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. https://en.m.wikipedia.org/wiki/Curry–Howard_correspondence

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.

https://en.m.wikipedia.org/wiki/Curry–Howard_correspondence

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It’s very freeing.
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https://en.m.wikipedia.org/wiki/Supercombinator

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.

“This statement is false” = this statement is true kind of thing.
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Pure is cleaner. Lines sharper. Boundaries ultimately resolve to limits.

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.

If I draw a line, I see the fuzziness of the edges. If I think a thought, I know some of the neurological processes happening within.

It doesn’t take away from their utility – it enhances the magic to me – but it does pull me away from platonic forms.

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Philosophically I’m probably what they call a “hard physicalist”, so much so that even pure abstractions are all physically modeled. Yet they still function as if pure abstractions despite having a physical basis.

So that’s the route I probably go with platonic forms.

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The humanity of pure abstractions is what I see – and none of this I’m saying is to take away from it – not at all – but this is the framework I think from:

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.

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I look at the truth of Pythagoras Theorem and see a human successfully mapping a skeleton of stress forces and finding a way to achieve a 2 dimensional skeleton structure that can handle its own stress forces regardless of size because there is now a RATIO that is dependable so long as the materials within are consistent within their own structures and there are no external forces applied such as gravity or wind.
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I suspect there is a “something more” in mathematical abstraction that I’m blind to.
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