Does the individual exist?

[stone space]

10. I remember back when I was an undergrad, many decades ago.

A Polish mathematician was visiting here, and stayed on for a couple more years, due to marshal law being declared in his own country.

His misfortune was my good fortune.

He gave a colloquium talk that had a fascinating open problem it in the foundations of geometry, specifically the geometry of lines.

The question was essentially whether or not one notion was definable from another notion.

I proved that it was undefinable, and the upshot is that in my geometry, lines are fundamental, and points can be proven "not to exist" in some rather strong technical sense. (Points are not even "pseudo-definable".)

The result was a new geometry.

For a while, I simply referred to my geometry as "pointless geometry", because points were not preserved under automorphisms (ie: the symmetries) of the geometry. The symmetries pulled points apart, so points couldn't exist.

I eventually stopped doing that, since it was a bit ambiguous.

It seems that mathematicians have used the term "pointless geometry" to refer to several other quite different and distinct concepts.

There's probably a psychological point here, and that is that a mathematician will name their concepts "pointless" at the slightest provocation, if they can at all get away with it.

I mean, who can resist the temptation?

And I thought was being original.