Doesn't the 'Infinite Regression Fallacy' Prove that Time Had a Beginning?

The ‘Infinite Regression Fallacy’ is that anything that appeals to an infinite regression is false. There cannot be an infinite regression because one cannot arrive at the present/current moment or item as it requires first traversing/counting/completing an infinite series to arrive at the current/present moment/object.

So applying it to the flow of time, doesn’t it prove that time itself, no matter how many contortions, convolutions, permutations or cyclic phases you want to envision, at some point in time, perhaps a VERY long time ago, time had to have a start?

And does that not then require an eternal object that exists outside of time to initiate the flow of time?

You say that one cannot “arrive” at the current time, but arrive from whence? Where are you starting?

I ask because one could use the same argument against the infinitude of the integers. One could insist that there must be a smallest integer since we would never be able to “arrive” at a given integer, say 0, if the negative numbers extended backward forever to negative infinity. The problem with this is the assumption that negative infinity behaves like an integer. It is not an integer, and once one realizes this, there is nothing compelling us to begin counting from it.

Likewise, if we accept for the sake of argument that the universe itself doesn’t have a beginning, all that matters is that, like the distance between integers, the length of time intervals between events is well-defined. Problems would only arise if you try to postulate a beginning and treat it as an event.

Yes, there is not a problem with the set of integers because we conceive of them as an entire set and not a progression of points.

The objection to an infinite regression is that in effect it has no starting point. You can no more arrive at the present/current item in after an infinite sequence than one could arrive at an infinite limit by going through an infinite sequence. Both are impossible.

And yes, negative infinity is not a number at all, it is an unbounded progression, and the symbol for infinity just a representation of the lack of a limit.

Altogether, if one is in the present, one cannot have arrived at the present via an infinite sequence of units of time of non-zero value. Therefore time would have to have a start.

At least that is how it looks to me, but I have not yet seen anyone apply the ‘Infinite Regression Fallacy’ to anything related to the flow of time itself. I was wondering why that was.

I can remember reading a nice reply to this argument once upon a time, I can’t remember if it was Flew or Kenny, or someone else along those lines. In effect, the argument is this: if there was an infinite series of time stretching out behind us, then during that infinite series, every possible combination of events/states would have occurred - every possible permutation - including this one. Hence this state could be situated in an infinite timestream without it requiring some beginning point.

Again, the problem is the presupposition that there has to be a starting point. There needn’t be a starting point for time anymore than there need be a starting point for the integers. It’s a false dilemma.

Indeed, the definition of “time” as it is used in physics does not a priori necessitate a beginning. If it did, the discovery of a beginning of the universe through Big Bang Theory wouldn’t have been as surprising as it was. If time did require a beginning, mathematicians could have demonstrated this requirement on purely logical grounds without appealing to theory or experiment.

Put another way, the problem is the assumption that time is used to list events (“here’s the first event, here’s the second, etc.”) rather than merely order them (“this event occurred before this one”). To assume that time must list rather than order is begging the question, and is what one must actually demonstrate for the argument against infinite regression to work.

Sure I suppose one could just assume that the impossible has happened, then argue from there. but to my view, it doesn’t make it any more plausible or possible.

Once again, the set of integers is not a sequential series of numbers in time. The complete set of integers is imagined simultaneously, and so it is not analogous to a sequence of units of time greater than zero length of time.

If there is no starting point to an infinite series of numbers that signify successive points in the flow of time, how does it start? It does not.

If you can go from an infinite regression to the present, then the opposite, going from the current/present time to an infinite limit in the future would also be possible, but we know that the latter is impossible, and so similarly the negative of that process is also impossible.

I don’t think it surprised any Catholic astrophysicists so much, particularly a certain Belgian priest… Wouldn’t we, believing in a Creator and His Creation, not tend to expect a beginning to Creation?

Now you are arguing from an absence of evidence for a claim I am not making.

That doesn’t work. Who knows, maybe some did but were ignored? Or maybe you are simply unaware of them?


Okay, let’s step back for a moment for some perspective. The question is “Why can’t we have an infinite regression?” The proposed answer is “Because there would be no beginning.” My challenge to this is “Why do we need a beginning?”

You haven’t addressed this challenge. Instead you’ve simply asked where we would start, but the very notion of starting assumes a beginning, so you’re just begging the question. Proving there is a beginning is your job. If you don’t do that, you’re basically just saying that we can’t have infinite regressions because we need beginnings and we need beginnings because we can’t have infinite regressions, which is circular reasoning.

If you can go from an infinite regression to the present, then the opposite, going from the current/present time to an infinite limit in the future would also be possible, but we know that the latter is impossible, and so similarly the negative of that process is also impossible.

This is based on the assumption that those “infinite limits” are events. They are not events, any more than the infinities are integers. That was part of the reason for the analogy to math. Since those limits are not events, the interval from the present to those limits needn’t be defined anymore than the distance from an integer to infinity.

For time to be a useful concept, it need only allow us to 1) order events, and 2) measure the “distance” between them. It can do both without invoking a beginning, hence a beginning isn’t logically necessary a priori

St. Thomas and St. Bonaventure took different sides on this question. The latter argued as above, that infinite regression is impossible. St. Thomas of course affirmed with the Church that time is finite, but did not think the arguments from reason alone disproved the possibility of an eternal universe. He said basically what Oreoracle says above. Here’s an excerpt from the Summa (I, Q46, a2):

Objection 6. …if the world always was, the consequence is that infinite days preceded this present day. But it is impossible to pass through an infinite medium. Therefore we should never have arrived at this present day; which is manifestly false.

On the contrary, The articles of faith cannot be proved demonstratively, because faith is of things “that appear not” (Hebrews 11:1)…

Reply to Objection 6. Passage is always understood as being from term to term. Whatever bygone day we choose, from it to the present day there is a finite number of days which can be passed through. The objection is founded on the idea that, given two extremes, there is an infinite number of mean terms.

In other words, the objection presupposes a finite length of time, then objects that infinity cannot fit into it, as Oreoracle pointed out.

Not if the beginning is singular.

Again, you are speaking of static sets of numbers. I am talking about SEQUENTIAL events in time. You are ignoring that dynamic to make your point.

No, it cannot. For a sequence of events to exist it must first start, else we cannot have arrived at the present, no more than we can ‘count’ to infinity.

The mathematical analogy is just that: an analogy. It is meant to illustrate a concept that would be difficult to communicate directly.

However, I do want to point out that, in physics, time is just a parameter/coordinate of a model. In other words, it is just a number as far as physics is concerned. :shrug:

No, it cannot. For a sequence of events to exist it must first start, else we cannot have arrived at the present, no more than we can ‘count’ to infinity.

You have not demonstrated that events need to be placed in a sequence. For the usage of time as seen in physics, it need only be able to order events (“this event occurred before that one”) and allow measurement between events (“this event occurred five seconds after that one”). There is no requirement in the everyday usage of time nor its use in physics that requires it to sequence events (“this event occurred first, this one occurred second, etc.”)

In physics time is a one way stream o f change. It is not merely a coordinate as coordinates do not imply direction.

And the events of the universes time line are already in a sequence. Your preference for a static analysis for a dynamic process is merely a convenient contrivance.

Any schoolboy know that one cannot count to infinity, but you will claim otherwise to avoid the obvious implication of the implication.

No. In physics, the “universe” is a 4-dimensional manifold with 3 spatial coordinates and a temporal coordinate. This is all conceived of “at once” within a single package, because every event is already right there–simply specify 4 coordinates and voila, it’s there. I can’t emphasize enough that, from this point of view, the universe is not something that changes. The “change” has already been taken into account by allowing the temporal coordinate to vary through the set of real numbers. The universe is a stationary, 4-dimensional object in this model.

This is no more problematic than graphing a line in 2-dimensional space. The objection that we cannot manually draw the entire line is irrelevant. Conceptually, everything exists in one package right in front of you, and there’s nothing contradictory in asserting that the line goes forward and backward forever.

And the events of the universes time line are already in a sequence. Your preference for a static analysis for a dynamic process is merely a convenient contrivance.

You can call it a contrivance all you want, but it isn’t contradictory. And since it isn’t self-contradictory, its negation (i.e., your position) isn’t tautological, meaning it isn’t demonstrable from logic alone and cannot be verified a priori.

It is not stationary and it moves through time in one direction only. Were it stationary we would be able to move back and forth through time, but we cannot in reality and in theory only with huge energy cost.

Lol, no mater what semantics you use, time is measured by a sequence of units and we cannot arrive at the present via an infinite number of those units.

Saying that time is static is absurd unless you can prove it by moving back in time.

It is contrary to what we all can observe, so whether it is self-contradictory is immaterial; time is a dimension the universe moves through. End of story.

Ah, I think I see where you’re misunderstanding me. You are thinking of the universe as the “set of stuff occupying space”. You are correct that this changes over time. However, this is not the definition of “universe” used in physics, as your conception is only 3-dimensional. You have basically ousted the time coordinate from the model and set it “outside” of the universe.

To a physicist, the universe doesn’t pass through time. The universe includes time.

The space time continuum is the whole process of three dimensional space moving through time.

To model the ‘universe’ as a vectorless set of coordinates in a static model is incomplete, over-simplistic and inferior to dynamic models.

Time is a sequence of smallest units of time, aka Planck time.

Minkowski space-time model has vectors in time and space, and this allows for things like causal events, and this also includes the basic sequence of events that you are trying to dodge.

Time flows. Itis a one way that moves in sequences called Planck time and this series of sequential time units cannot be of an infinite chain of events or else we cannot have arrived at the present.

I’m sorry, but this affirms to me that you don’t know what you’re talking about.

Planck time is the smallest observable unit of time. That doesn’t mean it is actually the smallest unit in existence. Indeed, our current physical theories assume that time is continuous, so there is no smallest unit. Calculus would hardly be applicable to physics if this weren’t the case, except perhaps for approximations.

Bah, prove that there is a smaller unit then.

There are smallest units of energy, a foundational realization to Quantum Mechanics.

And there is a smallest unit if distance as well.

Maybe in some abstract way one might argue that smaller units are possible, but no, actually they are not.

Well, as you probably know, our two main pillars of physics, General Relativity and quantum mechanics, are fundamentally incompatible with each other. That is why a unifying theory is being sought. In Relativity, time is continuous; in string theory (which is untested), time is still continuous; in the theory of loop quantum gravity (also untested), space is discrete; in quantum mechanics, we simply don’t have an answer.

So once again, these matters require further experimentation to resolve, not philosophical hand-waving to dismiss.

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