1 + 1 = 2, What makes mathematics valid? Options

[freefallz]

As stated in the topic description.

Also:
Is mathematics just a definition we use to represent our reality?

Should geometry be regarded as the consequence of mathematic results?

Not everyone is a mathematician, but all opinions are welcomed.

This post has been edited by freefallz: Jul 14 2005, 12:22 AM

[foopilot]

i really dunno lah im in yr 11 and i only got 100% in IC exam
this isnt really maiths its more lyk philosophy dont ask me !!!!

JoweI

[pataysaya]

ppl create standards? maybe..at least as i think..

[Jaimu-Jaimu]

Well firstly, we must acknowledge that the terms we use to describe mathematical or geometric truths are human-made and thus have no significance.

Secondly, we must also realise that mathematics/geometry are not contingent on our understanding or knowledge. If we come to an incorrect answer in mathematics or geometry, it is through our mis-use of the rules of mathematics rather than their failure to produce truth.

If they're not continent on human interpretation then they must have objective value.

Q. Is mathematics just a definition we use to represent our reality?

Mathematics as we know it (the rules, terms, equations etc.) our human-formulated devices for expressing an understanding of something that is objective and immutable.

We as humans, may not understand full the laws of mathematics and could even have them misunderstood in places but they do exist independent of us and we must grasp them.

Geometry as understood by us is the greatest form of a priori logic available. One cannot misinterpret geometry unless one has made a terrible error, to understand the rules is to arrive at the answer guaranteed. If you are given a "triangle" (Human-given term) then you already know that the degrees of the internal angles add to 180. To arrive at any other conclusion is to contradict the term triangle and it's necessary properties.

So in response:

Q. Should geometry be regarded as the consequence of mathematic results?

Geometry is a creation to explain mathematical results yes. The terms used in geometry can only apply to a given set that possess qualities that are necessary to group likewise elements that are likewise in mathematical property.

I should expand more but as I said, it is late and I am no longer a mathematician (So I'm not going to offer the proof that 1+1=2 as I am sure you or OB can provide that once more ).

[freefallz]

Yep so often when mathematics is employed to find 'relationships' between varies trends, science jumps on to draw some form of feasible conclusion. But in reality many relationships defined by mathematics are strictly imaginary. They hold no physic connection in reality.

It's interesting that you mentioned mathematics exist independently. Would this, be anyway supportive of the argument in the existence of God, or at least, higher order?

I think geometry is fabulous subject regarding logic. It's one of those topics in mathematics that reinforces the blatant implementation of logic, in comparison to algebra and calculus - where logic is less evident in the visual presentation.

That's my 1 cent.

[Suijen]

When you put it like that Jaimu, religion is just as logical as mathematics.

This post has been edited by Suijen: Jul 14 2005, 02:15 AM

[Jaimu-Jaimu]

Yep so often when mathematics is employed to find 'relationships' between varies trends, science jumps on to draw some form of feasible conclusion. But in reality many relationships defined by mathematics are strictly imaginary. They hold no physic connection in reality.

Yep. Any example of mathematical truth in the world is merely coincidental and adds/takes away nothing from the objective truth that is mathematics.

So must easier to deal with than the a posteriori nature of science for example.

It's interesting that you mentioned mathematics exist independently. Would this, be anyway supportive of the argument in the existence of God, or at least, higher order?

Well they've used it for an argument. It's a difficult one as there aren't really many similar cases that have objective reality such as mathematics to draw an analogy with.

But to postulate a God from mathematics is adding too much, too quickly. It merely sugguests an order or an organisation to things. Why there is this order is anybody's guess.

I think geometry is fabulous subject regarding logic. It's one of those topics in mathematics that reinforces the blatant implementation of logic, in comparison to algebra and calculus - where logic is less evident in the visual presentation.

That's my 1 cent.

Well it's been a friend of philosophers and logicians for centuries. It's been twisted and contorted so many ways that it's almost cliche' to use it any longer. There aren't many undoubted truths in the world but geometry holds quite a few of them, so it makes sense to use them right?

When you put it like that Jaimu, religion is just as logical as mathematics.

It would've been nice if you quoted me on the part that led you to think that way! *Checks post* I don't really see how you've got to that unless you're trying to advocate that mathematics only has existence in the empirical world through examples.

Mathematics ascribes terms and equations to things that if they are not true, the term no longer applies...thus the criterion for using the term goes unfulfilled and mathematics/geometry is none the weaker for the example.

In religion, I will use the example of God. If God being the omnipotent, omnibenevolent etc. guy that he is (2) all of sudden, orders the destruction of an entire city of people (Violating omnibenevolence) then the term God no longer applies to him as he has failed a necessary condition.

But there is a contradiction. There can be nobody as powerful as God. So if this omnipotent being that ordered the destruction of the city did so, then there can be no original God as to have two omnipotent beings is contrary to biblical teachings and the one that you are left (he who destroyed the city) does not fit the term "God" (Fails NC Omnibenevolence).

Ok...I'm really shooting in the dark trying to guess what you were referring to.

This post has been edited by Jaimu-Jaimu: Jul 14 2005, 02:25 AM

[freefallz]

When you put it like that Jaimu, religion is just as logical as mathematics.

Keep going, I'm all ears, I mean ...eyes.

[shiro]

Geometry as understood by us is the greatest form of a priori logic available. One cannot misinterpret geometry unless one has made a terrible error, to understand the rules is to arrive at the answer guaranteed. If you are given a "triangle" (Human-given term) then you already know that the degrees of the internal angles add to 180. To arrive at any other conclusion is to contradict the term triangle and it's necessary properties.

Not true.
This definition of a triangle is only for single-plane geometry.

[Jaimu-Jaimu]

Not true.
This definition of a triangle is only for single-plane geometry.

Would you correct it for me to try and keep the general point then? 2

I really am tired.

This post has been edited by Jaimu-Jaimu: Jul 14 2005, 10:12 AM

[華夏無產]

This reminds me of something I read a while ago. Some liberal "postmodernist" tried to "deconstruct" mathematics. Basically, they said that all of mathematics and science (even theories such as gravity) as are products of the "Eurasian" (European and Asian) dominated world, and are dominant only because of the arrogance of white people.

Basically, they say that all of mathematics can be relative....I guess if anything the Jewish system of that "1 Palestinian = 25 Jews" is an indication of that

[shiro]

Not true.
This definition of a triangle is only for single-plane geometry.

Would you correct it for me to try and keep the general point then? 2

I really am tired.

I don't remember how it goes, but a math teacher I had in university told us that if a triangle is placed on the surface of a globe, the angles will not add up to 180.
He said that only works for single-plane geometry.
I never really got into that kind of math, though...... never had a use for it.
I did alot more of the applied physics type.
Yeah Engineering! (haven't done math for so long now..... I have almost forgotten the headache that is physics equations)

[Jaimu-Jaimu]

^ Then is it still a "triangle"? That's a tricky one.

[Al Dukes]

You are talking about way too simple mathematics, once you start going beyond advanced calculus you will need to use a supercomputer to do the long hard work for you (with the help of a programmer).

[ob_muaj_ib]

As stated in the topic description.

Also:
Is mathematics just a definition we use to represent our reality?

Should geometry be regarded as the consequence of mathematic results?

Not everyone is a mathematician, but all opinions are welcomed.

it is a law of reality.

it does not matter what we use to represent or define it. a law is immutable.

it's name, it's shape, the words we use to describe, define it may change; but the law is immutable.

2=1

[freefallz]

^So what exactly are those laws? The laws of mathematics? Or the laws of logic?

[shiro]

^ Then is it still a "triangle"? That's a tricky one.

There are still three vertices, creating three angles.
I never got into anything beyond single-plane mathematics, though, so I don't know how that all works.

[ob_muaj_ib]

^So what exactly are those laws? The laws of mathematics? Or the laws of logic?

mathematics, according to what we call it.

these laws are unaffected whether or not if we understand them or call them.

from your basic, associative/multiplicative laws to einsteins formula to all the discovered and undiscovered laws of math/science.

i'm sure you're aware of the laws of math/science.

2=1

[My Hime]

everything we do is related to mathematics

[PervertBurger]

Me and Math don't mix.
I can do it, but I HATE it.
If there was a campaign to destroy all math in the world.
I would be its leader.

Calculus used to be cool..
until it got harder.

This post has been edited by PervertBurger: Jul 18 2005, 02:13 PM