addition and subtraction, left to right is correct

You can do addition and subtraction in any order and it's still correct

Social conventions are real, well defined things

So are the laws of nature, that Maths arises from

Some mathematicians like to pretend they aren’t, while using a truckload of them; that’s a hypocritical opinion

No, you making false accusations against Mathematicians is a strawman

That’s not to say you can’t change them

You can change the conventions, you cannot change the rules

But all of basic arithmetic is a social convention

Nope, law of nature. Even several animals know how to count.

you can redefine the numbers and operations any time you want too

And you end up back where you started, since you can't change the laws of nature

I mean, arithmetic order is just convention

Nope, rules arising from the definition of the operators in the first place.

not a mathematical truth

It most certainly is a mathematical truth!

But that convention works in the way we know, yes, because that’s what’s… well… convention

The mnemonics are conventions, the rules are rules

this is just a writing standard that is globally agreed on

No, it's a universal rule of Maths

The writing rules are defined by humans not by natural force

Maths is for describing natural forces, and is subject to those laws

That one thing and another thing are two things, is a rule from nature

Yep, there are even some animals who understand that, and all of Maths is based upon it.

Some people insist there’s no “correct” order for the basic arithmetic operations.

And those people are wrong

And worse, some people insist the correct order is parenthesis first, then left to right

As per Maths textbooks

Both of those sets of people are wrong

All Maths textbooks are wrong?? 😂

And in some languages a number can be used as a name of a variable or a function

Not in Maths it can't

so it can be anything really

No, it can only be a Factorised Term, ab+ac=a(b+c). You also can't call a function by any letter that you've used as a pronumeral

Wouldn’t we just assume function expressions are always “in parenthesis”?

No, because factorised Terms also are, ab+ac=a(b+c).

The way I was taught growing up, brackets are [these]. Parenthesis are (these)

They're all brackets. Parentheses is actually the part inside the ().

the 5 next to the parentheses indicates multiplication

No, it indicates Distribution, a(b+c)=(ab+ac), 5(8-5)=(5x8+5x5).

It should be limited - like Orders - to only Multiplication and Addition

Because you don't want people to know when to do Division and Subtraction? 😂

Because division is the same operation as multiplication

No it isn't, but they are both binary operators.

they have the same “weight” in the order of operations (meaning, you do them left-to-right)

And where are they going to do Division and Subtraction in the left to right if you've left them out? 🙄

O - oxponent?

To the Order of. 2² is 2 to the order of 2

so 5 literally cannot be a function if that’s the case

No, but it can be and is a coefficient of the Term 5(8-5)