In what context of the mind do numbers exist in the mind if the mind has no

[xcrunner2414]

perception of infinity? that is, infinity itself: that thing which cannot be defined in terms other than itself. How can you know what numbers are if you cannot perceive, and therefore acknowledge, infinity? Everything you know exists in a context, so in what context would numbers exist in the mind? Would they even exist?
and no, not infinity as in zero divided by zero, because that is still a number, its not a horse and a bird and love. I mean INFINITY! The thing that contains all things, but is also greater than all things.

 

[formeng]

Hi,
Well, perhaps you're right about no perception of infinity,etc., but I see it a little differently. First, I think you're talking about numbers, for which infinity is fairly well defined by mathematicians. Then in the same breath, you're talking about infinite existence of all things. If you're talking about a spherical universe, then infinity goes on forever, but if you're talking about a hyperbolic universe that's another question. Also, I would respectfully point out that cosmologists have some fairly definite perceptions of what an infinite universe would mean. For example, there would necessarily be another person exactly like you except for the placement of at most a few molecules. There all sorts of other interesting implications, but maybe I'd better stop here before I get too far afield of the subject of your question.

FE

 

[JL]

The Cantorian sense of infinity is very real.

Furthermore, infinity is not a number, though it can be well defined as any number greater than zero divided by zero.

 

[spoon737]

Why did you feel the need to ask this question four times? I answered the first time you asked this, but I may as well reiterate my point. Infinity is not necessary to put finite quantities into context. The mind is capable of assigning a value to a collection of objects which represents their quantity. This ability becomes more concrete when we realize that different collections of objects are comparable based on the difference in their quantities. These concepts are fundamental to mathematics, so much so that preschool aged children are able to understand them. No part of this concept involves infinity. Infinity does not put the idea of quantity into any new kind of context at this level.

Small children do not have the cognitive ability to perceive infinity. Aside from what I learned in the child development course I took way back in my first year of college, I know this because when faced with the idea of eternity/infinity, kids always want to know how big it is. The very fact that they are asking how big infinity is means they don't understand it, because infinity cannot be accurately described in terms of size. Size implies a boundary, a restriction, something that infinity does not have. And yet, these very same children DO have an understanding of numbers. Sure, it's basic, but it's there.

So we have examples of ancient civilizations with a developed sense of mathematics and small children who are capable of understanding quantity, neither of which had/have any real understanding of infinity. How then can you claim that the concept of the infinite is necessary to give context to numbers?