Was math invented or discovered?

What is the basis for reason? And mathematics?

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Scott Mayers
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Re: Was math invented or discovered?

Post by Scott Mayers »

Hobbes' Choice wrote:
Not sure what the problem here is.
We all of us had a rich experience of the world before we learned any maths, and we live most of our lives without daily reference to it.

Numbers are conceptual. Cups and apples exist without them. Does a cup need to know how many other cups in the cupboard before it can exist?

If no one had ever invented maths to count ONE world, would the world still have existed? Maths is a descriptive language.


The PARTICULAR language you use to model reality, like the math you use, actually MODEL a reality that exists prior to your bias to experience and communicate those experiences to others. The language is what you are treating is the reference to the reality when it is only modeling the reality in the only way we are able to relay it in common between other people. That is, we ARBITRARILY select symbols, like the words and languages we use ONLY to communicate the reality we share in common. But the reality we subjectively experience is, in essence, unable to be shared in any sincerely "objective" way. So we are FORCED to use a set of symbols that we agree to only for the means of relaying back and forth agreement.

The particular symbols we use for numbers and its relationships are still REFERRING to something 'real', even though the symbols are themselves NOT the actual things themselves. But this holds true for ANY reality we symbolize using language between each other. That is, just because you SEE something, while YOU can interpret it as 'real', communicating this to anyone or anything beyond yourself is still BEGGING, without any difference, that the words you use to reference and convey that experience to others is real as well.

So if you treat numbers as not real, nor is anything you can say is real, because all words, spoken or written, are themselves just SYMBOLS.

Now given ALL symbols to reference things, even if we may consider all unreal, Numbers are the MOST GENERAL inference we can be MOST CERTAIN of that is common between each and every person or thing.

Yet, unless you are a solipsist, all things you experience are symbols about the objective world to which you have no other choice but to infer are 'real'. So numbers are FROM the outside world, not simply something magically derived in and of you personally. The semantic meaning of some reality, such as, that "a coin has two sides", require that "twoness" is a property of the objective world, not your solipsistic invention. Thus numbers (the referents of the meaning, not the symbols) have a reality that we "DISCOVER".

I think the confusion DOES lie with confusing the difference between our "INVENTION" of the symbols that we use and to the referents of what those symbols denote by "DISCOVERY" in the real world. They are thus both true.
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Hobbes' Choice
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Re: Was math invented or discovered?

Post by Hobbes' Choice »

Scott Mayers wrote:
I think the confusion DOES lie with confusing the difference between our "INVENTION" of the symbols that we use and to the referents of what those symbols denote by "DISCOVERY" in the real world. They are thus both true.
No they are not both true. Languages are inventions. Reality persists regardless of them. The referred is not the same as the referent.
Confusing the sign with the signified is a classic error, but one, where mature reflection always renders the notion that languages are not discovered, be that logic, maths or the spoken word.
Scott Mayers
Posts: 2446
Joined: Wed Jul 08, 2015 1:53 am

Re: Was math invented or discovered?

Post by Scott Mayers »

Hobbes' Choice wrote:
Scott Mayers wrote:
I think the confusion DOES lie with confusing the difference between our "INVENTION" of the symbols that we use and to the referents of what those symbols denote by "DISCOVERY" in the real world. They are thus both true.
No they are not both true. Languages are inventions. Reality persists regardless of them. The referred is not the same as the referent.
Confusing the sign with the signified is a classic error, but one, where mature reflection always renders the notion that languages are not discovered, be that logic, maths or the spoken word.
The actual 'classic' error is assuming that (a) I don't know what you mean, when I do, and (b) that I am distinctly separating the symbols (models) from the reality (that which is 'referred' to, or more classically called, "denoted"). I can denote to you something while you are in the presence of me while simultaneously saying the word, "chair", and wait until you repeat it in hopes that you'll understand what I'm denoting. As such, "chair" does not exist any more than "5" because these themselves are the SYMBOLS being connoted of the thing I'm pointing to that might look something like this:
"Chair", I say pointing at this when you are present.
"Chair", I say pointing at this when you are present.
A chair.jpg (123.64 KiB) Viewed 1198 times
Now this is also an example of "ONE chair" of which I hope upon teaching you the meaning of "one" in context to multiple such denotations when I am teaching you my language.

So far, the chair being denoted is a REAL object, while the arbitrary symbol, "chair" is just a variable label, the model. [Ignore that we are using a picture here but are literally seeing this in front of me.]

The word "one", to which we may not initially speak when introducing SPECIFIC things, is induced later as a pattern to comparative realities in which we want to ADD the property term, "one", later as an extended meaning. We call this an adjective later that ADDS more information to narrow down something more specific. I would not say, "one chair" at all later because this would be superfluous without having something else I'm trying to point out. I then might show you two of those chairs and add, "two chairs". Certainly you would witness something I'm denoting AND those words simultaneously in hopes that you understand and confirm this if I see you repeat and use this to what I expect is sufficient for me to know you understand.

You won't initially understand what "one" nor "two" means until you contrast them with other denoted words and objects that relate these. Can you not notice that all of these are merely denotations referring to 'real' concepts we SHARE and are simply arbitrarily assigning those symbols to the concepts we experience? So we learn WHAT number is ONLY secondarily to the objects but once the meaning of the number symbols are understood, they DO refer to real perceptions of the same validity as the objects we are also perceiving. Neither is 'real' in that both are symbols. The sensation of sight of the chair or chairs are as equally part of the experience as their counts. You have to recognize that the actual chair is equally a relative 'symbol' of the word, "chair", to us. The actual chair is the model of the word we assigned even though these are simply arbitrary factors relative to each other.

That is, I could have denoted something else and assigned that object to the word "chair" too. Just because we usually assign the words AFTER we see the object does not make the object MORE real than the symbol. We could have reversed it by me saying the word first, then arbitrarily assign something I want to present to you that I beg you associate with it. Both are relative symbols and relative objects, neither being more nor less real of the other. But if you assume one is 'real', you just mean the SEMANTIC referent is the relative symbol assigned to it.

Numbers are the begged associations of the real concepts through time using different objects to denote them. But these FACTS still exist in nature, both as symbols AND realities.
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