The Stack Overflow podcast is back! Listen to an interview with our new CEO.
2 added 95 characters in body
source | link

Aristotle claimed that actual infinites aren't possible but potential infinities are possible.

In mathematics it appears that completed infinities are possible, for example omega, the completion of the natural numbers; but since you can always go beyond a completed infinity, Aristotles claim when properly interpreted in this domain still holds.

Now we can conceive a chain of causation ...->a2->a1->a0 that extends infinitely in the past; now what holds for succession above, holds also for predeccesors; so one can complete this; but again by the same argument above one can precede again; thus, in this sense, there can not be an infinite regression - there is either first cause, or a first cause in potentia; and by completion we arrive at a first cause again.

The moral of this story is that infinite regression doesn't neccessarily exclude a first cause.

Aristotle claimed that actual infinites aren't possible but potential infinities are possible.

In mathematics it appears that completed infinities are possible, for example omega, the completion of the natural numbers; but since you can always go beyond a completed infinity, Aristotles claim when properly interpreted in this domain still holds.

Now we can conceive a chain of causation ...->a2->a1->a0 that extends infinitely in the past; now what holds for succession above, holds also for predeccesors; so one can complete this; but again by the same argument above one can precede again; thus, in this sense, there can not be an infinite regression - there is either first cause, or a first cause in potentia; and by completion we arrive at a first cause again.

Aristotle claimed that actual infinites aren't possible but potential infinities are possible.

In mathematics it appears that completed infinities are possible, for example omega, the completion of the natural numbers; but since you can always go beyond a completed infinity, Aristotles claim when properly interpreted in this domain still holds.

Now we can conceive a chain of causation ...->a2->a1->a0 that extends infinitely in the past; now what holds for succession above, holds also for predeccesors; so one can complete this; but again by the same argument above one can precede again; thus, in this sense, there can not be an infinite regression - there is either first cause, or a first cause in potentia; and by completion we arrive at a first cause again.

The moral of this story is that infinite regression doesn't neccessarily exclude a first cause.

1
source | link

Aristotle claimed that actual infinites aren't possible but potential infinities are possible.

In mathematics it appears that completed infinities are possible, for example omega, the completion of the natural numbers; but since you can always go beyond a completed infinity, Aristotles claim when properly interpreted in this domain still holds.

Now we can conceive a chain of causation ...->a2->a1->a0 that extends infinitely in the past; now what holds for succession above, holds also for predeccesors; so one can complete this; but again by the same argument above one can precede again; thus, in this sense, there can not be an infinite regression - there is either first cause, or a first cause in potentia; and by completion we arrive at a first cause again.