Just on that, untermensche, there may be no "one", as you put it, but we can recognise one rock, from no rocks, or more
than one rock. So "one", as in "one rock", is a descriptive term, and I believe that even apes and monkeys can recognise the
difference between "one", and "many". I don't think that we could recognise infinity, even if we could see it.
As such, infinity has to remain a descriptive concept, just as "one", "none" and "many" are.
Cheers, Pops.
Show me something "infinity" describes.
Infinity is not a quantity.
To use it as a quantity in the real world is absurd.
I agree,
untermensche, infinity is not a quantity. But it is descriptive. You can have one rock. The term "one rock" describes this :-
You can have two rock.The term "two rock" describes this :-
You can have many rocks. The term "many rocks" describes this :-
In each case, we have two things the rockness quality, and the count. We can identify both, so both have descriptive value in the real world.
We have "rock", and we have "one. two, many". The question is, can we allow the term "many" to extend to infinity?
Alternatively, untermensche, one who argues that real completed infinity conflicts with reality is making a positive claim, and I for one
simply don't accept that.
It is applying an imaginary term that is not a quantity to reality.
Conflict.
And that is where you make a positive claim about reality,
untermensche, and so it is up to you to show that existence of infinities in the real world cannot exist.
As I said in my earlier post, I remain unconvinced by what has been shown to me, to support that claim that actual real infinities in the real world are impossible.
As such, I can say that: "I don't know, but no one has convinced me they are not, (yet)".
As I said, we need to establish some ground rules, some classifications as to what we accept or deny.
Let me give you a pre-amble, to explain my view of what an infinity is. This pre-amble is not here to say that such a condition can actually exist, merely to explain what it describes.
Let me interject that there are many things in the real world, which we cannot show, (in the sense that I think you mean), but which we probably would agree exist.
For example can you show me love ? Probably not. Yet it is a descriptive term we all use, and from it follows some of those IF X THEN Y, or IF NOT(P) THEN Q type conclusions.
This is pretty elementary stuff, but I hope will serve as a grounding for expansion :_
Numbers describe quantities. We can recognise quantities. If you are short changed some money, you will recognise it. There again is the two sided concept, money, and quantity.
If I tell you that I have three eyes in my head, and you look at me and only see two, then you cotton on straight away that I'm talking nonsense about the quantity of eyes I posses in my head.
Quantity can be applied to abstract concepts as well. If I ask you how many whole numbers there are, the answer is that there is an infinity of them. Although you might not recognise number as a real thing in the world, as concepts, they nevertheless have properties, if we agree on what numbers actually are.
For example, when it comes to whole numbers, I can begin to list what they are" "One two, three four ... a thousand, a million, a googolplex ... etc.". Now I cannot count to the last whole number, because there isn't one, whatever whole number I get up to, there will be more to come. The series of whole number never terminates. That is what infinity describes ~ something which you can begin to them, or see them, (like rocks), and assign a quantitative description to them, the process is iterative without termination. So infinity is a concept which describes something which may or may not be able to exist in the real world.
. . .
Show me something "infinity" describes.
Infinity is not a quantity.
To use it as a quantity in the real world is absurd.
I have agreed that infinity is not a quantity, but I have not yet proceeded to show an infinity in the real world - maybe I can and maybe I can't. To expand, I don't think that infinity is an actual quantity, because of what I have already described, and because the concept of infinity, although used in mathematics, has some non-intuitive properties.
Consider the following two sets :-
{A} All positive whole numbers. How many members in the set? Answer, an infinity. It just means that as a series, there is no terminal.
{B} All positive even numbers. How many members in the set? Answer, an infinity. It just means that as a series, there is no terminal.
But for every even number in set {B}, there are two members in set {A}. For the even number "2" in set {B}, there are then whole numbers "1" and "2" in set {A}.
So two infinities of different sizes ~ not very intuitive, and this leads me to say in agreement that infinity is not a quantity.
On the other hand, all of this does not say that infinities don't exist. But the crucial question is can an actual infinity of recognisable and real things in the real world exist?
So to say: "To use it as a quantity in the real world is absurd, (see above)" is just an assertion, isn't it?
Cheers,
Pops.