I wrote this extremely detailed response in another thread, and thought I would like to share it with the rest of you because the nature of mathematics is a very tricky one that many people fall prey to. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Mathematics is fundamentally about relationships first and foremost; numbers are a way to express those relationships. Hold out your finger. Let's call that "one." Now hold out another finger. Great. Let's call that "two." So now we have "two fingers" held out. But you see, this example necessarily RELIES on you defining a single finger as being "one." If you do not tell yourself first and foremost that a finger = 1, you COULD NOT say that two fingers = 2. What if I defined my hand as "one?" Well, I could put out both hands and say "I have two hands." But again, I COULD NOT say that two hands = 2, unless I first said that a hand = 1 This is important, because what counts as "one" changes depending on the thing you are attempting to describe. In the first example, 1 = a finger. In the second example, 1 = hand. This should tell you immediately that any numerical description you make of ANY PHENOMENA must be grounded in what you determine is equal to "one." The problem is, you can call ANYTHING "one" to suit your needs. I can call my hand 1, but you could come along and argue with me that it's actually 5. Nobody is right or wrong in this case, because our "unit" (the thing we call "one") is different. For me, the unit is a hand. For you, the unit is a finger. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Immediately, the question you should have is this: "what allows me to call something 'one?'" Well, you might think "I can just point to stuff and call it whatever I want, duh," but it's actually extraordinarily complex. The reality is, we can label anything as anything, so nothing is stopping us from calling things "one." However, the label "one" would have no meaning unless it was purposefully defined against its opposite. "one" means NOTHING unless there was such a thing as a "not-one." So you see, every time you call something "one," you are accounting for the possibility of a "not-one;" be it "two," "three," or "four." So when I label a single finger as "one," for that to have any meaning, I have had to already manifest a "two" without even considering any other fingers. Why is that? Well, how else could it be? If I label my finger as "one," without accounting for a "two," then calling my finger "one" has no meaning or utility. I might as well call it "potato" or "wioehtgoiasgjgioaweo." ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- So to recap: Mathematics is a study of relationships. Numbers facilitate this process. In order to describe something numerically, we must first define a "unit." Otherwise, it is impossible to do numerical mathematics. A "unit" only has meaning insofar as we view phenomena as "not-one." So here's the kicker: You actually DO NOT know that 1+1=2 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- You must first ask yourself "what is one?" "what is addition?" and "what is two?" You CANNOT know "1+1=2" unless you can answer these things. As we have shown, "one" is a completely relative term. What counts as "one" is decided either on a whim or by a specific human motive. That means that there is never a "one" for you to find somewhere out in the world, as it is ALWAYS a label your mind must assign. "But Rend, what about the spiritual gurus who say that all is one? Couldn't I find that out in the world?" Heh, they say that because it is what is communicable. The "oneness" that nonduality entails is nothing like the quantity "one" in mathematics. Furthermore, because we've shown that a "unit" only has meaning insofar as we view phenomena as "not-one," this tells you that ALL NUMERICAL DESCRIPTIONS are grounded in you personally viewing phenomena as fragmented. For example, who's to say I'm holding out 5 fingers? How do you know that it's not just 1 hand? What's a finger anyway? Isn't it just a part of the hand? So it's all just one big hand... there are no fingers... but wait, isn't the hand just a part of your arm?  Etcetera. You realize the only reason a "finger" exists is because you said it did? There is no "finger" there. Or is there? it's hard to tell. The point is, you call things "one," "two," or "three" only because you are able to distinguish and categorize. What if your distinctions and categories are wrong? What would you label as "one?" How do I know I'm not deceiving myself when I say "I have 10 fingers?" ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- So this should send warning sirens in your epistemology radar (what, you don't have one?) already. We thought we knew that "1+1=2" But we cannot even say what "1" is without appealing to a whole host of complexities. And the more we define and categorize, the more we must defend and rationalize. It's a vicious cycle. Here's the reality. You can't say what "one" is. No matter what you point to, it's all in your mind. Even if you say that "'one' is a mental construct! I've got it! I know what it is! Beat that, Rend. It's all mind-stuff, see? It doesn't have to be physical but all you did was give physical examples." you're wrong, and you don't know what "one" is Because, you see, now you have to explain to me what "mind" is. HAHAHAHA good luck. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- So the wise thing to do here, really, is to admit that you do not know when you really dig deep. The problem is most people do not dig deep. You can do this "deconstruction" process with literally ANY piece of "knowledge" you think you have. Your knowledge feels so solid, like a mighty oak tree, until you realize there are no roots on this tree. Now, that doesn't mean that you should give up on knowledge altogether, nor does it mean knowledge isn't useful. Knowledge is SUPER USEFUL! In fact, that's all it really is! Utility. 1+1=2 is super useful when you're counting your possessions, for example. So you want to "know" these things insofar as they serve your well-being, while simultaneously being cautious that ultimately you really just don't know.