Damascene Cosmology – On the Impossibility of an Infinite Regress

An infinite regress is impossible

Since the “if/then” is contingent upon an infinite regress being impossible, we must look to see if an infinite regress actually is impossible. Those who argue for an infinite regress usually make the followings points:

1)   It is not impossible to think of something that is infinite regressive. If we imagine a man is stacking books in a library and he’s stacking books on an infinite number of shelves, then it’s not impossible for us to imagine he’s been doing this for eternity.

2)   It’s not impossible to imagine something existing for eternity and impacting other things. If we think of an atom that has existed for eternity, we can imagine it wandering around space, moving and containing energy, without ever have being created.

If we take such views prima facie then an infinite regress does indeed seem possible. However, I would contend that such analogies misconstrue the issue of an infinite regress and do not align with reality. That is to say, while it is possible to imagine an infinite regress (and in fact mathematically we can use infinity in equations), there cannot be an actual infinite regress when applied to reality, especially in light of modern science.

When applying an infinite regress to reality, an infinite regress simply doesn’t seem possible in reality. Imagine that when you click on the “y” button on your computer it takes an infinite number of steps for “y” to show up on your screen. This would prevent “y” from ever showing up on your screen. That is because when you hit “y” it would go through step 1 to step 2 to step 3 and so on to infinity.

If x is supposed to lead to y, but there is an infinite number of processes P that take place between x and y then x would never lead to y. This is because x would need to go to P1, P2, P3, and so on to infinity before obtaining y. Since infinity is, well, infinite, x would proceed through an infinite number of steps in order to achieve y, meaning that x would never achieve y.

If this same computer did the same thing with opening software then we would have the same result. Let’s say you wanted to close your solitaire and open your word processing program so you could write an essay on the Ontological argument. If your computer took an infinite number of steps to close down the solitaire program and open up your word processing program, then the solitaire program would never close down and the processing program would never boot up. To make matters worse, before you can save your essay on the Ontological argument, you must first type an infinite number of pages. This means you could never save your essay!

While an infinite number of steps might work in mathematics, it is not congruent with reality. We know that to get from one end of the street to another there are a certain number of steps. If there were an infinite number of steps we would never reach the other side of the street.

In fact, when applied to reality, an infinite regress seems contradictory. If we use the above analogy of walking across the street, we are left with a problem; if it takes an infinite number of steps to get from one side of the street to the other, then we must have always been walking. At the point we began walking we ruined the idea of an infinite regress; we have a definite starting point. For an infinite regress to occur, there must not be a definite starting point. To say that we have moved from one point to another, or are attempting to do so, through an infinite number of processes, contradicts itself because there cannot be a beginning point regress.

The above doesn’t negate an infinite series of events, but instead an infinite series of events without a definite beginning. For instance, if we say that x leads to y, but all points began at r, then the progression is possible because we can trace it back to a point.

r                                    x                        y

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But when we look to an indefinite beginning, which would be an infinite regress, we understand that x must be preceded by P-1, P-2, P-3 and so on to infinity. If it is impossible for us to get from x to y due to the infinite number of steps that must be obtained, then how can we even get to x since an infinite number of steps precede x? If there is a step before x, say r, then how did we get to r when steps P-1, P-2, P-3, ad infinitum precede r? The point is, when an infinite regress is applied to reality we can never have a starting point, which means we can never obtain an actual event because an infinite number of events will precede the event.

…P-3 P-2 P-1 P       P1 P2 P3

<—————————————>

If we imagine we’re sitting in a book store and watching the owner stock the bookshelves, but there is an infinite number of bookshelves, then how is it that the store owner is stocking the bookshelves? When we look to his right we see an infinite number of shelves that need to be stacked and when we look behind him we see an infinite number of shelves that have (supposedly) been stacked. While it might be easy for us to imagine – even in a realistic sense – that he could continue on ad infinitum stacking the shelves as some sort of librarian Sisyphus cursed for eternity. But such an imagining can only occur if we allow for a finite beginning.

In this bookstore, we look to the left and see an infinite number of bookshelves. The problem is, none of these bookshelves can be filled because the bookstore owner could not begin at a definite point. If they began at a definite point, then we no longer have an infinite regress. If our bookstore owner is on row Pn and we expect him to get to shelf P3, then he must first get to shelf P1, then shelf P2, but he must first finish rows Pn-1 and so on to infinity. That is to say, our bookstore owner would never obtain shelf P3 or even get to row Pn if he was involved in an infinite regress. We could not even say he began at a certain point, for in an infinite regress there is no beginning.

If we apply the above concepts to the formation of the universe, then we are left with the reality that matter and energy cannot be eternal and had to start at a specific point. This means that matter as it is would either have to have been permanently formed the way it is or have never come together.

In order for matter M1 to form into a different form of matter M2, it would need to proceed through steps x and y. But for M1 to obtain M2, it would have first need to obtain M1 by processing through M-1, M-2, and so on to infinity. Just as we saw from the numerous examples above, this means that M1 would never obtain actuality.

For matter to be in its current form, then, since it cannot have an infinite series of events prior to the taking of its current form, it must have always been that way. But we know that this is not the case. We know that when a table is put together, we did that ourselves at a specific point in time. We know that the wood was not always that way. Evolution teaches us that such things have changed over time, meaning the matter of things is in constant flux, which means that it cannot be eternal.

Alternatively, if matter is eternal and subject to an infinite series of events, then the matter we see today should have never come about. Since we know the matter to exist and we know it came about, then it cannot be infinite, meaning that it came about at a specific point in time.

The clever naturalist might agree that an infinite series of events is impossible, but it’s not impossible to imagine a physical entity that has existed for an infinite amount of time. We could imagine a hypothetical atom that has been moving around for eternity and changing forms. Such a mind exercise would indicate that matter as eternal is not an impossibility and that an infinite regress might be possible. For instance, if we have an object A that is infinite in its own right that randomly causes Event P, then all things following P trace back to A, which is material and infinite in its own right.

The above analogy begins to fall apart when we consider that anything that is self-generating within the material universe (that is, something that generates another object separate from itself) it is always a compound object. There are no simple material objects that self-generate. This means that such an atom (or electron, or elephant, or flying spaghetti monster, or whatever you want to use as an example) would fall subject to the problem of infinite regress mentioned above.

If we say that the atom collided with something else in order to create something independent of itself, then we have two eternal objects wandering around that happened to collide. Thus, if x and y collide at time T1, we then get the result of r which is independent of x and y. But what is to prevent us from believing that they should have collided later at T2 or at T-1 or T-30? If both x and y exist within a confined space, but have existed infinitely, then why should they not have collided at an infinite period in the past? Furthermore, if we say that x and y exist within an infinite space, why should we suppose they would collide at all?

When considering the above, it shows that a compound object could not exist infinitely and bring about change, but does this negate the idea that an object could exist infinitely by itself? Certainly we can imagine x gaining form F1 to F2 to F3 onto infinity (though this does seem to violate what we previously learned about infinite regresses). If we give the naturalist the benefit of the doubt and assume that such an object can exists independently and somehow doesn’t violate an infinite regress, what are we left with? The answer is we’re left with nothing that is usable within reality. If such an object did exist, it would be changing within itself and not exacting change on anything else or bringing anything else into existence.

Now, a naturalist could argue that perhaps there was a simple material object that led to the creation of the entire universe. But everything within our experience is complex in some fashion and made up of different parts, thus the naturalist would be begging the question. They would ask us to assume the naturalistic state of mind for the sake of naturalism without having any reason to assume such a state of mind. We would have to assume naturalism is true in order to prove naturalism is true, and that is a fallacy.

Let us continue to look at the issue of an infinite regress even further by applying the idea of an infinite regress to matter, specifically when we consider the Second Law of Thermodynamics. The Second Law states that energy in a closed system decays toward a state of equilibrium. If you fill a bathtub, while the tub is filling up the heat is concentrated more towards where the water is pouring in rather than the furthest spot from the heat within the tub. If you turn the water off you have created a closed system. At some point, the water will become lukewarm and will have an equal distribution of heat within the tub. That is because the energy decayed toward a state of equilibrium and once that equilibrium is met it cannot be changed unless acted upon by an outside force.

Such an idea has posed quite a problem for scientists as we examine the Big Bang. The Big Bang is a well-established mathematical and scientific theory; the math predicted that the Big Bang existed and the evidence supports the theory. We know that approximately 14 billion years ago energy was released that resulted in our universe. While we do not know what the energy was contained in prior to the Big Bang, we are left with quite the perplexing question – how was this energy released?

Let us assume that all the energy that is currently present in the universe existed within a capsule prior to the event of the Big Bang. If this capsule was infinite, then the energy would have moved toward a state of equilibrium. Looking to the above examples of an infinite regress, if it was the energy within the capsule that caused the Big Bang, then the Big Bang should have occurred at T, but in reality such a time cannot exist. If we say that the Big Bang occurred on January 15 then we are wrong; if the capsule was infinite and the energy within infinite, then the Big Bang occurred at T, but such a time cannot exist, meaning that the energy could not be infinite.

Since the energy within the capsule could not have caused the Big Bang since the energy would have reached a state of equilibrium at T, then an outside force would be needed in order to release the energy within the capsule into the wider area of space. But if we suppose that there was a material outside source that released the energy from the capsule and caused the Big Bang, we are faced with the problem that to be material such an object must be complex, which then means the object is likewise subject to an infinite regress. All the naturalist does walk further into the infinite regress, but he does not solve his problem.

Now some would have us believe that the universe is currently expanding and will soon collapse on itself again to begin the process of expansion a short time later. However, aside from there being no evidence to support this theory and that such a theory still falls under the problem of an infinite regress, such a theory doesn’t make sense in light of the Second Law of Thermodynamics. To retract the universe would require the use of energy, but we know that energy is moving toward a state of equilibrium in our universe. If left unaided, our universe will eventually “die” by reaching a state of equilibrium where energy is evenly dispersed across the universe. In order for the universe to collapse on itself it would need a disturbance of the energy, but there is no evidence that such a disturbance can exist.

With all of the above I should hope the reader feels satisfied that an infinite regress is quite impossible. Though we can imagine an infinite regress, such imagination must take place inside of a vacuum and cannot be applied to reality. In reality, we cannot have an infinite regress of events or an infinite complex object. Therefore, an infinite regress is impossible.

Therefore, the unmoved mover would be by definition God

Since the syllogism is sound and the premises are true, it follows that the conclusion is true as well. Some might want to argue that if an infinite regress is impossible, then God must also be impossible since He can’t be eternal.

In the next section, I hope to show how God is both immutable and therefore not subject to an infinite regress.

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This was a scheduled post. I am currently out of town and subsequently have turned comments off since I cannot moderate or interact with commenters. If you have any questions, comments, or concerns about this post, please feel free to contact me.