I saw the question “Why is 1 + 1 = 2?” on Quora, a Q&A site, and I liked the answer I gave to it. I provided three alternative solutions. So here it is, three cases where someone might not consider one plus one to equal two.
My Quora post
If you ask any mathematician, they will tell you 1 + 1 = 2. Straightforward, unimaginative.
If you ask a nihilist what 1 + 1 equals, he or she will likely say the expression means nothing. If they are feeling particularly spirited, then they might say the bolder 1 + 1 = 0. If they are the extremely skeptical type, however, they might hold that 1 + 1 can not be equal to anything beyond itself. This last type type would reject even the notion that 1 = 1, (Aristotle’s “A is A”) on account of the number one on the left being distinguished tempo-spatially from the number one on the right. Even this letter Z being read here is not the same Z it was two seconds ago; at the very least, its pixels have refreshed.
If you ask someone who believes in an omnipresent deity or who holds that all things are united with all other things, he or she might not only say that 1 + 1 = 1, but would likely reject the notion that entities are distinguishable from one another in the first place. For such perspectives, one cannot be added to anything else, as it already encompasses everything. Isaac Newton’s law of universal gravitation is something they might point towards as well. Does anyone know what the universe plus one is? How does someone add anything to something that already encompasses everything? One does not, it might be said.
“Humankind has not woven the web of life. We are but one thread within it. Whatever we do to the web, we do to ourselves. All things are bound together. All things connect.” – Chief Seattle
If you ask a Gestalt psychologist what 1 + 1 equals, then they might say 1 + 1 = 3, or 1 + 1 = 4, or quite possibly any positive integer up to infinity. A popular adage in Gestalt psychology is “The whole is more than the sum of the parts.” One such example is Kanizsa’s Triangle. A photographic mosaic (larger picture made up of smaller pictures) is another example. Also to consider are optical illusions, such as the rabbit/duck, and the young lady/old lady. Ten bees spread out in a garden is no big deal; ten bees in a car is a swarm.
It’s a complex world we live in.