if math is out there waiting to be discovered, what once was a purely abstract notion then has to develop an existence unconceived of by humans.

Huh? What does that mean?

Subsequently, Mazur describes the Platonic view as “a full-fledged theistic position.”

Again, what the hell does one have to do with the other?

I know that Mazur is merely trying to describe the other side of the coin, but he does an awful job at it.

So the question remains; if a mathematical theory goes undiscovered, does it truly exist?

Of course. The universe doesn't invent itself according to our discovery of the relationships already ihnerent within it.

This is mixing...

if math is out there waiting to be discovered, what once was a purely abstract notion then has to develop an existence unconceived of by humans.

Huh? What does that mean?

Subsequently, Mazur describes the Platonic view as “a full-fledged theistic position.”

Again, what the hell does one have to do with the other?

I know that Mazur is merely trying to describe the other side of the coin, but he does an awful job at it.

So the question remains; if a mathematical theory goes undiscovered, does it truly exist?

Of course. The universe doesn't invent itself according to our discovery of the relationships already ihnerent within it.

This is mixing bad theology with mathematics. As Brian Davies says, “Let Platonism Die”.

The scientific method will time after time show that 2+2=4, this is a theory that is part of the mathematical model that is man-made and man uses in order to objectively attempt to model reality.
Those Aliens will most probably experience realty similarly to ways we do.
Man use emotion, reason(logic), sense perception and languange to aquire knowledge.
Mathematics, natural sciences, human sciences, history, ethics and the arts are areas of knowledge.
the theories that would be utilized by aliens would aim to objectively model reality would just as the man-made model we call mathematics enable 2+2 to equal 4 (assuming they had the same number base system)
They will h...

The scientific method will time after time show that 2+2=4, this is a theory that is part of the mathematical model that is man-made and man uses in order to objectively attempt to model reality.
Those Aliens will most probably experience realty similarly to ways we do.
Man use emotion, reason(logic), sense perception and languange to aquire knowledge.
Mathematics, natural sciences, human sciences, history, ethics and the arts are areas of knowledge.
the theories that would be utilized by aliens would aim to objectively model reality would just as the man-made model we call mathematics enable 2+2 to equal 4 (assuming they had the same number base system)
They will have to invent this science, invent integers to function as the basics of the theories.

Discover means that you become aware of something that is already existing.
1+1 as you use for an example does not necessarily equal 2. For example, if you have 1 pile of sand and add another, then don't you still have only 1 pile?
However, if you refer to the mathematical model 1+1=2. In reality this statement is arguable.

I think that that the aliens will find by using logic that 1+1 comes up to 2, and that will lead them to devise thier own model to describe this relationship. As mathematics appear to be universal, their model would be 'identical' to the human. Don't you think?

I'm a child myself, and about 10years ago i learned how to count. Of course i knew how to count before i 'learned' the universal language of mathematics. The point being I discovered relationships and used logic to express these.

For example: Newton is sitting under his apple tree and observes an apple falling. He concludes by experiments that every time he drops an apple it falls towards the ground. Although, even if he repeats the experiment a million times, how can he be certain that the million-and-one time the apple doesn't fall upwards? He can't. Although he uses reason to make the fairly good concluison that there is a relationship between the apple falling and the earths gravitatio...

I'm a child myself, and about 10years ago i learned how to count. Of course i knew how to count before i 'learned' the universal language of mathematics. The point being I discovered relationships and used logic to express these.

For example: Newton is sitting under his apple tree and observes an apple falling. He concludes by experiments that every time he drops an apple it falls towards the ground. Although, even if he repeats the experiment a million times, how can he be certain that the million-and-one time the apple doesn't fall upwards? He can't. Although he uses reason to make the fairly good concluison that there is a relationship between the apple falling and the earths gravitational force (Fg)
He called this relation the law of gravitation
this law was discovered.

He later invents calculus (some would call Leibriz the sole inventor as Newton never published his works).


Was calculus already existing before Newton thought of it, just as gravitational force?

Was calculus already existing before Newton thought of it, just as gravitational force?

Wouldn't the apple have fallen whether Newton was there or not?

Wouldn't the relationships in calculus exist whether we discover them or not?

"Discover means that you become aware of something that is already existing."

I can qualify the definition a bit better, but since you gave it (in a very generalized form), it works for our purposes well enough.

PS: Say we "invented" calculus. Couldn't we just invent 2+2 = 5? Would it work? Since we invented it, WE get to make up the rules. But would it work?

But if we "discover" what the rules are, those rules hold true regardless because t...

Was calculus already existing before Newton thought of it, just as gravitational force?

Wouldn't the apple have fallen whether Newton was there or not?

Wouldn't the relationships in calculus exist whether we discover them or not?

"Discover means that you become aware of something that is already existing."

I can qualify the definition a bit better, but since you gave it (in a very generalized form), it works for our purposes well enough.

PS: Say we "invented" calculus. Couldn't we just invent 2+2 = 5? Would it work? Since we invented it, WE get to make up the rules. But would it work?

But if we "discover" what the rules are, those rules hold true regardless because they are not dependent on us.

To use a previous example: The American continent would be here whether anyone ever discovered it or not.

Now these theories only describe what is discovered.

You keep making my case.

For the mathematical model it all comes down to most basic unit, the integers. Did man discover that a lollipop is actually 1 lollipop?

Ah! I think what you're calling the "invented" part is the syntax, the "language" of a system of discovery. Yes, we invent that.

Math, for example as compared to geometry. The rules of neither change because we invent ways of "modeling" or discussing the discoveries, and our rules of syntax can be flawed, but the thing discovered remains.

We call America Americana, instead... doesn't change the continent to another place.

Yes, we invent the lan...

Now these theories only describe what is discovered.

You keep making my case.

For the mathematical model it all comes down to most basic unit, the integers. Did man discover that a lollipop is actually 1 lollipop?

Ah! I think what you're calling the "invented" part is the syntax, the "language" of a system of discovery. Yes, we invent that.

Math, for example as compared to geometry. The rules of neither change because we invent ways of "modeling" or discussing the discoveries, and our rules of syntax can be flawed, but the thing discovered remains.

We call America Americana, instead... doesn't change the continent to another place.

Yes, we invent the language, but not the truths. As I wrote above:

"Math is the symbolic language by which we can discover quantitative relationships. Those relationships already exist."

Those relationships already exist...and we discover them.

We do not invent the math, we invent the language of the math.

Yes, we invent the syntax of math, the way in which we describe the math, (any symbolic language will do), but the math itself exists independently of us or any discovery.

If you and I are walking together on another planet, and we come across a structure inside of which an alien lives; and I call it a casa, while you call it a house, we invented the words "casa" and "house".

But we did not invent the "thing" we came upon.

Likewise, we do not invent the math, we invent the language that describes the math (casa, geometry), (house, calculus), (din, algebra) etc.

Of course we invented maths, it is so simple anyone could do it! All you need is logical thinking (reasoning) and you ca...

Yes, we invent the syntax of math, the way in which we describe the math, (any symbolic language will do), but the math itself exists independently of us or any discovery.

If you and I are walking together on another planet, and we come across a structure inside of which an alien lives; and I call it a casa, while you call it a house, we invented the words "casa" and "house".

But we did not invent the "thing" we came upon.

Likewise, we do not invent the math, we invent the language that describes the math (casa, geometry), (house, calculus), (din, algebra) etc.

Of course we invented maths, it is so simple anyone could do it! All you need is logical thinking (reasoning) and you can use maths.

So perhaps we are talking about the same thing if you are calling "math" by the language of the "thing" described, and not the "thing" itself, which I am.

As long as we both understand the difference, it's just semantics.

The relationships exist independent of our choices of language. Those relationships are not invented, they are discovered.

Mathematics is the symbolic language by which we utilize and discover those relationships. We invent the language; we discover the relationships.

So again, if you're calling math by "the language of math", then I agree. But if you're referring to the relationships uncovered by utilizing the language of math... then no, those relationships exist whether we invent any language to describe them or not.
---

Would you say that psychology was discovered too?

Psychology is a process, not an objective datum that stands on it's own, independent of our existence. It would be like saying Spanish was discovered. One might make such a case but it would be icky.

I cannot argue with that. It seems as we have forgot to define what we each meant by utilizing the word 'mathematics'.

I agree with you, mathematics was discovered.

The deviant arguments I've been proposing was in the sense of the math I get at school. I believe that was invented.

For example: in our Hease and Harris book it says that 'the shortest distance between two points is a straight line'. This is true in the mathematical model for three dimensional vectors. However, space is in reality 'curved'. Wouldn't the shortest distance between two points be in a 'curved' line?

I want to show the differences between 'math' and 'math'. One side holds the answer, another models the believe...

I cannot argue with that. It seems as we have forgot to define what we each meant by utilizing the word 'mathematics'.

I agree with you, mathematics was discovered.

The deviant arguments I've been proposing was in the sense of the math I get at school. I believe that was invented.

For example: in our Hease and Harris book it says that 'the shortest distance between two points is a straight line'. This is true in the mathematical model for three dimensional vectors. However, space is in reality 'curved'. Wouldn't the shortest distance between two points be in a 'curved' line?

I want to show the differences between 'math' and 'math'. One side holds the answer, another models the believed answer. One discoverable, one invented.

In my personal opinion, studying math or any other science is alot like solving a 1,000 pieces puzzle with a key-chain light. Not enough insight to see more than a fraction of the data, yet we make assumptions about the entire 'picture'

Can we ever know that the most basic mathematical theory 1+1=2?

As materia can appear, and dissapear in space, then 1 (for example) ozone molecule can become 0, or 2, or 3.. etc. This can be proved when observing that vacuum actually has a mass, though it theoretically should not.

Is 1+1=2 ultimate truth?