He brings the example of a spaceship flying into space and asks what would happen if it went on and on. Is there an end point or does one eventually loop back to the starting point? — spirit-salamander
In other words, the dimensional lines are straight and therefore the Universe is potentially infinite. — Gary Enfield
Since Aristotle, the philosophers say that there is only the potentially infinite. — spirit-salamander
Such statements by Greene as these are philosophically irritating:
"If space is now infinite, then it always was infinite. Even at the Big Bang. A finite universe can’t expand to become infinite." — spirit-salamander
That is a gross oversimplification. — SophistiCat
In the West Aristotelian dogma began to crumble during the Enlightenment, and in modern times the infinity of space, at least, was thought to be pretty much self-evident. — SophistiCat
Nowadays you would be hard-pressed to find a physicist who denies the possibility of some type of infinity on principle. — SophistiCat
Why is this "philosophically irritating"? (He is stating the mainstream position on the matter, BTW.) — SophistiCat
Okay, you're right. I was going by what I assumed was a consensus that may have existed in philosophy since Aristotle. In fact, I think if a survey were done today with academic philosophers, most would "abhor" the infinite mundane. — spirit-salamander
Giordano Bruno could also be mentioned. Not directly enlightenment, but strongly influenced the Enlightenment. — spirit-salamander
My point was about philosophers. — spirit-salamander
Or consider a sphere. The mathematics of paths is such that even on earth you could sail forever at a given setting and never arrive again (exactly) on a point you had already crossed once. Or Achilleus's problem of overtaking the tortoise who is an uncountable infinite number of points ahead of him, which, if Achilleus stopped at each of any points in a well-defined set of them, he would never overtake.The Universe is finite but unbounded. — Wayfarer
So do philosophers have to accept the actual infinite? — spirit-salamander
Consider the following...which would be the myth and why? — Alexandros
If you would accept the notion that each object in The Universe occupies unique coordinates and is subject to unique Universal forces, then one might conclude that each object in The Universe is "one of a kind," that is, unique in and of itself. If this is indeed the case, then what exactly does "2" mean? — synthesis
You have to accept the fact that mathematics sort of avoids this reality and "pretends" that 2 or 3 (or whatever number you choose) exists because it works (until it does not). — synthesis
No I don't. Nor should you. But we each choose our paths. You might consider joining forces with Metaphysician Undercover. His concern is the supposed equality between 2+2 and 4. :roll: — jgill
What does "one of a kind" have to do with counting two apples, one red and one green? — jgill
You have to accept the fact that mathematics sort of avoids this reality and "pretends" that 2 or 3 (or whatever number you choose) exists because it works (until it does not).
— synthesis
No I don't. Nor should you. But we each choose our paths. — jgill
There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. So we have to allow that "1" represents a different type of unity than "2" does, or else we'd have the contradiction of "2" representing both one and also two of the same type of unity. — Metaphysician Undercover
i don't understand your point, is it that nor numbers nor infinity exist? They point out to relations which do exist and are independent from physical reality. — Alexandros
Infinity can very well be treated in math. Regarding what you say about position and the one of a kind I think you are mixing quantifiable and qualitative. Mathematics doesn't pretend nor avoid reality, it is reality, I hope you understand the difference between the signs we use and the entities, relations and structures it points out. — Alexandros
maths is essentially an axiomatic system, anything goes so long as you don't contradict yourself within one. — TheMadFool
as we go towards 0 and infinity, are we just supposed to say, "Oh well?" Apparently. — synthesis
There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. — Metaphysician Undercover
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