a container that encapsulates the deeper meaning of existence beyond any formal systems. Goethe did a good job in his Faust to show how formal systems (preconceptions) have a grip on one's mind:
"Where sense fails it's only necessary
To supply a word, and change the tense.
With words fine arguments can be weighted,
With words whole Systems can be created,
With words, the mind does its conceiving,
No word suffers a jot from thieving."
I would be happy if you would read my essay and comment on it.