Geometry

'I can make a representation' is not, in any useful sense, a representation. While our 'mapping', 'representing', 'calculating', 'proving' metaphors are harmless - even heuristically powerful - in non-reflexive contexts, they are a barrier to the only kind of 'engagement with reality' that is consistent with the experience and logic of rendering ourselves intelligible.

If we try to 'map' the world of this engagement, we find ourselves, like Kripke, lost in a tangle of wormholes through the infinite dimensions of a Klein bottle world whose geometry varies with our attention. Each corridor is a corridor; each door is a door; each room is a room; but we cannot reliably predict which doors will appear in which corridors, and which rooms they will lead to - all corridors have doors, all doors lead to rooms, but any attempt to map them completely also reorders them in ways we can only partly predict.

We discover that we draw our maps by rearranging the geometry of the landscape. We cannot map our map-making.

But neither can we relinquish it. 'We can relinquish map-making' must, it seems, be a partial map - however ambiguous and qualified. Whether it's one of the parts that changes with our attention, in response to our epistemological needs, may or may not be a question we can address without further rearranging the landscape.

When we ask ourselves questions about fundamental qualifiers like 'changes' and 'stays the same', we experience kaleidoscopic disorientation. Does the meaning of 'stays the same' depend on things staying the same? Does it depend on 'same' meaning the same thing from one occasion of use to another? How would we know?

And yet engaging with this landscape is the only way we can do anything remotely like 'engaging with reality'. We must engage in the map-making activity, while resisting the delusion that this can ever be satisfactorily concluded ...