Is it possible that 1+1 doesn't equal 2?

Answer 1

Absolutely.
Mathematics is a system of conventions. The problem, as Wittgenstein pointed out, is that there is no real way to test whether we're all on the same page as to what the convention is.
This is how he expresses it.
Counting is a function, in which f(x)= x+1.
But what if you were talking to someone who was quounting? In quounting, f(x)= x+1 if x<28. If x is equal to or larger than 28 than x=28.
So the man who counts and the man who quounts both arrive to the same results right to the point where they reach 28. But while the counter goest on with 29, 30, 31... etc... , the quounter now goes 28, 28, 28...
So that while both were certain they were doing the same thing up to that point, it only appears then they weren't doing the same operation at all.

Answer 2

well, philosophically, the ONLY place that 1+1 = 2 is conceptually. Mathematically speaking, 1 always equals 1, A=A, a father is by definition a father of something. One plus one equals two, uno plus uno equals dos, itch plus itch equals nee.

However, beyond the conceptual, in the real world, lies the problem of definition. Say you have a chicken in the coop that is 1'-2" tall, and another chicken in the coop that is only 11" tall. One chicken is shorter than the other. Do you have 2 chickens? or 1.95 chickens? or 2.05 chickens? What makes a chicken a chicken? What gives one chicken more chickenness than the other chicken? Are all chickens supposed to be 11" inches? then what are we supposed to call the 1'-2" chicken?

That is the problem with definitions. A definition, at best, is a loose grouping of very similar entities. Like the old saying goes: "If it walks like a duck, and quacks like a duck, it's a duck". Or a chicken, in this case ;)

Definitions are nonetheless useful in the real world for logical expediency. A person from the city might not care that one of the farmer's chickens is slightly larger than the other. How does the city slicker logically reduce the number of chickens to only two chickens? Through applied concepts. A person has a rough idea of a chicken. He might not necessarily be thinking of a specific chicken, but he knows that if it's short, fat, squawks, and looks like a chicken, it's a chicken.

So the answer to your question is that it can't, but it does anyway. :) It exists conceptually, and is the basis for logic (and therefore, all human knowledge), but in relative terms, it can't exist.

Answer 3

I refer you to The Principles of Mathematics by Bertrand Russel. This book will set out to show that symbolic logic leads to 1 + 1 = 2.

Answer 4

If the expression 1+1 is merely a symbolic construction with a completely arbitrary value, then you could reassign what is represented by the symbols "1", "+", and "2".

Answer 5

Mathimaticaly, no.

In reality, very easily so.

In fact, mathematicaly speaking, 1 + 1 has roughly 2 to the -9813 percent of a chance to be something else. However, the likelihood of this being checked, or noticable, is incredibly low.

Answer 6

1 + 1 = 10 in binary.

Answer 7

I'm sure there's some new math, engineering calculation or science that has a different answer. Within the realm of basic math, though it can't be any other answer because that is the meaning and value that was ascribed to it. There would have to be a paradigm shift and discovery of unknown knowledge to change it now.

Answer 8

In chemistry yah.
If you take 1 mL water and 1mL oil it will, under most circumstances NOT mix to be 2 mL due to human error. For example you won't pour out EXACTLY 1ml... or drops of the substance will stick to the inside of whatever measuring device you are using...

Answer 9

Yes. For example in the case of rabbits, they could equal a much larger number.

Answer 10

It depends on the type of 1's.

There are positive 1's and negative 1's.

Do the math.