Lunalle wrote:You guys are brutal. Again, you are incorrectly twisting things around. Christopher Hitchens is talking about positive assertions, not negative assertions. This is a basic concept of formal logic. Following formal logic, you can dismiss the original claim of numbers being concrete, because there is no supplied evidence for it.
Yea there is evidence, I will show you. 1 + 1 always = 2 and not 3. Please give an example of 1+1 not = 2.
1+1=3 (Note, I'm not showing decimal places, if I were it would be 1.5 + 1.5 = 3.0), they are simply left out to save on space.
1+1=2.00... ONLY when 1 is exactly 1.00... (the ellipses signifies an infinite string of 0s)
The quote is applicable as you made a positive claim that numbers are not concrete, if I said the sun does not exist according to your definition of a positive claim I would need to provide no evidence.
Right, if you are using formal logic, and you don't think there is sufficient justification to say "the sun exists", you are under no obligation to say, or believe it. Feel free to say the sun does not exist.
Danieltwotwenty wrote:For someone who doesn't like to play semantics, definition and linguistic games you sure do them a lot.
Right, well when I'm using formal logic, I stick to the laws (and purpose) of formal logic. What I don't like is re-translating words to give them a different meaning, and using words to mean something they aren't defined to mean. There is a difference between mathematics, formal logic, rhetoric, slang, and literate dishonesty.
However, let me make a positive claim, so I can demonstrate it: Numbers are conceptual. I have not heard of anyone who has interacted with a number using any of their 5 basic senses.
So........... what does being conceptual have to do with numbers being concrete. Is having 1 apple conceptual or is 1 apple a real and tangible thing? What if I add another apple, does it become two apples or is it only conceptual? I am pretty sure there would be two real and tangible apples in my possession.
"Concrete" is an antonym (opposite) of "concept". While they're not direct logical negations (formal logic) they are opposite (rhetorical negation). I was using formal logic when I said they are not concrete (direct logical negation), and rhetoric when I said they are conceptual (rhetorical negation).
Back to formal logic:
1 is abstract
2 is abstract
Apple(s) is not abstract
You have apple(s), you do not have 1 or 2.
How many apples you have, is a concept to explain quantity in a universally understandable way.
Sure, you can interact with something which symbolizes the concept of a number, but not an actual number. There is no actual number, because a number is a concept. 1 is not 1, when it is anything else. For example, 1 is not really 1 when it is rounded from 1.25. (1.25 rounded is 1, but rounding is removing valid information). Similarly, 1 is 2 when it is 1.98 rounded (1.98 rounded is 2, but rounding is adding invalid information).
No this is not true all you have done is change the value. Lets use a real world example, if you have taken a bite from an apple and you are left with .98 of an apple and you round it up to 1 apple because you want to sell it, but you still only have .98 apple so it remains concrete, please tell me how the apple would be 100% because you rounded it up.
Another example is if you have 1.5 cookies but you round it down to one cookie to sell, does that mean there is only one cookie?
Here's the important bit:
Yes, rounding is changing the value, inaccurately. That's what rounding is. I mean, you wouldn't say "oh no, I only have 0.999999999999999999999999999999999999999999999999999999999999999999999999 of a cookie, because a crumb fell off when you picked it up, you would round it up and say you have 1 cookie.
In my 1+1=3 example, I have increased the accuracy of the value from 0 decimal places to 1 decimal place. You probably assumed that when I wrote 1, the value was actually 1.0..., which it was not, it was 1.50... This is a matter of accuracy vs. simplicity of display.
Generally speaking, with low numbers, we value accuracy higher than simplicity, and with high numbers we value simplicity higher than accuracy. For example, if I sold you 1 apple which had a worm in it, which ate a bit of that 1 apple, you'd probably be pretty upset. However, if I sold you a barrel containing 250 apples, and 1 apple had a worm in it, which ate a bit of that 1 apple, so you accurately had 249.98 apples, you'd probably chuck the apple with the worm in it, and be happy you have 249 good apples, even though you were technically cheated out of 0.02 of an apple (and chose to give up 0.98 of an apple).
Hopefully this is clear as mud.