Infinite Regress
An infinite regress is a series of causes and effects that go on indefinitely. If every event must have a cause, then any cause will also have a cause, and so on endlessly. Suppose someone asks what makes the grass grow. An explanation is provided by way of a cause. In turn, the cause of the cause of grass growing is questioned, and so on. Another, related way, of defining infinite regress is in terms of explanations that are not causal. Still, the explanation is dependent on a previous explanation, and so on. Many thinkers stop the infinite regress by supposing a first cause, or ultimate explanation such as God.
The infinite is typically defined as that which is endless, boundless, without limit. Such definitions imply that infinity is a numerical and physical concept, yet by definition, it cannot be measured.
The problem of infinite regress for mathematics is best illustrated, perhaps, by one of Zeno's paradoxes. Although it is not unsolvable, it may help to explain the basic problem of a mathematical infinite regress. In one paradox, Achilles races a tortiose, and because the tortoise is supposed to be much slower than Achilles, the tortoise is allowed a head start. According to Zeno, before Achilles can reach and pass the tortoise, he must first reach the place from which the tortoise started. By the time Achilles has reached that point, the tortoise has advanced to another, farther point. Now, Achilles must get to this advanced point, and so forth. The distance traveled is the sum of an infinite number of distances, and the problem is that before any distance is traveled, an infinite number of distances must be traveled. This represents an infinite divisibility of space (and also implies the same for time and number).
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