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 Post subject: Reality and existence
PostPosted: Sun Mar 06, 2005 9:35 pm 
If there's a better definition of real this won't mean much but here goes.

Let us define 'real' as something that interacts with the world. That is to say, something is real if it has a consequence. Then abstract ideas, such as mathematics, become real things. The consequenses of mathematics can be seen in what they eventually produce: cars, computers, planes, these things require mathematics before they can be designed, let alone built.

So, given this definition, can something be real yet not exist?


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 Post subject:
PostPosted: Sun Mar 06, 2005 9:56 pm 
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It's real, by your definition, but it doesn't exist.

Not until someone pulls the trigger and sends 135 grains of lead flying straight at you at 3300 feet per second.

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 Post subject:
PostPosted: Sun Mar 06, 2005 10:19 pm 
Of course it exists. It's right there.


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PostPosted: Sun Mar 06, 2005 10:21 pm 
Kodiak Claw wrote:
So, given this definition, can something be real yet not exist?


No, but things that exist aren't necessarily real.


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 Post subject:
PostPosted: Mon Mar 07, 2005 1:41 pm 
Gwalla, please give your definitions of 'real' and 'exists'. It sounds like your using my definition of 'real' for 'exists'


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 Post subject:
PostPosted: Mon Mar 07, 2005 3:56 pm 
Kodiak Claw wrote:
Gwalla, please give your definitions of 'real' and 'exists'. It sounds like your using my definition of 'real' for 'exists'


That's true. I believe that is actually closer to how they are normally used.

You neglected to provide a definition of existance for comparison.


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 Post subject:
PostPosted: Mon Mar 07, 2005 4:14 pm 
Exactly how do abstract mahematical ideas have consequences?


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 Post subject:
PostPosted: Mon Mar 07, 2005 4:44 pm 
Anh Minh wrote:
Exactly how do abstract mahematical ideas have consequences?


In their ultimate application to practical problems.


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 Post subject:
PostPosted: Mon Mar 07, 2005 7:08 pm 
gwalla wrote:
You neglected to provide a definition of existance for comparison.


He's got you there.


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 Post subject:
PostPosted: Mon Mar 07, 2005 7:29 pm 
KC - I think I know what you're trying to get at. What you need to do is find Moritz Schlick's paper entitled "Positivism and Realism."

...I've been trying to find a copy online and I can't.


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 Post subject:
PostPosted: Mon Mar 07, 2005 7:39 pm 
gwalla wrote:
Anh Minh wrote:
Exactly how do abstract mahematical ideas have consequences?


In their ultimate application to practical problems.

Yes, but what does it mean? That ideas have consequences because people think them?

Imagine a giant meteor had hit the Earth three centuries ago. Would that then mean that non-euclidean geometry wouldn't be real?


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 Post subject:
PostPosted: Mon Mar 07, 2005 9:26 pm 
Gerald wrote:
KC - I think I know what you're trying to get at. What you need to do is find Moritz Schlick's paper entitled "Positivism and Realism."

...I've been trying to find a copy online and I can't.

Hmm library has a copy of his collected papers, I'll take a look tomorrow


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 Post subject:
PostPosted: Mon Mar 07, 2005 11:25 pm 
Anh Minh wrote:
gwalla wrote:
Anh Minh wrote:
Exactly how do abstract mahematical ideas have consequences?


In their ultimate application to practical problems.

Yes, but what does it mean? That ideas have consequences because people think them?


No, because people use them to justify doing things.

Quote:
Imagine a giant meteor had hit the Earth three centuries ago. Would that then mean that non-euclidean geometry wouldn't be real?


Depends on whether you think ideas have an existence in their own right.


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 Post subject:
PostPosted: Sun May 15, 2005 2:48 am 
Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.


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 Post subject:
PostPosted: Mon May 23, 2005 4:11 am 
Drooling Iguana wrote:
Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.


Mathematics don't "interact" with the universe, they're laws according to which reality works. Two apples and two more apples is four apples, regardless of our brain.


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 Post subject:
PostPosted: Mon May 23, 2005 10:18 am 
sun tzu wrote:
Drooling Iguana wrote:
Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.


Mathematics don't "interact" with the universe, they're laws according to which reality works. Two apples and two more apples is four apples, regardless of our brain.

Unless you stuff them in the stomach of a cat which you then put in a box. Then all bets are off.

There are the laws of the Universe. Of which we know approximations. (Probably pretty good, in the case of apple counting, granted.) Those approximations can be put in the form of mathematics. But the mathematics aren't the Laws.


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 Post subject:
PostPosted: Tue May 24, 2005 1:26 am 
sun tzu wrote:
Drooling Iguana wrote:
Mathematics is simply a form of human thought. It is a tool we (and, presumably, other sapient species, if they exist) use to organize and communicate our thoughts. As such, it is merely a subset of our thoughts and therefore a function of our brain. Mathematics does not interact with the Universe. Our brains do.

Mathematics don't "interact" with the universe, they're laws according to which reality works. Two apples and two more apples is four apples, regardless of our brain.

No. Mathematics are a method through which we can understand and describe the universe (although mathematics on its own doesn't tell you anything. It has to be paired with real-world data to be useful.) Physics are the laws according to which reality works. We use mathematics to better understand physics, but they're not the same thing.


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 Post subject:
PostPosted: Tue May 24, 2005 12:29 pm 
No, physics is also a method of understanding reality, in terms of equations and forces. The laws of reality are just that- the laws of reality, and there's no way to dumb them down into a science, largely because we're mentally incapable of understanding them all.


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 Post subject:
PostPosted: Tue May 24, 2005 4:29 pm 
The General wrote:
No, physics is also a method of understanding reality, in terms of equations and forces. The laws of reality are just that- the laws of reality, and there's no way to dumb them down into a science, largely because we're mentally incapable of understanding them all.

Wow. That's wrong in so many ways I don't know where to begin, especially since you didn't make any actual arguments, just a bunch of assertions.

Suffice it to say that the laws of physics are the laws of reality, that science (which relies heavily on mathematics) is our best method of understanding them, and that there's absolutely no reason to believe that we're somehow "mentally incapable" of understanding those laws fully at some point. We're constantly making progress in our understanding of these laws and there's been no indication of some sort of looming barrier to our understanding that we won't be able to pass through.


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 Post subject:
PostPosted: Tue May 24, 2005 9:35 pm 
First of all, there's a difference between the science known as physics and the actual laws of physics.
And I feel we're incapable of understanding them in total not because of some magical mental barrier (though that's part of it; how many people really understand how the 7th dimension works?), so much as the fact that there doesn't seem to be any visible limit to them.


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 Post subject:
PostPosted: Sun Aug 21, 2005 11:13 am 
When discussing math one must keep in mind that numbers are only what they are because that is what a majority of humans say that they are. Imaginary numbers are a good examble. I stands for the square root of negative one, but if you got enough people to agree with you you could say that one is actually the square root of negative one. Another example, which I got from the book 1984, could be that while currently people would say that there is one smilely here 8-) with the right people saying otherwise it could actually be called three. Therefore numbers exist, but are only real for as long as we say they are, at which point they will also cease to exist.


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 Post subject:
PostPosted: Sun Aug 21, 2005 3:00 pm 
Gen. Burnsides wrote:
When discussing math one must keep in mind that numbers are only what they are because that is what a majority of humans say that they are. Imaginary numbers are a good examble. I stands for the square root of negative one, but if you got enough people to agree with you you could say that one is actually the square root of negative one.

Only in Z/2Z.

Quote:
Another example, which I got from the book 1984, could be that while currently people would say that there is one smilely here 8-) with the right people saying otherwise it could actually be called three. Therefore numbers exist, but are only real for as long as we say they are, at which point they will also cease to exist.

"Three" is "three" regardless of how you write it.


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 Post subject:
PostPosted: Mon Aug 22, 2005 4:03 pm 
Changing the name of something doesn't change the thing.
A rose by any other name...


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 Post subject:
PostPosted: Mon Aug 22, 2005 6:04 pm 
I think you may be missing my point. The reason you say that three is three is because that is what you've been taught to believe. we've been brought up in a society that says that this, :!: :!: :!: , is three. All I'm saying is that if someone was brought up differently then when you asked them how many three was they would say it was this, :!: . If you follow.


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 Post subject:
PostPosted: Mon Aug 22, 2005 7:01 pm 
Gen. Burnsides,

I think you may be missing the entire concept of mathematics. I can't tell if your point is that you can choose to call three by some other name, in which case you're arguing nomenclature, which is orthogonal to the current argument<sup>1</sup>, or if you mean to suggest that mathematics itself isn't invariant as most people are taught to believe. If you mean the latter, then let me assure you of your error; mathematics is indeed invariant between cultures, provided both cultures are advanced enough to develop it.

There is really only one major leap of faith you have to take in order to prove the existence of "three". You have to believe in the existence of "one". The unit. Anything, really, as long as you accept that it exists and can be dealt with as an individual thing. You can deny that anything at all exists, and it indeed becomes impossible to count things.

However, if you acknowledge that something (let's call it '1') exists, then you can put another something with it<sup>2</sup> (we'll call this activity '+'), and then yet another something, and you have more than one somethings. For convenience, we all agree that this is '3'. You can choose to call it speeblarg, or "one", but nomenclature alone cannot change the fundamental fact that there are --> :!: :!: :!: <-- this many.

The actual basis of mathematics, at least as discussed in this thread, is rooted in set theory, and contains a small fixed number of "postulates" which are generally considered to be self-evident, but must ultimately be taken on faith. Everything else follows logically and deductively from these postulates. If you want to successfully attack mathematics, you have to do it here.


<sup>1</sup> If you do not start with a common assumed nomenclature, then no communication is possible. Therefore, to argue that three may not be three due to a difference in nomenclature is spurious, and not a useful argument. The essence of communication (and thus the argument) carries with it an underlying assumption that all parties have a common vocabulary. You can neither communicate, nor (by induction) argue without one<sup>3</sup>.

<sup>2</sup> Not completely true - you can also deny the possibility of addition, as that is yet another of the fundamental postulates. However, I was trying to keep the argument simple.

<sup>3</sup> Ironically, this is the same spot where I see the fundamental disconnect form in many a political or religious "argument". Two sides will argue logical extensions which are both true from their point of view, because they did not begin by agreeing on common assumptions and definitions.


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 Post subject:
PostPosted: Tue Aug 23, 2005 12:41 pm 
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Vorpal Bunny Slipper
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Posts: 2707
Pi wrote:
The actual basis of mathematics, at least as discussed in this thread, is rooted in set theory, and contains a small fixed number of "postulates" which are generally considered to be self-evident, but must ultimately be taken on faith.


A slight quibble: It's not the postulates themselves that have to be assumed; it's a formal system, and you can start with whatever axioms you like. What you have to assume is that the postulates accurately describe and relate to the real world and our notions of real world sets.

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 Post subject:
PostPosted: Tue Aug 23, 2005 10:26 pm 
Fortunately, mathematics isn't subjective. You can teach people that one thing and one thing and one thing equals two things, but eventually someone will realize that there's an inconsistency.


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