The Platonic Mathematical World

[SerScot]

In part to resurrect this thread I not the fact that this discussion has moved to "thought". When talking about thought are we not taking on faith the fact that others can have internal monologs? After all I know I can think but how can anyone else establish that I can think if I do not share what I am thinking via the written word or by speaking? You can see that some sort of nural activity is occuring but cannot establish, with certainty that "thought" is occuring.

Are we not accepting, on faith, that people can have internal monologs?

[Avatar]

Only if you're not inclined toward solipsism.

--A

[SerScot]

Avatar,

True.

I had another thought. The reason I think Mathematics is more than mere mind games is that it cannot be altered. It always works the way it works. We can alter the world around us. Language changes over time. But Mathematics is still mathematics and it always works the same way no matter how we change our our views of the world or the universe.

It has to have something concrete that keeps it stable. It has to echo in more that our mere reality how else do we explain mathematics amazing stability when compared to everything else that is changes by the passage of time?

[Avatar]

Maybe it only stays the same because we keep operating by the same assumptions?

--A

[SerScot]

Avatar,

You're telling me that in ten thousand years no human has been able to change their assumptions about mathematics? Really? That's more than mere coincidence. Even if the base numbers used by the society changes the effects are always the same. 6+6=12 whether your base number is ten or twelve. That doesn't change, ever. Conceptually it is always the same.

Why doesn't it change while every other human construct changes over time? My contention is that it does not change because it is anchored in something larger than mere human psyche and as such it cannot change. If that is not the case what explanation would you offer for the assumptions within mathematics incredible resilience to the vast changes in human culture over millenia?

[Fist and Faith]

Don't pay attention to Av. He just likes getting us worked up.

[SerScot]

F&F,

Oh, I understand I'm simply curious to find out if there is another explaination for mathematics suprising durability. The Universe is always changing. It is defined by flux but mathematical concepts remain concrete, why?

[Vraith]

It doesn't change because there is nothing TO change...one is one by strict, pure, precise definition not by any actual property other than being one...by definition.
It does not touch the world, and the world is effectless on it.
One is not subject to gravity, inertia, or time...because it is naught.
One cannot prick it, and one does not bleed.

And mathematics and language have both changed in the same ways...as we understand more, we find more, things alter. The appearance of greater magnitude in linguistic change is due almost entirely to the fact that even the simplest word...grass, for instance...talks of an infinitely complex thing as if it were a unit. One is one, grass is legion.

[SerScot]

Vraith,

So Old English and modern English are the same?

[Vraith]

Vraith,

So Old English and modern English are the same?

Just as much the same as Euclidean geometry and topology and calculus and discrete.

[High Lord Tolkien]

I just want to post in this awesome thread!

[SerScot]

Vraith,

Vraith,

So Old English and modern English are the same?

Just as much the same as Euclidean geometry and topology and calculus and discrete.

But none of those cocepts change the way mathematics works fundemntally. They are just new ways of using the same old concepts.

[Vraith]

Vraith,

Vraith,

So Old English and modern English are the same?

Just as much the same as Euclidean geometry and topology and calculus and discrete.

But none of those cocepts change the way mathematics works fundemntally. They are just new ways of using the same old concepts.

I guess I don't see what you mean by fundamentally in this case...you can do/say things with each of them that can't be done with the others. Same with various languages. You can learn more than one system, once you understand the particular symbology and "grammar"...same with languages...just new ways of using old concepts: except they ARE new in part...what is sayable was not so before, whether math or speech.

[SerScot]

Vraith,

Vraith,

Just as much the same as Euclidean geometry and topology and calculus and discrete.

But none of those cocepts change the way mathematics works fundemntally. They are just new ways of using the same old concepts.

I guess I don't see what you mean by fundamentally in this case...you can do/say things with each of them that can't be done with the others. Same with various languages. You can learn more than one system, once you understand the particular symbology and "grammar"...same with languages...just new ways of using old concepts: except they ARE new in part...what is sayable was not so before, whether math or speech.

What I'm talking about is the difference between the semantic content of Language versus Mathematics. With the evolution of language the semantic content changes. There are no 1 to 1 correlations between languages each has slightly different semantic content. The same thing occurs as language evolves earlier meanings change as time passes.

That's not true with Mathematics. While vector and differential calculus were discovered by Newton and Leibniz toward the end of the 17th century the semantic content of the functions of vector and differential calculus do not change with time. They are still the same. What other phenomenon in our universe has such stability? Everything changes, but mathematics does not.

[Vraith]

What I'm talking about is the difference between the semantic content of Language versus Mathematics. With the evolution of language the semantic content changes. There are no 1 to 1 correlations between languages each has slightly different semantic content. The same thing occurs as language evolves earlier meanings change as time passes.

That's not true with Mathematics. While vector and differential calculus were discovered by Newton and Leibniz toward the end of the 17th century the semantic content of the functions of vector and differential calculus do not change with time. They are still the same. What other phenomenon in our universe has such stability? Everything changes, but mathematics does not.

Ah...well, related to other stuff I've said...the semantic content of mathematics doesn't change because, unlike ordinary language, it has no content except its definition. If you alter/evolve the semantic content of "tree," neverthless in my front yard the sap will flow come spring, summer be shaded, autumn I'll be raking thousands of tiny cool red and orange fires. The word and thing have other resources to live on, work to do. But if you change the definition of One, it ceases to be in any way, and so does all that follows from it.
Essentially, mathematics is an eternal language that has no nouns.
Sure, when one talks about One, one treats it as if it were a noun, but only in particular ways [not to be numberist, but they just aren't like us...because it stands for a concept, and we call those nouns in our language. But that translation is false...it is never meaningful, and there is no knowledge, until one says "One what?"

[Avatar]

Good posts Vraith.

--A

[SerScot]

Vraith,

What other abstract concept remains as constant as those in mathematics? Can love be defined, it's pretty clearly an abstract concept and arises from human culture and psyche but changes from time to time, heck from individual to individual.

One, a singlularity is an abstract concept until it is attached to one of something, you are correct. That being the case why does the abstract concept of "One" not fluxuate the way the abstract concept of "Love" does?

[Vraith]

Vraith,

What other abstract concept remains as constant as those in mathematics? Can love be defined, it's pretty clearly an abstract concept and arises from human culture and psyche but changes from time to time, heck from individual to individual.

One, a singlularity is an abstract concept until it is attached to one of something, you are correct. That being the case why does the abstract concept of "One" not fluxuate the way the abstract concept of "Love" does?

Because, one is abstract-objective, love is abstract-subjective? Because one is the definition of simplicity, love a multiplicity of turbulence/chaos/complexity.
One HAS to be one unchanging to continue on, love must change or die.
Your abstract forest is obscuring the One Tree.
A tree [or my particular maple, described in earlier post] will do what trees do...its functioning doesn't depend on your definition...but One literally IS it's definition...if the definition changes, the thing itself has to change...but if you do that, everything that depends on that definition [fractions, perhaps 2, 3, 4, etc] also must change. But also if you do that, you've made all of mathematics into a square wheel. Maybe there is something you can do with it, but you can't make it roll.

[SerScot]

Vraith,

That's my point.

The very fact that it cannot change without destroying it's utility is why I think it has some sort of concrete existence despite being an abstract concept.

[Vraith]

Vraith,

That's my point.

The very fact that it cannot change without destroying it's utility is why I think it has some sort of concrete existence despite being an abstract concept.

Believe it or not, while I was writing the last line of mine I was laughing to myself thinking "I know what's gonna happen next..." and it did and is still, which is me saying:

And that is exactly why I think it doesn't.

In truth I have other reasons, but they all attach/relate/have a necessary corollary of that.