Re:What Even Is a Number?
by TheOtherHobbes on Tuesday February 19, 2019 @04:56PM
(#19203244)
Numbers don't exist - unless you're a Platonist.
The experience of numbers certainly exists. The reason you recognise one-ness and two-ness in objects is because your brain experiences a difference between one-object and a-pair-of-those-objects.
The experience is subjective. If you have two objects that are identical except for the fact that one is red and the other is blue, you can parse them as one-each-of-red-and-blue or as two-identical-things. Both interpretations are logically consistent, but the most useful interpretation depends on the context, and your specific needs as defined by the context.
It's easy to underestimate how subjective math is.
I've long suspected that this is why math eventually dissolves into incompleteness theorems. You can't prove a subjective experience, and eventually all mathematical reasoning reduces to subjectivity - even something basic like true/false, which is essentially just an interpretation of experience. (And can be very unreliable.)
Math is really an introspective map of experiences and processes that we find collectively consistent. We like to tell ourselves it's external and objective. But how can we tell the difference between true objectivity and subjective consistency when we only have shared human subjectivity to use as a reference?
The experience of numbers certainly exists. The reason you recognise one-ness and two-ness in objects is because your brain experiences a difference between one-object and a-pair-of-those-objects.
The experience is subjective. If you have two objects that are identical except for the fact that one is red and the other is blue, you can parse them as one-each-of-red-and-blue or as two-identical-things. Both interpretations are logically consistent, but the most useful interpretation depends on the context, and your specific needs as defined by the context.
It's easy to underestimate how subjective math is.
I've long suspected that this is why math eventually dissolves into incompleteness theorems. You can't prove a subjective experience, and eventually all mathematical reasoning reduces to subjectivity - even something basic like true/false, which is essentially just an interpretation of experience. (And can be very unreliable.)
Math is really an introspective map of experiences and processes that we find collectively consistent. We like to tell ourselves it's external and objective. But how can we tell the difference between true objectivity and subjective consistency when we only have shared human subjectivity to use as a reference?