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Is the number "3" real?

There are three cars in my driveway right now. I can see and touch the cars, but I can't see or touch the number "3". Are numbers inherent to reality, or merely mental constructs?

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    Sep 22 2013: Your question is to be answered by looking at language. To transfer information from one to another humans have developed spoken/written/signed language. Every known thing, whether material or conceptual, has been given a name. Even quantities have been given names. The conventional English name for the quantity comprised of a single item is "one". When another single item is introduced to form a plurality of single individual items that quantity is named "two". Adding another single item to the group changes the group name to "three". Each time another item is added a new name is necessary. Without this system information could not be shared easily and accurately. Words do not have weight or take-up space. Words are not material and cannot be touched. Now go answer Fritzie's question and you will have your answer.
    • Sep 23 2013: Also about language, I'd like to complement your answer by saying that which item is considered to be "the same" as another (and only things which are "the same" can be encompassed in a single number) is also a matter of language. We choose what to group together and what to differentiate, according to standards which are based purely on our perception of the world or our purposes at that moment, i.e. the quality of an object we want to emphasize. A very obvious and trivial example: an orange could add up to a number of both fruits and orange objects, but an orange t-shirt couldn't add up to the first. Now, each orange and each orange t-shirt is obviously unique. They don't have exaclty the same shape and tone of orange, yet we choose to consider them as "the same". And what you choose to group together is crucial. You pick for example a talk I was just watching, the one about stress. They cite a research about "cases of stress", and they treat all "cases of stress" as being the same, and quantify them. But what if, due to some unknown particularities , some of them shouldn't be compared to the others? This could compromise the whole research.
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        Sep 23 2013: A single banana, a single pencil, and a single pocketknife form a plurality of individual, dissimilar items called a group. The quantity of items in that group is spoken/written/signed as "three". Do we agree the identicalness/sameness, or lack thereof, of each individual item in no way determines the name given to the sum total of those items? Thank you, Ryan!
        • Sep 23 2013: Hello, Edward. If by "sameness" we're talking about objective sameness, then we certainly agree. But what I was trying to say is that, in order to have any number, we have to choose what we are going to group together in order to form that number. Your banana, pencil and pocketknife do not exist alone in the world, they are surrounded by other objects. Choosing only these three within the whole array of possible objects is the subjective part of mathematics. Let's suppose the banana, the pencil and the pocketknife are on a table in a room. You could've chosen to encompass the table in your acount. Then you'd have four items. You could choose to encompass the room itself. Then you'd have five. Now you could say that the room is not a single entity, but is composed of four entities called "wall", one called "ceiling" and another one called "floor". You'd then have ten items instead of three. If there is a door in your room, you might want to include it as well, and then you'd have eleven items. Then you see the window, but you think it is irrelevant for your purposes and decides not to include it. Then you still have eleven. What I was trying to suggest is: mathematics is not as objective as we tend to think, because calculation can be done only after we have a criteria for what can be grouped together and what cannot. Three items are three items only within a previously estabilished criteria. Under some other criteria, they could be two, four or a million. I'm not sure if I'm expressing myself clearly.
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        Sep 23 2013: A "group" is a single entity no matter how many discreet objects it includes. I think you are saying that since there are 26 letters in the alphabet it cannot be determined which should be used to spell a word. Of course you would be correct IF THERE WERE NO CONVENTION, no consensus, no agreement, no uniformly adopted and applied standard. However, there actually is (thankfully) a convention for mathematics (and for spelling). We ALL agree the name of the number representing the quantity of items/entities is "three", and the name of the number representing the number of groups is "one". Same page Ryan?
        • Sep 23 2013: Not sure if we're on the same page. This discussion is full of complicated, abstract things. To make things worse, (besides my very anglophone name) I'm not an English native speaker, which means my language skills in this language are not as perfect as yours, and some of my language mistakes can compromise the meaning (while others, merely aesthetic, won't). Still, I'm very proud of my English skills, because mastering a foreign language to perfection is nearly impossible, and it takes time. I'd be able to explain the whole thing much easier if you could speak Portuguese, though. And well, I don't really know what to say now, because I tried to explain the idea two times already, and still can't make you see my point. I'll have to just recommend you sources which discuss similar things. You seem to be somewhat acquainted with linguistics. Have you ever read Ferdinand de Saussure's Course in General Linguistics? He doesn't talk directly about numbers (as far as I remember), but you can apply much of what he said about signs to understand numbers as well (which is what I'm doing here). Sorry for not going on with the conversation, but I really don't know what to say after all that.
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        Sep 23 2013: It's all good Ryan. No worries. Kudos on your English skills, I had no idea you were using a second . or third?, language. You should be proud of your skill. No I have not read de Saussure. My interest in linguistics is simple necessity. I often fail to grasp the meaning of an idea, so please don't be so hard on yourself. A better mind than mine might grasp the core of your idea right away. For now let's just exchange opinions. I say "three" is real. Live long and prosper!
    • Sep 23 2013: Hi, Edward. I agree with your comments on language. Is "three" purely conceptual? If so, and if it contains information that can be transferred, have we created something from nothing? How does "three" differ from "unicorn?"
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        Sep 23 2013: A branch of Linguistics, called Semantics, deals with the development, evolution, and especially the meaning of words. Just like naming a new baby. Folks agreed that the new Holmes baby boy would be named "John". All the family and friends agreed to follow the ruling and you have been "John Holmes" ever since. Everyone agrees what to call the number representing a group made-up of a single item plus another single item, plus another single item. That quantity is named "three". The quantity is not called "unicorn" because that name has been used to identify a mythical liiving creature. It is all about agreed upon meanings. Also, I think there is difference between "conceptual" and "real". The word/name "conceptual" implies something is still on the drawing board and has never been proven by use. Once a thing (a gizmo; an idea; a process; a method; a procedure; a name; etc.) is proven by usage it is no longer conceptual. "Three" is not conceptual. "Three" is not material. "Three" is real?. . . that depends on the conventional semantic purpose and meaning of the word/name "real". I say three is real.
  • Da Way

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    Sep 28 2013: To answer if 3 (or any number) is real you have to first establish if '1' and '0' are real. I.e. 'Is there existence'. If you accept that, and you assume all existence is composed of a fundamental particle or substance (the '1's, lets call it atom for now), then you may deduct that numbers are real irrespective of human preception.

    Lets take your 3 cars for examle. To count 3 you have to pre-define that the pattern of 'atoms' presented in front of you is 'a car'. Now you turn your head slightly and you see a space. You look further across and you see another group of atoms similar as before so you count it as 'another car'. You see a different group of atoms right next to it and u say 'oh, thats my cat, not a car' and so on. This is how you count your 3 cars. Just groups of '1's in large numbers forming a pattern.

    Back to the fundemental particle level, you see 1 0 0 1 0 0 1, where 0 is non-existence and 1 is existence. You count 3 as the quantity in your mind, thats the human interpretation part, ie an language we invented to describe the existence.
    But are the substances inherently there and possess a quantity whether you describe them or not? Yes they do.
  • Oct 4 2013: in philosophy this would be a reification
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    Sep 28 2013: real mental construct.
  • Sep 23 2013: the number 3 is in my opinion, inherent to reality and is a mental construct. We as "intelligent" beings love to put names to objects and perception. Objects do appear in 3's. But to be able to appreciate that, we have to form a mental construct of a 3. This will only apply to beings with concept in numbers... it is real to us. But it isn't real to a rock who cannot think.
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    Sep 23 2013: Can we touch other numbers as well ?
  • Sep 23 2013: The number "3" is an important symbol in mathematics as well as in language. In language, your concept of the number of cars in your driveway is quite essential when you want to "make use" or "get rid" of several or all of them. For example, when we go to a party in our friends' house with a circular drive. At some occasions when we want to leave early. Then we look at the position of our own car in the circular drive. If we see that there are 3 or more cars in front and in back of our car, then we better wait until the guests are starting to thin out. Except in a real emergency, it's a big hassle to identify the guests who own these cars. In general, even if you can't touch or feel the number of anything, but this concept in numbers is very important. I wonder, for instance that you can get the excuse from being found out about the number of beer cans in your car in a "drunk while driving" case, if you use the excuse argument of no touch, no feel about the number of cans of beer you have drunk.
    Of course, the entire business couldn't function if you say that the numbers are unreal. Regardless of what you "call" them as real or unreal, the human society simply couldn't operate with almost all the activities without the quantification procedures. Put it in another way, the so-called touchable things won't have much meaning without the quantity modifier. Heck, not only the quantity of currency notes has very important meaning in commercial transactions, the denomination on a note could have even more meaning and importance than the quantity of the notes.
    We can also look at the problem in this way. The COMPREHENSIVE "feel" or "touch" of 3 cars in your driveway is certainly different from the feel of two cars or one single car there.
  • Sep 22 2013: Definitely a mental construct - try 0 - 8>))
  • Sep 22 2013: 3 is not an object and has no presence, so I suppose it doesn't exist in the traditional sense. Instead it is a construct of the mind, designed to help us make sense of the world around us.
    Its more akin to an ideology or an idea. It only truly exists as a concept in our minds.

    Still utterly helpful though. Philosophizing or otherwise, mathematical concepts have a myriad of practical applications.
    • Sep 23 2013: I agree with both of your points. "3" seems to be a purely mental concept. Yet applied mathematics is extremely powerful. This raises the question, how can that be? If "3" is not inherent to objective reality (whatever THAT might be), how is it that removing one car (3-1) always results in two cars being present in the driveway?
      • Sep 23 2013: Just because a concept doesn't have a physical presence doesn't mean it can't be used to approximate real world events with great precision.

        The mathematics used in physics is essentially a theoretical model that behaves like the real world, because its specifically tailored after measurements to do just that. Trial and error is a very big part of the process.

        But look at me, philosophizing over nonsense. The important thing is, that from a purely practical standpoint, it works.
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    Sep 22 2013: I may think you are drunk.:)
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    Sep 22 2013: Do you define "real" as something you can touch?
    • Sep 23 2013: Hi, Fritzie. Your question illuminates a flaw in my example. No, I don't define "real" as something I can touch. I'm not even sure I can come up with a good definition of "real." My common sense notion of the cars, though, is that they exist whether or not my mental construct of them exists or not. Of course, the notion of "car" is a mental construct, as is any other verbalization I might give. Still, there seems to be some independent physical existence to which I am attaching the word "car."
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    Sep 22 2013: Mental constructs, It is in your mind that 3 exists otherwise in reality it doesn't. I may sound insane but for you number 3 can hold a different meaning while a person from primitive society may recall number 3 as something else. Though, it is all in your mind.
    • Sep 23 2013: Hi, Talha. I tend to agree with you. However, this raises other questions. For example, why does applied mathematics work? 3-1=2, to take a trivial example. If someone moves one of the cars, then inevitably, there are two cars left in my driveway. Am I somehow creating the entire phenomenon? Is the mathematics behind physics creative or explanatory?