numbers are an artificial human construct !

[SamBridge]

 

An observer can distinguish between those values, but an observer isn't required. Consider, for instance, gravitation. The force due to gravitation between two objects is, among other things, proportional to the objects' masses. More massive objects will attract each other more strongly than will less massive objects, other things being equal, whether anyone's around to measure that force or not.

 

Much of the rest of what you said boils down to the difference between something and how we describe that something. And yes, beyond a certain point, axioms come into play. If you're looking to ponder truth without resorting to any axioms at all, then I suppose you'd need to talk to a philosopher (for instance, the guy you've most recently been arguing about logic with in this thread ), which is something I'm not, about whether such a thing is worthwhile or even possible. You might this this article vaguely interesting: http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma

 

As for why 1 + 1 = 2, there are formal proofs to be found.

 

Edit: You added to your post while I was typing, and rendered my last sentence redundant. Also, I'm not sure anyone's claiming that the entirety of mathematics is independent of human thought. My entire point rests with the notion that while the labels we assign to various quantities are constructs, the variations in quantity themselves are not. I take our number systems to be labels assigned to quantities that exist independent of labels, if that makes sense.

It's a very difficult thing to understand, the only tool we really have is logic and our observations, but how do we actually prove even that logic=logic? Logic itself isn't observable, and even with our tool logic, how do we actually determine what a "quantity" or "value" means without an observer? We can't spontaneously become no longer an observer anymore to observe what that the solution is, that's a contradiction in of itself!

I do see what you're saying though, but even if I thought it was 100% correct, I don't think it can be logically proven either way, even the notion that logic=logic has to eventually boil down to some kind of assumption if it isn't one already.

Objects obviously have to exist outside of living things in order for them to have formed the conditions for life to have formed, but the universe does not sit there with a piece of paper working out math problems, it just goes about how it does.

Edited January 24, 2013 by SamBridge

[evansste]

Mathematics is a language that is used to describe quantities. It's as simple as that. Most of the confusion, and "math attacks" that are taking place on this thread really seem to boil down to definitions. For instance, all apples don't have to be identical in order for us to describe a quantity of apples. This is because of how we choose to define what an apple is. It usually has nothing to do with weight or size. So when I say "I'm going to give you two apples.", no one will have a difficult time understanding what that means because we are typically on the same page when it comes to knowing what an apple is. As is the case with any other language, the clarity of statements is dependent on the definitions that we choose to adopt as a society. Outside of this thread, not many people would have a difficult time understanding what an apple is. It makes perfect sense, unless you try to over-think it.

 

"This is all I have learned: God has made us simple, but we have made ourselves very complicated." --Ecclesiastes 7:29

 

 

 

[cladking]

 

 

Mathematics is a language that is used to describe quantities. It's as simple as that.

 

 

So when I say "I'm going to give you two apples.", no one will have a difficult time understanding what that means because we are typically on the same page when it comes to knowing what an apple is.

 

Yes. Exactly. But it is still on both persons' shoulders to know the referent and to know the nature of "two".

 

The former could be computers (Apples) and the latter is a human (/crow) construct that isn't normally confused. Math works fine in theory and in all known cases works in the concrete world so long as its nature is understood and terms are properly applied. Of course this isn't necessarily the case as evidenced by government finances. Logic works fine only so long as it is properly applied and defined. These definitions rest now on things like euclidean geometry rather than the real world and this too makes them a construct.

[SamBridge]

Mathematics is a language that is used to describe quantities. It's as simple as that. Most of the confusion, and "math attacks" that are taking place on this thread really seem to boil down to definitions. For instance, all apples don't have to be identical in order for us to describe a quantity of apples. This is because of how we choose to define what an apple is. It usually has nothing to do with weight or size. So when I say "I'm going to give you two apples.", no one will have a difficult time understanding what that means because we are typically on the same page when it comes to knowing what an apple is. As is the case with any other language, the clarity of statements is dependent on the definitions that we choose to adopt as a society. Outside of this thread, not many people would have a difficult time understanding what an apple is. It makes perfect sense, unless you try to over-think it.

 

"This is all I have learned: God has made us simple, but we have made ourselves very complicated." --Ecclesiastes 7:29

But then we have to have some boundary over how existent a "quantity" really is, because in math, numbers are quantities themselves. It's really not that simple, you have symbols, they make accurate descriptions, but you never actually just see the number "3" floating around in space. We know there has to be something, but at what pint do we draw a line between a simple language of symbols, and their representation of reality?

Of course logic will work properly were it's defined, but I'm talking about where maybe it isn't or that past a certain point it can't be because we have to assume that as an observer that what we are seeing is "1 apple = 1 apple".

It's kind of like that old philosophical problem. "If a tree falls in the woods and no one is around, does it make a sound?". Well if it did fall in the woods on Earth it would have to make a sound, but we don't know that it did or that it fell because there was no observer, there was no one around, we can't just go around assuming there's trees falling everywhere, we would have to know that they are falling, after they make a sound.

Edited January 26, 2013 by SamBridge

[michel123456]

Yes. Exactly. But it is still on both persons' shoulders to know the referent and to know the nature of "two".

 

The former could be computers (Apples) and the latter is a human (/crow) construct that isn't normally confused. Math works fine in theory and in all known cases works in the concrete world so long as its nature is understood and terms are properly applied. Of course this isn't necessarily the case as evidenced by government finances. Logic works fine only so long as it is properly applied and defined. These definitions rest now on things like euclidean geometry rather than the real world and this too makes them a construct.

(emphasis mine)yes. But you can surely construct some other maths based on other axioms that do not "work" in the concrete world. I guess there are an infinity of wrong maths versus a few correct ones (if not only one).

[cladking]

(emphasis mine)yes. But you can surely construct some other maths based on other axioms that do not "work" in the concrete world. I guess there are an infinity of wrong maths versus a few correct ones (if not only one).

 

So long as the basis of a math are logically consistent, sufficiently defined, and properly applied there should be no problems. Some systems are too simple to be useful (like counting one, two, more than two), and some could be so complex they cause computers to overheat but there are countless possibilities.

[michel123456]

So long as the basis of a math are logically consistent, sufficiently defined, and properly applied there should be no problems. Some systems are too simple to be useful (like counting one, two, more than two), and some could be so complex they cause computers to overheat but there are countless possibilities.

(emphasis mine)

There are problems in existing maths.

Dividing by zero and other infinities are not perfectly defined.

[cladking]

(emphasis mine)

There are problems in existing maths.

Dividing by zero and other infinities are not perfectly defined.

 

Yes! And it's one of the reasons I don't like euclidean geometry.

 

Math is very simple using our definitions but it might not be best at modeling the real world.

[SamBridge]

What actually makes something logical? And why does that does that thing make something logical?

[cladking]

What actually makes something logical? And why does that does that thing make something logical?

 

Definitions.

 

Logic is a property of nature. It's no matter if that's a human construct or not since humans are part of nature. If A follows B then B precedes A by the definitions of terms whether man invents the terms or not. Man is a natural part of the natural enviroment even whan he is also its observer.

[SamBridge]

Definitions.

 

Logic is a property of nature. It's no matter if that's a human construct or not since humans are part of nature. If A follows B then B precedes A by the definitions of terms whether man invents the terms or not. Man is a natural part of the natural enviroment even whan he is also its observer.

But why is it independent of man, and what makes it a property of nature? If it's a "definition", doesn't that mean it has to be defined by someone?

[cladking]

But why is it independent of man, and what makes it a property of nature? If it's a "definition", doesn't that mean it has to be defined by someone?

 

A scientist strives to remove human things from consideration. Ancient man did it through metaphysics and modern man does it through experimental parameters and controls. Nature is nature and this is what we're supposed to see and not our own eyes looking at it.

[SamBridge]

A scientist strives to remove human things from consideration. Ancient man did it through metaphysics and modern man does it through experimental parameters and controls. Nature is nature and this is what we're supposed to see and not our own eyes looking at it.

Yeah I know that, but why? Nature obviously works in some manner that has to do with values or qaunties, but why does 1+2=3 just because I mark 1 as a' and 2 as a'' and 3 as a''' and draw some correlation between them?

[cladking]

Yeah I know that, but why? Nature obviously works in some manner that has to do with values or qaunties, but why does 1+2=3 just because I mark 1 as a' and 2 as a'' and 3 as a''' and draw some correlation between them?

 

Think of it this way then. Even though the numbers are constructs the fact remains that nature doesn't know that. In order to get a baby elephant you need one elephant plus one elephant. By the same token having only one seed in an apple would be an inefficient means to get apple trees. Nature can't count rivers, tributaries, or water droplettes but water runs downhill and carves river channels. We just come along and want to count things.

[SamBridge]

Think of it this way then. Even though the numbers are constructs the fact remains that nature doesn't know that. In order to get a baby elephant you need one elephant plus one elephant. By the same token having only one seed in an apple would be an inefficient means to get apple trees. Nature can't count rivers, tributaries, or water droplettes but water runs downhill and carves river channels. We just come along and want to count things.

But the fact that there are numbers which can exactly model phenomena in nature would imply that nature can in fact in some way count or recognize quantities, at least if I am interpreting your context of nature as not super literal.

[cladking]

But the fact that there are numbers which can exactly model phenomena in nature would imply that nature can in fact in some way count or recognize quantities, at least if I am interpreting your context of nature as not super literal.

 

 

No!!! The elephant you add to an elephant to get three elepants can not be identical. It takes a male elephant and a female elephant to have a shot at making three elephants and the third one is just a little copy of both sets of genes. It's actually possible in some animals to have different fathers of twins. Nature doesn't count or care. Nature has no value system other than what is. You can't exactly model nature and this is what makes numbers a construct. All our models are constructs but our knowledge is correct to the degree the metaphysics and experimentation is correct.

 

At the risk of getting off-topic, real science is observation organized by logic. In the real world it is simply illogical to say that one elephant plus one elephant equals three elephants. You can address this problem in myriad ways but whether you use ancient metaphysics or euclidean geometry you need to keep in mind the definitions and that numbers are constructs or it's easier to go all wrong or to confuse an issue. You might not even get the cat out of the box until it's died. The real world doesn't care about numbers or cats. We need to do the worrying ourselves. Certainly the real world doesn't count cats but if there were more mice and other prey we might need to count cats. If the cats in the neighborhood were sabre-toothed tigers we'd better be counting cats to zero cats. We'd better be studying nature rather than magic.

 

Sure nature can count in a sense such as it "recognizes" when critical mass is achieved or when population dips too low for a species to recover. Nature tells a CO2 saturated lake when to erupt. But this counting isn't like counting stars or seas. We can model these things and gain real knowledge but we might apply such knowledge incorrectly if we don't understand all of the terms. We can't hold knowledge in mind that we don't understand so it can't be applied simultaneously woth other knowledge. I believe it is important to remember that "numbers" aren't absolute. Even the unitless (theoretical) numbers of math still are "saddled" with all the definitions of the operations applied to them. One plus one doesn't always equal two (and "2" might be expressed as "10" like in this very sentence).

[SamBridge]

No!!! The elephant you add to an elephant to get three elepants can not be identical. It takes a male elephant and a female elephant to have a shot at making three elephants and the third one is just a little copy of both sets of genes.

And as I've said before this point is invalid because you can simply change the units to make the math correct. I could easily say "2.34*10^78 moles + 2..41*10^78 moles" and that would account for the mass, and as for the genes I could say "probability of x base pair pairing with y = z according to the molecular model of Dirac's equation to model atoms because the carbon bond could be replaced by...ect".

[Daniel Foreman]

Well duh. Numbers are just another form of representative language. Aka, the word table represents tables in general yet no table specifically. If you wish to discribe a table in complex detail then you use mathematics.

 

Mathematics = specific language

English = Generalized language

 

The statement "I am feeling sad" is completely interprative. It can mean anything from you want to slash your wrists, to I saw a sad puppy which I'll forget about in the next 5 seconds.

 

The statement "I am feeling sad" in mathematics would have to be brought down to measurements, I guess the only accurate way of documenting how sad they are is to measure all the processes in their body at that time, and then isolate those that deal with feelings of sadness. Extremely complex and probably impossible by todays science.

So yes, numbers are a representative language designed to compare, measure, predict and proceduralize the universe, but they are not the universe itself.

 

Anyone who says different needs to re-evaluate their reality, and possibly grab a little medication along the way

Edited February 14, 2013 by Daniel Foreman

[SamBridge]

Well duh. Numbers are just another form of representative language. Aka, the word table represents tables in general yet no table specifically. If you wish to discribe a table in complex detail then you use mathematics.

 

Mathematics = specific language

English = Generalized language

 

The statement "I am feeling sad" is completely interprative. It can mean anything from you want to slash your wrists, to I saw a sad puppy which I'll forget about in the next 5 seconds.

 

The statement "I am feeling sad" in mathematics would have to be brought down to measurements, I guess the only accurate way of documenting how sad they are is to measure all the processes in their body at that time, and then isolate those that deal with feelings of sadness. Extremely complex and probably impossible by todays science.

 

So yes, numbers are a representative language designed to compare, measure, predict and proceduralize the universe, but they are not the universe itself.

 

Anyone who says different needs to re-evaluate their reality, and possibly grab a little medication along the way

It's not so obvious though because there is a correltation of patterns within the universe, there are predictable results that follow definite patterns which can be modeled using math, so how real numbers are is not exactly determined.