Philosophy of Numerus Numerans and Numerus Numeratus

[conway]

All that is abstract can be expressed as concrete. All that is concrete can be expressed as abstract. Abstraction and concrete are always interchangeable.

A unicorn is by definition abstract. Yet I can express a unicorn concretely with a simple picture or a stuffed animal.
A number is by definition abstract, yet in cases of physics, amongst others. A number can be expressed as concrete. Numerus Numeratus.

An apple is concrete. Its numerical value is concrete as ONE. Yet can I not imagine that exact apple in all its dimension within my mind. Therefore expressing the apple as abstract. Numerus Numerans.

Thus...all that is abstract is concrete. All that is concrete is abstract. Therefore no separation actually exists between these two ideas. Therefore Numerus Numerans, and Numerus Numeratus are the same thing. Just viewed from different perspectives.

This shows then that a higher ideal is needed to unify the concepts into one perspective. Thus...

Numerus Numerans Numeratus.

 

[Shaggy]

All that is abstract can be expressed as concrete. All that is concrete can be expressed as abstract. Abstraction and concrete are always interchangeable.

A unicorn is by definition abstract. Yet I can express a unicorn concretely with a simple picture or a stuffed animal.
A number is by definition abstract, yet in cases of physics, amongst others. A number can be expressed as concrete. Numerus Numeratus.

An apple is concrete. Its numerical value is concrete as ONE. Yet can I not imagine that exact apple in all its dimension within my mind. Therefore expressing the apple as abstract. Numerus Numerans.

Thus...all that is abstract is concrete. All that is concrete is abstract. Therefore no separation actually exists between these two ideas. Therefore Numerus Numerans, and Numerus Numeratus are the same thing. Just viewed from different perspectives.

This shows then that a higher ideal is needed to unify the concepts into one perspective. Thus...

Numerus Numerans Numeratus.

Hey, this is a really interesting idea. The way you talk about the abstract and concrete switching roles is kind of cool. It’s true that a lot of abstract things can be shown in physical ways, and physical things can be described abstractly. The whole numerus numerans numeratus thing makes it feel like it all connects. What got you thinking about it this way?

 

[conway]

Thanks. I am a philosopher. I find many philosophical flaws with mathematics. For which I am a heretic. Please see the thread "The Unified Number", in "other advanced math". For more insight into the concept.