I really don't see why people have an issue with this, as if there was something magical or philosophical to be discovered about something as logical and obvious as adding a unit to an already existing unit, so as to get... two units! How do YOU wish to take 1+1 ? Please Register or Log in to view the hidden image!
This is silly.Please Register or Log in to view the hidden image! One and two are words. One is the word we use for a single unit. Two is the word we use for a pair of units. If you put 2 single units together you will get a pair. End of discussion.
This is anything but not a stupid question. The truth of analythical statements resides in the non contradiction law, which is necessary but not enough in sintethical ones (the statements about fenomena).
The laws of arithmetics are usually derived formally from the system of statements called Peano's axioms. In Peano arithmetics you can mechanically derive (i.e. prove) from the axioms the statement that 1+1=2 (or 321+37=358). However, Peano's axioms only tell you what you can _do_ with natural numbers but they don't even try to say anything about why numbers behave like that. A more interesting approach philosophically is one that tries to explain natural numbers using the theory of sets. Here one says that 7 is nothing else but what is common to all seven-element sets. This definition seems to go in a vicious circle but it does not. (I don't have time to explain it but if you're interested why it's not circular, try to find something on Frege's definition of numbers.) In this approach addition is reduced to the union of disjoint sets, that is, to collecting the elements of two sets having no common member to form a resulting set. Of course, you can also prove that 1+1=2 or 321+37=358 in this approach too. So if you want a short answer, I would say 1+1=2 because the notion of a set and the laws of set theory imply it.
1+1 = 2 since 1 x 2 = 2 ; 1+1 = 3 if single ; 4 if twins ; 5 if triplets and so on...Please Register or Log in to view the hidden image!Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image!
No... our knowledge has a basis. Take one orange, take another orange, and put them next to each other. You now have 2. They could have changed the was we drew/said 2, but we would still need a symbol for it.
Of course, its like simple algebra - you have two - meaning double of one, which is an abstraction, dependent on your ability to touch, see, smell, taste and hear - double of an object which you define as an orange. And of course, the definition of an Orange is culturally relative.
They are two oranges but yet they are still an orange...right? So although 1+1=2 I could say that two is equal to 1+1=1+1 so in a way I could say that 1+1=1+1+1? Also if I were to see a reflection of an orange in a mirror and asked you how many oranges are there, what would you say? 1 or 2 or "infinite"?
What i would have said. Please Register or Log in to view the hidden image! However i can see your point Qfrontier but 1 object plus another 1 makes 2. Yes the words have been ascribed by man but because the symbol relates to a possible and very real concept i.e. it is possible to take 1 object (any object) and then gather another one and you have 2 of them then 1 + 1 = 2
I dare a philosopher to question 1+1=2. I will proceed to throw an orange in his face, followed by an other... Hrmm... two impacts. Two oranges ? Please Register or Log in to view the hidden image! Wow, I'm in a good mood... Please Register or Log in to view the hidden image!
Originally posted by qfrontier They are two oranges but yet they are still an orange...right? No. They would be orange(s). So although 1+1=2 I could say that two is equal to 1+1=1+1 so in a way I could say that 1+1=1+1+1? No. This doesn't follow with reality. Also if I were to see a reflection of an orange in a mirror and asked you how many oranges are there, what would you say? 1 or 2 or "infinite"? If you knew it was a mirror you would say 1. Otherwise you would say 2. You could get philosphical about the numerical system... but I'm sure this isn't the way.
- Are language and mathematics entwined? -So in your words Persol, for you what is reality? -Why would you say 2 if it wasn't a mirror reflection?
1+1 Granted, used to people would add 1+1 and get any number they wanted. NO problem. But at about the time bartering was introduced people with too many pigs and not enough porn would get burnt time and time again. Thus the standard was introduced. 1+1 =2.
I think your getting a bit confused Persol. 1 + 1 does equal 1 + 1 (1+1=1+1) as you said. This does not mean that 1+1=1+1+1 though because this is 2=3 and 2 does not equal 3. With the mirror there would still only be 1 orange because the other is just a reflection. It is not actually an orange; you try eating it! :bugeye: Someone might say that there are 2 oranges (if they didnt know one was a reflection) but they'd be wrong becuase there is only one! Why would there be an 'infinite' number of oranges because there was a reflection of 1 orange?? :bugeye:
Originally posted by Neville I think your getting a bit confused Persol. Nope... meant what I saidPlease Register or Log in to view the hidden image! 1 + 1 does equal 1 + 1 (1+1=1+1) as you said. This does not mean that 1+1=1+1+1 though because this is 2=3 and 2 does not equal 3. This is exactly what I said. With the mirror there would still only be 1 orange because the other is just a reflection. It is not actually an orange; you try eating it! :bugeye: Someone might say that there are 2 oranges... The question was "what would you say?" My answer stands. If I knew it was a mirror then 1 orange, if I didn't know then I'd say 2. That doesn't mean I'd be right when I said it. Why would there be an 'infinite' number of oranges because there was a reflection of 1 orange?? :bugeye: I didn't understand that either.
Originally posted by qfrontier - Are language and mathematics entwined? At the 1+1 level I'd say no. You can demonstrate 1+1 without language. At higher levels though language is needed. -So in your words Persol, for you what is reality? Whatever I know. The trick is to continue to try a 'know' more and more. -Why would you say 2 if it wasn't a mirror reflection? I said "if I didn't know it was a mirror". I'd say 2 because I see 2 oranges. I don't know that one of them is just a reflection. Therefore I see 2 and would say 2.
Theoretically, if you put 2 mirrors on both sides of the orange facing each other, you would see an infinite number of oranges. In reality you will not see infinity because it is impossible to place the mirrors perfectly parallel to each other.
