How could you prove 1+1=2?

[Blobbenstein]

You might say 'get one apple and then get another apple; put them together and then count how many apples you have.'

But apples are not simple things. They are complex objects(atoms and quantum stuff etc), in a complex universe, processed by a complex mind. All of which we probably only scratching the surface of understanding.
So it seems like you would be using a highly complex, and non-understood, system to prove something that one would thing was fairly simple.

To me, putting those apples together, is actually defining an axiom; that 1 plus 1 is 2...it only seems self evident.

what do you say?

 

[Andy_T]

Maybe you need to ask in another forum ?

 

[Calliegirl]

 

[Blobbenstein]

but that is just the same as my apple argument. Shuttlecocks are not simple objects. We do not know really how they, or the universe they are in, function.

 

[Blobbenstein]

Maybe you need to ask in another forum ?

well, I thought I would ask it here.

 

[Ann Chovie]

You might say 'get one apple and then get another apple; put them together and then count how many apples you have.'

But apples are not simple things. They are complex objects(atoms and quantum stuff etc), in a complex universe, processed by a complex mind. All of which we probably only scratching the surface of understanding.
So it seems like you would be using a highly complex, and non-understood, system to prove something that one would thing was fairly simple.

To me, putting those apples together, is actually defining an axiom; that 1 plus 1 is 2...it only seems self evident.

what do you say?

Can I use oranges instead? Its just that I find it hard to contemplate this deeply as I have just spotted a maggot hole in my apple.

 

[Second Summer]

You might say 'get one apple and then get another apple; put them together and then count how many apples you have.'

But apples are not simple things. They are complex objects(atoms and quantum stuff etc), in a complex universe, processed by a complex mind. All of which we probably only scratching the surface of understanding.
So it seems like you would be using a highly complex, and non-understood, system to prove something that one would thing was fairly simple.

To me, putting those apples together, is actually defining an axiom; that 1 plus 1 is 2...it only seems self evident.

what do you say?

I think I see what you're saying. Since the physical world we live in is not fully understood, I think the only type of proof that will satisfy you will be one that is pure logic, like in a mathematical proof, e.g. along the lines of the page Andy linked to.

 

[Blobbenstein]

I think I see what you're saying. Since the physical world we live in is not fully understood, I think the only type of proof that will satisfy you will be one that is pure logic, like in a mathematical proof, e.g. along the lines of the page Andy linked to.

but that page is in the physical world as well...I think I started a similar thread a while ago.
There would, I think, be no "pure logic" without a universe with minds in it to understand.

 

[Blobbenstein]

what I mean to say is that 1+1=2 is self evident anyway, as is a lot of the steps in any formal proof, so I don't see a proof really addressing the problem.

 

[Second Summer]

but that page is in the physical world as well...I think I started a similar thread a while ago.
There would, I think, be no "pure logic" without a universe with minds in it to understand.

Not only the page, but we too, are in the physical world. "Pure logic" only means that the proof can be imagined entirely in our minds, and does not require physical evidence as part of the proof, as in the case with counting the apples. "Pure logic" doesn't mean the medium on which the proof is commonly distributed is non-physical, or that the minds needed to interpret and understand the proof is non-physical.

 

[Blobbenstein]

but does logic exist without a mind to understand it?

 

[Second Summer]

but does logic exist without a mind to understand it?

Logic is by definition non-physical and therefore doesn't exist as such, regardless of whether there are anyone there that understands it.

 

[Blobbenstein]

Logic is by definition non-physical and therefore doesn't exist as such, regardless of whether there are anyone there that understands it.

but how do you know? What does 'non-physical really mean, or imply?

how can something exists if it isn't physical in some way?

 

[Second Summer]

but how do you know?

I was told it was so. It's by definition.

What does 'non-physical really mean, or imply?

how can something exists if it isn't physical in some way?

It means it's imaginary, that it doesn't exist. The thing which distinguishes mathematics from other non-physical things like, say, language or God, is that it's entirely logical.

 

[Blobbenstein]

I was told it was so. It's by definition.

It means it's imaginary, that it doesn't exist. The thing which distinguishes mathematics from other non-physical things like, say, language or God, is that it's entirely logical.

yes, but how do you know it is logical without being able to process iit with you mind?

How can something be imaginary without a mind to imagine it?

 

[Second Summer]

yes, but how do you know it is logical without being able to process iit with you mind?

I'm not quite sure what you are asking. How can I know something is logical or not without processing it with my mind on some level? I can't. Does it matter?

How can something be imaginary without a mind to imagine it?

All things that don't exist are imaginary. It is true, such things can only be imagined by some kind of mind/intelligence. Still, a thing doesn't have to be imagined in order to have the property of being imaginary. For example: the pink parrot with an elephant trunk and tusks with spotted tail feathers and claws like an eagle. It's imaginary. As such it never came into existence. It was probably never imagined until just now. Still, it has always belonged to the set of imaginary things. It's like in mathematics where they have sets with an infinite amount of things, like the set of natural numbers. Not all of them have yet been imagined, and never will be.

 

[Blobbenstein]

I'm not quite sure what you are asking. How can I know something is logical or not without processing it with my mind on some level? I can't. Does it matter?

well, it matters to proving that 1+1=2.

if you don't know if a proof is logical unless you use your mind, and you can't be sure about how your mind, or the universe it is in, works, then you can't really be sure if 1+1=2. Just think how complex matter could be, and then on top of that think how complex a human mind could be.

 

[Blobbenstein]

I've been wondering if maths, and things like pi, are observer dependent.

 

[Blobbenstein]

You've probably heard of Gödel's incompleteness theorems, IS.....I think it concludes that whatever you try to prove, in maths, you always have to start with an assumption that you cannot prove..


edit:"Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic."

but I don't think the trivial axioms are trivial.

 

[Mr Crunchy]

As any computer programmer will tell you, 1 + 1 = 10.

My belief is that mathematics is fundamentally the study of how the human mind perceives the universe. Given a set of assumptions or axioms, what conclusions can we draw? It abounds with intangible objects such as imaginary numbers and infinite dimensional spaces. Numbers themselves are just an abstraction that conveys our concept of cardinality.

Mathematicians and philosophers have pondered for millennia about whether mathematical concepts such as numbers and shapes "exist" outside our minds as absolutes and whether logic we impose on them is universal or just our agreed upon conventions.

It's a tantalizing question but in the mundane routine of day-to-day life, the elementary systems we have unanimously accepted serve us well to keep things going. If I pick up an orange and then another one, I do hope they only charge me for two.