Intuitionalism is powerful and I think the best bridge between pure abstraction and pragmatism.
For me, the magic lies here but performs a similar function for computing and mathematics as it does for language and mathematics for you.
Supercombinators have practically religious value in combinatory logic but they work not only theoretically but pragmatically.
I try not to get too into it and treat it as “handwaving functions” in theories of types but then again I’m fine with 1=0 without it causing a break in space time.
I can see the appeal of pure.
But then I look at the glass I’m pushing my thumbs on that causes these letters to show up behind the glass and I click a little arrow which makes the words go to a place you are at, also behind a piece of glass that you interpret as having value (hopefully) and respond to by tapping on glass or a keyboard.
So, that’s what always keeps me from fully enjoying pure things.
It doesn’t take away from their utility – it enhances the magic to me – but it does pull me away from platonic forms.
So that’s the route I probably go with platonic forms.
Humans communicating with other humans across time.
A purely mental landscape has been created / discovered and continues to be explored.
Pure abstractions particularly in mathematics are a map of human cognitive processes functioning, removed and put on paper and into theories of logic and circuitry which humans mapped in electronics to produce what we’re communicating with now, an incredible human achievement just in its infancy.
All stemming from cooperative human thought.
Human capabilities are seemingly unbounded and can create systems which can operate by themselves – “ye shall be as gods” – including pure mathematics which does not even require time to consider as functioning, even though you CAN take a clock and measuring calculation time, whether human or human invented computer.
Humans are drawn to these purely abstract forms because humans find certainty addictive. It is a pleasurable sensation of satisfaction. Things equate. You are certain that if you follow these steps you will end up in the same place.
Knowing your way around the labyrinth with confidence.
And if you don’t know the way, you know that if you follow these procedures you will get to the right place even if it is not the place you expect because the mapping of function is so dependable it can take you into places no humans have ever been : and yet were always latently capable of.