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1. Originally Posted by The_Liquid_Laser
I can't believe that you are making a distinction on this minor level of abstraction, and yet at the same time think that numbers are real entities. If you consider measurement abstract, then numbers are much much more abstract, lol.
The number "1" is a representation of real world object; what the object is is irrelevant. This is important: it doesn't matter what the object is. No matter what the object is, in this universe adding one object to another object results in two objects. In this way, quibbles over the nature of any given object are sidestepped to tell us something real about the universe: that adding one object to another object results in two objects.

Accordingly, as this yields real information about our universe, I would say it is anything but abstract.

2. Originally Posted by Mycroft
The number "1" is a representation of real world object; what the object is is irrelevant. This is important: it doesn't matter what the object is. No matter what the object is, in this universe adding one object to another object results in two objects. In this way, quibbles over the nature of any given object are sidestepped to tell us something real about the universe: that adding one object to another object results in two objects.

Accordingly, as this yields real information about our universe, I would say it is anything but abstract.
1 can also represent units of measurement. "1 meter" is not an object. It's a description of a unit of length. On the other hand "1 meter" does measure something concrete. When you have a label, whether it be "1 meter" or "1 orange" or "1 dollar", you are describing something concrete. When you remove the label and just have "1", you have an abstraction. You have taken an adjective and made it a noun. You are calling "1" a thing when such a thing doesn't really exist as an object in reality. It only exists as an adjective. That is why numbers by themselves are abstract.

Now let's going back to our example about measuring hours. A clock measures hours in a cycle of twelve. It does this because days progress in a repeated cycle. The repeated cycle of 12 (or 24) hours represents reality, because the days themselves are cyclical. In reality 10 + 5 = 3 when talking about hours because time happens in a cycle. The cycle is reality.

3. Originally Posted by The_Liquid_Laser
1 can also represent units of measurement. "1 meter" is not an object. It's a description of a unit of length. On the other hand "1 meter" does measure something concrete. When you have a label, whether it be "1 meter" or "1 orange" or "1 dollar", you are describing something concrete. When you remove the label and just have "1", you have an abstraction. You have taken an adjective and made it a noun. You are calling "1" a thing when such a thing doesn't really exist as an object in reality. It only exists as an adjective. That is why numbers by themselves are abstract.

Now let's going back to our example about measuring hours. A clock measures hours in a cycle of twelve. It does this because days progress in a repeated cycle. The repeated cycle of 12 (or 24) hours represents reality, because the days themselves are cyclical. In reality 10 + 5 = 3 when talking about hours because time happens in a cycle. The cycle is reality.
A "meter" does not exist. All that exists is a length. An "hour" does not exist. All that exists is time. Numbers can certainly be used to represent even such man-made objects as units of measurement; as I stated, numbers represent objects. However, man-made objects like units of measurement have no existence in and of themselves and, consequently, tell us nothing about the universe.

However, this does bring into sharp relief an important point: numbers, as representations of objects, are not units of measurements themselves.

4. Originally Posted by Mycroft
A "meter" does not exist. All that exists is a length. An "hour" does not exist. All that exists is time. Numbers can certainly be used to represent even such man-made objects as units of measurement; as I stated, numbers represent objects. However, man-made objects like units of measurement have no existence in and of themselves and, consequently, tell us nothing about the universe.

However, this does bring into sharp relief an important point: numbers, as representations of objects, are not units of measurements themselves.
We are both just saying the same thing over and over lol.

5. Originally Posted by The_Liquid_Laser
We are both just saying the same thing over and over lol.
For once we are in agreement.

Although, yes, you are correct in that numbers can be used to represent man-made objects in addition to metaphysical objects and I update my definition accordingly.

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