Collins’ Argument Paraphrased

Collins’ cosmological fine-tuning argument is deceptively simple, yet requires an extensive vocabulary of abbreviations, various hypotheses, and scientific and philosophical terms. Here, I will attempt to offer a version of the argument that is more accessible, without losing any of the power or simplicity of the original¹.

1. Given the fine-tuning evidence, it is very, very surprising that a life-permitting universe (LPU) exists, under a naturalistic single universe hypothesis (NSU).

2. Given the fine-tuning evidence, it is not surprising at all that a life-permitting universe exists, under a theistic hypothesis (T).

3. The theistic hypothesis was advocated prior to the discovery of the fine-tuning evidence, and thus is not ad hoc.

4. Therefore, by the likelihood principle, LPU (the existence of a life permitting universe) strongly supports T (the theistic hypothesis) over the NSU (naturalistic single universe hypothesis).

(Collins 2009, p. 207)

The fine-tuning evidence of which Collins writes is the fact that the laws, constants, and initial conditions of our universe must fall within a very narrow range in order for a universe to be life permitting. A life permitting universe is one which can support the existence of, what Collins calls, embodied moral agents; complex physical beings possessing intelligence and the ability to make moral choices and affect one another. The naturalistic single universe hypothesis states that there is only one universe and that the values of the constants, laws, and initial conditions are a unexplainable brute fact, and could have had any value from a very wide range. The theistic hypothesis states that there is an omnipotent, omniscient, eternally existing, and free creator of the universe. And the likelihood principle states that the degree that a piece of evidence counts towards one hypothesis over another, is proportional to the ratio of how surprising the evidence is under each hypothesis.

The justification for the first premise comes from the fact that there is a very large range of values that each physical constant could have taken, but only a very small range of values which would have allowed the resulting universe to be life-permitting. And, given the naturalistic single universe hypothesis, there is no reason to expect each constant to take one value, as opposed to any other. That each constant took a value which allows the universe to be life-permitting, then, is very surprising under NSU.

The second premise is justified by appealing to God’s motivations, which we can know by reasoning from the attributes that Collins takes Him to have. Collins explains that the only reasons God would have to do anything would be to increase the moral and aesthetic value of reality (2009, p. 254). From that, it is reasonable to conclude that the existence of embodied moral agents does add significantly to the moral and aesthetic value of reality. Therefore, it is not surprising at all that God would create a universe (with aesthetic value in its own right) which could hold such creatures.

The third premise seems obvious, in that the theistic hypothesis was widely held well before the fine-tuning evidence came to be understood.

As for the conclusion, the likelihood principle is fairly uncontroversial and derivable from Bayes’ Theorem. If the first two premises are true, then LPU does serve as powerful evidence for T and against NSU.

The Understatement of the Century

Imagine a trial where the defendant stands accused of stabbing a man to death in the victim’s living room. The accused takes the stand, and admits to being in the victim’s house at the time of the murder. Does this evidence support the “defendant is guilty” hypothesis or the “defendant is innocent” hypothesis?

It seems easy to see that it would be unsurprising that the defendant would be in the house at the time of the murder, if he is guilty. It also seems quite surprising that the defendant would be in the house if he were innocent. Using the likelihood principle, this evidence counts toward the guilty hypothesis and against the innocent hypothesis.

Were this singular piece of evidence to be the extent of our knowledge of the events in question, this conclusion seems quite reasonable. But how would our evaluation change, were we to also know more specific facts about the case? If the defendant were locked in the basement of the victim’s house at the time of the murder, it would still be true that he was in the house at the time of the murder. But the additional, more specific evidence seems able to render the initial likelihood calculation irrelevant when determining which hypothesis is supported by the evidence.

What exactly is the relationship between more general pieces of evidence which seem to favor one hypothesis over another, and the more specific evidences which point in the opposite direction? And, most importantly, what does this have to do with the fine-tuning argument?

As for the first question, Paul Draper calls this the fallacy of understated evidence. “This fallacy (i.e., mistake in reasoning) is committed when one uses some relatively general known fact about X to support a hypothesis when a more specific fact about X (that is also known to obtain) fails to support that hypothesis. (Draper, 2008)” We can see that this applies to the case of the man accused of murder; the general fact is that he was in the victim’s house at the time of the killing, the specific fact is that he was locked in the basement while the murder took place.

As for the second question, Draper accuses Collins of unintentionally committing the fallacy of understated evidence by, “understating what we know about life, Collins makes the fine-tuning data appear to support theism more than it really does. (Ibid.)” He agrees with Collins that the mere fact that intelligent life, of some sort, exists is less surprising under theism than naturalism. But Collins ignores the more specific evidence that humans are the only form of intelligent life known to exist. Draper takes this more specific evidence to point strongly toward naturalism.

Menschliches, Allzumenschliches

Let us consider a second, more specific piece of evidence:

HE: The only intelligent life we know to exist is human.

Then, the following argument can be formed:

5. Given the fact that intelligent life exists, it is not surprising at all that the only intelligent life we know to exist is human, under a naturalistic single universe hypothesis (NSU).

6. Given the fact that intelligent life exists, it is very, very surprising that the only intelligent life we know to exist is human, under a theistic hypothesis (T).

7. The theistic hypothesis was advocated prior to the discovery of the fine-tuning evidence, and thus is not ad hoc.

8. Therefore, by the likelihood principle, HE (humans are the only form of intelligent life known to exist) strongly supports NSU (the naturalistic hypothesis) over T (the theistic hypothesis).

Under the naturalistic single universe hypothesis, it is no surprise at all that HE is the case. In evolutionary terms, intelligent life is expensive, requiring huge amounts of resources. Given that intelligent life exists, we should expect that it would be relatively unsophisticated, only incrementally better morally, aesthetically, in intelligence, and in emotional sophistication than its evolutionary ancestors, and far more common in the universe than more advanced life.

However, under the theistic hypothesis, HE is very surprising. If God’s motivation can be understood entirely in terms of adding moral and aesthetic value to the universe, that the most morally and aesthetically valuable intelligent life is human, seems very unlikely. An omnipotent God would have the power to create life which was not constrained by its evolutionary history, which was not limited in morally and aesthetically irrelevant ways, and which was “better” intellectually, physically, and emotionally. Given that intelligent life exists and the truth of the theistic hypothesis, HE is very, very surprising indeed.

The conclusion of this argument mirrors the conclusion of Collins’. As HE entails that a life-permitting universe exists, by using the more specific evidence, we should expect to obtain a more accurate conclusion. And, if this conclusion is true, it should dampen, if not extinguish entirely, the persuasive power of Collins’ fine-tuning argument.

Of Angelic Aliens…

One possible objection to this reasoning rests on the idea that, although humans are not the only kind of intelligent life we would expect God to create, our existence is a net-positive, all things considered. So the creation of humans could very well play a role in maximizing the moral and aesthetic value of reality.

I will agree with the first part of that objection; it does seem that humans, for all our flaws, are a net-positive in terms of moral and aesthetic value. But I would disagree with the second part; our existence cannot fit with a plan to maximize the moral and aesthetic value, carried out by an omnipotent being.

It seems very easy to conceive of a species of intelligent life, which was morally and aesthetically superior (if only marginally) to humans, able to live and thrive in exactly the same kinds of environments as humans, and which would be far more likely candidates for existence under the theistic hypothesis. It would be very surprising, if all of our intuitions of what kind of intelligent life is possible were false. Therefore, it would be very surprising were HE to be true, even if it were also true that humans play but a small role in a larger plan to maximize the moral and aesthetic value of reality.

…and Panglossian Possibilities

A different sort of objection to the probability calculation involving HE, is that it is possible that humans are much, much more morally and aesthetically valuable than we give them credit for, that it is possible that God has knowledge of some kind of moral consideration which makes the existence of humanity consistent with the maximization of moral and aesthetic value.

On the face of it, I would agree; this is certainly a possibility. God, with his perfect view of the moral landscape, would possess a better perspective on the relevant moral issues regarding the value of humanity. But what we are concerned with, for the purposes of this argument, is not mere possibility, but the likelihoods of those possibilities.

If the theist maintains that she would not expect to know the relevant moral considerations which would affect what actions God would take in order to maximize the moral and aesthetic value of reality, this does nothing to undercut how surprising it would be, to us, that morally and aesthetically superior beings would not raise the moral and aesthetic value of reality more than morally and aesthetically inferior beings.

So, without some kind of explicit justification for the idea that, contrary to our own moral intuitions and reasoning, God does have a good moral reason for creating humans, which is also non-ad hoc and does not fall victim to Collins’ probabilistic tension criticism for extended hypothesis, we are completely justified in continuing to believe that HE is surprising.

Conclusion

The fine-tuning argument does show that the existence of intelligent life is more likely if theism is true, rather than if naturalism is. Were the singular fact that intelligent life exists make up the totality of our evidence, this argument would require the rational person to significantly revise their degree of belief in theism upward, and their degree of belief in naturalism downward. Unfortunately for the proponents of the fine-tuning argument, LPU is not all the evidence we have available to us. If the mere specification of the kind of life which is known to exist is enough evidence to cancel out the epistemic effects of the fine-tuning argument, then there seems to be no repairing it.

Notes

[1] I have endeavored to reproduce the argument without introducing any subtle errors. To be sure, any that are found are due to my rendering of the argument, not the original. I would urge anyone interested in learning more about fine-tuning arguments to read the original, as it is a model of clarity and precision.

Works Cited

Collins, Robin. “The Teleological Argument: An Exploration of the Fine-Tuning of the Universe.” The Blackwell Companion to Natural Theology. Ed. William Lane Craig and J. P. Moreland. Oxford: Wiley-Blackwell, 2009.

Draper, Paul. “Collins’ Case for Cosmic Design (The Great Debate).” The Secular Web. Internet Infidels Inc., 2008. Web. 26 Apr 2010. .

The cosmological argument is one of the oldest arguments for the existence of God. It has its roots in the work of the Greek philosophers Aristotle (384–322 BCE) and Plato (427–347 BCE). Today, we have two popular versions of the argument: theKalam and the Leibnizian arguments. Both attempt to show that there must have been a first cause or sufficient reason for the universe to exit. However, one seldom hears of the original cosmological argument as it was made famous by Thomas Aquinas (1225-1274). Aquinas’s argument is handy if one wants to avoid heavy debates on the philosophy of time and the principal of sufficient reason that other cosmological arguments bring to the table.

The simplest statement one can find of Aquinas’s argument is found in his Summa Contra Gentiles:

We see things in the world that can exist and can also not exist. Now everything that can exist has a cause. But one cannot go on ad infinitum in causes… Therefore one must posit something existing of which is necessary. (Summa Contra Gentiles 15.124)

We can see that this argument, rather than focusing solely on cause and effect as Kalam does, or on sufficient reason as the Leibnizian does, attempts to combine the two by examining causal chains and their modal status. David Beck, a modern day defender of the TCA, gives the example of a train. If we visualize a train being pulled, we ask ourselves “What is the cause of the cart in front of us being pulled?” The answer is of course the cart in front of it, but what is pulling that cart? Well the cart in front of it. The problem is that we see that all the carts are dependent on the one in front of it to move, but this cannot go on forever otherwise the carts would never be in motion. We can break the causal chain by positing a being which depends on nothing for its movement; the engine which by its very nature is able to move. This illustration is clearly an analogy for existence. The contingent beings are the carts, and God is the engine: the thing of which by its very nature exists and does not depend upon another thing for its existence.

We can summarize our reasoning thus far in the following way:

P1. A contingent being exists.
P2. What explains this being’s existence must be in a set that contains either only contingent beings or contains at least one necessary (non-contingent) being.
P3. A set that contains only contingent beings cannot cause this contingent being to exist.
C1. Therefore this set contains at least one necessary being.
C2. Therefore a necessary being exists.

Premises one and two are not at question. The third premise is true due to the fact that if there was ever a time when nothing existed, then nothing currently exists, since contingent beings are finite in temporal duration and cannot cause themselves to exist. It follows then that if even one contingent thing exists, whether it be the universe as a whole, a chair, or my best friend Steve, then there exists a necessary entity.

What then can we deduce about then nature of this necessary entity? Firstly, Occam’s Razor eliminates the possibility of there being more then one necessary being, since positing a plurality of beings does not seem to be necessary for the explanation. From this, we can conclude that monotheism is true. Secondly, since this necessary being is the cause of space and time, the necessary being must transcend space and time, and therefore exist non-temporally and non-spatially (at least without the universe). This necessary being must therefore be changeless. The cause must also be immaterial since something can only be timeless if it is unchanging, and something can only be changeless if it is immaterial. It must also be unimaginably powerful, since it created all of space, matter, and time. Finally and most remarkably, such a transcendent cause must be personal, for how else could a timeless cause give rise to a temporal effect (like the universe)?¹ The only entities that we know of which can be timeless and immaterial are minds and abstract objects (numbers, sets, laws, theories, colors, etc). But abstract objects can’t cause anything. Therefore the being which exists, must be an unembodied mind. If the cause were just a mechanically operating set of necessary and sufficient conditions, then the cause could never exist without the effect. If the cause were timelessly present, the the effect would be timelessly present too. The only way for the effect to be timeless and the effect to be in time would be for the cause to be a personal agent with free choice. Thispersonal agent chooses to create an effect in time without any prior determining conditions.

Thus we are brought not only to a transcendent cause of the universe, but to its creator. So, from the Thomistic cosmological argument alone we can may conclude that a personal creator exists, and is uncaused, necessary², unique, beginningless,changeless, timeless, immaterial, very powerful, and personal. From this, it is reasonable to conclude that God exists.”

1. This deviates from Aquinas’s original presentation of the argument and presumes the past duration of the universe to be finite. Though there are good reasons for believing the past duration of the universe to be finite (The Kalam cosmological argument takes this approach), Aquinas’s goal was more modest: his argument is compatible with a universe whose past duration was infinite. However, I wish to extend the force of Aquinas’s argument, and hence I do not assume the eternality of the universe in this essay. [↩]
2. In the factual sense. [↩]

The Argument

(1) If it is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe), then it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(2) It is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(3) It is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

Axiom S5

Premise (1) is an instantiation of the Axiom S5 of the S5 modal logic. It states both:

(A) If possibly p, then necessarily possibly p

(B) If possibly necessarily p, then necessarily p

To understand these axioms, it is first important to understand six different types of modal status. Modal logic is our logic of possibility (among other things), it allows us to discern which propositions are true, false, necessary, possible,   contingent or impossible. Possible worlds are a tool which we use to assist in understanding these three types of modal status. A possible world can be thought of as a set of compossible propositions or in a simpler manner, a way in which reality might have been. Now, it is not important to discuss whether or not possible worlds are real in the sense of actually existing things. While this is the view of the modal realists, we can simply think of possible worlds as abstracta, propositions or even conceptions.

Propositions under modal logic are classified into the six aforementioned classifications (the term ‘obtains’ means ‘achieves trueness’):

A proposition is true if it obtains in the actual world (for example: Obama is the first black president of the United States)

A proposition is false if it fails to obtain in the actual world (for example: Obama is the first white president of the United States)

A proposition is necessary (or necessarily true) if it obtains in all possible worlds (for example: All bachelors are unmarried)

A proposition is possible if it obtains in at least one possible world (for example: There are no human beings)

A proposition is contingent if it obtains in some possible worlds and fails to obtain in others

A proposition is impossible (or necessarily false) if it fails to obtain in all possible worlds (for example: 2+2=5)

So what the Axiom S5 reveals to us is the following:

(A*) If there is some proposition that is possible, then it is necessarily possible

(B*) If there is some proposition that is possibly necessary, then it is necessary

To understand further: (A*) states that if some proposition is possible, that is, it obtains in at least one possible world then it must obtain in at least one possible world. This follows from the definition of possible, such that if a proposition p is possible, it is true in every possible world that p is possible.

Additionally, (B*) shows us that if there is some possible world where the proposition p is necessary, then it follows that p is necessary (and obtains in all possible worlds). That is, consider there is some possible world w1 in which the proposition ‘Banana’s are yellow’ is necessarily true. So, in w1 the proposition ‘Banana’s are yellow’ is true necessarily – the proposition will obtain in all possible worlds. Since in w1 the proposition is necessarily true, it must be true in all possible worlds (otherwise it wouldn’t be necessarily true). Again, we see that this is true by definition.

Now that we understand the Axiom S5, let us re-examine the argument.

The Argument (again)

(1) If it is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe), then it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(2) It is possible that it is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

(3) It is necessary that (there exists a very powerful and intelligent supernatural being and it is contingent that he is the creator of the universe).

As we can see, premise (1) is merely a form of the conditional found in (B) and so if (2) is true (3) follows and the argument is sound.

Conclusion

A defense of (2) will cause this article to become far too technical for its intended purposes. I will simply direct anyone interested in a defense of (2) to Gale’s paper entitled “A New Argument for the Existence of God: One that Works, Well, Sort Of.”

If the argument is sound it establishes a necessary being that is creator of the universe. Of course, there are no established attributes beyond this so that being is not necessarily any particular religious version of God. In fact, it seems that the conclusion is wholly consistent with the creator of the universe being malevolent. Further argumentation is certainly required to establish further attributes of the proposed necessary being.

I write again on the topic of the Kalam Cosmological Argument (KCA) in an attempt to summarize and simplify the position of philosopher Quentin Smith. Smith and Craig have been long time correspondents and have shared two extremely interesting discussions.

In these discussions the KCA has largely been the focus. In their 1996 debate, Quentin Smith during his positive period argued not only that God did not create the Universe, but rather, the suggestion is logically impossible.

Smith begins by outlining the difference between a continuing cause and an originating cause.

Continuing cause: Something is a continuing cause of the universe only if it causes each state of the Universe.

Originating cause: Something is an originating cause of the universe only if it causes the earliest state of the universe.

Thus, he states that:

If the universe began with the Big Bang and has no originating cause, it has no continuing cause. For the origin of the universe is a state of the universe, and if it is not caused the criteria for a continuing cause (causing each state of x) cannot be satisfied.

Smith’s thesis: It is logically impossible that there be a first state of the Universe caused by God, and furthermore that every cosmological argument for the existence of God are actually arguments for his non-existence.

Smith attempts to prove this by showing that Craig’s thesis that the universe has an originating divine cause is logically inconsistent with all permissible definitions of causality.

He undertakes this by beginning with an explanation that he is speaking of the cause of the universe’s beginning, not the cause of God’s act of willing that the universe. The purpose of this clarification is to note that we are not talking about agent causality. Agent causality would by the type associated with action. The relationship between myself and my willing my arm to move would be such an example. The notion of causation that is up for discussion is that of event causation. He is specifically speaking of the relation between God’s act of willing (which is an event) and the beginning of the universe (also an event).

Smith operates under the presumption of Big Bang cosmology (as does Craig) and holds that the universe and time began to exist with the Big Bang. He says that from this, one can rule out an originating cause according to ALL definitions of causality which include temporal priority as a logically necessary condition.

He is making the claim that in every definition of causality that affirms that the cause is earlier in time to the effect rules out any notion of an originating cause.

He begins with Hume’s definition of causality.

Hume’s definition of causality: Something, c, is a cause of something, e, if and only if these three conditions are met: (1) c is spatially and temporally associated with e, (2) c is earlier in time than e, and (3) every particular like c is always conjoined with a particular like e.

Perhaps we can simplify with a focus on the specific point Smith makes:

God is the cause of the universe at the earliest time only if God is earlier than the earliest time.

We have a clear logical contradiction; nothing can be earlier than the earliest time.

Ergo, for any system of causality which is derived from Hume’s where a cause is earlier than the effect,  cannot affirm God as the cause of the beginning of the Universe.

Smith then moves on to discuss what he calls “Nomological definitions of cause”. Nomos is a Greek word meaning the law, so any Nomological definitions of causation are definitions which include a law of nature.

He proposes the following definition of causation:

Nomological definition of causality: c is a cause of e if and only if there’s a law of nature, called the law of nature L, that enables a statement that e occurs to be deduced from the premise that c occurs and another premise asserting the law L.

An example of something which meets this criteria is the following:

Let’s first propose our law of nature. Let us say, gravity. Let us also suppose that I, Mitch, throw a ball in the air and it falls to the ground.

Throwing a ball in the air (c) is a cause of the ball falling (e) if and only if there is gravity (L).

This enables us to state that e occurs via deduction of c and L:

Mitch throws a ball up into the air, (C)

What goes up must come down (simple statement of gravity) (L)

Therefore, the ball that Mitch has thrown will fall. (E)

Unfortunately for theists, the nomological definition is logically inconsistent with a divine cause of the Big Bang because God, by definition is supernatural and not governed by the laws of nature.

Thus far, Smith has shown that God cannot be the cause of the Universe when analyzed with any definition of causation which places a cause before an effect, and that God cannot be cause of the Universe when analyzed with any definition of causation which allows a deduction of effect from a combination of cause and natural law.

Should one still want to posit God as the originating cause of the universe, than one would have to do so according to a definition of causation which does not include time or natural law. These are known as atemporal and singularist definitions of causality.

An atemporal cause is called atemporal because it does not mention time or allows simultaneous causation (an effect occurring at the same time as the cause).

A singular cause is a cause which allows one event to cause an effect in a single case.

Smith notes that there are not many definitions of causality like this, but points to David Lewis’

Lewis’ definition imports conditions that are contrary to the ones that happen. It is a hypothesis of imaginary situations.

David Lewis’ definition of cause: c causes e if and only if (1) c and e are events and both occur, and (2) it is the case that either if (i) c had not occurred, e would not have occurred (if the cause did not occur, the effect would not occur) or, as an alternative to that, (ii) if there is a causal chain linking c and e and each link d in the chain is such that if d had not occurred, then e would not have occurred.

To simplify: God’s willing(c) causes the beginning of the universe(e) if and only if (1) God’s willing and the beginning of the universe both occur (God wills the beginning of the universe and the universe begins), and (2) it is the case that either if (i) God’s willing had not occurred, the beginning of the Universe would not have occurred or as an alternative to that, (ii) there is a causal chain linking God’s willing and the beginning of the universe and each link of this chain is such that if d (a link) had not occurred, then the universe would not have began.

Smith states that there is no causal chain between divine will and the Big Bang so (ii) is inapplicable, so we can concentrate on condition (i).

Condition (i) states: if c had not occurred, e would not have occurred

We can understand (i) in context to state that if God did not will the universe to begin, it would not have begun.

Smith states then that from (i) it stands that if (e) had not occurred, then (c) would not have occurred. We can state this because this definition of causality has no notion of time associated with it.

Hence where (i) states: if c had not occurred, e would not have occurred

We can reverse the predicates to state:

(i2) If e had not occurred, c would not have occurred

Now, where c is God’s willing and e is the universe beginning:

(i) states that if God’s willing had not occurred, then the beginning of the universe would not have occurred

And (i2) states that if the beginning of the universe had not occurred, then God’s willing would not have occurred.

In (i2), the Big Bang is effectively the cause of God’s willing! But, this is absurd.

Lewis addressed this problem in saying we have “a reverse causal dependence of c on e, contradicting our supposition that e did not cause c”. He also solves the problem by denying the statement of (i2) (that if e had not occurred, c would not have occurred). He says that instead, it is true that “c would have occurred just as it did, but would have failed to cause e.”

So, it becomes possible that the cause could occur, or the event which was the cause could occur but the effect would never have happened.

We have the following propositions then, when working with this definition of causation that is atemporal:

(i) if God’s willing had not occurred, the beginning of the universe would not have occurred

(i2) if the beginning of the universe had not occurred, God’s willing would not have occurred.

Because (i2) is absurd, we must use Lewis’ solution to the problem:

(i3) God’s willing occurs, but fails to cause the universe to begin to exist.

It should be evident then, that Lewis’ definition cannot be applied to the matter of God willing the Big Bang because how can an omnipotent being fail at doing what it sets out to do? It is logically impossible that an omnipotent being will the Big Bang to occur, and yet the Big Bang does not occur.

To those who are wondering why we cannot simply work with (i), without reversing the predicates, the answer is simple. If we are going to disallow a reversal of the predicates, we are stating that the cause MUST come BEFORE the effect, and we would be utilizing a temporal definition of causation to do so (as in the Humean example). Because Lewis’ definition is atemporal, we cannot invoke such.

Smith also outlines “Necessary and Sufficient Conditions”, with the following three definitions of causality:

Necessary and Sufficient Conditions:

1. x is a cause of y if and only if x is a sufficient condition of y – Sufficient Condition
2. x is a cause of y if and only if x is a necessary condition of y – Necessary Condition
3. x is a cause of y if and only if x is a necessary and sufficient condition of y – Combined

To clarify, the difference between a necessary and sufficient condition is the following:

A necessary condition for some state of affairs S is a condition that must be satisfied in order for S to obtain.

Example: A necessary condition for getting an A in philosophy class is to hand in your term paper. If you do not hand in the paper, you will not get an A and if you get an A, you obviously have handed in the paper.

A sufficient condition for some state of affairs S is a condition that, if satisfied, guarantees that S obtains.

Example:  A sufficient condition for getting an A in philosophy class is getting an A on every piece of graded work. If a student gets an A on every piece of work, then the student gets an A overall.

Handing in the essay is not a SUFFICIENT condition for getting an A in the course, since you can hand in the paper and not get an A overall.

Getting an A on every piece of work is not a NECESSARY condition for getting an A in the course. It is possible to get an A even if one fails to get an A on some piece of work.

Smith’s contention is that none of the three aforementioned definitions can apply to God.

God’s willing the Big Bang is a sufficient condition of the Big Bang, so (1) appears to be satisfied by God’s creation of the Big Bang. But (1) fails as a definition of a cause because numerous things suffice the definition. As Smith states, a thermostat reading 65 degrees is a sufficient condition under normal circumstances of the temperature being 65 degrees, but this reading is not the cause of the temperature.

Then, we can move on to (2) and propose that it is necessary that the Big Bang be caused by God, if it is to occur at all. From this, it seems that God’s willing can satisfy (2), but (2) is not the definition of a cause since there are many causes that are not necessary conditions and many necessary conditions that are not causes. As Smith further explains: “The movement of a feather on my desk is caused by my pushing the feather with my hand, but this pushing is not a necessary condition of the feather’s moving, since the feather may move by a gust of wind blowing. Further, air is a necessary condition of humans existing, but the air does not cause humans to exist.”

Moving on to (3), the condition which combines both Necessary and Sufficient notions may be satisfied by God’s willing the Big Bang, but again it is not a definition of a cause. There are many causes which are not both necessary and sufficient conditions of their effects (the example of the feather, and humans). Further, Smith suggests that this definition is violated by probably causes such as the radioactive decay of a uranium atom which requires a probabilistic definition of causality.

Smith entitles his next section “A Correct Formulation of Any Divine Relation to the Big Bang.” He also suggests that there is an argument that God is not the cause of the Big Bang, and that this argument remains sound regardless of which definition of causality is used.

He bases the argument on the premise: if something is a logically sufficient condition of something else, that doesn’t cause it.

More formally written as: for any x, if x is a logically sufficient condition of y, then x is not the cause of y.

He gives an example of a body being in motion. A body’s being in motion is a logically sufficient condition of the body’s existence, but the body’s being in motion is not the cause of the body’s existence.

God’s willing the Big Bang is a logically sufficient condition for the Big Bang, for “God wills the Big Bang and the Big Bang does not occur” are logically incompatible since he is omnipotent. If an all-powerful God wills x and x does not occur, the all-powerful God is not all-powerful . This is an obvious contradiction. God might be able to do everything that is logically possible but he cannot what is logically impossible.

Smith makes sure to point out that this conclusion does not mean we cannot speak intelligibly about God and his relation to the Big Bang. We may still say that a mental event in God’s mind is a logically sufficient condition of the Big Bang’s occurrence. Smith proposes, in fact, that we should say this rather than say that God causes the Big Bang.

Smith states that such can be proposed as:

There is a certain relation, R, in which God stands to the property F, F being the property of being the Big Bang such that by virtue of God’s standing in relation R, to the property of the Big Bang, it is logically necessary that the property or characteristic of being a Big Bang happens and thus, there is a Big Bang.

Simplified, this just means that while God is not the CAUSE of the Big Bang, there is some mysterious sufficient condition linking the two. Smith notes that one can still speculate about this.

Smith’s conclusion explains that proving that God cannot cause the Big Bang, does not necessitate that he does not exist or that the Big Bang is not logically necessitated by God but it does show that he could not have been the cause. The implications, he explains, are that arguments from necessary truth, a priori truth, or empirical truth of some causal principle CANNOT be a relevant premise to establish that the Big Bang is the logical result of God’s standing in relation R (some relationship that is not a causal one… an unknown relationship) to the property of being a Big Bang.

One such example is William Lane Craig’s Kalam Cosmological argument:

1. Everything that begins to exist has a cause.
2. The universe begins to exist.
3. Therefore, the universe has a cause.

This argument does not support the thesis that God exists or is the cause of the universe’s beginning to exist. The very argument, in fact, entails that the Universe’s existence is NOT a consequence of any act by God, since God could not have caused the universe to exist.

Smith also explains that even inductive arguments, based on the fact that everything we observe has a cause, cannot be used to support that thesis that God caused the Big Bang since this would support a thesis incompatible with theism; namely, the Big Bang has a cause.

Furthermore, every cosmological and teleological argument for the existence of God are in fact arguments for God’s non-existence, since these arguments are arguments for the thesis that the universe has a cause.

Smith gives an example in the form of a teleological argument (argument from design):

1. Artifacts are caused to exist by intelligent beings.
2. The universe resembles an artefact.
3. Therefore, it’s probable that the universe was caused to exist by some intelligent being or beings, with some purpose in mind.

If this argument is a proper argument from analogy, then God probably does not exist, since God is not a cause but a logically sufficient condition of the universe’s existence.

Smith further asserts that since the cosmological and teleological arguments have thought to be the strongest arguments for God’s existence, and since they support atheism rather than theism he is essentially granting all the theistic arguments as being sound, especially the cosmological and the teleological. Now ask, “What does this prove?”

He concludes by saying that he is arguing that they prove that God doesn’t exist because their conclusion has got a God who causes the beginning of the universe, which is logically impossible! Smith states that the theist position is rather weak now as it’s hard to imagine how one could ever inductively or deductively establish, or find self-evident, that the Big Bang has a logically sufficient condition of its occurrence which requires that God brought it about. Therefore, the belief in the existence of God is less reasonable than even the “most cautious theologians have standardly supposed.”

Craig’s case:

The theistic case was not yet dead in the water, as William Lane Craig touches upon a few matters in his own speech period.

Craig restates Smith’s argument as follows:

1. If the claim that God caused the Big Bang cannot be analyzed in terms of extant definitions of causality, then God cannot have caused the Big Bang.
2. The claim that God caused the Big Bang cannot be analyzed in terms of extant definitions of causality.
3. Therefore, God cannot have caused the Big Bang.

Craig does not believe this argument to be sound.

Of premise (1), he states that he sees no reason to think that it is true. He says that in general, arguments that have some intuitively intelligible notion and cannot be analyzed in light of certain philosophical theories should make us reject the theories, not the common sense notion. Craig argues that God creating the universe is intuitively intelligible and if the present theories do not support this, than all the worse for them. It shows, he says, that the theories need revision. He also asserts the same for the definitions of causation and concludes that there is no good reason to think that (1) is true.

Diving deeper into the core subject matter, Craig analyzes (2). He says it is clearly false and that Smith himself admits it! He points to the fact that Smith in his discussion of necessary and sufficient conditions, does not deny that God’s willing the universe or the Big Bang is a case that satisfies the definitions proposed. Rather he attacks the adequacy of the definitions themselves. Craig claims that what Smith is really asserting is:

(2) The claim that God cause the Big Bang cannot be analyzed in terms of any adequate extant definitions of causality.

But, he says, this is problematic because it is generally acknowledged that there s no adequate definitions of causality to date.

Craig concludes by saying that even under the assumption that Smith’s definitions are adequate, God’s causing the universe satisfies at least some, so (2) is clearly false.

He points to Lewis’ analysis of causation:

Lewis’s definition of cause: c causes e if and only if c and e are both events, and both occur, and if c had not occurred e would not have occurred.

Craig says that God’s willing the Big Bang obviously satisfies the definition: God’s willing and the Big Bang are both events which occur and if God’s willing had not occurred, the Big Bang would not have occurred.

But, Smith rejoins with “if the Big Bang had not occurred, God’s willing would not have occurred,” implying that the Big Bang is the cause of God’s willing. This is obviously not the case says Craig, but this calls into question Lewis’ analysis not whether God satisfies it.

Craig also touches upon the notion of metaphysical time, stating that if we hold with Newton, Swinburne and others that God exists prior to the Big Bang in a metaphysical time then there is no objection to be had by adopting an analysis of causality which involves temporal priority of cause to effect.

Smith responds:

Smith is quick to point out that Craig’s claims about the lack of agreement on a correct definition of causality are true for ANY philosophical theory or subject. That is the very nature of philosophy, and once people agree upon certain things it moves on to become a science. Smith concludes that this point is then moot.

Smith then states that there is something common to every single definition of causality he gives that all philosophers agree upon, that of an event that does not logically entail the event that’s the effect. He proposes the following example:

“Take what every philosopher says, the sun shines on the stone, and the effect is the stone becoming warm, and I say, O.K., that’s a law of nature, but can we derive that just from pure logic? Is it a logical contradiction to say the sun shines on the stone, and the stone does not become warm? No. To have a logical contradiction, you have to say something like: the sun shines on the stone, and the sun does not shine on the stone. So all these definitions of causality, even though they differ in a number of respects, all agree in this very fundamental point, that the cause is not logically sufficient for the occurrence of the effect. And that’s precisely how they all differ from the relationship of God to the Big Bang.”

In response to Craig’s analysis of Lewis’ definition, Smith confesses he does not see the point:

“But I confess that I did not follow that argument very well because I couldn’t see how Lewis’ definition was satisfied by God and the Big Bang at all. For there’s a part of David Lewis’ definition that, if some event c is going to cause some even e, then Lewis holds that if the event e had not occurred (which would be the Big Bang), then c (God’s willing) would not have occurred. And that does not apply to the case of God and the Big Bang. Lewis holds that, in this case, if e had not occurred (the Big Bang had not occurred), then c (God’s willing) would have occurred just as it did, but have failed to cause e (the Big Bang). But that’s inconsistent with the notion of theism, which implies that if God’s willing occurs, it is a logically sufficient condition of the Big Bang.”

Lastly, in conclusion to the entire discussion Smith mentions that if one is to accept a concept of metaphysical time they must do so by rejecting physical cosmology. That would include a rejection of Einstein’s Relativity and Big Bang cosmology. He says that even if one supposes that there was a time before the Big Bang, this does not solve the problem! The crucial issue, he says, is that God’s willing the Big Bang is a logically sufficient condition of the Big Bang and once we have that condition, we violate every existent definition of causality.

Craig says that maybe these definitions are false, how is this different than stating that we should redefine causality so that it allows God’s willing of the Universe?

As would be evident at this point, this discussion offers a much greater critique of cosmological arguments than my own and even goes further to state that they are atheistic arguments, not arguments for God.

In the following, I will show why the Kalam Cosmological Argument fails to establish its conclusion that God exists.

First, we must understand the argument:

(1) Everything that begins to exist has a cause of its existence.

(2) The universe began to exist.

(3) Therefore, the universe has a cause of its existence.

I will not touch upon any attempted refutation of (1) on the basis of virtual particles as the results are still inconclusive. Though, it is perhaps interesting to note that (1) is presented as an a priori category of the human mind. That is to say that causality seems to be a precondition of all human thought, as Kant touched upon.

Insofar as Craig’s argument attempts to conclude that the cause of the Universe was a single personal being, that is simply a non-sequitur. It remains a possibility that several entities took part in the creation.

Also, Craig asserts that the Universe was brought into existence by something that is beyond, and greater than it. I fail to see why the creator(s) of the Universe must be beyond, or greater than it. It seems that Craig is proposing the following:

A creator is always greater than its creation.

Do we have good reason to suppose this? I think not. Parents give birth to children who turn out to be much greater than they were, for example. Craig doesn’t seem to provide justification that the relationship between Creator(s) and Universe is different than that of parent and child.

It also seems that the Kalam rests on this idea that the Universe was created from nothing (ex nihilo) but this does not seem to be justified within the Kalam either. An understanding of the Kalam leads to an understanding that an assertion is being made that the Universe is not eternal, and was rather created. Though where is the exclusion that the Universe was not created out of some other thing. As Michael Martin proposes:

“One possibility is that the creator or creators of the Universe created it out of something that existed in some timeless realm. Another is that the material existed from eternity and that the creator or creators took this and formed the universe at a particular moment and, with it, causality and change.”

There simply cannot be any idea of causality or causal sequences prior to the creation of the Universe.

Craig further suggests that the cause of the Universe is a personal agent(s). But as Michael Martin explains, to do so is to appeal to the principle of determination. The principle reads:

If there are two equally possible results and one occurs, the result must be explained in terms of the choice of a personal agent

Why should we suppose this to be true? In our world and even in science, what would happen if for every situation in which there were two possible set of affairs and one arose, we appealed to a personal agent. What would become of coin flips? Rather than saying that the reason as to why it dropped on one side as opposed to the other was due to a personal agent, rather than the natural forces operating on the coin. We can safely reject this principle, and by doing so, we can safely reject that if the Universe was created it must have been at the hands of a personal being. Perhaps there are non-personal causes which are timeless themselves, but create events in time.

We should also be skeptical when Craig states that the Universe had a beginning in time. When Craig seeks to establish this point he presents this idea that actual infinities are impossible. In order to simplify, I will give a (very) brief explanation of Potential Infinity vs. Actual Infinity.

Potential infinity refers to a procedure that gets closer and closer to, but never quite reaches, an infinite end. For instance, the sequence of numbers 1, 2, 3, 4 …

This sequence gets higher and higher but never ends, it will never actually reach infinity. We just use the term infinity to denote the direction in which the set of numbers if moving towards. As Eric Schechter says, “chasing this kind of infinity is like chasing a rainbow or trying to sail to the edge of the world — you may think you see it in the distance, but when you get to where you thought it was, you see it is still further away.

Actual infinity, (think, completed infinity) is an infinity that one actually reaches; the process is already done. For instance, the completed set of numbers {1, 2, 3, 4…}

By having a completed set, we are identifying the set as one object. A set which has infinitely many members. This does not mean a large amount of finite members, this literally means the set already has “infinitely” many members. It is completed, whereas the potential infinity is working towards completion but will never arrive there.

Perhaps a clearer explanation is that which Aristotle suggests. A potential infinity is one that you may keep adding to, an actual infinity is one that you may not because it is completed. All of the members of the actual infinite set exist together simultaneously as a final totality.

Craig goes on to admit that actual infinities are perfectly consistent in mathematics, but says they are logically impossible to have in the real world. He fails to show that there is any logical inconsistency to be had by having an actual infinite exist in the real world.

He does, however, give the following example:

“Suppose further that each book in the library has a number printed on its spine so as to create a one-to-one correspondence with the natural numbers. Because the collection is an actual infinity, this means that every possible natural number is printed on some book. Therefore, it would be impossible to add another book to this library. For what would be the number of the new book? Clearly there is no number to assign to it…. Therefore, there would be no number for the new book. But this is absurd, since entities that exist in reality can be numbered”

Firstly, it is important to note that though Craig says this is absurd, it surely is not illogical. As Wainwright tells us, the argument is unsound, because books can be added and numbered by simply renumbering the books already in the library. The new books would then be given the numbers of old books (books that have already been assigned numbers) and the old books would be assigned new numbers.

Craig’s argument that one cannot construct an actual infinity by successive addition is reconstructed by Martin as:

(1) For any point, it is impossible to begin at that point and construct an actual infinity by successive addition.

(2) In order to construct an actual infinity by successive addition, it is necessary to begin at some point.

(3) Therefore, an actual infinity cannot be constructed by succesive addition.

First off, (2) begs the question. There is an alternative that an actual infinity can be constructed by successive addition, IF the successive addition is without a beginning. Craig assumes that an actual infinity cannot be constructed this way, but that is precisely what is being questioned! Hence, Craig begs the question.

At this point, there would usually arise an appeal to scientific evidence. Craig does so by stating that the evidence supports the hypothesis “the Universe had an absolute beginning”. Though, as Milton Munitz shows, that would preclude any scientific investigation of this beginning:

“Science is grounded in the use of the Principle of Sufficient Reason and therefore, always leaves open the possibility of finding the explanation of any event. To say there is some unique event marking the beginning of the universe for which no [scientific] explanation can be given, is to say something contrary to the method of science. It is for this reason … that any conception of the beginning of the universe, when defended under the aegis of some supposedly scientific cosmology, is an indefensible notion.”

Simply because there is no explanation now, does not mean there will not be one in the future. Munitz further states:

“Even if, there is reason to prefer a model whose account of the past history of the universe includes a reference to an event called in that theory ‘the origin of the universe,’ it does not exclude the possibility of finding some more refined theory, in which inference can be made to events even earlier than the once identified as “the beginning” in the theory of the coarser grain. The search for a more refined theory that would explain the event considered ‘the beginning of the universe’ (in the cruder theory) would be part of the normal interest of science.”

Lastly, as Martin states:

“…even if the universe has beginning in time, in the light of recently proposed cosmological theories this beginning may be uncaused. Despite Craig’s claim that theories postulating the Universe ‘could pop into existence uncaused’ are incapable of ‘sincere affirmation,’ such similar theories are in fact being taken seriously by scientists”

It is evident that the Kalam Cosmological Argument, as presented by William Lane Craig, fails to establish its conclusion.