Why is infinite regression held to be impossible?

[JDaniel]

The creationist arguments and its variants rely on supposing that an infinite regression is impossible. I wonder, why precisely is such an infinite series held to be impossible.

If one places two mirrors facing each other, there is one mirror the image of the other, which contains its own image, which contains the image of the other, which contains its own image, et cetera ad infinitum.

If one divides 10 by 3, the answer is 3.3333333333333, etc. ad infinitum.

The value of pi, is held to be 3.14159, etc., etc.

If become aware that I think, I think that I think, and I think that I think that I think, etc. ad infinitum.

Are each of these not infinite regressions?

If the universe itself contains these infinite regressions, why should there not be an infinite regression of causes?

Qoeleth:

What makes one think that an infinite regression is so different from an infinite progression, that the laws of logic and reason must come to a halt? Consider what St. Thomas says in the Summa Theologiae: “But no species of number is infinite, for every number is multitude measured by one.”

What does this mean. Simply, it means that any number is measured by one, that is, the unit. No matter what kind of number one chooses, including fractions of whole numbers, multitude is number measured by the number one (in all of its forms). As such, the species of the number nine is the final one, which when added to the preceding eight ones, produces what we call “nine.” Likewise, the number “minus nine” is the negative form of multitude measured by eight plus one “one’s.”

Infinity means unachievable multitude. In a regression, just as in a progression, one (or more) can always be added, or subtracted, from the previous number state considered to be infinity. It does no good to say, “Well, it’s close enough.” Being unachievable means that getting to the current Now is impossible. You can’t just posit an end number, or beginning number, and call it infinity. Nothing can traverse an infinity - in either direction. Only that which is of itself infinite, is able to traverse itself. If our universe was infinite, there is no compelling impetus that this world should be extent here and now. And, even if we were to postulate an infinity consisting of parts, any given hypothetical part would be infinite.

God bless,
jd

 

[levinas12]

There is a fundamental problem with most people’s conceptualizations of regress here. Time is a dimension of the universe. Did you get that? Of this universe. Outside of the universe there is no time. Time does not exist outside the universe, therefore “regress” as we know it involving going back farther and farther in time does not work because time has a beginning. “Before” the big bang time, and therefore temporal regress, did not exist.

I agree.

But, putting the Big Bang aside, does the very notion of an infinite time series stretching into the past involve a vicious infinite regress? Is there a purely philosophical argument in favor of or against the eternity of the world?

These questions are why philosophy is such a delicious armchair pursuit. Like mathematics and logic.

Again, look at Kant’s first antinomy in the Critique of Pure Reason (even though Kant’s purpose was to discredit medieval and ancient philosophy, he went on to produce his own batch of interesting “armchair” ruminations).

By the way, Hawking argues that the Big Bang does not necessarily mean that the universe had a “beginning” in time (at least in the sense that a finite line segment has a “first” point).