In my previous post, I discussed the so-called circular trap and how it does not really seem escapable. I also mentioned that that wouldn’t stop me – I’m basically going to ignore it because otherwise nothing can be discussed. Onwards.
This, of course, leaves us with the question of where to start if we want to move beyond the circular trap. I’m a logician at heart, so I’m going to start with an axiom. And since the circular trap is still fresh in our minds, the axiom I’m going to start with is intentionally circular. In fact, it is:
Axiom 1: Axioms are valid starting points.
Nice and circular, and generally implied whenever somebody reasons from axioms in any situation. Because of this, and because of its extremely tight circularity, I tend to regard this axiom as the beating heart of the circular trap, so it seems like a reasonable starting point. This is where I plant my flag, flying proudly unsupported by anything but itself.
Of course, this axiom on its own doesn’t really get us much in the way of practical consequences. We’re going to have to add a few more axioms to our collection before we can coherently think about all the things we want to think about. But the validity of all the other axioms we use will rest on the validity of this axiom, so I shall leave them for the next post.