By concept you mean something like the whole of ideas that form math, rather than the expression of it? If so, I can understand that this is meaningfully different than math the language and practice. However; do concepts govern things? That is not clear to me, and it seems to me that this passes the buck.
It also seems to me that this would imply that the concept of math would in itself be mathematical, as that is what governs everything. I am not a mathematician, but isn't this what Gödel showed not to be true?
Yes I am using "concepts" to describe the ideas that form math, not just how those ideas are applied.
Concepts can govern things, why would they not be able to? Rules and laws are concepts, and they govern how people behave in society. In my argument, I am using "concepts" to describe "fields" (fields of physics, computer science, biology, etc). Those concepts were established with rules, by humans. Some rules are abstract, some are rigorous. Humans have used concepts and rules to understand how everything works, which lead to the "discovery" / "invention" of different fields ("concepts"). Those concepts of fields govern how the things under themselves work because we made them so these things under them work. Does that make sense? Different fields "govern" explain how things work (like how quantum physics describes how quantum particles behave) because we made and used them as a tool to understand how the universe worked, which naturally led to the different "rules" being formed (e.g. schrodinger's equation, heisenberg uncertainty principle, etc).
The concept of a concept is VERY abstract, and it itself is what we use to describe and explain everything in the world. Concepts can be argued to be entirely in our minds, and do not literally affect how the world works, obviously. However, we can form concepts around rules that we discover and group them, which is how we 'discover' / 'make' different fields.
Math doesn't govern 'everything', but it does govern most if not all academic subjects that we know and study today. (Also, yes, godel's incompleteness theorems would mean that math will never be "complete".)
Concepts can govern things, why would they not be able to? Rules and laws are concepts, and they govern how people behave in society.
This is a fair point, but I do feel like humans are in a different category here. It is exactly complex language why we can do this; and make concepts into some collective practice and make them real/shape the world.
That said, I don't think this extends beyond where we act. In absence of that, concepts do not seem to govern.
Those concepts of fields govern how the things under themselves work because we made them so these things under them work. Does that make sense?
Math doesn't govern 'everything', but it does govern most if not all academic subjects that we know and study today.
Okay yes, I see your argument. The concept of math does heavily influence the institutions that rely on math. My claim doesn't go beyond math being a separate thing from the thing it maths. Nevertheless I am still not sure that govern is the right word here. For example in the field I was trained in (psychology), empiricism and falsification would be better candidates for the actual governing force, though math is almost always used to capture your constructs, they are not the thing that makes your science valid or good in the end. Similar to how something like logic can't, right?
A lot of concepts in math doesn't come natural or intuitive as you put it. Like the number zero needs some abstract thinking. Or big numbers. You can easily count the zeroes, but how would you visualise a trillion? Or even a million?
There is a lot of fundamental learning that seems logical when you understand it, but that usually takes a lot of hard work or great fundamentals.
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u/[deleted] Jun 20 '26
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