The largest number

patiodog wrote:

Irrational numbers cannot be counted.

Irrational numbers are only numbers as far as they are presented as numbers. So pi is not a number but 3.141 is.

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Ah.

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Of course pi is a number: it has a value. It is the length of the circumfrance divided by the length of the diameter. Just because it cannot be expressed in whole numbers does not mean that it is not a number. Your counting criteria seems misplaced. You must always arbitrarily chose an interval to count with. If you are counting by 1 or 0.1, as you said earlier. This means that both of these are numbers. This means that I can count by anything I want.

1,2,3,4,5,...

5 is a number because I can count to it.

5,10,15,20,....

20 is a number because I can count to it, but in this case, we assumed that 5 is a number from the start -- we did not have to prove it was a number by counting up to it first.

This means that counting has nothing to do with whether a number is a number.

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Thalion wrote:

Of course pi is a number: it has a value. It is the length of the circumfrance divided by the length of the diameter. Just because it cannot be expressed in whole numbers does not mean that it is not a number. Your counting criteria seems misplaced. You must always arbitrarily chose an interval to count with. If you are counting by 1 or 0.1, as you said earlier. This means that both of these are numbers. This means that I can count by anything I want.

1,2,3,4,5,...

5 is a number because I can count to it.

5,10,15,20,....

20 is a number because I can count to it, but in this case, we assumed that 5 is a number from the start -- we did not have to prove it was a number by counting up to it first.

This means that counting has nothing to do with whether a number is a number.

I can say that for any two lines the ratio of one line to another can always be expressed as a number. But I don't have a concept of dividing one line by another line. The concept of ratio is applied to numbers and not lines. So I must first express the two lines as numbers. If I now choose to divide one number by the other number and cannot get an exact result, I might say that this ratio is an irrational number. I would not be correct in saying this. I should say that the ratio falls between two numbers, say 3.14 and 3.15. But there is nothing about my two lines that demands the existence of any number.

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What? I just showed that lines have nothing to do with numbers. Any single number is a multiplicity of smaller numbers (1 is 10*0.1, an infinite combination), and any multiplicity is one number (5*1 is 5). Thus, every number is a priori a number. You don't have to count up to it. It just is in the realm of pure reason. A number of objects must be counted, but numbers in of themselves simply are. From this thread and the other thread it seems obvious that you don't believe that anything exists besides what is physically observed, but reason and logic do exist. Go read my response on the other thread.

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Thalion wrote:

What? I just showed that lines have nothing to do with numbers. Any single number is a multiplicity of smaller numbers (1 is 10*0.1, an infinite combination), and any multiplicity is one number (5*1 is 5). Thus, every number is a priori a number. You don't have to count up to it. It just is in the realm of pure reason. A number of objects must be counted, but numbers in of themselves simply are. From this thread and the other thread it seems obvious that you don't believe that anything exists besides what is physically observed, but reason and logic do exist. Go read my response on the other thread.

Any number, no matter how small or large, can be countable, or it would not be a number. Pi is not countable so is not a number. In fact, it obscure as to what pi is. It's all very well to say it is a ratio, but that's neither geometry nor mathematics. We can make a number by a standard method and call it pi. But we can't say 'here is pi'.

There are no stand-alone numbers. Numbers that are not in an application are numerals. A bag carrying a bunch of numbers holds a bunch of numerals. Accordingly, you cannot say 'every number is a priori'. Also, there is no such concept as 'every number'.

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The largest number

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