You’re right, there are people that disagree, I spoke too extremely. Nevertheless, I am not going to challenge the existence of infinities in the abstract, and I don’t think the points I made require me to.
I have changed my mind. I think that infinites can exist. “Infinite” is not the name of an individual, but the name of a set of individuals. If there are many infinites, we can say that:
infinite = infinite - 1.
Nothing absurd.
it depends on how much you sub divide something in order to consider it infinate. Time may be considered infinate,… yet it does have a starting point. For time is the measurment of physical events,… and time and space is a side effect of matter.
How can anything be infinate? It is numerable on some level. All infinate means is that to many to understand. Unless your saying that it’s possiable to have an unlimited amount of anything. Numbers are unlimited. But even christiand believe that the universe is growing at the speed of light, therefore is numbered by the speed of light times how long it’s been around.
The Peano axioms are a set of axioms that define the set of natural numbers. One of the properties they have is that every number has a successor. You can easily see from this that the natural numbers cannot be a finite set. Proof: suppose the natural numbers are a finite set S with some number of elements n. This finite set has a largest element, call it x. The successor of x is also in the natural numbers by the Peano axioms. But S cannot contain the successor of x since the successor would be bigger than x, and x is the biggest element in S. Therefore S is not the natural numbers.
It follows from this proof that no finite set can be the natural numbers. They are therefore what is called “countably infinite”.
Having shown the position of the mathematical establishment, I will proceed to respond to Samkhya’s position.
As I’ve shown above, there is considerably more sophistication in the concept of the natural numbers than “dots forward or backward”. The natural numbers are in fact a sort of logical structure, one of the properties of which is that it is not a finite set.
A position like “a number does not exist before someone thinks about it” is a philosopher complaining to a mathematician “i’m not sure you can do that”. The mathematician says “I just did!”