Is there a way to refute '1+1 = 2'?

[Fan of Science]

Spiral Out: Just think of a number line with the set of natural numbers marked. Start at the point that corresponds to the number one. Then, move 1 to the right, which represents the operation of "adding 1," and you'll end up at the point marked with a 2, the "squiggly line." The operation of addition is essentially sliding along the number line.

[Synthesis]

That's nonsense. The number 2 is an abstraction, as all mathematical objects are. Being ignorant of the meaning of these mathematical abstractions does not in any way undermine them. It simply means you have not taken the time to learn mathematics before commenting. It's not just math that has this level of abstraction, so do other subjects, like economics. As an example, the amount listed in your bank account is not a reference to any specific, unique, set of dollar bills.

The number two is an abstraction of exactly what? If you wish to apply the term abstraction to economics, then consider the abstraction of labor-value earned into its money-form.

[Fan of Science]

Synthesis: The labor-value theory in economics has been debunked long ago and so no I will not waste my time trying to argue that a non-empirical value claim is in any sense true. The number 2 is an abstraction that little children learn. They learn what is common about 2 chairs, 2 dollars, 2 houses, 2 women, 2 schools, 2 cars, etc. That's the part that you completely reject.

[Magicpotion]

The number two is an abstraction of exactly what?

I've always conceptualised the number two as an abstraction of polar-opposites on a spectrum.

Day and Night
Hot and Cold
Up and Down

Although these things may be unified in reality (all is one), we conceptualise them as two different things to compare, contrast and show the variety within the spectrum.

[Jacqueline Sheehan]

Biologically speaking, 1+1 might = 3.

[SubatomicAl1en]

you can't refute 1+1+2. It is simply pure logic that is implemented into our universe. What if in some other universes laws and logic work differently?

[SubatomicAl1en]

It's like asking "could the speed of light be slower or faster?"

[LuckyR]

Sure: 1+1=10

Simple, really.

[Sculptor1]

Sure: 1+1=10

Simple, really.

Clearly.
And
12+4=A

AND

Let's not forget the connoisseur's:

7+1=10

[Hans-Werner Hammen]

The aequation = an assertion "1+1=2" logically follows from a presupposition, ONE assertion Of symbols symbolizing an order OF numbers
1, 2, 3,...
Let the symbols be different
2, 1, 4, 3, 6...
then 2 + 2 = 1, and 1 + 1 = 3

[LuckyR]

Sure: 1+1=10

Simple, really.

Clearly.
And
12+4=A

AND

Let's not forget the connoisseur's:

7+1=10

I was writing in binary, what are you doing?

[Sculptor1]

Clearly.
And
12+4=A

AND

Let's not forget the connoisseur's:

7+1=10

I was writing in binary, what are you doing?

The first is hexadecimal, and the latter is octal.

[LuckyR]

I was writing in binary, what are you doing?

The first is hexadecimal, and the latter is octal.

Ah so, but 1+1 is still 2.

[Sculptor1]

The first is hexadecimal, and the latter is octal.

Ah so, but 1+1 is still 2.

Unless its binary, in which case it is 10.

[Sealight]

I think people who argue about the true value of the statement '1+1 = 2' try to look deeper into the matter.
There is no such a thing as '1+1 = 2' in physical world. In physical world one can say '1 apple + 1 apple = 2 apples' which I doubt is true since not all apples are the same.
In Algebra it is true by the way of constructing integer numbers. Still in Math but outside Algebra the statement is not necessarily true. Look at Banach-Tarski paradox that basically states '1+1 = 1' https://en.wikipedia.org/wiki/Banach%E2 ... ki_paradox
So, it is a very narrow area where '1+1 = 2' is true and that area is Algebra that doesn't cover the whole Math. And Math is not everything. So I would say that probability that '1+1 = 2' is true is very negligible and almost zero.