Category: Argumentative Strategies Series

Argumentative Strategy Series: The Analog Strategy

Let us consider a well-worn argument:

P1 Everything that begins to exist has a cause.

P2 The universe began to exist.

C Therefore, the universe has a cause. (Reichenbach, Bruce. “Cosmological Argument”Stanford Encyclopedia of Philosophy. 2021. Web.)

When nonbelievers first encounter this argument, it is likely they find it suspicious even if they cannot immediately identify why. My first written refutation of the argument zeroed in on the fact that it appears to commit the fallacy of composition. As an inexperienced and naive thinker, it was a real eureka moment for me. As it turns out, this is a common retort.

Russell replies that the move from the contingency of the components of the universe to the contingency of the universe commits the Fallacy of Composition, which mistakenly concludes that since the parts have a certain property, the whole likewise has that property. Hence, whereas we legitimately can ask for the cause of particular things, to require a cause of the universe based on the contingency of its parts is mistaken.

Reichenbach, Bruce, “Cosmological Argument”The Stanford Encyclopedia of Philosophy (Fall 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.)

My interest here is not whether or not this rebuttal works against the Kalam. We can all agree that proponents of the argument will reject this rebuttal and certainly won’t regard it as a defeater. To my mind, it does work and although it is not the best rebuttal or strongest defeater for the argument, it is worth understanding why it works. Unfortunately, one would still have to deal with the obstinate apologist refusing to hear your case. In cases like this, the analog strategy works perfectly.

Basically put, the strategy would have one devise an argument so similar to the original that it would be difficult to deny the analog without also denying the original. This is admittedly tricky, but if successful, this could save a lot of time otherwise spent on trying to convince someone who refuses to budge and doubles down. Discussions on the Kalam give us a perfect segue: another common refutation is the possibility of a multiverse. Whether one goes with M-theory or Everett’s Many Worlds Interpretation of quantum mechanics, other universes are a consequence in some theories in cosmology and quantum mechanics. It does not, as some apologists erroneously claim, result from a refusal to admit that God created the universe. Carroll alluded to this refutation in his debate with Craig.

So without further ado, here is a Kalam analog that theists will almost certainly reject:

P1 For every particular thing that exists, there is always more than one of that particular thing

P2 The universe exists

C Therefore, there is more than one universe

A standard refutation to this argument will likely point out that I have committed the fallacy of composition. People will likely say that the universe is unlike everyday objects. They might find it patently absurd that made a logical inference from many cats, ants, and planets to many universes. Another standard refutation of the Kalam can be mapped onto the analog: what is meant by “particular thing that exists”? Although I find the argument prima facie intriguing, I would concede; my argument does not succeed at logically proving the existence of other universes. Whether a dissenter points out the fallacy or whether they quibble with the semantics of the argument, there refutations have force. Now is when sleight of hand occurs and you hold up a mirror.

The theist will have to strongly consider whether the analog is a charitable reflection of the argument they think is true. In this particular case, if they are suspicious of my inference from many entities to many universes, then they are obligated to be equally as suspicious of the inference from every entity in the universe being an effect to the universe being an effect. There is only one other option: they will have to show that the analog is dissimilar to the original in some critical way. If they choose that route, I do not see a way forward. If after employing this strategy, they still double down, then you know you are not dealing with someone who is reasoning properly. They likely have an emotional attachment to the argument or accept it because of motivated reasoning. Whatever the case, any further discussion with such an individual is fruitless.

Ultimately, the analog strategy is an effective and powerful tool to have in one’s reasoning kit. As shown here, when used properly, proponents of flawed or outright unsound arguments have to reckon with the efficacy of certain refutations. Where they might have waved these refutations away, they now have to consider the possibility that the argument they thought was true is actually false. The strategies I have offered so far make one thing abundantly clear, and it is perhaps one thing most philosophers are reluctant to admit, certainly not something I am ashamed to admit: persuasion involves manipulation and deception. These terms tend to have bad connotations, but reasoning, like playing a game of chess, must involve setting traps for your opponent. In order for philosophy to be more truth-obtaining than it currently is, these strategies have to be learned and used effectively, so that we can begin to eliminate erroneous arguments and schools of thought.

Argumentative Strategies Series: The Negation Strategy

By R.N. Carmona

Every deductive argument can be negated. I consider this an uncontroversial statement. The problem is, there are people who proceed as though deductive arguments speak to an a priori truth. The Freedom Tower is taller than the Empire State Building; the Empire State Building is taller than the Chrysler Building; therefore, the Freedom Tower is taller than the Chrysler Building. This is an example of an a priori truth because given that one understands the concepts of taller and shorter, the conclusion follows uncontroversially from the premises. This is one way in which the soundness of an argument can be assessed.

Of relevance is how one would proceed if one is unsure of the argument. Thankfully, we no longer live in a world in where one would have to go out of their way to measure the heights of the three buildings. A simple Google search will suffice. The Freedom Tower is ~546m. The Empire State Building is ~443. The Chrysler is ~318m. Granted, this is knowledge by way of testimony. I do not intend to connote religious testimony. What I intend to say is that one’s knowledge is grounded on knowledge directly acquired by someone else. In other words, at least one other person actually measured the heights of these buildings and these are the measurements they got.

Most of our knowledge claims rest on testimony. Not everyone has performed an experimental proof to show that the acceleration of gravity is 9.8m/s^2. Either one learned it from a professor or read it in a physics textbook or learned it when watching a science program. Or, they believe the word of someone they trust, be it a friend or a grade school teacher. This does not change that fact that if one cared to, one could exchange knowledge by way of testimony for directly acquired knowledge by performing an experimental proof. This is something I have done, so I do not believe on basis of mere testimony that Newton’s law holds. I can say that it holds because I tested it for myself.

To whet the appetite, let us consider a well-known deductive argument and let us ignore, for the moment, whether it is sound:

P1 All men are mortal.

P2 Socrates is a man.

C Therefore, Socrates is mortal.

If someone were completely disinterested in checking whether this argument, which is merely a finite set of propositions, coheres with the world or reality, I would employ my negation strategy: the negation of an argument someone assumes to be sound without epistemic warrant or justification. The strategy forces them into exploring whether their argument or its negation is sound. Inevitably, the individual will have to abandon their bizarre commitment to a sort of propositional idealism (namely that propositions can only be logically assessed and do not contain any real world entities contextually or are not claims about the world). In other words, they will abandon the notion that “All men are mortal” is a mere proposition lacking context that is not intended to make a claim about states of affairs objectively accessible to everyone, including the person who disagrees with them. With that in mind, I would offer the following:

P1 All men are immortal.

P2 Socrates is a man.

C Therefore, Socrates is immortal.

This is extremely controversial for reasons we are all familiar with. That is because everyone accepts that the original argument is sound. When speaking of ‘men’, setting aside the historical tendency to dissolve the distinction between men and women, what is meant is “all human persons from everywhere and at all times.” Socrates, as we know, was an ancient Greek philosopher who reportedly died in 399 BCE. Like all people before him, and presumably all people after him, he proved to be mortal. No human person has proven to be immortal and therefore, the original argument holds.

Of course, matters are not so straightforward. Christian apologists offer no arguments that are uncontroversially true like the original argument above. Therefore, the negation strategy will prove extremely effective to disabuse them of propositional idealism and to make them empirically assess whether their arguments are sound. What follows are examples of arguments for God that have been discussed ad nauseam. Clearly, theists are not interested in conceding. They are not interested in admitting that even one of their arguments does not work. Sure, what you find are theists committed to Thomism, for instance, and as such, they will reject Craig’s Kalam Cosmological Argument (KCA) because it does not fit into their Aristotelian paradigm and not because it is unsound. They prefer Aquinas’ approach to cosmological arguments. What is more common is the kind of theist that ignores the incongruity between one argument for another; since they are arguments for God, it counts as evidence for his existence and it really does not matter that Craig’s KCA is not Aristotelian. I happen to think that it is, despite Craig’s denial, but I digress.

Negating Popular Arguments For God’s Existence

Let us explore whether Craig’s Moral Argument falls victim to the negation strategy. Craig’s Moral Argument is as follows:

P1 If God does not exist, objective moral values do not exist.

P2 Objective moral values do exist.

C Therefore, God exist (Craig, William L. “Moral Argument (Part 1)”. Reasonable Faith. 15 Oct 2007. Web.)

With all arguments, a decision must be made. First, an assessment of the argument form is in order. Is it a modus ponens (MP) or a modus tollens (MT)? Perhaps it is neither and is instead, a categorical or disjunctive syllogism. In any case, one has to decide which premise(s) is going to be negated or whether by virtue of the argument form, one will have to change the argument form to state the opposite. You can see this with the original example. I could have very well negated P2 and stated “Socrates is not a man.” Socrates is an immortal jellyfish that I tagged in the Mediterranean. Or he is an eternal being that I met while tripping out on DMT. For purposes of the argument, however, since he is not a man, at the very least, the question of whether or not he is mortal is open. We would have to ask what Socrates is. Now, if Socrates is my pet hamster, then yes, Socrates is mortal despite not being a man. It follows that the choice of negation has to be in a place that proves most effective. Some thought has to go into it.

Likewise, the choice has to be made when confronting Craig’s Moral Argument. Craig’s Moral Argument is a modus tollens. For the uninitiated, it simply states: [((p –> q) ^ ~q) –> ~p] (Potter, A. (2020). The rhetorical structure of Modus Tollens: An exploration in logic-mining. Proceedings of the Society for Computation in Linguistics, 3, 170-179.). Another way of putting it is that one is denying the consequent. That is precisely what Craig does. “Objective moral values do not exist” is the consequent q. Craig is saying ~q or “Objective moral values do exist.” Therefore, one route one can take is keeping the argument form and negating P1, which in turn negates P2.

MT Negated Moral Argument

P1 If God exists, objective moral values and duties exist.

P2 Objective moral values do not exist.

C Therefore, God does not exist.

The key is to come up with a negation that is either sound or, at the very least, free of any controversy. Straight away, I do not like P2. Moral realists would also deny this negation because, to their minds, P2 is not true. The controversy with P2 is not so much whether it is true or false, but that it falls on the horns of the objectivism-relativism and moral realism/anti-realism debates in ethics. The argument may accomplish something with respect to countering Craig’s Moral Argument, but we are in no better place because of it. This is when we should explore changing the argument’s form in order to get a better negation.

MP Negated Moral Argument

P1 If God does not exist, objective moral values and duties exist.

P2 God does not exist.

C Therefore, objective moral values and duties exist.

This is a valid modus ponens. I have changed the argument form of Craig’s Moral Argument and I now have what I think to be a better negation of his argument. From P2, atheists can find satisfaction. This is the epistemic proposition atheists are committed to. The conclusion also alleviates any concerns moral realists might have had with the MT Negated Moral Argument. For my own purposes, I think this argument works better. That, however, is beside the point. The point is that this forces theists to either justify the premises of Craig’s Moral Argument, i.e. prove that the argument is sound, or assert, on the basis of mere faith, that Craig’s argument is true. In either case, one will have succeeded in either forcing the theist to abandon their propositional idealism, in getting them to test the argument against the world as ontologically construed or in getting them to confess that they are indulging in circular reasoning and confirmation bias, i.e. getting them to confess that they are irrational and illogical. Both of these count as victories. We can explore whether other arguments for God fall on this sword.

We can turn our attention to Craig’s Kalam Cosmological Argument (KCA):

P1 Everything that begins to exist has a cause.

P2 The universe began to exist.

C Therefore, the universe has a cause. (Reichenbach, Bruce. “Cosmological Argument”. Stanford Encyclopedia of Philosophy. 2021. Web.)

Again, negation can take place in two places: P1 or P2. Negating P1, however, does not make sense. Negating P2, like in the case of his Moral Argument, changes the argument form; this is arguable and more subtle. So we get the following:

MT Negated KCA

P1 Everything has cause iff it begins to exist. {(∀x)[(C)x (E)x]}

P2 The universe did not begin to exist.

C Therefore, the universe does not have a cause.

Technically, Craig’s KCA is a categorical syllogism. Such syllogisms present a universal () or existential quantifier (∃); the latter is introduced by saying all. Consider, “all philosophers are thinkers; all philosophers are logicians; therefore, all thinkers are logicians.” Conversely, one could say “no mallards are insects; some birds are mallards; therefore, some birds are not insects.” What Craig is stating is that all things that begin to exist have a cause, so if the universe is a thing that began to exist, then it has a cause. Alternatively, his argument can be considered an implicit modus ponens: “if the universe began to exist, then it has a cause; the universe began to exist; therefore, the universe has a cause.” I consider this a much weaker formulation and since Craig or anyone else for that matter doesn’t come across things that didn’t begin to exist, interpreting his first premise as a biconditional makes more sense. Hence, the negation works because if the universe did not begin to exist, then the universe is not part of the group of all things that have a cause. This is why my original formulation began with Craig’s P1 because I consider it a biconditional. Notice that even if p and q are false, Craig’s P1 is still true. One way to make a biconditional true is if p and q are false. All that’s said by the Negated or anti-Kalam is that the universe is not within the domain of things that begin to exist. Therefore, the universe does not have a cause.

Whether the universe is finite or eternal has been debated for millennia and in a sense, despite changing context, the debate rages on. If the universe is part of an eternal multiverse, it is just one universe in a vast sea of universes within a multiverse that has no temporal beginning. Despite this, the MT Negated KCA demonstrates how absurd the KCA is. The singularity was already there ‘before’ the Big Bang. The Big Bang started the cosmic clock, but the universe itself did not begin to exist. This is more plausible. Consider that everything that begins to exist does so when the flow of time is already in motion, i.e. when the arrow of time pointed in a given direction due to entropic increase reducible to the decreasing temperature throughout the universe. Nothing that has ever come into existence has done so simultaneously with time itself because any causal relationship speaks to a change and change requires the passage of time, but at T=0, no time has passed, and therefore, no change could have taken place. This leads to an asymmetry. We thus cannot speak of anything beginning to exist at T=0. The MT Negated KCA puts cosmology in the right context. The universe did not come into existence at T=0. T=0 simply represents the first measure of time; matter and energy did not emerge at that point.

For a more complicated treatment, Malpass and Morriston argue that “one cannot traverse an actual infinite in finite steps” (Malpass, Alex & Morriston, Wes (2020). Endless and Infinite. Philosophical Quarterly 70 (281):830-849.). In other words, from a mathematical point of view, T=0 is the x-axis. All of the events after T=0 are an asymptote along the x-axis. The events go further and further back, ever closer to T=0 but never actually touch it. For a visual representation, see below:

Asymptotes - Free Math Help

Credit: Free Math Help

The implication here is that time began to exist, but the universe did not begin to exist. A recent paper implies that this is most likely the case (Quantum Experiment Shows How Time ‘Emerges’ from Entanglement. The Physics arXiv Blog. 23 Oct 2013. Web.). The very hot, very dense singularity before the emergence of time at T=0 would have been subject to quantum mechanics rather than the macroscopic forces that came later, e.g., General Relativity. As such, the conditions were such that entanglement could have resulted in the emergence of time in our universe, but not the emergence of the universe. All of the matter and energy were already present before the clock started to tick. Conversely, if the universe is akin to a growing runner, then the toddler is at the starting line before the gun goes off. The sound of the gun starts the clock. The runner starts running sometime after she hears the sound. As she runs, she goes through all the stages of childhood, puberty, adolescence, adulthood, and finally dies. Crucially, the act of her running and her growth do not begin until after the gun goes off. Likewise, no changes take place at T=0; all changes take place after T=0. While there is this notion of entanglement, resulting in a change occurring before the clock even started ticking, quantum mechanics demonstrates that quantum changes do not require time and in fact, may result in the emergence of time. Therefore, it is plausible that though time began to exist at the Big Bang, the universe did not begin to existthus, making the MT Negated KCA sound. The KCA is therefore, false.

Finally, so that the Thomists do not feel left out, we can explore whether the negation strategy can be applied to Aquinas’ Five Ways. For our purposes, the Second Way is closely related to the KCA and would be defeated by the same considerations. Of course, we would have to negate the Second Way so that it is vulnerable to the considerations that cast doubt on the KCA. The Second Way can be stated as follows:

We perceive a series of efficient causes of things in the world.

Nothing exists prior to itself.

Therefore nothing [in the world of things we perceive] is the efficient cause of itself.

If a previous efficient cause does not exist, neither does the thing that results (the effect).

Therefore if the first thing in a series does not exist, nothing in the series exists.

If the series of efficient causes extends ad infinitum into the past, then there would be no things existing now.

That is plainly false (i.e., there are things existing now that came about through efficient causes).

Therefore efficient causes do not extend ad infinitum into the past.

Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God. (Gracyk, Theodore. “Argument Analysis of the Five Ways”. Minnesota State University Moorhead. 2016. Web.)

This argument is considerably longer than the KCA, but there are still areas where the argument can be negated. I think P1 is uncontroversial and so, I do not mind starting from there:

Negated Second Way

We perceive a series of efficient causes of things in the world.

Nothing exists prior to itself.

Therefore nothing [in the world of things we perceive] is the efficient cause of itself.

If a previous efficient cause does not exist, neither does the thing that results (the effect).

Therefore if the earlier thing in a series does not exist, nothing in the series exists.

If the series of efficient causes extends ad infinitum into the past, then there would be things existing now.

That is plainly true (i.e., efficient causes, per Malpass and Morriston, extend infinitely into the past or, the number of past efficient causes is a potential infinity).

Therefore efficient causes do extend ad infinitum into the past.

Therefore it is not necessary to admit a first efficient cause, to which everyone gives the name of God.

Either the theist will continue to assert that the Second Way is sound, epistemic warrant and justification be damned, or they will abandon their dubious propositional idealism and run a soundness test. Checking whether the Second Way or the Negated Second Way is sound would inevitably bring them into contact with empirical evidence supporting one argument or the other. As I have shown with the KCA, it appears that considerations of time, from a philosophical and quantum mechanical perspective, greatly lower the probability of the KCA being sound. This follows neatly into Aquinas’ Second Way and as such, one has far less epistemic justification for believing the KCA or Aquinas’ Second Way are sound. The greater justification is found in the negated versions of these arguments.

Ultimately, one either succeeds at making the theist play the game according to the right rules or getting them to admit their beliefs are not properly epistemic at all; instead, they believe by way of blind faith and all of their redundant arguments are exercises in circular reasoning and any pretense of engaging the evidence is an exercise in confirmation bias. Arguments for God are a perfect example of directionally motivated reasoning (see Galef, Julia. The Scout Mindset: Why Some People See Things Clearly and Others Don’t. New York: Portfolio, 2021. 63-66. Print). I much prefer accuracy motivated reasoning. We are all guilty of motivated reasoning, but directionally motivated reasoning is indicative of irrationality and usually speaks to the fact that one holds beliefs that do not square with the facts. Deductive arguments are only useful insofar as premises can be supported by evidence, which therefore makes it easier to show that an argument is sound. This is why we can reason that if Socrates is a man, more specifically, the ancient Greek philosopher that we all know, then Socrates was indeed mortal and that is why he died in 399 BCE. Likewise, this is why we cannot reason that objective morality can only be the case if the Judeo-Christian god exists, that if the universe began to exist, God is the cause, and that if the series of efficient causes cannot regress infinitely and must terminate somewhere, they can only terminate at a necessary first cause, which some call God. These arguments can be negated and the negations will show that they are either absurd or that the reasoning in the arguments is deficient and rests on the laurels of directionally motivated reasoning due to a bias for one’s religious faith rather than on the bedrock of carefully reasoned, meticulously demonstrated, accuracy motivated reasoning which does not ignore or omit pertinent facts.

The arguments for God, no matter how old or new, simple or complex, do not work because not only do they rely on directionally motivated and patently biased reasoning, but because when testing for soundness, being sure not to exclude any pertinent evidence, the arguments turn out to be unsound. In the main, they all contain controversial premises that do not work unless one already believes in God. So there is a sense in which these arguments exist to give believers a false sense of security or more pointedly, a false sense of certainty. Unlike my opponents, I am perfectly content with being wrong, with changing my mind, but the fact remains, theism is simply not the sort of belief that I give much credence to. Along with the Vagueness Strategy, the Negation Strategy is something that should be in every atheist’s toolbox.

Argumentative Strategies Series: The Vagueness Strategy

Let’s start with well-known, often disputed verses:

For the Lord your God is God of gods and Lord of lords, the great, the mighty, and the awesome God, who is not partial and takes no bribe. Deuteronomy 10:17

God has taken his place in the divine council; in the midst of the gods he holds judgment. Psalms 82:1

There is none like you among the gods, O Lord, nor are there any works like yours.Psalms 86:8

And the king shall do as he wills. He shall exalt himself and magnify himself above every god, and shall speak astonishing things against the God of gods. He shall prosper till the indignation is accomplished; for what is decreed shall be done. Daniel 11:36

Recently, I brought up the fact that modern Christians are polytheists. On the one hand, they believe in the God of the Bible and on the other, the so-called god of philosophers or as they would put it, the god of monotheism. A commenter on my post over on WordPress brought up the fact that the early Jews were polytheists. He provided a number of verses like the ones above. I responded to him and stated that Christians have a go-to copout. They’ll argue that this is merely a recognition that people at the time worshipped other gods, gods that were mere idols. That, however, demonstrates that they are either ignorant of historical context or they know of the context and yet ignore it. We can discuss the polytheistic origins of Judaism further, but that’s not my purpose here.

My purpose here is to debase the notion of a god of (mono)theism, to disrupt that convenient narrative. A Christian on Facebook recently offered an ontological argument he confused with Godel’s Ontological Argument. That wasn’t the argument he offered. He offered another ontological argument in where ‘God’ could be replaced with ‘Allah’ or ‘Ahura Mazda’ and the result wouldn’t change. Two other people then responded and said that the refutation fails because the argument sets out to prove the god of monotheism.

The god of (mono)theism, as William Lane Craig posits, is timeless, personal, omniscient, and so on. I’ll set exegesis aside because there are ways to prove otherwise given passages in the Bible (e.g. why did god ask Adam questions in Genesis 3 if he’s omniscient?). What I want to offer instead is a new argument against the notion of a so-called god of (mono)theism. We know from mathematics that there are different infinities. Since infinity is already a large value, if we can even call it such, there’s no way for the human mind to apprehend one infinity or another, let alone distinguish them. So given that line of thinking, there’s an element of vagueness we can introduce to debase the notion of a god of (mono)theism.

Take, for instance, timelessness. A Christian will posit that their god has no beginning; he’s eternal and exists outside of time. All well and good. Let’s say there’s another being who had a beginning outside of the universe billions of years ago, e.g., Satan. What disqualifies this being from being timeless as well, especially given that we can’t ascertain the beginning of this being’s existence? In other words, if god is present at point 0 and then Satan at point 0.00000005, what difference is there? There are some beginnings that result in a virtual eternity and so, just like there are different infinities, there are different eternities, different versions of timelessness.

The same goes for omniscience. What if there’s a being that knows all things except one thing; let’s suppose this being doesn’t know how to play billiards. What is the difference between an omniscient being who knows all things and another being who knows all things save the required know-how to play billiards? Again, as there are different infinities, there are different levels of omniscience and we simply wouldn’t be able to distinguish between a being who knows everything and one who knows everything except for how to play billiards.

Omnipotence, omnipresence, the capacity to be personal, and so on, all fall victim to vagueness, and as such, the same defeater that exists for Godel’s Ontological Argument, namely that parallel arguments work just as well (see Oppy 1996), also exists for the notion of the so-called god of monotheism. There is no such entity. It is logically possible that, given vagueness, there are millions of beings that fit the description. However, one should not draw ontological conclusions on the basis of logical considerations. Just because there could be a million such beings doesn’t mean they actually exist; likewise, just because one such being is logically possible doesn’t mean it actually exists. The god that apologetic arguments allude to is a product of Christian obfuscation.

Given that Christians are overly fond of deductive arguments, I will do my best to formulate an Argument From Vagueness, which isn’t necessarily an argument on its own. Let’s consider Plantinga’s Victorious Ontological Argument:

  1. A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
  2. A being has maximal greatness if it has maximal excellence in every possible world.
  3. It is possible that there is a being that has maximal greatness.
  4. Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
  5. Therefore, it is necessarily true that an omniscient, omnipotent and perfectly good being exists.

Now, consider a parallel Argument from Vagueness. D1 is crucial to the argument.

D1: A being with maximal excellence* has omnipotence* (which is to be so close to all-powerful that its lone incapacity is negligible; it once failed to push a universe to the left), omniscience* (which is to be virtually all-knowing; it doesn’t know how to play billiards), and perfectly good* (which is to be virtually morally perfect, but it once told a white lie). Maximal greatness* is to have maximal excellence* across all possible worlds.

  1. A being has maximal excellence* in a given possible world W iff it is omnipotent*, omniscient*, and wholly good* in W.
  2. A being has maximal greatness* if it has maximal excellence* in every possible world.
  3. It is possible that there is a being that has maximal greatness*.
  4. Therefore, possibly, it is necessarily true that an omniscient*, omnipotent*, and perfectly good* being exists.
  5. Therefore, it is necessarily true that an omniscient*, omnipotent* and perfectly good* being exists.

Once this counter-argument is offered, what a Christian has left is the bare assertion that a being with maximal excellence* isn’t truly god because it has negligible limitations. The question remains: how do we know that the purported attributes of god are true? It is, as it will always be, a matter of faith. There is no way to ascertain that god is eternal, omnipotent, and omniscient. We can ask whether he is perfectly moral, but that’s a separate issue entirely. The thrust that Arguments From Vagueness drive is that there’s no justification for speaking of any infinity with such certainty. There may be an infinity so near to the one a theist reveres that the differences are negligible. That’s precisely what these arguments are designed for.