1 + 1 = Invalid: cannot add distinct objects

[VulcanRevenge]

Before we delve into this idea I would like to say that this isn't some conspiracy theory, nor is it some strange idea about how everything is different than we think it is. In fact I wouldn't be surprised to know there is a lack of surprise or epiphany amongst readers of this post. I strictly wish to discuss what I have observed to be a common fallacy of how people organize, and categorize living beings, objects, and ideas (and yes these are categorizations in and of themselves, oh the irony)

As to the relevance of this fallacy, it has been according to my observation that a person who is of the understanding of this fallacy tends to show similar reactions to events as other people who view the world in this way. In other words, this fallacy has visible and vivid repercussions in many aspects of a person's behavior.

Let's start with an interesting question. Imagine you are the principal of a prestigious elementary school and you are interviewing children to test their mathematical capabilities. You are interviewing a certain frustrating child who doesn't seem to understand the question you are asking. You say, "If I have two apples in my right hand, and three apples in my left hand how many apples do I have?" The child briefly looks at your hands and answers, "You have two apples in your right hand and three apples in your left hand." You try to clarify by saying, "So how many would I have all together?" The child responds in the same way, "You would have two apples in your right hand and three apples in your left hand." Trying not to lose your patience you try to ask a different question, "Okay, so if there were three people in a room and another person walks into that room how many people are in that room now?" the child responds, "Who are the people?"

The child has the inability to categorize. Where most would see this as a major disability, some would understand the deep logic behind this idea. The idea is that there are no categories, that every object, and living being is inherently unique simply by existing. There are no two objects in the universe that are exactly alike. There are no two atoms that are exactly alike. In real life is there really a way to "add" objects together? Are you then assuming that by putting the objects in juxtaposition they become more than one of the same exact object?

With this train of thought we can also say that in the true world, there is only one number. On the deepest level of categorization there would only be one of anything. I am in no way suggesting that we shouldn't categorize because the only way we advance in learning is through categorization. All learning is based on categorizing and relating situations. For example, we can assume that if you bite an apple that a part of that apple will come off and into your mouth whereas the apple will have a large part of it missing in the exact place where you took a bite and of the same size that your mouth was when you took a bite. However, saying that since a certain object will react in a certain way 100% of the time so another object of it's same type will act in the same way 100% of the time is incorrect. How can something be that certain? The only thing that is certain is uncertainty. I'm sure most of us have experienced a dud firework, a device that will work only after being kicked, or a person that just won't listen no matter how hard you put effort into trying to help them do so.

You might be thinking at this point, "what's the point? Nobody assumes anything to be entirely accurate anyway." This is where our opinions would differ. Have you ever experienced anger? This emotion comes from a variety of ways and one of them can be unmet expectations, expectations you were certain an individual or an object would meet. How about frustration? Another emotion that can come from a wide range of sources one of which can be when your ideas you're certain of come into clash with another logical source.

Uncertainty is everywhere. However, it isn't something to get depressed about, it's only something to realize and accept. Anger, embarrassment, pride, and frustration can be products of placing too much certainty on too few people and objects. If understood incorrectly however, this idea can destroy emotions such as confidence, hope, and love. This is why uncertainty should be understood as something that applies to all things but only to a somewhat limited degree. Just for example, I would say the most accurately someone could predict an event is about 99%. If we believe that number to be 100%, those negative emotions can come from the remaining percent of times our prediction is incorrect, whatever it really may be. If uncertainty is understood in all things, these negative emotions tend to be frequently avoided.

The only thing that is certain is uncertainty. As I am writing at this moment, I understand that what I am writing isn't even certain, that there is probably someone out there who understands completely differently than I do and can logically disprove my argument. To that person, I thank you for the competition so that I might refine my own ideas and learn from yours.

I do not ask that we do nothing or have no expectations, nor do I ask that we have no opinions or stop trying to learn about something we are uncertain of. My only desire is that we are wary and careful about what we place our confidence in and what we are certain of. It is imperative that we always leave room for error and uncertainty.

[Mulie]

It was a nice, thought-provoking read, but there's nothing to debate in this thread.

[Patashu]

if you can't categorize objects you're p. screwed because everything scientific is discovered via induction and extrapolation to the unknown

saying 'everything is different' isn't very useful since it ignores the fact that objects can still be similar and express similar phenomena but it doesn't give us any better tool to use in place of it

[customstuff]

Very good first post. Longer than any of my posts! Welcome to FFR and I somewhat agree, but somewhat not...

[NFD]

This reminds me of www.timecube.com

[TC_Halogen]

Welcome to FFR!

Such a thought-provoking idea, I'll give you that much. Here's my side on it: while no two atoms are the same, things are categorized in such a way that they can be grouped together. While they are not in fact 100% identical, I would say that it's just human nature.

Your thought on this topic though is plausible in my opinion, which is why I can't really come up with a clean-cut rebuttal to it.

[Patashu]

I'm pretty sure, actually, that the only thing making two particles of the same type distinct is their place and energy.

There's no way to tag an electron and find it again later.

[elchocolato]

We can be certain 100% because of science Unless you bring it down to the quantum level where you've got Heisenberg's uncertainty and what not, but I suppose that's a whole other topic, and one that really doesn't pertain to eating apples...but then again this thread doesn't really pertain to eating apples either. I think I'm just hungry and can't move my eyes past that sentence "...if you bite an [sweet, delicious, mouth-watering!!!] apple...". Mmm.

[Cyanite]

This is just splitting hairs, really.

When you have two apples in one place and three in another, and you claim to have five in total, you don't categorize them under the guidelines of "identical in every physical way". You're just acknowledging that all five are apples, in one shape or another, and they can be categorized under that basic idea.

Honestly just the fact that someone would put this much thought into such a basic principle is somewhat ridiculous in itself.

oh, and welcome to FFR

[devonin]

Originally Posted by Mulie

It was a nice, thought-provoking read, but there's nothing to debate in this thread.

This is a true statement. Thanks very much for the thread and the thought that went into it, but you're basically saying "If we assume X instead of Y, the result is X instead of Y" to which the only thing we can say is "Yup"

And for reference, as soon as the child makes a statement like "You have two apples in one hand and three in the other" they are already grouping things and understanding categories. The proper response to the question would have been "What's an apples" because an inability or unwillingness to group similar objects together because they are not identical would necessarily include a refusal to understand or acknowledge the whole concept of plurality in the first place.

[Reach]

In additional to what Cyanite said, there are various ways to conceptualize 1+1, not just through objects themselves.

Consider only proportions. 1+1 must = 2 through simple understanding of proportions; that is, if you double the amount of X, well, by definition you have double the amount of X. That's really what's happening here, and in math you can formalize this system and call it an axiom.

Whether or not what you're adding is 'exactly identical' or not is irrelevant; it's an abstract concept. From there, you can take that abstract concept and apply it to real world problems.



With respect to uncertainty, sure, everything is uncertain, but it doesn't matter. If you care that much about uncertainty, it's called quantum mechanics, and you can describe the universe using probabilities. Either way, it's math, and you're still using the exact same abstract concepts and applying them to the real world.

[Izzy]

1+1=2 simply because that's how we developed the mathematical system. We declared that it did by defining what 1 is. Math isn't definite in anyway to reality since it is artificial. I don't see the point of this. More of a dumb play on words imo.

[0MG]

To say that no two atoms are exactly alike is only saying that they are in different fixed positions possibly at different times, and therefore are different. But taking an individual atom, and then juxtapositioning it in into the same place of the other atom would therefore make it the same thing. Nonetheless to say it IS the same thing because there are obviously two identical atoms that aren't each other. That would rectify a whole new issue. There comes a point of irrelevance of whether or not something is the same or not. An apple can weigh more than another apple by .0000000000000000000001 of an oz, but it still is the same thing. They aren't each other like I said before, but they are the same.

[Izzy]

This is also most likely some copy paste post. Doubt he will respond.

[0MG]

Originally Posted by Izzy

This is also most likely some copy paste post. Doubt he will respond.

What?

[Izzy]

The opening poster only has 1 post. His post is either a bot or just someone going around forums posting some copy paste crap.

[devonin]

We've had similar posters in the past. They are rarely bots, but are often people who have accounts on many forums and simply make a thread and post it to all of them.

The last one we had was called Coberst, if you do a search for him you'll see what we mean.

[VulcanRevenge]

Yes, I said in my post that it IS necessary to categorize, it's important that we do, because if we don't then it's impossible to grow and learn from information. For example, you wouldn't be able to say "oh, I shouldn't kick that person in the shin because I'm angry with them because the last person I kicked in the shin just returned it back even worse." You wouldn't categorize human beings in the same group and would expect every human being to act completely and utterly differently.

Izzy probably hit it right on the head however, "1+1=2 simply because that's how we developed the mathematical system. We declared that it did by defining what 1 is." That's a large part of what I'm trying to say, that our mathematical system is a human creation based on something that doesn't necessarily entirely and accurately exist in the real world. There are many people who don't realize that, and I guess that's what my post is, it's a mind-opener rather than a debate topic, but apparently there are still things to debate here. (And no this is no copy paste trash, this is my original post that is no where else on the internet).

Devonin, "The proper response to the question would have been "What's an apples"", you are exactly right, I meant to change that, and I knew someone would pick up on that. I was having a really hard time trying to illustrate the example, any other ideas would be helpful.

OMG I forgot to respond to you. I have a question for you to answer. Maybe those two apples are similar, and if you place an object in the same exact position, shape, atomic makeup, electron movement, and all else as another object then yes, I would agree with you, theoretically the two objects would be exactly the same. Here's the question, is that possible in the real world? So, two objects may be very similar, but will they react exactly the same way in every situation possible? Of course, we as human beings cannot cause every possible situation for that object, but even for what we can do to the objects will the two objects react the exact same way in all those situations?

A lot of scientific experiments are based on this concept. They try a new drug on mice. They have about a hundred mice, many people would say all these mice are exactly the same, and then there is only a percentage of them that react similarly. Many people take that percentage and take it to an extreme, sometimes forgetting the remaining percentage and sometimes believing it is consistent amongst every single similar object. That is a fallacy.

[devonin]

Yes, I said in my post that it IS necessary to categorize, it's important that we do, because if we don't then it's impossible to grow and learn from information.

So it sounds like, in fact, the child in your example who cannot do this -does- actually have a serious disability. Understanding the "deep logic" behind this (which the child probably doesn't anyway) in no way mitigates the fact that this is a skill that everyone needs to have to function properly in society.

So, two objects may be very similar, but will they react exactly the same way in every situation possible? Of course, we as human beings cannot cause every possible situation for that object, but even for what we can do to the objects will the two objects react the exact same way in all those situations?

That question doesn't actually challenge any assertion that he made. His point is that the definition of "apple" isn't so precise that it applies to one and only one instance of appledom in all of creation.

Our definitions for categories of things contain enough leeway to allow for the sort of categorization you say is impossible.

Apple: : the fleshy usually rounded red, yellow, or green edible pome fruit of a usually cultivated tree (genus Malus) of the rose family ;

Clearly all the apples in the person's hand fit into that definition, such that referring to them all collectively as "apples" is perfectly legitimate.

"the same" doesn't -actually- mean "Completely identical in all respects" That's why we have both the word 'same' and the word 'identical'

Many people take that percentage and take it to an extreme, sometimes forgetting the remaining percentage and sometimes believing it is consistent amongst every single similar object.

Those people are stupid though, and shouldn't be held up as representative of anything but their own stupidity. Anybody who would see "We tested 100 Y, and 30% exhibited this behavior X" and say "Therefore it will do X to 100% of Y" is just an idiot and can be safely ignored.

[Izzy]

Originally Posted by VulcanRevenge

Izzy probably hit it right on the head however, "1+1=2 simply because that's how we developed the mathematical system. We declared that it did by defining what 1 is." That's a large part of what I'm trying to say, that our mathematical system is a human creation based on something that doesn't necessarily entirely and accurately exist in the real world. There are many people who don't realize that, and I guess that's what my post is, it's a mind-opener rather than a debate topic, but apparently there are still things to debate here. (And no this is no copy paste trash, this is my original post that is no where else on the internet).

Glad to see you came back.

I remember awhile back I created a thread about time and how I didn't think it existed. I argued my point for awhile, but I don't believe anyone really understood what i was getting at. This is the same thing though. Time and even the first three dimensions are just concepts that we created and defined. They don't really exist since we made them to be used to solve problems that are probably also entirely artificial. Just have to accept that everyone is probably wrong about everything.