Proving a Beginning for the Chain of Phenomena

The Skeptic put his empty coffee cup down on the table, placed a pen and a sheet of paper beside it, and said:

Skeptic: “I have thought a great deal about finite and infinite regress. What you said about the chain of causes and effects being actualized caught my attention. In fact, the difference between an infinite set of numbers and a set of causes and effects that has led to the final phenomenon in a chain is precisely this: the chain of causes and effects could have produced this final phenomenon only if all of its members had actually come into existence. In other words, the counting of the phenomena has actually taken place, whereas the counting of an infinite set of natural numbers can never, in practice, be completed.

Even if we had an endless lifetime and spent it counting, whenever we stopped from exhaustion, we would still have to resume counting the next day, and there would be no end to it. The counting of all the natural numbers could never actually be completed.

I tried to formulate an argument that incorporates this idea of ‘actualization.’”

Believer: “I looked into arguments against infinite regress and found some others that I could present to you, but I would like to hear your argument first.”

A New Argument Against Infinite Regress

Skeptic: “Let us consider a chain of successive phenomena, the last of which we shall call A.

A is the effect of B, B is the effect of C, and so on, continuing backward to a point where we do not know whether the chain has a beginning. In other words, we do not know whether it is finite or infinite.

What we do know is that each of these phenomena is the effect of the phenomenon preceding it and the cause of the phenomenon following it.

So we know that all the preceding phenomena came into existence one after another until the chain reached phenomenon A. In other words, A is directly the effect of B and indirectly the effect of C, D, E, and so on. Therefore, without all of those preceding phenomena having come into existence, A could not have come into existence. The emphasis here is on the word all.

Now let us ask a question:

If we retrace this path in reverse, is it possible, in practice, to encounter all the preceding phenomena?

The answer is yes.

But why?

Because once before, all the preceding phenomena traversed this path, coming into existence one after another until they actually brought phenomenon A into existence. That alone is sufficient reason to accept that traversing this path is possible, because it has already been traversed once and its traversal has been actualized.

Now let us ask a second question:

If this chain has no beginning and is infinite, and we traverse the path in reverse, is it possible, in practice, to encounter all the preceding phenomena?

The answer is no.

But why?

Because although reaching any individual member of an infinite sequence is possible, counting or reaching all the members of an infinite sequence is actually impossible. The reason is obvious: because the sequence is infinite.”

Believer: “I think your argument can be summarized as follows:

1. Counting all the members of a finite sequence is possible.

2. Counting all the members of an infinite sequence is impossible.

3. All the members of the chain of causes and effects that produced phenomenon A have already come into existence—or, in other words, have already been counted—because phenomenon A exists. A could not have come into existence without each and every one of them having first come into existence.

4. If we travel along the chain in the reverse direction, we can once again count the entire chain of causes and effects leading to A, just as this counting has already been actualized once before.

Conclusion: The chain of causes and effects leading to phenomenon A must be a finite sequence.”

Skeptic: “Yes... that is exactly what I meant.”

Believer: “I was going to present the ‘Argument from Correlatives1’ against an infinite regress. Perhaps what you have just presented could be regarded as another formulation of essentially the same argument. Of course, you have used the mathematical concepts of the finite and the infinite, and that distinguishes your argument from the Argument from Correlatives. In any case, there is no longer any need to present that argument, since what matters is that we have reached the conclusion.”

The Skeptic laughed and said:

Skeptic: “If an argument resembling the one I just gave has not been proposed before, I shall allow myself to call it the ‘Argument from the Possibility of Counting2.”

The Believer laughed as well.

Believer: “Call it whatever you like. Now, may we continue?”

Skeptic: “For the time being, I accept that no chain of causes and effects can be without a beginning. I am now waiting to hear the rest of the argument from causation.”

The First Cause and Some of Its Characteristics

Believer: “We now arrive at the conclusion that there must be a First Cause—a cause without which no phenomenon could ever have come into existence. Let us call it the Necessary Existent. But this First Cause—the Necessary Existent, or the Cause of Causes—cannot, in certain respects, be like other phenomena.

In fact, for the Necessary Existent not to require a cause of its own, it must differ from phenomena in certain ways. What characteristics this First Cause actually possesses may be beyond our ability to understand or investigate, but we can say what characteristics it must not possess. It must not possess characteristics that belong exclusively to phenomena, because it must not itself be an effect and must not require a cause.”

Skeptic: “And what are those characteristics?”

Can the Necessary Existent Be Temporal and Subject to Change?

Believer: “A temporal phenomenon has the potential to undergo change. Even if it undergoes no change and remains otherwise exactly the same, the very fact that it exists in time means that its existence is successively renewed.

Suppose this pen in my hand undergoes no change whatsoever: its spatial coordinates and outward appearance remain entirely unchanged. Yet if it is temporal—as it is—its temporal coordinate changes. The pen of the previous moment had its own existence, while the pen of the present moment is a new pen with a new existence. This new existence is new in the sense that, although the pen possesses all the same coordinates and characteristics as the previous pen, its temporal coordinate is new. Thus, something new has come into existence. In other words, its existence is renewed at every moment. This renewed existence is itself a new phenomenon and therefore requires something to bring it into existence.

The pen at moment t1 has its own existence and coordinates. At t1, no pen with the temporal coordinate t2 existed. The pen with the temporal coordinate t2 came into existence at t2. We do not know what the cause of the existence of this new pen at the present moment is. Perhaps its cause is the pen of the preceding moment, or perhaps it is something else. Whatever its cause may be, what matters is that it requires a cause. In other words, a temporal being, because its existence is renewed at each new moment, requires a cause. And if the Necessary Existent were also temporal, it too would require a First Cause.

If the Necessary Existent were temporal, then we would not be dealing with an eternal Necessary Existent. It too would need to be brought into existence anew at every moment. Each moment of its existence that comes into being would itself be a phenomenon requiring a cause and a creator. Its existence, therefore, would have to originate from yet another First Cause. Having a lifespan and existing in time are thus impossible for the Necessary Existent. It must be timeless if it is to be the First Cause.

It is also clear that any being that undergoes change or transformation belongs to the category of phenomena, because every new state that arises through such change is a state that did not previously exist and therefore requires a cause. A Necessary Existent of this kind would itself require a First Cause, and could no longer properly be called the Necessary Existent.”

Can the Necessary Existent Have Any Deficiency?

Believer: “Therefore, the Necessary Existent must not undergo any change or transformation. For example, if the Necessary Existent possesses knowledge, nothing can be added to that knowledge; and if it possesses power, nothing can be added to or taken away from that power. Its knowledge must be complete and without deficiency, and its power must likewise be complete and without deficiency.”

Skeptic: “I accept that the First Cause cannot be temporal. But why are you speaking of its being without deficiency? How can you prove that it cannot have any deficiency?”

Essence

Believer: “Every limited being has an essence.”

Skeptic: “What do you mean by essence? I mean, how are you using the word, and how do you connect it with being limited?”

Believer: “By “essence,” I mean what a thing is—its “whatness.” This table has a mass of twenty kilograms. Its mass is part of its essence. If we want to describe what this table is, we have to mention things such as its mass and dimensions. This table has a mass of twenty kilograms. If it had a mass of nineteen kilograms, it would no longer be this table; it would be a different table. If its dimensions were different, it would again be a different table. I would even go further and say that if its position in space and time were different from what they are now, it would no longer be ‘this table at this moment,’ but another table.

“The essence of this table consists in its particular position in space and time, its dimensions, mass, color, hardness, and its other unique characteristics. What makes these characteristics specific is that each has a definite and limited value or quality. For example, the position, mass, hardness, and dimensions of this table can each be described by a specific value, and each of those values represents a limit of the table.

“This table has a certain width. It does not have a greater width, and it does not have a smaller one. Its width is exactly what it is, and nothing else.

“At this moment in time, which we will call t1, the table is in this corner of the room and has these particular spatial coordinates. These are limits. If they change, we are dealing with a new existence. For example, as time passes and we reach moment t2, we encounter a new existence, different from the existence of the table at t1.

“The color of the table at this moment is exactly the color you see—not darker and not lighter.

“In short, if we ask exactly what this table at t1 is, we would have to list all its limits and qualities until we reached a description that applied only to this table at this particular moment. The moment any part of that description changed, we would be dealing with a different table.

“So when we give a precise answer to the question of what this table is—its essence—we have to describe its exact values and qualities. None of those values or qualities could be even slightly different while our description still referred to this same table at t1.

“To define this table precisely, we are limited to these particular values and qualities. So we can say that what this table is—its essence—is limited by these boundaries. In this sense, the essence of things is tied to their limits. Therefore, we say: anything that has an essence is limited. Of course, in our discussion, this is what I mean by the word essence or whatness. The same word may be used differently in other discussions, but we are not concerned with those other meanings here.

“Now, any being whose essence or whatness is defined by such limits, we will call a possible existent.

“For any object, different essences can be imagined. An imaginary table might be here or there. It might have a mass of twenty kilograms or thirty. All of these are possible. Its limits could take different values. If one particular set of these values comes into existence, then a being with those definite limits comes into existence.

“An imagined table with imagined limited dimensions and mass, existing within imagined limits of space and time, becomes a real table if it actually comes into existence. Otherwise, there is no real table. We call this possibility of existence, and beings of this kind possible existents.

“But we have said that the First Cause existed eternally and had to exist for the rest of existence to arise. So that first being is a Necessary Existent, not a possible existent. Anything with limits is a possible existent, while the Necessary Existent, or First Cause, has no limits.

“It also has no deficiency, because to have a deficiency means to lack something. Deficiency means lacking some degree of existence. A being whose existence has no limits cannot meaningfully be said to possess a measurable amount of existence that could be greater or smaller, let alone deficient.

“So deficiency has no meaning in relation to it, just as limits have no meaning in relation to it.

“Notice that this does not mean the Necessary Existent has infinitely large numerical measurements. You can subtract from a numerical infinity and speak of change. Whatever the existence of the Necessary Existent may be, it cannot be measured, so it makes no sense to describe its measure as small, large, extremely large, or infinitely large. Limits and quantity—whether small, large, or infinite—do not apply to it.”

Skeptic: “I still don’t understand why a possible existent could not be eternal.”

Believer: “Didn’t you hear all the reasons I just gave?”

Skeptic: “It is true that an imagined limited being may or may not become real. It may come into existence, or it may remain only a possibility. But the fact that something is a possible existent in the sense you described does not prove that it could not also be eternal and serve as the First Cause of everything else.

“In other words, you have not proved that, in reality, it is impossible for a limited being with an essence to have existed eternally.

“I accept your argument that the First Cause cannot be temporal. But you have not shown that a limited being cannot be eternal. It would only need to lack temporal limits—that is, its existence would not have to be renewed moment by moment. Your argument did not show me why it must also lack every other kind of limit in order to be the First Cause.

“You seem to assume that anything with limits such as mass, dimensions, or other qualities must also have temporal limits, and therefore the First Cause must be free of all limits. But from what you have argued so far, it seems that being free of temporal limits alone would be enough. The other limits do not appear to conflict with being the Necessary Existent.”

Believer: “If the Necessary Existent were limited, that would mean that it lacked certain perfections. And lacking all perfections would mean that it lacked some degree of existence. But something that lacks a degree of existence cannot possess the highest degree of existence.”

The Skeptic looked confused. After a short pause, he said:

Skeptic: “I think everything you just said means the same thing.”

Believer: “What do you mean, the same thing?”

Skeptic: “You are treating ‘lacking perfection,’ ‘being limited,’ and ‘lacking a degree of existence’ as equivalent. That is fine if you want to define them that way. But then your argument amounts to this:

If the Necessary Existent is limited, then it is limited. And being limited means being limited. And something limited cannot be unlimited.

“That is not really an argument. Who said that the Necessary Existent has to possess the highest degree of existence?”

Believer: “Existence has degrees. As some Muslim philosophers say, existence comes in different levels. The Necessary Existent occupies the highest level of existence.

“In this hierarchy, every level of existence is more limited than the level above it. In other words, it has less existential fullness than what stands above it. Therefore, if the Necessary Existent were limited, there would have to be some higher existence above it in relation to which it was weaker and more limited.”

Skeptic: “Can you say the same thing in another way?”

Believer: “Look. Existence has levels. For example, stone and soil are at a lower level than plants; plants are at a lower level than animals; and animals are at a lower level than humans. A stone is more limited than a plant because it does not grow. A plant is more limited than an animal because it does not move. And an animal is more limited than a human because it does not think.”

The Skeptic looked at the Believer in disbelief.

Skeptic: “You have created your own standard and used it to rank different things in your mind. Then you concluded that because you expect the Necessary Existent to be at a higher level, it must therefore be unlimited?

“If you changed your standard, many animals might turn out to be less limited than humans, many plants less limited than animals, and many nonliving objects less limited than plants. For example, if the standard were the number of senses, animals such as sharks, which can also detect electromagnetic fields, would have a sensory ability that humans lack. By that standard, humans would be more limited than they are.

“Many plants can survive without humans or animals through photosynthesis, while humans and animals could not survive without plants.

“And even if we did suppose that the Necessary Existent had to occupy a higher level, by your own standard it would be enough for it to possess just one ability beyond those of humans and other beings. It would not have to be completely unlimited. It could occupy a higher level and still have limitations.

“Overall, I don’t understand why you give this mental ranking so much importance and assume that such a hierarchy really exists among different beings outside your mind.

“And even if such a hierarchy did exist, why should we assume that the Necessary Existent can be placed within it at all? And why should we assume that its existence is unlimited in every respect?”

The Believer thought for several minutes. Then he took some notes from his pocket and looked through them.

Believer: “I need to look into this more carefully and see why, in Islamic philosophy and logic, the gradation or hierarchy of existence is treated as something obvious.

“To be honest, now that I think about it, I realize that I myself do not have an argument proving that the existence of a human being is inherently higher or lower than the existence of a stone. I can accept, to some extent, that they may have different kinds of existence, but I cannot find a reason to show that those existences are inherently rankable, with one intrinsically higher or lower than the other.

“My ranking depends on a standard, and as you said, I choose that standard myself. If I chose another standard—for example, hardness—the stone would rank higher. If I used stability of chemical composition as the standard, the stone would again be more stable and might remain largely unchanged for a very long time, while the chemical balances and stability of the human body change and deteriorate much more quickly.

“If we set aside these mental standards, the existence of a stone is just as much ‘existence’ as the existence of a human being.”

Suddenly, the Believer noticed something written on one of his papers.

Believer: “Yes, here it is... I remember now. There are other arguments for showing that the Necessary Existent is not limited.”

Skeptic: “I’m listening.”

Believer: “Limitation means deficiency. To have limited existence means to have this much, but not that much. A limited being must depend on other things in order to make up for what it lacks. The Necessary Existent is pure existence and depends on nothing; therefore, it cannot have any deficiency.”

Skeptic: “Once again, you are relying on an arbitrary assumption. According to you, for a thing to be deficient means that it lacks something. But whatever it supposedly lacks exists only in your mind and mine. It is we who imagine a thing alongside various other possibilities and then declare that, relative to what we have imagined, the thing is deficient.

“For example, I might say that this table is missing a leg, because I can imagine it having five legs. I could just as easily say that it is missing twenty legs, that it is missing a flowerpot on top of it, and that it is also five square meters short of perfection. Or I could say that this table is absolutely perfect, because my conception of a complete and flawless table is precisely what this table already is.

“You see, deficiency and perfection exist only in our minds. Whatever a thing is, and however it is, is pure existence. Anything else that we imagine it to lack belongs to nonexistence; in reality, those supposed deficiencies do not exist at all. All that exists is this table. Whatever this table does not have exists only in my imagination, and if these imaginings of mine disappeared—or if I myself ceased to exist—this table would no longer have any deficiency at all.

“Here, you have used the words bounds and limitation in two different senses.

“The first is the sense we were discussing when defining essence: having definite bounds and measurements and determinate qualities—in other words, the features by which the thing in question could be defined. In this sense, by a thing’s bounds we mean whatever enters into the definition, description, and explanation of its essence. Its bounds are what the thing is.

“But in your latest argument, you used limitation to mean deficiency. That is, you interpreted a thing’s limits in terms of what the thing is not, rather than what the thing is.”

Believer: “I don’t think there is really any difference between the two.”

Skeptic: “If we take limitation to mean deficiency, then the fewer deficiencies a thing has, the less limited it must be. For example, if a table has four legs instead of three, then naturally it has less of a deficiency, and therefore it must also be less limited.

“But limitation in the first sense—having determinate qualities and definite bounds—had nothing to do with being deficient or perfect. A three-legged table has its own bounds, and a four-legged table has its own bounds. We cannot say that one has fewer bounds than the other, or that one is less limited than the other.

“Limitation in the first sense has nothing to do with deficiency and perfection, which are concepts that exist only in the mind. Bounds in the first sense do not depend at all on whether you and I, with our deficiency-finding minds, exist. Whether we exist or not, this table has its own bounds.

“Bounds in the second sense, however—that is, bounds understood as deficiency—depend on the existence of minds like ours that identify deficiencies. If we exist and find fault with this table and attribute a deficiency to it, then the table is deficient; if we regard it as perfect, then the table is flawless.

“Without your imagination and mine, there would be no deficiency at all in reality. Whatever exists, whatever it is and whatever bounds it has, is pure existence. So keep in mind that being pure existence is not incompatible with being limited.”

The Believer tapped his fingers on the table as he thought. At last, he looked at the Skeptic and said, “Let’s continue the rest of this discussion next week.”

Skeptic: “All right. I’m tired too.”