Theism and Contemporary Cosmology

ACKNOWLEDGMENTS

Chapter

1. INTRODUCTION

2. FAITH AND REASON

The Medieval Portrait: Thomas Aquinas
The Modern Empiricist Portrait
The Fideist Portrait: Kierkegaard and Barth

3. THE STRUCTURES OF ARGUMENTS

4. THE KALAM COSMOLOGICAL ARGUMENT

Everything That Begins To Exist Has A Cause For Its Existence
The Universe Began to Exist
Therefore, the Universe has a Cause

5. NATURALISTIC EXPLANATIONS FOR THE BEGINNING OF THE UNIVERSE FROM CONTEMPORARY COSMOLOGY

The Steady-State Model
The Oscillating/Cyclical Universe Model
The Inflationary Universe Models
The Vacuum Fluctuations Model
The Unbounded Universe Model

6. ATHEIST MICHAEL MARTIN ON THE KALAM'S INFERENCE TO A PERSONAL CAUSE

The Kalam's Conclusion and Ontological Vagueness
Transdimensionality and the Causal Inference

7. CONCLUSION

END NOTES

I would like to thank the following individuals for reading earlier drafts/portions of this work and making helpful suggestions: Michelle Guthrie, N. Kyle Cooper, Sean Choi, Jeffrey Jay Lowder, Mitch Hodge, Matthew Butler, and Kristopher Nicholson. Furthermore, the use of the computers in the Astronomy classroom in the Physics department at the University of Nevada, Las Vegas for the research on the constellations was a tremendous asset to the "walkthrough" on determining the age of the universe. I would also like to thank Pamela Dudley and the reprographics division at Legal Express in Las Vegas, Nevada for binding this document in an appropriate format. Finally, I want to thank the staff at Lacrosse University in Covington, Louisiana for the opportunity to research the subjects contained in this thesis. Without the support and help of these individuals and institutions, this work would not have been possible.

Throughout the years of philosophical and religious history, many have witnessed a battle on what could rightly be the most important topic to transcend the annals of history: The existence of God. Perhaps no greater issue is debated today than that of the possibility of God's existence. The approach that one takes on such an important philosophical issue as this one will tremendously shape the world view of that person. The existence of God is surely the par exemplar of this truth. Quite naturally, there are those of us who favor the proposition that God exists and see such an issue paramount to a religious faith. But there are other competing beliefs about God's existence that call such conclusions suspect under reasonable criticism. With the inclusion of reasonable inquiry in contemporary debates over the existence of God we find ourselves defending a fundamental assumption about who is or is not at work in our universe. It has indeed been progress since the Rationalist era as we have now rightly granted the readmission of reason back into the question of God's existence. This is certainly progress. Previously, many philosophers have given up the ideological fight to declare one way or the other whether or not God exists (and in some cases they have avoided the question altogether). Instead, discourse about the existence of God is now relegated to popularist media. On many levels of contemporary media it is even fashionable to make belief in God surrealistic. On a scholarly level, ever since theists have traveled the road of fideism and atheists have ventured through the forests of naturalism and positivism, we have found ourselves asking the same questions all over again. This may imply that our readmission of reason back into faith is an unavoidable phenomenon and that reason is to be properly regarded as the handmaiden to faith. Lest this statement serve as a premature conclusion, I shall address the antecedent issue of faith's relationship to reason in this work. If a critic already denies any application of reason to faith then the material on proving God's existence below will only be imbued with a premature disparagement. Therefore, this will make our discussion of faith and reason essential.

You may be asking yourself, "Why is the existence of God still an issue when such a struggle antedates even the earliest philosophical thinkers?" Or, "Why have we bothered to come full circle only to end up repeating ancient controversies?" I suspect that the answers to these questions are found in the evolution of philosophical arguments. It seems that each generation is permeated with a different twist on the existence of God. For the Greco-Roman era, the existence of God (or gods) enjoyed very little opposition. But 18^th century Rationalism and the Positivists of the Vienna Circle conveyed a disdain for God's existence such that even the notion of God was incoherent. And it is easy to see how one's view on the existence of God can serve as a foundation for other areas of philosophy. For example, think about discussions on ethical issues and basic civil liberties.

There is no doubt that our concession of God's existence or our denial of such defines our perception of how the world operates and sustains a foundational plateau. In other words, how we answer the question "Does God exist?" will tell us what our world view will encapsulate. Let me illustrate this by means of analogy. If we believe that goblins coerce all human actions, then we would have, admittedly, a peculiar world view. But this world view would imply all sorts of interpretations for the real world. For example, numerous individuals who were and are on death row would be there for crimes of which they are not guilty (since the goblins are the constraining causal agents of their actions). Similarly, no beautiful work of art would be the production of the artists whose names appears in the corner, and no great work of philosophical history would be the product of those whose names are contained therein. Instead, we would have to attribute every human action to the mysterious goblins behind the intellects. Now, nobody seriously considers this analogy as a reflection of truth about the world; but it serves to illustrate how one can view or interpret the world we all share and enjoy. Now consider something else. You have just read an analogy that you found to be an imaginary piece of fantasy used to illustrate a point. But did you stop to think that due to your world view you were making judgments about the goblins of intellectual causation? Perhaps your rejection of a goblin world view is itself the product of antecedent presuppositions (and it no doubt is). If you are an Empiricist, you may have decided the question of goblin interaction simply by observation. Now, goblins driving human intellects is one thing but the existence of God entails an entirely different interpretation on our world. As a confessing theist, I suspect that a Creator freely created, either in time or timelessly, the universe in which we live. ⁽¹⁾ If any reader of this article is a professing theist, then they would perceive the world as being the product of an intelligent being that somehow exists independent of temporal and spatial constraints. In some cases they may see themselves as individuals who have strived to worship such a God and to commune with Him, as in the Christian persuasion. If one is an atheist or an agnostic then they would perceive an entirely different world view. Their world view makes no individual person the product of any transcendent intellect. The universe and everything in it is just the cosmic furniture in which we find our existence. How an atheist or agnostic lives her life is truly a matter of personal endeavor and self-defined circumscription. In any case, any attempt to mix the different world views in this case is clearly like that of oil and water.

In this work, we shall consider the role that reason has with respect to belief in God and how contemporary cosmology, as evidence, compels us to that belief. The particular argument we will be focusing on is the kalam cosmological argument in its deductive mode. Although arguments are not necessarily considered as evidence, per se, I believe that the advances of contemporary natural science and the theoretical sciences provide physical evidence for the kalam argument (which is discussed below). After the argument is presented, we will examine its strength in light of contemporary cosmology and philosophical scrutiny. Since this argument has come under much criticism, I shall attempt to leave no stone unturned.

In the previous chapter we saw how God's existence (or lack thereof) can shape our world view. We need to begin examining our approach to explicating the role of reason in the issue of faith in God before we can confidently assert any arguments for the existence God as a worthwhile enterprise. Historically, Christianity itself has always taught that reason plays a significant role in evangelism (at least up until the Enlightenment). The Christian ⁽²⁾ believes that from an inward epistemic experience from the Spirit of God there is a personal affirmation that God is known and genuinely real. On the other hand, the Christian (and usually the theist in general) is equally committed to providing reasons to both skeptics and pilgrims of religious convictions. This represents a real dichotomy in the theist. But to what extent does the role of critical thinking have with respect to a theistic apologetic? Throughout the centuries there have been theists who have affirmed the reality of God and yet postulated constraints for the boundaries of reason. Each era of human history, ever since the rise of Aristotelian philosophy in Christian, Islamic, and Jewish theism, has expressed an opinion on the matter. We shall briefly consider some of those views here.

Thomas Aquinas was born in the castle of Roccasecca just outside of Naples around 1224. At the early age of five, Aquinas was placed in the Benedictine Abbey of Monte Cassino as an oblate. He remained there for nine years until the Emperor Frederick II expelled him and the other monks. Aquinas then joined the University of Naples when his flirtation with the theology of the Dominican friars caused dissension in his home. He was kept from attending the University of Paris until 1245 when he enrolled and studied under his companion St. Albert the Great. After his studies, Aquinas managed several positions of lectureship and greatly contributed to the Papacy in Italy. He was summoned by Pope Gregory X to the Council and while en route from Naples to Rome at the age of 49 he passed away. Aquinas' life is characterized as one of study and minimal outside social involvement. For Aquinas, Aristotelian philosophy and the Scriptures were the most important elements in his studies as well as his upbringing. Nary a word can be said against Thomas' devotion to God. These elements that characterize Thomas's life make him an essential voice on the subject of relating faith and reason.

A Thomistic analysis of the philosophy of religion leads us to conclude that Aquinas accepted a view of religious beliefs such that they were ascertained by faith. This mirrors Augustine's account of a sort of fideism. But not so fast. Thomas was surely conveying that the doctrines of Christianity were mysterious such that they did not enjoy empirical or rational certitude. For example, there are no empirical evidences that prove the doctrine of the Trinity or any certainty in evidence that would show that God was incarnated as a man. Moreover, the resurrection of the saints is not self-evident or experientially attested (since such an event is yet future). But Aquinas does suggest that there are evidences that make those doctrines believable. For example, he points to various prophetic pronouncements and miraculous support for the "proofs" of faith. ⁽³⁾ These miracles and prophecies undergird the authenticity of the Scriptures as the expressed revelation from God. Thus what makes the doctrine of the Trinity reasonably true is that it is inscribed by God in the Scriptures which themselves are confirmed by the prophetic and miraculous signs of authenticity. Of course the question that naturally arises is, How can Thomas vindicate the miracles which he purports proves the Scriptures true? Thomas found the answer in Augustine's notion that the Church stood as the miracle of Christianity. For Aquinas and Augustine, the fact that Christianity was embraced by "simple and lowly men" render its present existence a confirmation of the truth of those previous miracles. ⁽⁴⁾ Therefore, we could envisage Aquinas' progression of faith and reason by Figure 2-1:

Figure 2-1: Aquinas' conception entails that the Church itself points to Miracles & Prophecies, while such point to The Scriptures, which ultimately point to specific ChristianDoctrines.

In Aquinas' understanding of faith and reason, both appear to be equally tenable avenues to truths about religious matters. Sometimes faith is required for those things that are not demonstrable with certainty and other times reason points to the truthfulness of certain claims.

It is presumptuous to suggest that the modern (or British) empiricists denied belief in the existence of a divine being, or God, simply because they were empiricists. Often, empiricists are wrongly globalized as naturalists, which is to say that the only reality that exists is the perceivable physical world of time and space. This unfortunate conflation of empiricism has led many to surmise a disavowing of theistic belief subsequent to the Middle Ages simply because empiricism offered an evaluation of physical reality. In contemporary vernacular we understand this to be an early form of the controversy surrounding the relationship between religion and science. But the following analysis will show that modern empiricism did not a priori eliminate our ability to know about God.

It seems historically true that if the various empiricists thought that a proper epistemological structure was only what can be perceived via the five senses, the fact remains that the most ardent critics, such as Thomas Hobbes and David Hume, would not have given tacit admission to the existence of God. ⁽⁵⁾ However, any attempt at rationalizing God or any organized religion, says Hume, is surely a vacuous enterprise for religion is not in any sense a "relation of ideas." Thomas Hobbes vigorously derides the notion of an immaterial world of a deity or angelic beings in his most notable work Leviathan; yet he accedes the notion of God all throughout his writings, perhaps thinking that belief in God was not a matter of reason but solely about revelation. Similarly, Francis Bacon, an empiricist philosopher who helped to shape scientific investigation, perceived God as a matter of revelation and not reason. ⁽⁶⁾ The mistake often committed by careless investigators is for one to conclude that because an empiricist's philosophy does not possess a rational or experiential means of acquiring knowledge of God then God must not exist. This would be to make a metaphysical conclusion from an epistemological standpoint, which is a mistake. Surely how one comes to know certain things has little (if any) bearing on the ontological status of those things. This is how the genetic fallacy is often committed.

The empiricists by and large give explicit affirmation of their belief in God. Bacon writes, "Men must soberly and modestly distinguish between things divine and human . . . the oracles of sense and of faith." ⁽⁷⁾ John Locke writes, "The knowledge of the works of God proportions our admiration of them." ⁽⁸⁾ And Locke even contends that the Gospels in the Bible are God's written revelation. ⁽⁹⁾ It is also interesting to note how the great Idealist George Berkeley's "immaterialism" is contingent upon the existence of a divine perceiver, God, in order to bring reality to unseen objects. In this scenario one would be required to believe in God in order to exist! Woolhouse writes,

"In a sincere attempt to display the importance of God in the

scheme of things, Berkeley sought to rebuild the 'new philosophy'

on the more solidly religious foundations of a complete and thorough-

going spiritual immaterialism." ⁽¹⁰⁾

Although it sounds contradictory to speak of a "spiritual immaterialism," Berkeley means to suggest that the epistemological process of perception of objects are mere apprehensions of ideas in the mind. ⁽¹¹⁾ And this only becomes a reality when it is ultimately understood that God's awareness of our universe gives it existence. Alas, one cannot help but perceive an early pronouncement of quantum physics. But as a philosophy of religion, knowledge about God is not so much a reasonable supposition but a necessary foundation for grounding existence. And if we follow Descartes and assert that some ego in the world really exists (even if it were the only existent) then it follows, from Berkeley's scheme, that God exists. ⁽¹²⁾

In order to tie in what the empiricists perceived was the proper relationship between faith and reason, there needs to be a stark contrast between the two. The British empiricists would not permit outright contradiction between claims of faith and the logic of reason. Faith claims could only be accepted if they were consistent with and to some extent even implied by reason. But as we have seen, the role of faith is construed as entirely unrelated to the role of reason, yet reason and faith cannot contradict each other. If a contradiction arose between the two roles then reason ought to be favored. Perhaps in an empiricist's world view one could provide a cosmological argument in order to corroborate theism with that of reason and then acquire via revelation the reality of God's existence.

The Danish philosopher Søren Kierkegaard suggested that the role of reason in matters of faith was too excessive. People simply do not appreciate the subjectivity of the experience of God in their lives and preferred merely intellectual assent toward matters of faith. As a reaction to the rationalistic Lutheran Christianity of his day, he presented an existentialist theory of meaning that entails a three-category view of human existence that could be acquired wholly apart from reason. In fact, reason should have nothing to do with it! Each category, or stage, is a progression toward achieving the virtues of meaning, purpose, and value in life. For Kierkegaard, the problems and sufferings of life bespeak the existence of God. The first category of existence is the aesthetic stage. On this level human beings are primarily concerned with personal gratification and living for self-complacency. This does not necessarily mean that the aesthetic man is a gross hedonist, rather, he is simply very circumspect about his life. Everything revolves around the aesthetic man. But Kierkegaard explains that this ultimately leads to unhappiness. Pursuers of meaning, purpose, and value are ultimately compelled to arrive at the ethical stage. This category of man is the attempt of the "struggling individual" ⁽¹³⁾ to find conformity in recognizing certain moral and absolute goods. The problem for the ethical man is that it also leads to despair. Such a man sees living the life of the ethical a fruitless task and an impossible achievement. The last stage and impending conclusion of the struggling individual is the religious stage. With the realization that the aesthetic man cannot bring happiness in personal pleasures and that the ethical man simply mirrors the problem of an infinite satisfaction in values (along the lines of Thomas Aquinas), the next level requires a drastic "leap of faith" to the realization of the existence of God. This "irrational" step compels us to view the meaning, purpose, and value of life through the perspective of divine providence. In this sense the notion of the truth of Christianity is subjective because it is quite real to the perceiver. Professor Solomon writes:

A "subjective truth" is a psychological truth about the author. The object

of the author's belief may be false, but it is true that the author has that

belief. This account could also explain how it is that "subjective truth" is

for only one person. ⁽¹⁴⁾

God then becomes the source of ultimate meaning and satisfaction and brings to the perceiver a deep sense of resolution. But reasonable arguments and rationalistic inquiries into the truths of Christian doctrine impede the subjective self-actualization of the individual who struggles to find that resolution.

The great influential Protestant thinker Karl Barth is credited for making fideism a contemporary issue. For Barth, knowledge of God apart from revelation is incomprehensible. We must look to God's historical revelation which is found in the person of Jesus Christ. Thus the Bible is not itself the revelation of God but a container of the true revelation of God: Jesus. Barth's philosophy stems from his reaction to post World War I liberal theology. Having been educated under Adolf von Harnack and Wilhelm Herrmann who supported German imperialism, Barth rebelled against liberalism and sought theological reflection in the spirit of the Reformers. ⁽¹⁵⁾ This reaction led Barth to be an avid champion of divorcing faith from reason. People must come to the truth of God's existence by accepting the revelation contained in the Scriptures and by opening their hearts to receiving that revelation. The inability for the human mind to use reason to access God is, in Barth's analysis, due to a complete transworld depravity often paraded by the theological position known as Calvinism. ⁽¹⁶⁾ This depravity renders the human being totally disabled from the ability to believe in God unless God first illuminates the person's mind to do so. For Barth, the access to God is so incomprehensible that human reason cannot codify the steps required to obtain knowledge of God. Hence God enables the person to believe in God and then insures their response to Him by His irresistible Spiritual presence.

For the some individual believers, there is a non-evidentialist sense in the way one believes that God exists. She accepts a personal testimony acceded by the heart and clings to this incorrigible experience as self-validation for her religious theism. The famous philosopher of religion John Hick concurs with this instrospection. He admits that there are "different ways of conceiving and experiencing the one ultimate divine Reality" ⁽¹⁷⁾ either through evidence or direct personal experience. Such an experience is "generally cognitive of reality except when we have some reason to doubt it." ⁽¹⁸⁾ Thus a religious experience, such as knowledge of the existence of God, ought not to be dismissed without good reason but may be adhered to pending no defeaters to the experience.

Christian theists also agree with this understanding as is often codified by Professor Alvin Plantinga of Notre Dame University. Plantinga teaches that human beings are created with belief-making faculties that, when unhindered by depravity, can produce true beliefs. ⁽¹⁹⁾ Moreover, such beliefs can be properly basic. A properly basic belief is a belief that does not depend on another belief for its acceptance by the believing agent. For example, someone observing a tree five feet in front of them would immediately believe that the tree is really five feet in front of them. A simple observation such as this would not entail that the perceiver has assessed certain philosophical propositions in order to conclude, "I now believe that a tree is really five feet in front of me." Such a belief is immediately known and initially unquestioned. When these belief-making mechanisms are functioning properly and they espouse the belief "I had an experience with God that made Him real to me" then we would have good personal grounds for accepting the existence of God as true. Such a belief may be perceived, in Plantinga's words, as a properly basic belief justifiable apart from evidence. ⁽²⁰⁾

With respect to the personal reality of God's existence as advocated by Hick and Plantinga, the fideist and the classical apologist agree. There is nothing that ultimately brings one to belief in God other than the fact that the free creature's will undergoes a life-changing experience. Regarding this revelatory pathway to knowledge, the New Testament itself declares:

"I am the good shepherd, and know my sheep, and am known of mine"

(John 10:14; KJV; emphasis mine)

and

"For ye know the grace of our Lord Jesus Christ" (2 Cor. 8:9; KJV;

emphases mine).

And perhaps the most vivid passage on the endowment of the knowledge of God in Christian theists can be found in Ephesians:

God . . . may give unto you the spirit of wisdom and revelation in the

knowledge of him: The eyes of your understanding being enlightened;

that ye may know what is the hope of his calling, and what the riches of

the glory of his inheritance in the saints (Eph. 1:17-18; KJV; emphasis

mine).

In this passage, we see that the source of a knowledge of God for the Christian specifically comes not from reason but from God Himself. This should make the fideist very happy. Furthermore, the Spirit of God also has the role of convicting non-believers of their spiritual reluctance. Concerning this, the New Testament states:

But I tell you the truth: It is for your good that I am going away.

Unless I go away, the Counselor will not come to you; but if I go, I

will send him to you. When he comes, he will convict the world of

guilt in regard to sin and righteousness and judgment: in regard to sin,

because men do not believe in me; in regard to righteousness, because

I am going to the Father, where you can see me no longer; and in regard

to judgment, because the prince of this world now. (John 16:7-11; NIV)

But, you may wonder, if the Holy Spirit is the one who compels and convicts people of their conviction-producing faith then why should the evidentialist or theological rationalist have a voice at all? The answer is that through reason and argument one may benefit from the inner spiritual conviction. It seems as though the participation of reason assists the creaturely will in forming a belief in God. How is this accomplished? Indeed, influence is a classic tool in persuading anyone in considering the object of belief. For example, if you wanted to sell a product that you found extraordinary and wanted others to benefit from it then you would no doubt reason with your potential buyer that the benefits of having this product far outweigh the reality of not having it. You may even say to yourself that such a product sells itself and really curtails the need for a salesperson to go door-to-door in search of potential buyers. This is echoed by well-meaning Christians who declare, "I am just going to preach to people and leave it to God to win the souls." But even the owner of our analogous product knows that many people are not aware of such an item and that others simply need reasons to bridge the gap of their need with their buying it. Similarly, theists must include in their discussion the tool of apologetics. The word "apologetics" comes from the Greek word apologia which means "to give a defense." ⁽²¹⁾ If a non-believer begins to criticize theism or calls a certain issue into question, then the individual engages in what is called "apologetics." Apologetics, similar to the temperance of various martial arts and self-defense techniques, is generally used to deflect criticism. After all, no one would barge into someone's home with a product and begin defending it from critics without provocation. You would kindly and gently present your case for the potential buyer's appeal and begin defending the product only if circumstances require you to do so. If the product is truly that good, it may be revealed through the presentation. But if someone decides not to purchase it, it might be due to a weak presentation and not necessarily the product itself. I suspect the same is true of theistic apologetics. Theists tend to know that God exists, but they may just have a hard time conveying this message to the satisfaction of the recipient.

The final reason why someone may not choose to buy a product is because they have closed their minds to the notion of ever receiving it under any circumstances. If salespeople encounter such closed-mindedness then we would only be wasting time and energy attempting to convince them. But again, such failure is not necessarily the fault of the product but perhaps of the potential buyer. In the cases of refusal we have seen above, neither one is necessarily to be attributed to the product itself. On the other hand there may be good reasons to reject the adequacy or the acclamations of the product. Either way, the seller needs to advance positive case for the product and then deflect criticism when prompted. Let us now match the analogy to the appropriating theistic arguments. If believers in God expect to convince anyone else of their personal faith then one must logically go beyond the subjective experience. After all, no one can know what someone else is experiencing without external exhibition. What good would it do if one acknowledged their belief in God and did nothing to convince others? Of course the Kierkegaardian fideist could suggest that the person's assessment of their existential predicament would compel them toward the religious persuasion. But it seems incomplete and vacuous to think that self-reflection would somehow necessarily drive the struggling individual toward belief in God. There must be some avenue of knowledge that is accessible. Maybe the individual will always consider God as a possible existent. But the question seems open-ended and unresolved. For I can think of no specific reason why anyone should abandon the aesthetic or ethical lifestyle unless they thought that their personal unfulfillment is not a truth about their existence. The critic would be within her logical rights to surmise:

What the fideist would have to demonstrate is that:

But how can any fideist assert that? Statement (2) speaks of the falsity of statement (1), and the fideist is not supposed to be interested in supporting her beliefs or denying others. If the fideist is sure that the critic falsely believes (1) then (2) must be somehow probable. So the fideist could probably assert:

This would be Hick's and Plantinga's approach to the issue. But even this statement bespeaks an existential truth not evident to the critic even though it may be true to the believer. In fact, I accept that (3) is unequivocally true (in agreement with Hick and Plantinga) but is lacking enough persuasion to convince the critic that (2) is true. It seems that on a Kierkegaardian level the fact that (3) is perceived as false to her is surefire confirmation that God does not exist. Now the fideist is in a pickle.

It seems that the remedy is to append statement (3) above to protect the subjective truth of God's existence and yet maintain a semblance of probability to the critic. Thus one could say:

Although (3) may serve to be personal vindication of God's existence to my own satisfaction (wholly apart from reason), only (4) can be advanced by the theist who wants to convince the critic that God exists. As can be seen, if the critic believes (1) then nothing in (3) should change that. However, if the theist affirms (4) then this has a direct challenge to atheism regardless of the truth of (1)! Now the theist can be commensurate with the critic's denial of God's existence. The two competing world views are now in a shared arena where the issue can be battled. This should not serve to overturn the truthfulness of (3) since a theist can remain rational and still believe that (3) is true apart from supporting evidence. For the theist who personally acknowledges her belief in God on the basis of an internal experience of God is not threatened by the truthfulness of (4). The only thing that (4) accomplishes is that it is possible to convince others that God exists. It is only when the theist must show others that God exists does (4) become necessary. I think that the fideist and the rationalist can share a Thomistic middle ground here and affirm the knowledge of God from a personal perspective and yet demonstrate to others that theism is rational and should be considered.

In the context of debate or simple discussion about the existence of God, the theist is presenting their case for the reality of a Being they believe created the universe. The non-theist does not accept such a proposition and, thus, may advance criticism. As we have seen, reason plays an integral part in influencing others. It seems that on a level of pure fideism, the critic sees no reason to come to a belief in God. But a rational demonstration of how theism can be true might appease the critic's requirements for considering the truth of theism - yet theism may still be personally believed wholly apart from reason. As a salesperson tries to convince others that their product is worth the investment, the theist can also share in their belief in God by showing others that He exists. A theist can be rationally justified in their belief in God wholly apart from evidence (as Hick and Plantinga explain) but that reason plays a pedagogical role in influencing others toward the same belief.

I remember when I was in high school, an acquaintance of mine told me that if I believed in God then I did not use logic and reason in my everyday thinking (an insult to be sure). Of course, since I was just a teenager learning basic principles in various subjects along with everyone else, I was taken back by this remark. He told me that if I really believed in such fairy tales then I was not using any intellectual sense. He simply felt that logic and reason were diametrically opposed to a belief in God. With my buttons having been pressed, I managed to pose the following question, "How can our universe exist at all unless someone greater than it created it?" He just went on to another subject and we eventually lost sight of the initial discussion. Nonetheless, many theists have come across similar circumstances where belief in God is put under the microscope of rational scrutiny. However, we have already established that reason can possibly show that God exists. So the non-theist no longer has the monopoly on rational discourse. Thus the question that naturally arises is, "Where do we start?" Understanding and establishing the nature of the kalam cosmological argument's structure will be the paramount focus of this chapter. By perceiving how the argument is structured one will be given the opportunity to visualize the point of the argument and to see how the existence of God is to be concluded from a collection of evidence and concepts. In this chapter we will look at the general structures of logical arguments, the particular structure of the kalam cosmological argument, and the particular premises as they relate to the argument itself.

Without delving deep into a written lecture on reasoning and critical thinking here, we will only be concerned with the differences between the structure of the kalam argument versus the structures of other arguments. Basically, what we need to understand is the nature of an argument in general, the structure of good arguments in particular, and which category the kalam argument will fit into.

A collection of statements is said to be an argument when two necessary elements are involved. These elements are the supporting statements, or premises, toward the support of a claim, or the statement known as the conclusion. For example, if I say that roses are red and violets are blue because our uniform experience verifies this then I have just given an argument. This argument can be constructed as follows:

premise: Our uniform experience indicates that

roses are red and violets are blue.

conclusion: Therefore, roses are red and violets are blue.

Although the contents of an argument are uncompromisingly important, we need to see how the relationship between the premise(s) and the conclusion operate. In order to strip ourselves from any bias we will use letters, or variables, to represent statements of alleged fact. After all, just looking at this illustration automatically tells us that such a relationship is uncontroversial since our collective experience most certainly does suggest that roses are red and violets are blue. But before we look at any more examples of arguments (particularly those using variables in place of statements), let us look at a rough sketch at my intended goal. Just like the captain of a ship needs to chart his course of destination, I will also chart a course of argument structures for our final destination.

Here we see that an argument can either be deductive or inductive. A deductive argument is an argument such that if the premises are factually true then the conclusion is guaranteed to be true. So it is logically impossible to have true premises and a false conclusion. An inductive argument is structured so that the relationship of the premises to the conclusion is such that if the premises were true then the conclusion would only probably be true. So, it may be that the premises are true but this does not guarantee that the desired conclusion is true. The illustration about roses and violets I used above is a demonstration of an inductive argument. Since we do not need to be concerned with inductive arguments in our structure of the kalam cosmological argument then we will simply examine the deductive branch of an argument. ⁽²²⁾

In the argument tree above you will notice that the deductive branch splits into valid and invalid. An argument is said to be invalid when the structure of the deductive argument yields true premises and a negligible conclusion. In this case it is all over for the argument. But if the deductive argument turns out to be valid then this tells us that there is never a time when the premises are true and the conclusion false or that the conclusion cannot possibly be other than what it is. Consider the structure of a deductively valid argument:

p1: If X then Y.

p2: X.

C: Therefore, Y.

We may substitute the variables with an example:

p1: If I live in Nevada then I live in the United States.

p2: I live in Nevada.

C: Therefore, I live in the United States.

This argument is deductive because the structure claims to guarantee the conclusion. It also turns out to be valid because no matter what truth value I substitute for the variables X and Y in the previous argument (either "true" or "false"), I will always have a true conclusion with true premises. In the second argument it is impossible for me to live in Nevada and not be in the United States. This setup guarantees our confidence in the structure.

Our final consideration of general deductive arguments is the question of soundness. An argument is said to be sound if the premises are genuinely connected to the conclusion. This is the most difficult part of determining if the argument is ultimately a good one or not. For example:

p1: If I eat breakfast this morning then the Yankees will win

the next World Series.

p2: I ate breakfast this morning.

C: Therefore, the Yankees will win the next World Series.

There is no doubt that the argument is deductive. It also happens to be valid. But there is something suspicious about my eating breakfast this morning causing a Yankee victory in the next World Series. As much as I would like it to be true, the argument is doomed to be unsound.

So, how does all of this play into the kalam cosmological argument? We can answer this by using variables to illustrate its structure and, consequently, analyze with our argument tree. The kalam cosmological argument takes the form of a quasi-syllogism. This argument structure rationalizes a truth about a particular member from its class based upon the same truth about the class itself.

This can be exemplified as follows:

p1: All men are mortal.

p2: Socrates is a man.

C: Therefore, Socrates is mortal.

The truth about a particular member (Socrates) is that he has a true property (mortality). This is inferred from premise 1 which tells us that every member of the class (all men) has the same truth (mortality). The kalam argument then fits the quasi-syllogism structure and can be represented as:

p1: Every X has p.

p2: Y is a member of X.

C: Therefore, Y has p.

In premise 1 the word "every" is used instead of "all." This difference is inconsequential. To say that all men are mortal is to say that every man is mortal. Thus, the same message is being conveyed. Both words in this sense are said to be universal. Now, this structure above is certainly a deductive argument. The conclusion must follow with uncontested certainty from the premises if they are true. The argument is also valid since every possible combination of truth values substituted for the variables never yields true premises and a false conclusion. This only leaves the question of soundness. Since soundness considers the actual statements themselves then we will have to examine the statements individually to see if they reasonably connect to the conclusion. This is where our assessment of deductive arguments operates.

I have met a variety of people ranging from those who see evidence for God's existence and are wholly persuaded and those who review the evidence and outright reject it. For this reason I prefer to preface my presentation of the evidence for God's existence with some simple words of caution and a stipulation about how arguments figure into the decision-making process. I am not claiming to be able to present evidence for God's existence in such a way as to yield mathematical certainty. Philosophers who have invoked this argument believe that the case for God's existence based on the kalam argument is a cumulative one. After all, deductive arguments ultimately find their success or failure in their ability to be sound, not in whether or not the conclusion is palatably conceivable. Occasionally I witness theists with such bold expectations about the evidence. They think that upon delivering the evidence, an atheist or agnostic will become overwhelmed by the evidence's magnanimous force and will immediately concede theism. Nay, human nature is far too stubborn. Reality has taught many of us that one can only provide the evidence, then the individual must decide for herself. How that evidence is psychologically processed is reserved solely for the listener or reader.

There is just one final piece of information. The reader should know that argument you are about to read is not new. I do not intend to advance a revolutionary piece of disclosed evidence for God. In today's suppression of arguments for theism, theists are now making an unprecedented leap from evidence to esoteric proclamations. Take for example the popular literature on the presumed failure of the classical arguments for God's existence. These theists are aiming at a trend that finds peculiar defenses in such things as Equidistant Letter Sequencing or uncontrollable laughter during a church service as new evidence for God. As far as I am concerned, if theists can only make their case by resorting to questionable defenses then we have sorely neglected the rich arguments that great men and women of passed centuries have advanced. This is an attempt at a resurgence of what many today consider one of the most powerful evidences for the Christian faith: The kalam cosmological argument. Due to present-day advancements in cosmology, there is a sweeping force of theoretical speculation that is attempting to respond to the kalam cosmological argument. And to this we shall now turn.

The kalam cosmological argument is the product of a history of philosophy and refined evidence. It utilizes astronomy and astrophysics to empirically demonstrate that a cause for the universe is necessary if we are to make sense of its existence. In addition, some powerful philosophical arguments have been injected into these arguments as further support for what appeared to Medieval philosophers as unquestionably obvious. "Kalam" is the general Arabic term for "argue" or "discuss," but no precise definition corresponds to it in English. ⁽²³⁾ It has been a term associated with the "dialectical theology" promoted by Islamic philosophers during the peak of Aristotelian Christianity, and it represents the notion that, given the impossibility of an actual infinite, the universe could not have existed for all eternity since time itself is a set of discrete segments pointing indefinitely back into the past. In their scientific defense of the beginning of the universe, they saw the celestial sphere as empirical evidence for their philosophical conclusions. In Christian antiquity, great philosophers such as Thomas Aquinas and Bonaventure have also advanced cosmological evidences for the existence of a cause for the universe. Each philosopher who has pushed for a cosmological argument in support of the existence of God has stylized his own argument as a supplement to other cosmological arguments. There is no doubt that history has shown us such great literary presentations, but the present has taught us that ideologies and arguments are fair game for critics. Given the current advances of scientific knowledge about our universe and its origin, we have seen such Medieval and contemporary cosmological arguments weather even the most vilifying criticisms. Perhaps that is what makes cosmological arguments so appealing. They have survived the test of time. In contrast, I find that atheistic arguments have been refined, redefined, revamped, and even abandoned in order to seek that academic loophole that would allow the skeptic to safely regroup. But the final arbiter as to whether or not the kalam cosmological argument provides the good evidence to show God's existence will be the reader.

The kalam argument is a simple construction. As noted in a previous section, it claims to be a deductive argument that has the form of a quasi-syllogism. For simplicity's sake, here is a reconstruction of the kalam cosmological argument in its skeletal form:

p1: Everything that begins to exist has a cause for its existence.

p2: The universe began to exist.

C: Therefore, the universe has a cause.

The argument itself is pretty straightforward but it does not end here. Remember that deductive arguments also have to survive the test of validity and soundness. The validity question can be answered right away. It seems that if the premises are true, then the conclusion definitely follows. There are additional reasons to perceive this argument as structurally effective simply because so many atheists have criticized this argument, not on the basis of false premises per se, but on the basis of the conclusion's insufficiency to point to God even if such an argument turns out to be undeniably sound. Skeptics usually say, "Even though there is a cause for the universe's existence, that doesn't mean that the cause is 'God'!" It seems that the presence of this question serves to show that the argument itself is valid but missing other elements necessary to declare the cause to be God (of course we will deal with this cumulative argument later once we have substantiated the conclusion). It is the question of the soundness of the argument that is the final one to be answered and the one which is not readily accepted by skeptics of theism. Yet non-theists have not been able to come up with a convincing response to it. As the reader discovers the individual support for each premise, my hope is that the reader sees the argument's success and how it provides ample support for the justification of belief in God despite attempts to the contrary.

The first premise in the kalam argument claims to conform with the general uniform intuition that something is not spontaneously brought into being without any cause. Nothing in nature or in the theoretical sciences prompts anyone to push for an incredible belief that something can or did mysteriously "pop" into existence without a cause. This premise seems to stand as a monument to this intuition. It just seems to be a simple fact of life that everything that exists has a cause for its existence. We would naturally question anyone with an alternative claim.

Our pre-noetic structure, or our intellectual makeup prior to its sensing the physical world, seems to guide our interpretation of sense data in the experiential world. Many philosophers have posited the notion that our intellects begin as blank slates prompting raw empirical input. They, that is the empiricists, identify this state of intellectual emptiness as the tabula rasa or the "blank tablet." Classically, ancient empiricists like Aristotle have argued against Plato's belief that our understanding and realizations about the world are based on a transcendent world encasing the Forms, or archetypal structures of identification, as the explanation for our awareness of certain objects and relationships. For Plato, causation may imply the Form of "Cause" being manifested through a particular event, say the causing of a computer to switch on, in order to bring comprehension of the event to the observer. Aristotle did not accept this world of the Forms because he believed that if Forms did exist, they would be a priori bound up in the particular manifestations themselves. So, how does Aristotle account for the existence of universals if they are only generalizations of particular occurrences? Philosopher and theologian Ed L. Miller writes:

Aristotle's answer is that the universal and necessary elements

of knowledge - the foundations of all subsequent reasoning -

are built up in the mind through induction. ⁽²⁴⁾

The process of induction is the inference of general characteristics necessary to identify a particular object or occurrence (or universals) to the particular object or event itself (or a particular). So, Aristotle believed that the source of our understanding of universals came through the induction of collected experiences leading us to conclude those characteristics that are necessary for that item or event to be categorically identified. Simply put, a universal is the whatness or essence of an object (i.e. What makes X an X to begin with?) and a particular ostensibly points to this or that as a representation of a universal. Thus, a chair is a particular object while chairness is its universal attribute. Both Plato and Aristotle concurred with this. But they disagreed how knowledge of universals became evident to the human intellect. Plato believed that the universal (or Form) defined a particular. Aristotle believed that a series of experienced particulars led to our understanding of the universal. But which one is correct?

The preferred answer came not from Aristotle or Plato but through the school of Idealism. Idealism is the view that our intellects are "constructed" with "built-in" categories of objects and events in relation to each other. The reality of these objects depends on whether one is a subjective idealist or an objective idealist. The former believes that reality relies on perception for its existence. For example, the great British empiricist George Berkeley taught through the Three Dialogues that sensations are experiences that exist in our minds and that we only have direct awareness of those sensations. ⁽²⁵⁾ Contrary to John Locke, Berkeley's notion of a substratum (an underlying reality for experienced objects) cannot even be conceived of because we cannot access anything beyond our sensations. Furthermore, our ideas about experiencing external objects are "fleeting, changing, [and] ephemeral" while the substratum is said to have a "fixed and real nature." ⁽²⁶⁾ As if in anticipation of the modern-day Copenhagen school of quantum theory, Berkeley suggests that the external world exists in the perception of it. The "immaterialism" of Berkeley is descriptive of the epistemological process of perception of objects which are mere apprehensions of ideas in the mind. ⁽²⁷⁾ Therein lies their reality. However, Berkeley wanted to avoid the mistake of the Solipsists who believed that objects outside of sensory experience actually cease to exist. Thus he suggested that there must be a divine mind that constantly senses the external world so that it never ceases to exist.

The latter, objective idealism, suggests that reality simply exists apart from the perception of it. Historically, all men including George Berkeley, Reneé Descartes, Immanuel Kant, and John Locke have defined and defended differing views of idealism. For the purposes of this essay and in the interest of brevity, we shall presume a common sense approach to the situation (that is, one that is irrespective of either view of idealism). This will incline us to opt for a synthesis of both idealism and empiricism. Think how we could devise something like a one thousand sided figure or a mathematical infinity if only empiricism were exclusively true. We would, according to Aristotelian empiricism, be obliged to sense a variety of particular infinities and one thousand sided figures in order to universalize them. But this is clearly absurd. It is absolutely necessary that we have at least some sort of pre-noetic structure that possesses a way of defining particulars in their absence (we may even see that infinity is not even a real property in the world in which to sense; this implies some sort of idealism). ⁽²⁸⁾ Therefore, we seem to have at least some pre-experiential intellectual structures which assist in our defining the actual world.

When we think about the sentence "everything that begins to exist has a cause for its existence" it seems intuitively clear that such a systematic expression surpasses all experiences. We can be confident in the obviousness of this expression as it signifies cause-effect relationships in the actual world. Neo-Kantian Stuart Hackett makes the following comment:

Either the categories are thus a priori or they are derived from

experiences. But an experiential derivation of the categories is

impossible because only by their means can an object be thought

in the first place. Since the categories are preconditions of all

possible knowledge, they cannot have been derived from an ex-

perience of particular objects: the very first experience would be

unintelligible without a structure of the mind to analyze it. ⁽²⁹⁾

In other words, it makes no sense to suppose that we can derive the first notion that everything which begins to exist has a cause via experience unless something non-experientially distinguishes this notion with which to begin. But even if one denies the a priori category of the causal principle, it still strongly appeals to the intuitions of even the most ardent skeptic. Natural philosopher and empiricist David Hume once remarked:

But allow me to tell you that I never asserted so absurd a Proposition

as that anything might arise without a cause: I only maintain'd, that

our Certainty of the Falshood of that Proposition proceeded neither

from Intuition nor Demonstration; but from another Source. ⁽³⁰⁾

This implies that even one who questions the validity of cause-effect relationships has to admit its veracity in order to share in the common belief that causation at least appears to be consistent. I suppose that even empiricists unite on the most basic of beliefs when it comes to seemingly obvious truths such as this one. This makes our first premise of the kalam cosmological argument well established.

Without neglecting the intellectual benefit quantum mechanics has had in our thinking culture, we need to consider one final objection that only a person living in or beyond the 20^th century could propose. Modern day cosmological speculations about the utilization of quantum theory in the universe's origin are attempts to dismiss the notion that all things that begin to exist require a cause. In quantum physics, some critics suppose that a high level theoretical entity called a virtual particle may be exempt from the causation principle arguing that such theoretical entities are non-Newtonian in nature. This fancy scientific footwork used to elevate an exception to our premise that everything that begins to exist has a cause is only an imaginary distraction, much like David Copperfield's dancing assistants. But there really is a man behind the curtain! Upon closer inspection, the educated scientist is somewhat enlightened about the virtual particle. First, causal critics have to make the universe a virtual particle in order to make it an exception to the causal principle. ⁽³¹⁾ But if we are to press the issue, I find no correlation between a virtual particle and the universe's original singularity. All speculations about the universe's singularity entail a point of infinite mass at t=0. There is no similarity in definition or folk knowledge about it. Besides, why do we not observe additional universes "popping" into existence uncaused if virtual particles are the culprits? ⁽³²⁾ If the critic supplies reasons to suggest that such a particle is unique then it is difficult to see how it can be identical to the general understanding of virtual particles today. The conclusion that the universe is not a virtual particle is, to me, a proper analysis. So, what if the universe were only analogous to a virtual particle? ⁽³³⁾ This would also seem to fail since the universe's origin does not appear to have behaved like a virtual particle. But perhaps there are specific similarities with respect to initial conditions prior to Planck time (10^-43 of a second after the initial singularity). Quantum physicists speculate that there existed a superforce and a superparticle prior to the hot Big Bang state of the universe. The superforce is the force from which the gravitational, strong, weak, and electromagnetic forces are derived. Similarly, the superparticle is divided into bosons and fermions following the Planck era. This superparticle could conceivably be broadly construed as a virtual particle. Granting the superparticle analogy, virtual particles derive their existence from quantum vacuums, which is not the same thing as saying "nothing at all." That is, a classical Newtonian vacuum is understood to be the absence of any energy or matter. But a quantum vacuum is the state of a particle that has not yet been provided the necessary qualities to be observed. Lastly, there is one final destination for the virtual particle argument: It relies on a metaphysical view of quantum mechanics not yet adhered to by the majority of physicists. Quantum physics is a theoretical science that remains in its underdeveloped infancy. The fact that quantum events are just comprehensible manifestations of unobservable entities demands that such a system be interpreted with caution. This is why most physicists opt for the Copenhagen interpretation of quantum events associated with Niels Bohr. ⁽³⁴⁾ Quantum particles serve to provide answers to scientific problems but have no real bearing on reality. Such a view sees quantum physics as a science similar to astronomical theories about WIMPs and Dark Matter. Although they may be constructive and functional, there are no firm conclusions drawn about the unseen.

Therefore, without having to spend too much time and energy dealing with what could only be criticized in a philosophical arena and not in the observable world, the premise that everything which begins to exist has a cause for its existence seems to be a well-established principle underscored by experience.

This premise is perhaps the vital organ of the kalam cosmological argument and, if successfully refuted, would certainly put this argument into academic arrest. There would be no need to worry about a clearly intuitive notion that everything which begins to exist has a cause for its existence since the other leg of the argument would be undermined. This simple statement, yet one which has been the target of both philosophers and scientists, is the key to the validity of the kalam cosmological argument whose implication is to believe in an ultimate cause of the universe. Defenders of the kalam argument have split the support for the belief that the universe began to exist into two categories: (i) Philosophy shows that there cannot be an infinite regression of time since that would imply the absurd notion that an actually infinite number of things exists in the real world. (ii) Science shows us through the best astronomical model of the origin of the universe and through the Second Law of Thermodynamics that the universe began to exist. If at least one of these independent categories of inquiry turns out to be true then we have no rational choice but to concede the truth that the universe began to exist (which is the logical necessity of this deductive argument). So we will now take a closer look at each of these two categories and why no rationally thinking person should reject them.

In order to make the case that our universe must have a beginning, we will concentrate in this section on the more abstract reasons to reject the real possibility of an actually infinite past. This particular argument suggests that if no real actual infinites exist and no actual infinites can be achieved through successive addition, then the only option for quantitative values is to be limited to a finite count (which may progress indefinitely). Since the total number of past events in the history of the universe is a quantitative value, then the total number of past events in the history of the universe would be finite:

Our conclusion will expectantly yield the only other option to an actually infinite number of past events, which is to say that our universe began to exist some finite time ago.

It is impossible to have an actually infinite number of things.

The famous mathematician Georg Cantor developed a system of categorizing groups of numbers as members of a collective set. This systematic arrangement is commonly identified as set theory. A mathematical set is a collection of mathematical members belonging to that set, whatever it may be. We can label, manipulate, and compare members of a set to another value, set, or whatever a mathematician can come envisage. Let me provide a physical example of a set of people. Suppose that we wanted to talk about a small group of friends whose names are Joe, Frank, and Wendy. We can call this group set A:

As you can see, within set A (the set that includes a closed circle of friends) are three friends. This total number of friends is called the cardinal number. Thus, in this example, the cardinal number of friends that we have is three. But what if we wanted to talk about only two of the three friends? How would we categorize them mathematically? When we begin pointing to members within a set, we call this reference a subset or proper subset depending on how we make our reference. But a general subset to our example may include just Joe and Wendy. So, if A₁ represented the two friends we wished to discuss then:

As you can see, set A has three members while subset A₁ only has two members. With this example in mind we can now graduate to a more abstract usage of set theory. Consider the following:

We can clearly see that any subset extracted from set A would have a cardinal number no greater than five (A₁ 5). It is possible that A₁ could stand for {1, 3, 5} or {2, 4}. As long as our imagination is free to wander, we can come up with any number of combinations. If we begin comparing two sets then we can begin to see how mathematics begins to work its arithmetical and comparative magic. Suppose there are two subsets (A₁ and A₂) that are compared with set A, so:

According to the principle totum parte maiuis (or "the whole is greater than a part") we can never have a situation where a subset of A can be larger than the original set A (keeping in mind the rule about cardinal numbers) ⁽³⁵⁾:

So, no matter how we formulate a subset, it must always conform to this principle. But when we intimate the simple realm of finite numbers into the realm of transfinite numbers then our world principle begins to break down. Sure, one could easily look at this and say that this principle works with finite numbers but not with transfinite numbers and, thus, could avoid the complications altogether. But I see this response unwarranted because numbers represent logical values. It supposes that transfinite mathematics can be categorized as an illogical subcategory of mathematics, obeying no rules of non-contradiction. This could lead to all sorts of unreasonable conclusions. Consider that if I count to the highest finite number of objects then the rule that the "whole is greater than its parts" applies. But if I add one more number then the rule supposedly breaks down. So:

But why should one more number make any difference to the rest of the set? Now, I am not suggesting that the abstract world of mathematics will not permit certain allowances that the real world cannot mirror. Instead, I am suggesting that a look at numbers with respect to the totum parte maiuis principle requires that although no contradictions can obtain there is a peculiar result offered by conclusions drawn from transfinite arithmetic. But, more fundamentally, this is why the finite/transfinite distinction exists in the first place. Transfinite numbers still must obey basic logical principles. It is only when they correspond to actual physical events that their internal game can no longer be played.

Consider the following ancient approach to the problem of motion in the early Eleatic school of Parmenides. Zeno of Elea, born around 489 B.C., came to the defense of the non-existence of motion against Pythagorean pluralism. The dilemma of pluralism proffered to the Pythagoreans suggested that either everything that exists is infinitely large or infinitely small. If this is true then since individual components (or "units") of the universe possess no magnitude we could not possibly expect that a totality of these components could add up to produce magnitude collectively. To exemplify, anything multiplied by zero is still zero. This led Zeno to conclude that a plurality of "units" in the composition of reality is an absurd notion. Concerning motion, the problem of infinity again buttressed the Parmenidean concept of a single Reality. Because of this problem, the existence of such would preclude any honest belief that it truly exists as anything but an illusion. This is where Zeno's famous paradox of Achilles and the tortoise served as support for this notion. Zeno, in response to the Pythagoreans, asked us to imagine a race where Achilles and a tortoise are going to compete. Achilles, being the sportsman that he is, grants the tortoise a head start. But when Achilles begins his run after the tortoise has reached a certain distance then the supposition that a straight line on the racetrack has an infinite number of points promotes a paradox. Zeno shows that Achilles, in order to catch up to his opponent, must first arrive at the point where the tortoise was. In so doing, the tortoise naturally has advanced to another point on this racing line. Even if the tortoise only moves a relatively short distance, Achilles still has the task of reaching that point before proceeding any further. But, again, the tortoise has already moved on to another point on the line provided that nothing stunted his travel. On the surface, Achilles seems to be closing in on the tortoise, but since he must first traverse the same points already covered by the tortoise then he will never overtake his opponent.

Figure 4-1

According to this diagram, we see that in order for Achilles to catch up to the tortoise he must approach points 1 and 2. But when Achilles makes his move the tortoise is also moving toward points 3, 4, and 5. And Achilles must reach those points before he can at least catch up to his opponent. But since the tortoise is obviously not going to stop but keep running, then Achilles still has the task of reaching those same points that the tortoise has already covered. Thus, assume (t) = the tortoise and (A) = Achilles:

If (t) is at 5 then (A) must traverse 5 to catch up . . .

Notice in the prior diagram that points 3, 4, and 5 are closer together showing that the tortoise is slowing down. But this is inconsequential to the tortoise. He still retains victory since he knows that Achilles must reach those same points before he can catch up. The tortoise need only advance one more point, no matter how short a distance, in order to insure that Achilles could never catch up. The fact that a line contains an infinite number of points entails that the tortoise can go as slow as he wants and never lose a race with even the quickest opponent, so long as the tortoise can begin the race with at least a one point handicap over his opponent. ⁽³⁶⁾

With this illustration in mind, consider the mathematical formula expressing the impossibility of reaching the destination on an infinite line:

- 1 =

Because there are an infinite number of bisections that can obtain by dividing some whole number an infinite number of times then there are an actually infinite number of midpoints between two whole numbers. Fractions serve to exemplify how this is accomplished:

1 1 1 1 1 2 4 8 16 . . .

It seems that we could multiply any whole number with an infinite number of divided fractions and never achieve a result equaling the next whole number. This seems to show that an infinite number of midpoints can never be achieved.

Is it true, then, that Achilles can never catch up with the tortoise as long as the tortoise keeps moving no matter what the rate? Of course he can. The problem with Zeno's paradox is that there is no such thing as an actually infinite number of midpoints. Instead, we see the number of times a whole number can be divided as indefinite (or potentially infinite). Given the finitude of the real points on the racetrack where Achilles and the tortoise are racing, Achilles need only cover more finite points per every set of points covered by the tortoise. This is what we call rate.

Given a certain finite distance d to be traversed in some length of time t, then we can calculate how long it would take for the tortoise to cover d:

So, in order for Achilles to win the gold medal, he must have a rate (r₂) exceeding the tortoise's:

Given this, it is impossible to see how the tortoise could win the race as long as the rate is within the bounds of the time allotted.

Therefore, if an actually infinite number of things really exists then such a number results in logically contradictory results. In this illustration we saw that an infinite set can have an infinite number of subsets removed from it and still contain an infinite number of members left. The lesson we ought to learn from Zeno's paradox is that there cannot really be an actual infinite since this would imply that a lagging racer could never reach his winning opponent no matter how long he had and how slow the winner moved. These considerations rationally force us to suppose that an actual infinite is just an idea fostered by the mind and not something that can exist as a property in reality. Since time itself is a set of discrete members of seconds, days, years, and so on, then time must be a finite set of members. This means that the universe must have begun to exist.

It is impossible to obtain an actually infinite number of things through successive addition.

Mathematicians have puzzled for centuries on the precise meaning of infinity as it relates to the actual world. Some have eliminated the puzzle by suggesting that infinity is merely something that exists in the mind (as we have seen above). ⁽³⁷⁾ Others maintain that infinity possesses some ontological status in the real world. ⁽³⁸⁾ In an attempt to demonstrate the difference between the reality of an infinite and the idea of an infinite, Aristotle had suggested the terms actual infinite (the completed whole value of infinity) and potential infinite (an indefinite count susceptible to infinite addition). ⁽³⁹⁾ Analytic philosopher Bertrand Russell (1872-1970) believed that an actual infinite could be achieved as long as the counter possessed an actually infinite number of years to accomplish the count. In the example given in Sterne's novel, we have a man by the name of Tristram Shandy. ⁽⁴⁰⁾ Sterne writes about Tristram Shandy as an extraordinarily slow individual committed to writing an autobiography. However, he is so slow that it takes him one year of writing in order to complete only one day of his personal history. This means that the most recent event that could be recorded is the day that occurred only one year ago. As Shandy writes on an additional day, it takes him an additional year to complete the events of that day. On the one hand it seems that if Shandy could write for an infinite number of years then he could eventually have complete his essay. On the other hand it seems that the longer Shandy writes, the further he distances himself from the days to write on. Russell uses this example and believes that an actual infinite can be achieved through successive addition only if Shandy has an infinite number of days to complete the task.

Bertrand Russell suspected that a true life Tristram Shandy paradox could be solved. For Russell, it is the individual who possesses an infinite number of days. Of course mortal individuals possess merely a finite number of days. According to Russell, this is the key to solving the apparent problem. The paradox posits an autobiographer who writes on every day passed. Since it takes Shandy one year (=365 days) to complete one day, then in terms of a one-to-one correspondence with temporal history it would appear to be futile on a finite level:

Observed History: 1 day, 2 days, 3 days, 4 days, 5 days, . . .

Recorded History: 365 days, 730 days, 1095 days, 1460 days, 1825 days, . . .

On the surface it would seem mathematically impossible for Shandy to complete writing on all the days passed. Since each day yields an additional 365 days to write then it would seem that the longer Shandy wrote the further behind he would get. Russell solves this mathematical problem by suggesting an actually infinite number of years as the required antecedent for finishing the task (and to be sure it is certainly a necessary antecedent). For the sake of written mathematical concepts, the symbol often used to refer to a mathematical infinite is the Aleph Null (Ao). As one observes the following equation, the paradox appears to suggest something not true of usual, finite numbers.

The implication here is that since any number added to infinity is still infinity, then the idea that an additional member adds to the set is defeated. One component of the equation (Ao) is quantitatively equal to the sum of both components (Ao and 1). The reader should notice the violation of the totem parte maiuis occurring here. This is a good mathematical illustration with the problem of the reality of an actual infinite we already looked at. But concerning the adding of individual discrete parts to total an infinite set, Russell asserts that given an infinite number of years to write plus the infinite number of days written about results in an infinite amount of time that actually transpired. Thus, the amount of time to write (if obtained) would be equal to the amount of time given to write about. Therefore (Let d = days to write on; y = years to complete; t = time obtained):

Russell believed that when the presence of infinity is seen all at once, then the concept of infinity is something that can exist as a quantitative property in the real world (he does not mean exist in the Platonic sense). ⁽⁴¹⁾

At this time I will briefly present two opposing views on Russell's assessment of the Tristram Shandy paradox and the problem with an actual infinite through successive addition.

Atheist philosopher Quentin Smith presents the Tristram Shandy paradox in his essay on the existence of infinity in the past. His purpose is to show that it is feasible to exist in a universe that does not have a beginning (this is in contrast to the non-Thomistic belief that the universe began to exist). Smith, with regard to Russell, makes this observation:

the number of past days written about is a proper subset

of the infinite set of past days, and a proper subset of an

infinite set can be numerically equivalent to the set even

though there are members of the set that are not members

of the proper subset. Just as the infinite set of natural

numbers has the same number of members as its proper

subset of equal numbers, yet has members that are not

members of this proper subset (these members being the

odd numbers); so the infinite set of past days has the same

number of members as its proper subset of days written

about, yet has members that are not members of this proper

subset (these members being the days unwritten about). ⁽⁴²⁾

Smith maintains that the Tristram Shandy paradox is internally consistent in the light of sets and proper subsets. ⁽⁴³⁾ If it is true that

A₁ = {2, 4, 6, 8, . . . 0}

A₂ = {1, 3, 5, 7, . . . 0}

then:

1) The total numbers of proper subset A₁ = The total numbers of set A. ⁽⁴⁴⁾

2) But, proper subset A₁ does not contain the numbers of proper subset A₂.

3) Therefore, proper subset A₁ contains the same numbers as set A while simultaneously not possessing numbers found in proper subset A₂.

Smith shows that set theory validates the Tristram Shandy story and shows that the completion of his autobiography is ultimately possible.

Theistic philosopher William Lane Craig, one of the most stern contemporary defenders of the kalam cosmological argument, responds to Smith by asserting that both Russell and Smith have missed the real issue involved in the paradox. Craig responds to Russell that

the problem with this argument seems to be that while an

infinite number of years is a necessary condition of record-

ing an infinite number of days at the rate of one day per year,

it is not a sufficient condition. What is also needed is that

the days and years be arranged in a certain way such that

every day is succeeded by a year in which to record it. But

then it will be seen that Tristram Shandy's task is inherently

paradoxical; the absurdity lies not in the infinity of the past

but in the task itself. ⁽⁴⁵⁾

Craig claims that instead of Shandy writing forever and catching up on history, he would eventually be infinitely far behind. ⁽⁴⁶⁾ Craig further points out that the picture Russell paints entails a beginningless task. That is, if one were to ask "Where in the temporal series of events are the days recorded by Tristram Shandy at any given point?" ⁽⁴⁷⁾ then, according to Craig, one could only answer that the days are infinitely distant from the present. It appears that for every day Shandy is writing there is an infinite distance from that day to the last recorded day. Craig shares with his critics that Russell's assessment fails to consider the real problem of consecutively counting to infinity.

On the question of an actual infinite, my sympathies are with Craig. I think both Russell and Smith have failed to consider the one-to-one correspondence in the actual world as it relates to the world of mathematics. At this point I will limit my response to Bertrand Russell's view of the Tristram Shandy paradox. My observation of the matter seems to yield two problems with Russell's justification.

First, if we observe what is really going on in the paradox then it becomes apparent that it is logically unsolvable and not merely epistemologically unsolvable. When we see that for each day there are 365 subsequent days of writing, then I fail to see how Shandy "catches up" on the autobiography. Mere comparisons of infinite sets and subsets bespeak the paradox's lesson. It is precisely because an infinite proper subset equals an infinite set why successive addition fails to obtain. It appears, then, that we are discussing two different worlds: the finite and the infinite. ⁽⁴⁸⁾ So, if we uphold the principle of correspondence then it would appear that Tristram Shandy falls behind with each additional day he must write on. This makes the task unending.

Second, if we grant Russell's solution by granting immortality to Shandy then it would appear that the problem is merely extended instead of solved. In other words, there is no reason to adhere to an actual infinite via successive addition by simply pushing back the length of the task to the time of the task. The question now becomes, "Will temporal segments of duration through successive addition arrive at an actual infinite?" ⁽⁴⁹⁾ Would we not still be dealing with successive addition to the infinite? At this point it would be absurd to respond by suggesting that such an achievement is based on finite time because the argument now concerns time itself. The detractor could avoid this problem by reestablishing a definition for time such that it is perceived as being static instead of dynamic. The notion of discrete segments of durative temporal points could be construed as a singular point of presentness. It is only through the individual consciousness of an observer that separate segments of time exist and that individual segments are merely illusory. But even a phenomenological perception of time, such as this one, would not serve to defeat the problem because now we are relegating the existence of temporal infinity to a mere mental thought. As we saw before in the example of Achilles and the tortoise, it is only in the world of conceptual mathematics do there exist the types of paradoxes advanced by Zeno and Russell. Even a conceptual analysis of time requires the one-to-one correspondence if the history of the universe is to be envisaged. And this places the detractor back into the very seat that was being avoided. ⁽⁵⁰⁾ No matter what the context of temporal duration, the question is inevitably about the actual universe in which we exist. It is that temporal segments adding up to infinity are alleged to exist apart from consciousness either by nature or by virtue of a conscientious correspondence to temporal segments. In order to see this illustrated, suppose that we mentally affirm this mathematical sentence: