God, Math, and the Nature of Reality – Two Professors: Satyan Devadoss Dagan Karp at Claremont

http://www.veritas.org/talks – Two professors discuss life’s biggest questions at The Veritas Forum at Claremont, 2014.

VIDEO by The Veritas Forum

Does the Universe Go On Forever or Come to An Edge? and If Time Continues Forever, Is That An Actual Infinite Amount of Time?

In 2011 Dr William Lane Craig spoke at the Forum of Christian Leaders (FOCL) in Hungary. While they he spoke on the topic, „Five Arguments for Theism” and took questions from the audience to accompany his lecture. In this clip, Dr Craig answers the question, „Does the universe go on forever or does it come to an end?”

Spatial infinity of the universe

There is no evidence that the universe is infinite in the spatial sense. All the evidence is consistent with the universe not only being finite in time, but also being finite in space. And you wouldn’t come to an edge of the universe, if the universe is finite. The universe could have the geometry of the surface of a sphere, for example, like the surface of the earth, which is finite. But, if you go around the earth, you never come to an edge where you fall off. You’ll just come back to where you started again. Similar to the geometry, the universe could be spherical like that so that it could be finite and yet, unbounded.

VIDEO by drcraigvideos

If Time Continues Forever,
Is That An Actual Infinite Amount of Time?

Let me address the question about the infinity of the future. I think it is important to differentiate between two concepts of the infinite. The actual infinite and the potential infinite. According to Aristotle, actual infinities never exist. Infinity exists only in potentiality. For example, if you take any finite distance, you can divide it in half, and then in half again, and then in half again. And that can go on to infinity. And what Aristotle would say is that that finite distance is potentially infinitely divisible. It is infinite in the sense that infinity  is a limit which you can endlessly approach, but at which you will never arrive. And that’s in contrast to the idea of an actual infinite, where you have an actually infinite number of definite and discreet finite individuals that make up this collection.

The notion of a potential infinite, which is Aristotle’s idea, dominated  mathematics right up to the 19th century and is the role of the infinite in calculus, where infinity is just a limit. The idea of the actual infinite was pioneered by Gayard Cantor and is the role of the infinite in set theory, which thinks of sets, like the sets of natural numbers, as having an actual infinite number of members in the sets. Now, how is this relevant to the question about the future? What I would say is this. If time is dynamic, in the sense that the future does not yet exist, but is a realm of pure potentiality only, the, what that means is that the series of events that have occurred at any time is always finite, but increasing toward infinity as a limit. So that, the numbers of events in any point in time toward the future is always finite, but growing. That is to say that it is a potential infinite. And, I agree with Aristotle that there’s nothing objectionable about a potential infinite. So, I would differentiate  between the future and the past in that respect. If, the universe is beginning less, then there has actually occurred an infinite number of events. But, if the universe will go on forever in the future, the number of future events will never be actually infinite. We will never arrive at infinity. It is infinite purely in the sense of potentiality. It will go on and on forever, but will always be finite, but growing toward infinity as as the limit.