Explaining, as a mathematically disinclined individual, why 1+1 does not equal 2
It is common knowledge that adding one and one equals two, mathematically, 1+1=2. I believe that in a theoretical sense, this is true. It has been, and as long as traditional arithmetics state and retain the same rules, will continue being true, at least in an intangible and conceptual way.
I would argue that, for the sake of arguing, anything can be proven true if you decide to argue for it. To assume that 1+1 does not equal 2, and to redefine mathematics as someone who hasn’t any degree in mathematics, much less any proficiency in it, I need to assume a different, likely more philosophical, standpoint, as assuming a mathematical standpoint would be insensible for my position. I proclaim, with due hesitancy, that while 1+1 does equal 2, the equation does not always equal 2. In fact, whether 1+1 is always equal to 2 is frankly, by philosophical definition, indeterminable.
Stating that 1+1 always equals 2 requires a dissection of the statement. One is a number with a numerical value of a single unit; it is sometimes defined in different ways, but in most ways it is defined to be the multiplicative unit. Always, by the definition of Oxford Languages, implies ‘at all times; on all occasions.’ This is where, and the only place where, I find room to make my argument. To determine if 1+1 is always 2, then we, by grace of this definition, would have to infinitely add 1+1 and validate that it’s still equal to 2 until the end of time. Some arguments are made, those which attempt to prove 1+1=2, that define the equation as necessarily true, and if proven untrue would throw off the basic assumptions that are generally useful. However, just because someone hasn’t found a case where 1+1 is not equal to 2 (and because it is argued that it is irrational) does not mean it is always equal to 2, because it has not been tried infinitely.
The concept of adding ‘1 and 1’ cannot be merely implemented in our physical plane of existence. Primarily, we need to conceptualize 1 and relate it to the real world. Suppose, we define one unit of ‘1’ in real life as an apple, translating, therefore, to 1=apple. Hence, 1(apple) + 1(apple) results in 2(apples). Therefore, in real life, our definition of ‘1’ must adapt to the scenario at hand. The definition of 1 could potentially differ between individuals. Additionally, it becomes imperative to question what reality actually is. Could it be our personal mental constructions determined by our senses? And is this perceived reality identical for everyone? If a truth in my reality could potentially be a falsehood in someone else’s, that would mean the perceived ‘1’ in my reality might be different from another individual’s perceived ‘1’ in their own reality.
Furthermore, it’s impossible for us to truly know ‘reality’ because that would mean that we know all things, all facets of a reality made of things, and, ergo, all facets of all things in our reality, which, in due part unto human ignorance, is and will, presumably, always be, a universal and anthropic truth. But we don’t know the things we don’t know and our reality is based on the limited responsiveness of our senses and comprehension abilities, so, therefore, it disqualifies the notion that we are aware of all things, meaning we as humans can and will never know the truth of our reality.
By my asking for you to open your mind to my presupposition, I may also contend that, in a more mathematical, or rather logical, fashion, 1+1 may not always be equal to 2, may not usually be equal to 2, and may not, in reality, be equal to anything. In modern quantum physics it’s commonly known that the closer we look at reality and our physical world (my, as aforementioned, supposed reality), the more it seems as though nothing is actually tangible or ‘true,’ for that matter. A quantum particle has the ability to be existing and non existing at the same time depending on if it is observed. Things can be true, things can be false, and quantum physics can deem things both concurrently true and false. The closer we look at quantum particles, the more we see that everything is made of nothing. Therefore, and by reasonable implementation of these logical boundaries, if everything is made of nothing then, in execution, I would say 1=nothing and nothing(0) + nothing(0) is still equal, by no stretch of the imagination, to nothing. So, therefore, 1+1=0.
In relation to my statement that, while 1+1 conceptually and in an intangible manner, usually equals 2, though it doesn’t always equal 2, and considering that, when translated into our reality, id est an apple, or quantum particles, for that matter, assuming the adding 1+1 until the end of time and factoring in an infinite number combinations of existing or non-existing quantum particles in those apples, it can be assumed that, at some point, those apples will cease to exist, and, therefore, my thesis that 1+1 will not always equal 2, is, axiomatically, true.
