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What is God?

Aspects of God

Understanding the concept of God is crucial in delving into philosophical theism. In this article I'll discuss the ontological argument, the cosmological argument, the argument from morality, and some basic criticisms. I won’t go too much into the more religious aspects of theism (such as specific religious beliefs of God, e.g. Judaism, Christianity, and Islam), only the philosophical. The idea of God falls into the realm of philosophy known as philosophy of religion. Various ideas of God and deities have been put forth, but this web page will deal mainly with God as a Supreme Being. Below are the attributes often attributed to such a being:

  1. Omnipotence
  2. Omniscience
  3. Omnibenevolence
  4. Omnipresence
  5. Eternity
  6. Immutability
  7. Aseity
  8. Incorporeality
  9. Simplicity
  10. Ineffability
  11. Infallibility
  12. Supreme and universally binding authority
  13. Perfection

The above list is mainly characteristic of God as a Supreme Being; a supernatural and incomprehensibly powerful force of maximal perfection. Various other takes on the issue of theism have existed though. Below is a list of some major terms in this matter:

Ground rules

What's the best default belief? Some atheists have claimed that atheism is. However, some theists believe theism (at least for them) is a basic belief, just as the general reliability of sense experience is. Thus the burden of proof is on the atheist, at least according to this argument. I however propose that agnosticism (and thus suspending judgment) is the best and most rational default position here. Think of the matter as a pair of scales, with theism on one side and atheism on the other. If all rational support is equal, the scales balance and agnosticism becomes the most rational position to take. Now perhaps the scales are not equal, perhaps the evidence (which symbolizes weights on the scale) tip the balance in favor of atheism or theism. In that case, we need to weigh the evidence accordingly. We will first start with some arguments in favor of theism.

Classic Arguments for the Existence of God

A number of arguments have been used to support the existence of God. The cosmological argument has to do with the cosmos. It says that in the long chain of cause-and-effect in the universe, there had to be a first cause (this version of the cosmological argument is called the kalam cosmological argument). This can be based on the principle of the universe existing for a finite period of time (there are various attempts to support this, e.g. the Big Bang theory and scientific evidence suggesting the universe to be some 10 to 20 billion years old). Theism explains the origin of the universe by using God as the first cause. A related one is the teleological argument, claiming that the structure of the universe (e.g. the fact that our universe consistently operates in intricate mathematical patterns) seems to suggest design, and that an intelligent creator of the universe (such as God) is most likely responsible. The ontological argument is often based on defining God as “that which nothing greater is possible” or something similar to it, and is the argument we will deal with next.

The Ontological Argument

Perhaps the most interesting argument used to rationally support the existence of God is the ontological argument. There are many forms of ontological arguments, but I’ll only use one derived from Anselm’s approach. The ontological argument for the existence of God was first structured in the Proslogion of Saint Anselm, Archbishop of Canterbury (1033-1109 A.D.); though it was actually Immanuel Kant, an 18th century German philosopher, who first called the argument “ontological.” Ontology is a branch of metaphysics concerned with the nature and relations of being. Ontology attempts to answer such questions like, “What is real?” Thus Anselm’s ontological proof attempts to answer the question of whether or not God is real. “What’s metaphysics?” you may ask. Metaphysics is itself a branch of philosophy that studies the nature and causes of things. Metaphysics asks questions like, “Does matter exist?” and “Does the immaterial (e.g. the soul) exist?”

Anselm defines God by saying God is that “which nothing greater can be conceived.” A slightly different definition will be used here, defining God as that “which nothing greater is possible.” One way to interpret this phrase is to define “God” as maximal perfection, i.e. the greatest possible being (and this is the definition that our ontological argument will use). Some may criticize this definition by saying that’s not what they mean when they use the term God. But that really doesn’t matter. If the argument proves that such a being exists, then it does so regardless of what one wishes to call the being of maximal perfection. Furthermore, it’s unclear why a rational person should be reluctant to call such a being God, or why God wouldn’t be the greatest possible being.

The ontological argument is an a priori argument, i.e. one that relies only on reason and not on sense experience. Curiously, the upshot of the whole ontological argument implies that God has necessary existence. What is necessary existence you may ask? There are many ways reality could have been like, i.e. many different possible worlds. Necessary existence is existence in all possible worlds (the fact of 2 + 2 = 4 is a quick example of necessary existence, since this mathematical truth exists in all possible worlds). So if the argument is sound, then God cannot fail to exist. Does it work? You be the judge.

The type of ontological argument I’m using is a reductio ad absurdum argument. In a reductio ad absurdum argument, the negation (opposite) of the conclusion is assumed, and then demonstrated that the opposite of this conclusion leads to an absurdity (such as a contradiction). Incidentally, Anselm himself used a reductio ad absurdum argument in the book Proslogion to explain his ontological argument.

If therefore that than which nothing greater can be conceived exists in the understanding alone [and not in reality], then this thing than which nothing greater can be conceived is something than that which a greater can be conceived. And this is clearly impossible. Therefore, there can be no doubt at all that something than which a greater cannot be conceived exists in both the understanding and in reality.

To explain this sort of thing more clearly, I’ve written a similar version of this argument (which has paraphrased significant amounts of what Anselm wrote). And so without further ado, here it is:

  1. God is that which nothing greater is possible (from Anselm somewhat), i.e. the greatest possible being (by definition).
  2. It is at least possible for God to exist in reality (from Anselm). That is, whether or not God actually exists in the real world, He at least exists in some possible set of circumstances. That is, God exists in at least one possible world. So, God might have existed in the real world.
  3. If something exists only in the mind (i.e. does not actually exist) but is possible (in the sense that was defined in 2), then that something might have been greater than it is. For example, a majestic mountain that exists only in the mind (i.e. a nonexistent, imaginary mountain) might have been greater: the mountain existing in reality.
    1. Suppose God (the greatest possible being, from 1) exists only in the mind and not in reality (i.e. God does not actually exist; which is the negation of what this argument attempts to prove).
    2. Then there is a possible being (from 2 and 3) that is greater (than the being in 4), namely God existing in reality.
    3. So it is possible for something to have been greater than God (from 5).
  1. Since God is that which nothing greater is possible (from 1), then it is possible for something to be greater than that which nothing greater is possible (from 6).

Conclusion: Statement 7 is absurd. It can’t possibly be true because it is self-contradictory. Therefore, God must exist in reality as well as the mind.

Justification for the second premise (which says it is at least possible for God to exist) can be done by examining the definition of God as maximal perfection, i.e. the greatest possible being. To illustrate the concept, let’s take an aspect commonly attributed to God. God is said to have perfect power: omnipotence. But can God create a round square? Can he defy such basic rules of logic? The theist under this definition of God could reply that God is only omnipotent to the greatest possible extent. Thus, this theist could respond by claiming that God cannot do what is logically impossible, but He can do anything that can be done. If a certain level of one of God’s traditional qualities is proved “impossible,” this theist could then lower the bar on that aspect of God down to where that quality is possible, such as from, “God is omnipotent and can do literally anything,” to “God is omnipotent to the greatest possible extent.” In short, God is defined as the greatest possible being. If a being is possible, it cannot be impossible. As the example illustrates, were it the case that the being was perfect to an extent that is not possible, it would not be the greatest possible being. Given its coherent meaning then, it would be irrational to claim that the greatest possible being cannot possibly exist.

If you’re like me, you’re thinking there’s some kind of underhand trick with words in this ontological argument. Naturally then, you might be wondering about the objections to the ontological argument. Well, stay tuned. I’ll deal with that soon. Of course, if the argument is wrong, there must be a reason why it is wrong. There are only two ways a deductive argument like this one can fail. One is that at least one of the premises is incorrect. In that case, the question would be “which premise fails and why?” The other way is that the argument is invalid, i.e. the argument does not logically follow (from its premises) somewhere along the way. If that is true, which line of the argument does not logically follow from the statement(s) it’s based upon?

Objections to the Ontological Argument and Rejoinders
Gaunilo’s Criticism

Gaunilo (who was a monk of Marmoutier and a contemporary of Anselm’s) criticized Anselm’s argument saying that one could apply the statement to a lot of things, the most famous example he used was, “the greatest conceivable island” and prove the existence of the island using parallel reasoning of Anselm’s ontological argument. Similar to the ontological argument, we slightly modify the definition of Gaunilo’s island to mean “the greatest possible island” instead of the original “the greatest conceivable island.”

“Proving” the existence of Gaunilo’s island can be done by replacing God with that island in the ontological argument. In his own words (in In Behalf of the Fool):

Now if someone should tell me that there is such an island [an island that which no greater can be conceived], I should easily understand his words, in which there is no difficulty. But suppose that he went on to say, as if by a logical inference: “You can no longer doubt that this island which is more excellent than all lands exists somewhere, since you have no doubt that it is in your understanding. And since it is more excellent not to be in the understanding alone, but to exist both in the understanding and in reality, for this reason it must exist. For if it does not exist, any land which really exists will be more excellent than it; and so the island already understood by you to be more excellent will not be more excellent.”

Gaunilo’s criticism applied below:

  1. Gaunilo’s Island is that which no greater island is possible (by definition).
  2. It is at least possible for Gaunilo’s Island to exist in reality. That is, whether or not Gaunilo’s Island actually exists in the real world, it at least exists in some possible set of circumstances. That is, it exists in at least one possible world. So, Gaunilo’s Island might have existed in the real world.
  3. If something exists only in the mind but is possible (in the sense that was defined in 2), then that something might have been greater than it is. In this case, a Gaunilo’s Island that exists only in the mind (i.e. a nonexistent, imaginary Gaunilo’s Island) might have been greater: Gaunilo’s Island existing in reality.

    1. Suppose Gaunilo’s Island (the greatest possible island, from 1) exists only in the mind and not in reality.
    2. Then there is a possible island (from 2 and 3) that is greater (than the island in 4), namely Gaunilo’s Island existing in reality.
    3. So it is possible for an island to be greater than Gaunilo’s Island (from 5).

  1. Since Gaunilo’s Island is that which no island is greater (from 1), then it is possible for an island to be greater than that which no island is greater (from 6).

Conclusion: Statement 7 is absurd. It can’t possibly be true because it is self-contradictory. Therefore, Gaunilo’s Island must exist in reality as well as the mind.

The same sort of thing could be used for “the greatest possible chicken,” “the greatest possible sock” or even the “greatest possible pile of crap.” But this is nuts. Something has to be wrong here.

My Thoughts

The unfortunate thing about Gaunilo’s criticism is that it doesn’t tell us what went wrong. Is it one of the premises? If so, which one and why? Is the argument invalid? If so, which line of the argument does not logically follow from the other(s) that it’s based upon? Alas, Gaunilo’s criticism is silent on such matters. Since the objection claims that something’s wrong but does not explain why, I think we should be a little leery. Nonetheless, Gaunilo’s objection is interesting and would seem to discredit the ontological argument if there is no adequate rejoinder. I think the criticism still deserves a response if it is to be rejected as unsound.


One response is that Anselm’s ontological argument only applies to the greatest possible thing. It’s not absurd to believe that something greater than the greatest possible island exists (e.g. an intelligent person) but that would not be the case for God, a being that is the epitome of maximum possible perfection. God is that which nothing (and no being) greater is possible. So, unlike the island, it would be absurd to think that something is greater than the greatest possible thing.

Another response is that there is no limit to how great an island can be. The properties that contribute to the greatness of an island have no intrinsic maximum (borrowing the term from philosopher C. D. Broad). For any great island, there is another that could be greater. The “greatest possible island” is thus like, “the greatest possible integer.” No such thing can possibly exist because neither has an intrinsic maximum.

Yet another response is that the notion of a “greatest possible island” isn’t all that coherently meaningful for an ontological proof that was used for God, and so the parallel is misleading. This is because there isn’t anything that makes for greatness in islands, chickens, socks and the like; it’s all a matter of taste. Truly objective standards of greatness for these sorts of things simply do not exist. There is nothing inherent in the definition of “island” and “chicken” that entails such perfection that was used when the argument described God. Thus, it isn’t so much as possible that there really be a greatest possible island. The concept of an island (sock, crap etc.) does not inherently include the notion of supreme perfection, instead the vague aspect of “perfection” is artificially pasted on to the core concept, while the concept of God (maximal perfection, “that which nothing greater is possible”) cannot be separated from its hardcore intrinsic meaning: maximal perfection. With God there is only one clear and coherent concept of maximal perfection, and so the argument that flows forth from this can’t be used to support any other concept. What about God? Aren’t his attributes of greatness subjective? Not at all. One way the theist could justify defining God as maximal perfection is to look at the summary property of God’s attributes. God is perfectly powerful, perfectly good, perfectly wise, perfectly knowledgeable, and so forth. Being perfectly powerful (omnipotence) for instance, is an objective quality. Thus God (as defined here) is a legitimate concept, unlike the greatest possible island/number/chicken etc.

Disputable Point

Is the concept of perfection (in this case, maximal perfection) sufficiently unique to the definition of God so that one can rationally credit the idea of necessary existence to maximal perfection and not the other concepts (Gaunilo’s Island, greatest possible chicken, etc.)? Gaunilo’s criticism, however compelling it may be, doesn’t give us a modicum of explanation as to why the ontological argument fails. If no such reason is given, should one still accept the ontological argument?

The concept of God (when defined as “the greatest possible being”) lacks an intrinsic maximum and is thus not logically possible

You might have seen this objection coming when you saw the one of the responses to Gaunilo’s Island. This objection says that the concept of God is like the greatest possible integer. There is always one greater. God (as defined in this ontological argument) is an incoherent concept, and possesses no adequately coherent meaning because there are no intrinsic maximums. Incidentally, C.D. Board himself brought up this objection when he used the term intrinsic maximum.


It would seem that there are intrinsic maximums for the qualities of God. For instance, God’s omniscience can be defined as knowing everything that can be known, and God’s omnipotence can be defined as being able to do anything that can be done. There aren’t any greater possible conditions for those aspects of knowledge and power. They are intrinsic maximums.

Kant’s Objection: Existence is not a predicate (a property).

Immanuel Kant (1724-1804), the very same 18th century German philosopher who first called the argument “ontological,” made this objection. It has been widely accepted among philosophers who reject the ontological argument. A predicate is a property/characteristic/aspect we attribute to something. For example, a red strawberry has “red” as one of its predicates. In a sentence, a predicate is used to denote additional information about the subject. In Kant’s own words (and in his book, Critique of Pure Reason):

Being is evidently not a real predicate, that is, a conception of something which is added to the conception of some other thing. It is merely the positing of a thing, or of certain determinations in it. Logically, it is merely the copula [i.e. the verb linking the subject and the predicate] of a judgment. The proposition, God is omnipotent, contains two conceptions, which have a certain object or content; the word is, is no additional predicate—it merely indicates the relation of the predicate to the subject. Now if I take the subject (God) with all its predicates (omnipotence being one), and say, God is, or There is a God, I add no new predicate to the conception of God, I merely posit or affirm the existence of the subject itself, with all its predicates, in relation to my concept, as its object.

There is a difference between predicating something (e.g. “this person is tall”) and saying something exists. Consider the list of predicates below:

But existence merely says, “God is.” As for the word is, it is only a copula (i.e. a verb that links the predicate with the subject). It is not a predicate itself. Unlike real predicates, existence doesn’t say anything about what God is like (e.g. omnipotent, perfectly good, etc.), only that God is. Existence as a predicate is meaningless to use because, according to Kant, it tells us nothing about the subject (confer calling a strawberry “red” or a person “tall”).


Kant’s justification for existence not being a predicate seems unsound. He claims that existence is merely the copula for the predicate and the subject, such as the word is in “God is omnipotent,” and any other form of “[subject] is [predicate].” Suppose that existence is just the copula. If that were true, then attaching a predicate to a subject with the copula would presuppose the subject’s existence. But we predicate non-existent things all the time. Suppose I say, “Santa Claus is a jolly fat guy.” I really don’t mean to imply that Santa actually exists when I describe him.

My Thoughts

The only kind of existence the copula seems to imply is conceptual existence, not real (actual) existence. All predicated subjects have at least conceptual existence (i.e. any predicated subject is a concept; it exists in the mind). So given that this is already known, one could argue that conceptual existence doesn’t add anything new to a subject. But even if conceptual existence is not a predicate, how useful is this claim in attacking the ontological argument? The ontological argument used here suggests that a God with actual existence is greater than a God with actual non-existence. Actual existence may be required to be a predicate here, but not conceptual existence. It would appear that, for Kant’s objection to work, it would have to show that existence other than conceptual existence (e.g. actual existence) is not a predicate. Whether or not such existence is a predicate, it seems clear that Kant’s copula justification for it does not seem to work.

A related response is that existence does seem to be a predicate. Suppose an inquiring child who has always believed that Santa Claus existed asks me if this is so. I tell the child that Santa Claus does not exist, and the child believes me. The objection of existence not being a predicate would seem to say that the child has not learned anything new about Santa Claus, but surely that is a bit peculiar. To say that the child has not learned anything new about Santa Claus when the child learns of Santa’s nonexistence seems dreadfully nonsensical. When a mathematician says that there exists prime numbers between 12 and 21, is she not denoting a characteristic of prime numbers? The objection would again seem to say no. But clearly the child has learned something about Santa Claus, and the mathematician has mentioned a characteristic of prime numbers. Thus, existence does seem to be a property one can attribute.

Disputable Point

Does the claim of existence being merely a copula give a fully accurate description of what existence really is? If so, then the objection works. If not, and if the last response of the section makes sense, then existence really is a predicate. But do the examples of Santa Claus and prime numbers really adduce existence as a property that one can attribute? If yes, then the objection doesn’t work. If not, then it does not establish existence as a predicate and the third premise will require some other justification.

Existence is not a “great-making” predicate.

This objection focuses on the claim of existence not being a great-making property and says that the reason “the greatest possible island,” and “the greatest possible chicken” don’t work as arguments to prove their respective existences is because “existence” doesn’t actually make something greater. To use another example, is the existence of Stalin, the Devil, Hitler, and maniacal mass murderers (say that three times fast) greater than their failure to exist? Obviously not. This is because existence is not a “great-making” property.


Maybe existence doesn’t make things like maniacal mass murderers great, but it seems to make some other things great, like mountains, beauty, or God. All else held constant, beauty that exists is greater than beauty that does not exist. Similarly, an existing God is greater than a non-existing God.

My Thoughts

How does the attribute of existence make God greater? Does an existing God have more knowledge or more power? As a matter of fact, yes. A non-existing God does not really have omnipotence, omniscience, etc. for the simple reason that this God would not exist. A God who exists in reality, however, would be far greater in every one of such attributes. One could conceivably use this fact to argue in favor of in favor of existence being a great-making property, at least when it is applied to God.

Disputable Point

Pretty easy to find here. Is existence really a great-making property? Or to the nitty gritty: is an existing God greater than one that does not exist? If the answers to these questions are yes, then the objection fails and premise 3 is true. If the answers are no, then the objection stands and the ontological argument collapses.

Do the responses satisfactorily answer the objections? Is the concept of greatest possible perfection sufficiently unique to the definition of God? Is this concept of perfection properly meaningful for the first premise to be true? To be honest, I’m still not entirely sure what to make of it all. How about you?

The Cosmological Argument

First some terminology. Aristotle once suggested the terms potential infinite and actual infinite. Roughly speaking, a potential infinite is a collection that grows towards infinity without limit, but never actually gets there. Take for instance a finite past starting from a beginning point. No matter how forward you go into the future, you’ll never actually reach a point where the universe is infinitely old. You can always add one more year. An actual infinite is a collection that really is infinite, such as the set of all real numbers. In mathematics, an actual infinite is represented as aleph null and a potential infinite is represented as ∞. The distinction between actual and potential infinites will be important later on. One form of the cosmological argument is also known as the first cause argument. This is because according to the argument, the universe began to exist, and something had to cause it. And since we’re talking about the entire universe (excluding God) being created, this cause would be the first cause to occur in reality. Thus the cosmological argument typically has this sort of format.

  1. Anything that begins to exist has a cause.
  2. The universe began to exist; it does not/cannot have an infinite past.

Therefore the universe had a cause (from 1 and 2).

First we must ask ourselves, why is this used as an argument for God? The theist argues that the fact the universe was created (and thus had some sort of creator) gives rational support for theism. It becomes difficult for the atheist to account for this fact (if it is so) of the universe being created in any acceptable manner, which is why the atheist would rather like an uncaused universe (as a universe that's infinitely old) and would typically believe in that instead.

Still, the objection could be waged, “This doesn’t prove God. There are infinitely many other possibly kinds of creators for the universe besides the theist’s view.” For instance, for the cause of the Big Bang theory, perhaps a flying spaghetti monster created the universe.

The problem is that if I were the atheist, I wouldn't accept that explanation. If you are an atheist, you probably don’t accept it either. The theist might reply that these are not acceptable alternate explanations, and that's what we need if we want to compare atheism and theism. So this sort of argument could be considered an inference to the best explanation (i.e. which one explains it best) rather than a rigorous proof. There is the underdetermination of theories, a well known problem in the philosophy of science that says no matter what the data, there will always be multiple alternative explanations. The mere fact that one can come up with alternatives to match the data isn't particularly noteworthy to our discussion. It would be relevant if the alternative explanation was an acceptable one (i.e. one the atheist is willing to accept) but that does not appear to be the case with the flying spaghetti monster. Given we are playing the game of inference to the best explanation, if the best explanation atheism has to offer is an infinite past, then perhaps this is what we ought to contrast the cosmological argument to.

The essence of the cosmological argument is to establish that the universe was created by an outside agency. To see why let’s look at two forms of causation:

The idea of agent-causation goes back to agency theory, a metaphysical theory of free will in which the agent is the person or self. This theory states that instead of previous causes determining an event, an agent (person, self) causes it. An agent is something that creates effects without being determined by prior causes. In the examples above, the results were not uncaused, nor were they the effects of some random or deterministic event, but were the result of willful volition. Not only must the first cause be an agent of some sort (if the universe is caused) but the theist could also argue using agency theory (and perhaps also some inductive logic associated with all observed agents) that the first cause is some kind of volitional entity.

Disputable Point

This idea would require one to accept agency theory. If one already accepts this as the correct explanation for the alleged existence of free will, then we have no inherent problem in accepting an agency as the first cause. But what about those who accept determinism (the belief that all events are determined by prior causes)? Determinists would not accept agency theory and thus would immediately reject this explanation. A disputable point would then be whether or not agency theory is acceptable. Additionally, if the past were infinite, agent-causation would not be required at all. Remember that (according to the argument) anything that begins to exist requires a cause. If the universe did not begin to exist, the argument would not work. An atheist could thus dispute the second premise of the first cause argument, but there are some arguments that attempt to support the veracity of that second premise (as we’ll see later).

Those who opt for an infinitely old universe say that each event is caused by another event, and that the chain of causation goes back forever. For a finite past, the first cause cannot be event-causation (since that event, which began to exist, would require another event to cause it) so that leaves agent-causation. A theist would argue that a finite past means that some sort of outside agency created the universe. The fact (if it is so) that some kind of outside agency created the universe would provide at least some degree of rational support for theism. If one is to accept a finite past, about the only way to avoid agent-causation is to have the universe begin uncaused, i.e. the universe (with its finite past) began to exist and nothing caused it. Indeed, several atheistic philosophers have taken this route. But this would violate ex nihilo nihil fit (from nothing, nothing is produced) and the theist could claim that abandoning that principle is horribly irrational.

Furthermore, the theist could argue that some aspects are discernable about this outside agency. Creating the entire universe is a big job, so whatever created it must be extremely powerful. Since an infinite regress of changes cannot exist (because that would, among other things, imply an infinite past) the first cause must be changeless, at least sans the universe. Since the universe has a finite past (an infinite past cannot exist according to the argument) time itself begins to exist along with the rest of the universe. Thus, whatever created the universe had to transcend time, i.e. is atemporally timeless. If the teleological argument is sound, then this extremely powerful and time transcending agency is also probably extremely intelligent (e.g. the agency imprinted highly sophisticated mathematical patterns in the universe, suggests a high degree of intelligence on the part of this creator). From the deduction we have so far, this creator is extremely powerful, (at least probably) extremely intelligent, changeless, and atemporally timeless. Do these aspects for a creator of the universe sound familiar? Thus the theist could claim that while the cosmological argument is not a proof, the fact (if it is so) that some extremely powerful outside agency created the universe provides a pretty substantial evidential “weight” for the existence of God (confer the analogy of the scales).

But for this to be so, the premises need to be justified. Looking at the argument again:

  1. Anything that begins to exist has a cause.
  2. The universe began to exist; it does not/cannot have an infinite past.

Conclusion: the universe had a cause (from 1 and 2).

The argument implies that there had to be some first cause. The first premise could be justified by appealing to ex nihilo nihil fit, a Latin phrase that means, “from nothing, nothing is produced.” The theist could say this is because being cannot come from nonbeing, though one could claim that the truth of ex nihilo nihil fit seems pretty self-evident just as the phrase “hairless men have no hair” is.

What about the second premise? Why can’t an actual infinite exist? Don’t we have an infinite quantity of real numbers? The theist could reply that those numbers are abstractions, not concretely existing things. The issue is not whether or not an infinite can exist in the mind or is valid mathematically, but whether or not it can exist in the real, physical world. Also, one could specifically target the idea of an infinite past without rejecting the general concept of an actual infinite.

There are various ways to justify the second premise. One way is to argue using the scientific evidence. The evidence would suggest that the known physical universe is some 10 to 20 billion years old, starting with the Big bang. This fact is agreed upon by nearly all scientists and typically even atheists. Other forms of justification are philosophical, appealing to the use of reason alone. One claim is to argue against actual infinities in general, which would thus argue against an actually infinite series of events. Another method is to specifically attack an infinite past by appealing to various paradoxes that result from having an infinite past. We will briefly examine each. But first let's start with the scientific argument.

The essence of the argument is fairly succinct. The universe began to exist about 15 billion years ago, with its first moments being rapidly expanding in an event known as the Big Bang. The Big Bang is believed to be true as a result of much scientific evidence, so the theist can use that to support her claim. Now 15 billion years is an old age, yet it is finite. The universe began to exist, ergo something must have caused it.

Objection: Scientific evidence suggests something can begin to exist without a cause

For instance, there have been observed instances of virtual particles coming spontaneously from a vacuum before annihilating each other. Since they come from nothing, they have no cause.

Rebuttal: A quantum vacuum is not nothing

The above objection is based on a misunderstanding of quantum mechanics. Contrary to what one’s intuitions might naturally assume, a vacuum is not literal nothingness. Rather, it is a seething foam of (among other things) fluctuating energy, from which the particles temporarily borrow energy from and then return it. So the cause of the particles is this quantum vacuum, not a literal nothingness. Also, to say that the quantum vacuum caused the universe has a number of scientific problems. For instance, if the vacuum had always existed, then it should have spawned universes from every point in space by now, but this contradicts observation. The vacuum fluctuation models have now been abandoned even by its original proponents. Additionally, the theist could present some philosophical arguments against the existence of anything in the universe (vacuum or otherwise) existing forever. (More later.)

A similar yet mistaken objection is to mistake causality for determinism. For instance, there are some events in quantum mechanics, such as which atom will decay next in radioactive elements, that appear to be random. But to say that this has no cause would seem inaccurate. A more correct description of the cause seems to be time and chance acting on inherent properties of matter.

Disputable Point

Still, one could salvage an infinite past by claiming the universe existed in some form prior to the Big Bang and we just haven’t discovered evidence for that yet. But does this violate Ockham’s razor? Isn’t the more straightforward and best explanation that the universe really did begin to exist billions of years ago? But even if that is true, the atheist could still claim that there is a chance that the universe existed forever and it’s just beyond our scientific means to detect.

However, the theist could point to philosophical justification by saying the reason the universe is of finite age (albeit billions of years old) is that an infinite past can’t exist. Additionally, the fact that the physical universe (at least as we know it) did begin to exist seems very confirmative for the idea that the past is finite and not infinite. The philosophical arguments supporting this idea is what we’ll explore next.

In an Infinite Past, Would the Present Ever Be Reached?

There are various arguments that have to do with not being able to reach the present if the past were in fact infinite. One of them involves the axiom of not being able to form an actual infinite through successive finite addition. We can again justify this using the counting example. Consider again the story of an immortal person named Count Int who is attempting to write down all the natural numbers and reach infinity with his trusty pen and never-ending supply of paper, taking him exactly one second to write down each number. He starts with one and successively adds one each second (1, 2, 3, 4...). Will he ever reach a point in time where he can honestly say, “I’m done, I’ve reached infinity”? No, the number will just get progressively larger and larger without limit. He can never reach infinity anymore than he can reach the greatest possible number. There will always be a bigger yet finite number in the next second. The Count will never lay down his pen because there is an infinite quantity of those numbers.

Since we’re using numbers, this example can be instantiated to reality whether it be distance (1 meter, 2 meters, 3...) time (1 year, 2 years, 3...) or whatever. In any case, it seems clear that a complete traversal of an infinite region (when done via successive steps of finite size) cannot be done. For instance, suppose a person named Joe Walker tries to completely traverse Infinity Avenue walking at the rate of one meter per second. Infinity Avenue is infinitely long and begins at Hilbert's Hotel. Starting from the hotel, he walks 1 meter, 2 meters, 3, 4... and though he walks tirelessly (just as Count Int is tireless) Joe Walker cannot succeed. The infinite distance is impossible to traverse via successive finite steps, with the only “barrier” to its successful traversal being the sheer magnitude of this impenetrable distance.

However, an infinite past requires that an infinite number of years be traversed before the present is reached, and thus the universe could never have reached the current point in time. And time is certainly traversed via successive finite steps (year after year). So while an actual infinite might be valid mathematically, in reality it just doesn’t work with an infinite past. An infinite past requires an impossible traversal.

Objection: an infinite region can be traversed

The set of all finite numbers is infinite. When counting (1, 2, 3, 4...) each number will be reached eventually. Recall the counting example (starting with 1, adding one each second; 1, 2, 3, 4...), in which our job was to count all finite numbers. Now if we can’t traverse all the finite numbers, which finite numbers won’t we get to? There aren’t any of course. Each one will eventually be gotten to. We thus traverse them all (1, 2, 3, 4...).


In the counting example (1, 2, 3, 4...), it is true that any finite number we can name will eventually be gotten to (whether it be a million, a trillion, or whatever). But will the Count ever manage to count all finite numbers? Ironically, no. The Count will never lay down his pen. This is because no matter how far he gets, there will always be more numbers to count (he can eventually get to a million, but there’s still more numbers to count; he can eventually reach a trillion, but there’s still more to count etc.). The Count never lays down his pen. The Count being able to reach any finite number only implies that he can traverse any finite distance; it doesn’t imply that he can traverse an infinite one.

If the Count eventually reaches infinity, where does he cross the threshold between a finite number and an infinite one? What is the last finite number he writes with his pen before writing “infinity”? Remember that the Count always gets his next value by adding one to the previous value (1, 2, 3, 4...e.g. when he’s at 2 he adds one to get 3, and when he’s at 3 he adds one to get 4). If he eventually reaches infinity, what finite number does he add 1 to in order to get infinity? If all natural numbers could be counted, then along the path of successive finite addition (1, 2, 3, 4…) where does he traverse all those numbers? After what natural number does the Count lay down his pen? Nowhere. Instead, there will always be more numbers to count regardless of what number he has reached so far (a million, a trillion, or whatever), and thus his job (counting all those numbers) is never done.

Disputable Point

Can the Count ever write down all those numbers?

Objection: the story of Count Int is a false analogy

A false analogy is one where there are relevant differences that outweigh the similarities. In this case, the story of the Count is a false analogy because the only reason why the Count cannot reach infinity is because there is no end. With a beginningless traversal there is a difference: it does have an end (the present point in time). Also, the story of Count Int has a beginning, whereas an infinite past does not. Therefore, a beginningless traversal of an infinite region is possible even though the Count’s traversal is not.


The story of Count Int mirrors the backtracking of time; going from the present to the past (1 year, 2 years, 3, 4...) and as explained we can never make a complete traversal of the infinite region. But this backtracking involves a beginning and no endpoint. A beginningless traversal involves neither of those things. It makes sense that a traversal could never finish if it has no end. But from the past to the present, there is an endpoint. What to make of this?

As mentioned earlier, there are actual infinites in mathematics. For instance, the mathematical infinity that comes “right after” natural numbers is symbolized by ω. But that doesn’t mean it can be reached via successive finite addition (the Count would still never reach it for instance). And so it isn’t clear why an endpoint would make an infinite traversal via successive finite steps possible. Suppose Joe Walker tries to reach a point infinitely far away. To do this he must completely traverse the infinite region. He walks 1 meter, 2 meters, 3, 4...and yet Joe can never get there. It isn’t that the traversal will take a really long time, it’s that the infinite traversal is impossible. Note also that the only “barrier” for Joe’s traversal to that point is the sheer magnitude of this impenetrable distance.

Compared to a traversal with a beginning, one view (e.g. philosopher J.P. Moreland) is that the absence of a beginning point actually makes things worse for an infinite traversal, not better. It seems clear that going from zero to infinity (as Joe trying to reach a point infinitely far away) is impossible, but traversing an infinite past to reach the present is even worse because it “cannot even get started. It is like trying to jump from a bottomless pit.” [1]

It is true there is an endpoint in the beginningless traversal, and it is true there is no beginning in a beginningless traversal, but these are not relevant differences; the same years have to be traversed at the same rate either way. Thus, if the infinite distance is impenetrable in one direction (backtracking from the present to the past) it makes absolutely no sense to think the other direction could be any more successful (the past to the present). To get to the present (or any point finitely away from the present) would require an infinite amount of time and thus could never be reached. Mathematically, both types of infinities (when traversing from either direction) are precisely equal. A step-by-step complete traversal is impossible with Count Int and Joe Walker. So why should a beginningless traversal be any different?

Disputable Point

Is the existence of an endpoint (or the nonexistence of a beginning) a relevant difference, given that all the same years must be traversed at the same rate either way?

The Argument from Morality

The argument from morality uses the existence of objective ethics as evidence for the existence of God. This can come in varying degrees, such as God being absolutely necessary for the existence of objective ethics or simply that God is the best explanation for the existence of objective moral values (compared to atheism). By ethics being objective it is meant that ethical truths (e.g. torturing infants for fun is wrong, the Holocaust is morally wrong) are valid and binding regardless of what people believe. Note that the claim is not that an atheist cannot recognize the existence of moral values (an atheist could believe, however mistakenly, that God is not necessary for objective moral values), nor is the claim that belief in theism is necessary to live a moral life (an atheist could follow the rules of morality and still disagree, however mistakenly, on the metaphysical basis of those rules). Nonetheless, the argument does claim that God is the metaphysical basis for objective ethics. An argument for this might go something like this:

  1. Morality (by definition) is an ought (e.g. “Murder is unethical” means “You ought not to commit murder”) and its principles are commands (e.g. “You ought not to commit murder” means “Thou shalt not kill”).
  2. If any kind of morality is to exist, something (some kind of commander) has to give such requisite commands.
  3. If objective morality is to exist, this commander (the source/essence of ethics) must be ultimate and supreme in authority, since the declarations of ethical truths would transcend what anyone else thinks or believes (e.g. if a person says the Holocaust is morally right that person would be wrong, because true ethics says otherwise and true ethics carries ultimate authority).
  4. Such a supreme being is necessary for objective ethics to exist (from 2 and 3).
  5. Objective morality exists (self-evident truth, e.g. the Holocaust is morally wrong regardless of what the Nazi culture believed, regardless of what Hitler believed etc.).

Therefore such a supreme being (as God) exists (from 4 and 5)

One could then argue that only God is ultimate in authority and thus God exists, or at least that the existence of God provides the role for a supreme being that is ultimate in moral authority and thus theism has explanatory power (thus providing at least some degree of evidential support for theism). In either case the implication is that God explains the existence of objective moral values. Morality is an ought, and God is the supreme judge of what ought to be.

Objection: God is not needed for objective ethics

The atheist could still maintain that God is not necessary for objective ethics. Why can’t ethics be like logic, not needing a conscious mind for its statements (like 2 + 2 = 4) to be true?


Consider this more general approach of the argument from morality. One could claim that if ethics does not have its basis in God but instead our beliefs of morality were the result of socio-biological evolution on a tiny speck in the universe containing billions of stars and planets, then our beliefs and feelings of the way things should be lack an objective reference point. Reference points for should statements often lie in cultures (e.g. “People should eat spaghetti with eating utensils instead of fingers”) or else sources for should statements reside within individuals (e.g. “Clowns should be in circuses”). But what objective reference point is there for ethical should statements (e.g. slavery should not happen)? It isn’t the individual or the culture. Without an objective reference point, moral beliefs would instead be expressions of feelings and opinions of the culture/individual, such as “I don’t think this color should be on that painting” or “spaghetti should be eaten with eating utensils.” But with the existence of God, ethical ideas (e.g. one shouldn’t steal) would reside within a metaphysical basis of supreme authority, providing an objective reference point. Ethics being grounded in God explains why ethics transcend humanity and why they are binding whatever humanity thinks. The existence of God provides a source for objective morality, whereas atheism does not. And therefore God is the best explanation for the existence of objective moral values. After all, if I say things should be one way and you disagree, how is one right and another wrong? What is the source of the standard we’re judging on that makes it authoritative?

Disputable Point

Okay, so the difference is that logic describes what is and ethics describes what ought to be. Does the latter require God? Is God really necessary as a basis for objective moral values?

The theistic arguments above might sound like divine command theory. Divine command theory says something is morally good/bad because God commands so. One argument that has been often used against divine command theory goes something like this:

  1. If God commanded rape, then rape would be ethical.
  2. Rape is not ethical.

Therefore divine command theory is wrong.

At first I thought this was a really good argument, but on closer examination it doesn’t quite work out, at least in part because divine command theory isn’t necessarily what we’re talking about when we say that God is the best explanation for objective ethics. In Plato’s Euthyphro, Socrates asked, “Do the gods love holiness because it is holy or is it holy because the gods love it?” This is what is known as the Euthyphro dilemma. Applying that principle in the case of ethics, this version of the Euthyphro dilemma becomes, “Is it good because God commands it, or does God command it because it is good?” But some philosophers have claimed that this is a false dichotomy. One alternative view is that ethics exists in the form of a personification, and that God is that personification of ethics. Under this view, ethics results from the nature of God rather than the commands per se. Still, the atheist could claim that ethics does not exist in the form of a personification, i.e. that a personification of ethics does not exist. One could use the same argument above replacing “God” with a “personification of ethics.” But watch what happens when we try to apply the same argument:

  1. If the personification of ethics commanded rape, then rape would be ethical.
  2. Rape is not ethical.

Therefore the personification of ethics does not exist.

But wait a minute. It should be immediately clear that if premise #2 is true, that if rape is indeed unethical, then there aren’t any possible circumstances by which any personification of ethics could command rape. Also, the argument is invalid. The conclusion doesn’t logically follow from the two premises. The structure of the argument is a travesty of modus tollens. Modus tollens has the following structure:

Modus Tollens
In English In Symbolic Logic
If A then B
Not B
Therefore, not A
A --> B
therefore ~A

This is valid, i.e. the conclusion logically follows from the premises. Suppose we have:

A = God/personification of ethics commands rape
B = rape is not ethical

When we plug in A and B into the modus tollens structure, the valid conclusion would be that A is not true, i.e. it is not the case that God/personification of ethics commands rape. It doesn’t logically follow that the personification of ethics doesn’t exist or even that divine command theory is false.

Disputable Point

Yet another route is to abandon ethical objectivism altogether. A number of atheists have conceded that God is required for objective morality but reject ethical objectivism in favor of some form of ethical relativism or noncognitivism. So another disputable point is whether or not ethical objectivism is true.

The next section deals with a few basic criticisms on the attributes of God. What about the problem of evil? I'll save that one for later.

Basic Criticisms and Rejoinders
Can God create an immovable stone?

There are quite a few variations to this. “Can God create a rock so heavy that he can’t lift it?” Or, “Can God create an immovable mountain?” If the answer is “yes,” then that would mean that God can’t move the mountain, or couldn’t lift the rock, and therefore God isn’t omnipotent. If the answer is “no,” then God can’t create the immovable stone, can’t create a rock that He couldn’t lift etc. and therefore God isn’t omnipotent.  Neither answer looks good for one who believes in a God that can do anything. How can the theist respond here?


Here’s my own version of a story I saw somewhere else.

Human:    Hey God, you can do anything right?
God: You betcha.   [Evidently, God is a Minnesotan.]
Human: I don’t think you can, and I can prove it. Let’s see you create an immovable stone.
God: No problemo.
* Creates an immovable stone. *
Human: Quite impressive.
God: Thank you.
Human: Now put that stone on top of that hill.
God: That’s not fair! You’re toying with semantics and petty logic.
Human: Big deal! If you can’t do this it means I’ve proved you wrong. Now let’s see you do it!
God: Let me think about this one... Got it.
* Disincorporates the universe, then reconstructs it with the stone on top of the hill.*
You see, I can play games with logic and semantics too.

The point of the story is that “creating an immovable stone” and the like really isn’t a test of God’s omnipotence. Even assuming that God might not have the power to do what’s logically impossible, God can still lay the foundations of the universe, create beings in His own image, possess essentially unlimited (the limits being only what is logically possible) ability to create and manipulate space, time, matter, and energy; and can kick your butt in every trivia game show you can imagine. Playing games with semantics doesn’t prove anything and in fact misses the point.

A similar question could be asked, “Can God do what is logically impossible? Can he create a round square etc.?” One way to respond to this question and the “immovable stone” one is that God’s omnipotence doesn’t mean that He can do literally anything, but he can do anything that can be done. The answer to the “immovable stone” question would be “no.” Now this might prompt one to say, “Aha! So God can’t do absolutely everything!” But then the theist would say, “So what?” God can do anything that can be done. Omnipotence, even if it’s only omnipotence to the greatest possible extent, is surely enough for any rational theistic worldview.

God’s omniscience versus free will

The argument first starts off by saying that we humans obviously have free will. But do we really possess free will? Are we really capable of choosing our own actions? Experiment for yourself. To see if you have free will, intentionally do something, anything at all. For instance, try to move your arm. Can you do it? I think I can. And the evidence (direct perceptions) would seem to indicate that we do indeed have free will. A famous law of logic we'll be using in this argument is the law of noncontradiction. This law states that for any specified proposition p, it is impossible for both p and not p to be true; e.g. it is impossible for me to exist and to not exist at the same time.

Suppose there is a God with such attributes described on the list above. That would mean that he’s omniscient and thus knows the future. We creatures have the ability to do various things. To simplify matters, let’s have A be a placeholder for an action, whether it be the action of doing something or the action of refraining from doing something. The key thing to keep in mind here is that A represents a decision if we had free will. We can then use the following argument:

  1. God is omniscient (a trait from the definition of God).
  2. God knows everything that you will do (from 1).
  3. If it is known in advance that you will do A, then you have no choice but to do A (because not doing A would violate the law of noncontradiction).
  4. God knows you will do A (from 1 and 2).

Conclusion: You have no free will in whatever you do (from 3 and 4).

So how can an omniscient God also allow creatures to have free will?


Premise #3 is false. Foreknowledge does not imply predestination. To understand exactly why this doesn’t work, it’s helpful to about a division of logic called modal logic. To help explain some basic concepts of modal logic, let me tell you a little story about OmniSim. Our world is reality. Nevertheless, there are many other ways reality could have been like, i.e. many other possible worlds other than our own (actual) world. Suppose we have a supercomputer called OmniSim that can simulate all possible worlds. Every world that is possible has a simulated environment in this supercomputer.

Let's have p be a placeholder for a statement. Possibly true means p is true in at least one possible world. There exists at least one possible world in OmniSim where p is true. A statement that’s true in some possible worlds but also false in other possible worlds is called a contingent statement (because it can be either true or false).

Statement p being necessarily true means p is true in all possible worlds. Using the supercomputer analogy, statement p would be true in all of OmniSim’s simulated worlds. Examples of a necessary truth would be 2 + 2 = 4 and the law of noncontradiction. All of these things are true in all possible worlds. To sum it all up:

Terms that Describe Modal Status
Term Meaning
possible True in at least one possible world.
contingent True in some possible worlds, false in other possible worlds.
necessary True in all possible worlds.

What does any of this have to do with rebutting the argument? The reason this argument is slippery is that it confuses the meaning of necessarily true. Looking at premise #3 again, “If God knows you will choose A then you have no choice but to do A.” To use the argument in modal terms, “If God knows you will choose A, then you will necessarily choose A.” Why is this true? If I will do A in a possible world (e.g. ours), I can’t simultaneously do not A in the same world because that would violate the law of noncontradiction; I can’t do A and not A at the same time. But notice this holds only for the world(s) in which I do A. It doesn’t logically follow that just because I will do A in the actual world that I will do it in all possible worlds.

In other words, just because I will actually do A doesn’t mean I necessarily (in the modal logic sense) had to do A. Rather it could be that I will do A in the actual world because I freely choose A, i.e. that I had the ability to choose an alternate possible world where not A could have been my decision (I had free will) but I just chose A instead for the actual world. To give an example, just because I will drink hot chocolate doesn’t mean I necessarily had to do that, rather it could be that I chose that outcome out of the many possible circumstances (i.e. many possible worlds). And thus here we have the problem with the premise, actuality does not imply necessity. Someone knowing that I will do A only implies that I will in fact do A, it does not logically follow that I will do A in all possible worlds (i.e. that I necessarily had to do A).

One way to illustrate this and to refute premise #3 is through a counterexample (and example that disproves a theory, proposition, premise, etc.). For this counterexample against #3, let’s have A be the action of voting for George W. Bush. Suppose I use a time machine to travel from the present to the year 1995. I know that the American people will elect George W. Bush in the year 2000. But clearly, this foreknowledge does not imply predestination. I don’t take away the people’s free will simply by knowing what will happen. How is this a counterexample? The point is that foreknowledge and free will are not logically incompatible. Time travel may not be physically possible, but so long as it is logically possible (and it is) it can be used to prove that a combination free will and foreknowledge is logically possible and are thus not logically incompatible. Bear in mind that God (if he exists) is not limited to physical laws anyway. (One could prevent time-travel paradoxes this way; the powers that be permit one to exist in the past and fully observe it, but does not permit one to interact in it. Again even if this idea is not permissible by physical laws it is logically possible and that’s the only requirement here.) But what if people choose to vote for Al Gore instead? In that case, I would correspondingly have always known that when I traveled from the present to the year 1995.

It’s the same with God’s omniscience. Let’s face it, either I will choose action A (whether it be voting for a particular candidate or whatever) or I won’t. Suppose one chooses A. If God knew it ahead of time, would that remove the individual’s free will? No it wouldn’t, anymore than if I knew it when I traveled back in time. What if, at the last minute, the person chooses not to do A? Then God would correspondingly have always known that the individual wouldn’t do A. It’s like traveling back in time before George W. Bush was elected. Simply because I know that the people would vote for George does not in the least imply that I have removed their free will, just like God knowing who would be elected does not imply that He removed their free will.

A problem with the “foreknowledge implies predestination” thing is a lack of a mechanism. Going back to the time-travel example, how did I remove their free will merely by knowing what will happen? Magic? The simple answer is that I didn’t remove their free will through mere knowledge, because knowledge by itself can’t cause anything. It doesn’t seem at all plausible, for instance, that my knowledge of them voting for George W. Bush actually somehow causes them to vote for Bush, any more than knowledge causes things to fall when gravity becomes known. As the thought experiment seems to indicate, foreknowledge does not necessarily obstruct free will because mere knowledge doesn’t actually cause anything.

The only way to maintain the alleged logical incompatibility between foreknowledge and free will (presuming we have free will to begin with) is to claim that the time-travel thought experiment (going back to the past) somehow removed free will. But again, there is a lack of a mechanism. Knowledge of the past (e.g. voting for a presidential candidate) does not entail its predestination (e.g. knowing that they did vote for him doesn’t mean that they had to vote for him). When the time-traveler (with knowledge of history) goes back to the past, what removed their free will then? Magic? It seems even less reasonable to suppose that this magic necessarily follows in this thought experiment, since mere knowledge can’t cause anything.


[1] J.P. Moreland et al, Does God Exist? Prometheus Books, 1990; p. 230