Having had numerous discussions with both anti-theists and theists, I’ve found that there are a lot of flawed arguments going around. This is an attempt to point out some of those fallacies. This is a living document, with more arguments and counter arguments being added as needed.

Prelims

Proving Negatives

This is blatantly contradictory to our usual epistemological mechanics. Proof, in the most absolute sense possible, only exists in mathematics. What we generally mean by “proof” is “support with evidence.” In mathematics, we can prove nonexistence either directly, or in many cases, through proof by contradiction. In “the real world” we essentially do the same thing statistically. This is done by what what is called “hypothesis testing.”

To understand hypothesis testing, we first need to start with proof by contradiction. It goes as follows. You start by assuming that what you want to disprove is actually true. Call that statement p. Then we use existing knowledge to reach a conclusion that we already know is false. Since we assume that our system must be logically consistent: not true and false at the same time, we conclude that p must actually be false.

But the assumption that p is true, is only relevant within our proof. And if we do not reach a contradiction, then we can say nothing about p. In other words, if we make a series of logical inferences from our assumption p, and do not come up with a contradiction, we don’t know whether p is actually true or not, and we just admit that.

Now, in “the real world” we do not have things so easy, but that’s fine. Instead of our statement p, we start with a similar statement that we want to disprove, call it h0. We try to show that assuming h0, our observations have a low probability of being true, given that h0 is true. But since we know that our observations are true, we are LIKELY to have a contradiction. All a hypothesis test is, is a statistical version of proof by contradiction.

And since our null hypothesis is essentially our assumed statement p, the assumption of truth only has relevance within our hypothesis test, and just as with proof by contradiction, if we do not reach a contradiction, then we cannot say anything about our null hypothesis.

So to summarize, we set our null hypothesis to whatever it is we wish to disprove. We then try to show that our observations are unlikely, given our assumed hypothesis. If we do so, then we can reject the null hypothesis. If we fail to do so, then we cannot say anything about our null hypothesis. Furthermore, there is no “null hypothesis in life.” A null hypothesis only makes sense within the bounds of a hypothesis test.

How does this apply to proving negatives? Well, if we start with the assumption of existence for something, and we have a list of known expectations of what we would observe under the assumption that such a thing exists, then we can make a series of observations and try to show that it is improbable to see such observations, assuming existence. This does not disprove existence absolutely, but if the actual observations are improbable, assuming existence, then we can be reasonably certain of nonexistence.

For a more detailed argument on proving negatives, read Thinking Tools: You Can Prove a Negative by Steven D. Hales Ph.D. or pick up a copy of one of his books on logic.

Burden of Proof

The next topic is burden of proof. Many people seem to think that only existential claims suffer from burden of proof. Yes; I call it suffering. It is a burden after all. One of the arguments used is that negative claims cannot be proven, but I already pointed out the issue with that. So, what would happen if we assumed negative claims lacked burden of proof? Well, “no claim suffers from burden of proof” is a negative claim. So it would be on the other person to show that any claim suffers at all.

Furthermore, we can generally take a claim of nonexistence or existence, and find claims of existence and nonexistence respectively, which imply the other. For instance, “there is a god” is implied by “a universe without a god does not exist.” It is obtuse, sure. But it works. It’s a negative claim, and it implies that there is a god. How could the claim “there is a god” suffer burden of proof, but not a claim that implies it? It is nonsensical. We would always just seek out the equivalent claims of nonexistence to absolve ourselves of the burden.

Unanchored Backward Chaining

The Elephant

Suppose that I want to show that my neighbor does not have an elephant in his back yard. I can do this by first noting that elephants are very large, make a lot of noise, and leave footprints, especially if the ground has been wet. Is this an absolute fact? No. Maybe there is an elephant somewhere that does not have any of these characteristics. But we have made quite a few observations and infer that elephants have these features. But to make sure, I ask my neighbor if he agrees with these statements. If he does, I can proceed. This makes the list of assertions a well established foundation.

Now that I have this foundation, I can make a series of observations in the neighbor’s back yard. Suppose I haven’t seen any big animals towering above the measly fence which separates our two yards, that I haven’t heard any noise coming from my neighbor’s back yard, and that I see no footprints when I walk through the yard, even though it rained a few days prior.

I can add these observations as a second layer on top of my foundation, and from that, add the top layer: the conclusion that my neighbor does not have an elephant in his back yard.

Backward Chaining

It is pretty easy for a human to reach a conclusion from a given set of assertions, by working forward. In computer science, it is sometimes easier to work backwards, starting with the conclusion, and through various substitutions of the initial assertions, determine whether or not the conclusion is true or not, based on those initial assertions. This is a process called backward chaining and it is a valid process.

Unanchored Backward Chaining

Now here is where things get interesting. In the initial elephant example, I more or less worked in a forward manner. Sure, I was thinking about what foundation would be useful in determining whether or not the conclusion was true, but I made sure my foundation was solid and then made sure that I could build from that foundation to my conclusion. Before starting my argument, I made certain that the person, with whom I am arguing, agreed with the initial assertions, and then used those assertions as an anchor for the remainder of my argument.

But many arguments relating to religious claims work in a very different way. First, a conclusion is asserted to be true and the goal is to “prove” the statement true. Now, instead of working on an established foundation, a claim is made which leads to the conclusion that the original claim is true. But there is no substantiation for that second claim. Once pressed, the person seeks to find another claim which can then substantiate the second claim, and so on. Because there is no solid foundation from the start, I call this process unanchored backward chaining.

Creationism and Anti-theism

Two instances in which unanchored backward chaining is common are in arguments relating to creationism and arguments relating to claims that there are no gods. Both start with their respective conclusions and try to progress backwards.

As an example, creationists sometimes rely on a concept known as “irreducible complexity.” The idea behind the irreducible complexity argument is that some features of life are simply too complex to have evolved randomly. Certainly if this is the case then creationism or intelligent design are more or less the only explanations for life existing in its current form.

But for irreversible complexity to hold, there would have to be no paths available through which evolution can produce a given result. As such, the claim that life is irreducibly complex is unsubstantiated. But for the average creationist, they are comfortable with the level of argument and therefore feel satisfied that they have indeed substantiated the claim. Meanwhile to someone who does not support creationism, they would continue to ask for the next link in the chain.

We can see the same process in attempts to discredit the existence of a god. One example is the following assertion: “The fact that no God has contacted us in an unambiguous manner is contrary to the nature of God as depicted in most religions and therefore evidence that such a God doesn’t exist” (Glen Tarr, Quora answer, accessed October 15, 2015).

Is this substantiated? It doesn’t seem to be. Why is it contrary to the nature of God, as depicted in most religions? Indeed, the Christian god seems to want people to believe without evidence rather than when presented with clear evidence. This is apparent from the story of doubting Thomas. True, Christianity is just one of many religions in the world, but it is a very prominent religion.

Another chain can be added to this one: god wants certain things from us and this is why a lack of unambiguous communication is evidence against a god (Glen Tarr, comment discussion, October 14, 2015). But why would this be the case? Because it is easier to get humans to do what such a god wants them to do? Certainly, but even using that claim is just another link in the chain. Why would a god act in a way which is easiest?

Validity of Use

This does not mean that unanchored backward chaining “wrong.” It can be used when investigating various claims. Indeed, you may need to use this process, in order to find an anchor link and determine whether or not the claim seems reasonable. But an unanchored link should not be used within an argument because it is far too easy to undermine an argument which relies on it. Once an anchor is established, the only way for a opponent to invalidate the conclusion is to break a link in the chain: show that one of the links is wrong. With an unanchored chain, all an opponent has to do is reject the newest link. This, combined with the initial desire to prove the conclusion right, results in a possibly endless search for evidence to support the conclusion.

Absence of Evidence

Absence of evidence is not evidence of absence. Just because we do not find evidence for the existence of something, does not mean that it does not exist. As in the earlier elephant example, to find evidence of absence, we need to first establish what would constitute evidence of existence. We would then need to make a series of observations and show that such observations are contrary to the assumption of existence. That brings us back to hypothesis testing.

For instance, I cannot say that the wind likely does not exist, because I cannot see it. There is no expectation that I should be able to see the wind, even if it does exist. Likewise, I cannot say that a failure to see leaves moving is evidence of absence of wind, if there are no trees around. A failure to establish reasonable expectations of existence, and to make proper observations which are contrary to assumed existence, means that nothing can be said of nonexistence.

Occam’s Razor

Occam’s razor is a philosophical tool. A razor is any tool used to cut down the number of arguments, positions, etc. Usually razors are statements of probability: a statement is less likely to be true if a given razor’s condition is met. However, Occam’s razor never really satisfies this. William of Occam himself was just looking for a tool to better help him argue for the existence of a god. It was a conjecture on his part. Various formalizations of Occam’s razor do exist. However, none of the mathematically justifiable forms actually do anything to address “truth:” we do not know, from Occam’s razor, whether or not one of two competing theories is less likely than the other. It’s simply a tool that allows us to say “we should use one over the other to make predictions.”

To use Occam’s razor properly, we look at two competing models consistent with a given set of data. The model which makes the least number of assumptions is preferred, only because the additional assumptions must be valid in order for the model to be valid. Yet we know nothing of the probability of any assumption being valid or invalid, and therefore nothing about the difference in probabilities of the two models being right. Who knows, maybe all the guesses cancel themselves out?

Dr. Yaser S. Abu-Mostafa has multiple books about machine learning which cover this topic, including Learning from Data.

The Abrahamic God(s)

One would think that such a specific god would be easy to falsify, but it’s not. There is one exception, but we have to start with a foundation. The Christian god, in its most common form, is a god that sentences people to eternal suffering, for not believing. Now, if we start with the foundation that a just punishment is one that is commensurate with the crime, and that not believing has at most a finite negative impact on those around us, eternal damnation simply is not just. Furthermore, it is generally considered that the Christian god is omni-benevolent. It must therefore only issue just punishment. But it is concluded, upon the aforementioned foundations that eternal damnation is not just. And so an omni-benevolent Christian god, who sends people to hell for all eternity, for not believing, cannot exist.

The problem with extending this to all god claims, or even most Abrahamic god claims, is that the concept of eternal damnation is not universal. Jews do not believe in eternal damnation. Indeed, Jewish doctrine says little about the afterlife in general. But the basic idea in Jewish doctrine is that hell is not a system of eternal punishment, but a system of cleansing for the soul, to prepare it for heaven, kind of like a cosmic dish washing machine for the soul. This cleansing would then be finite, and commensurate with any crime committed, and therefore just. So the argument above does not work for the Jewish god. This isn’t to say that we have an argument for such a god, just not against.

Shifting Burden of Proof

Both anti-theists and theists do this. Russel’s Teapot was a response to theists trying to push atheists into countering the existence of a god, rather than defending the claim of existence. But burden of proof, as mentioned in the prelims, is always on the person making the claim. It is always appropriate to demand evidence from someone who makes a claim.

Shifting burden of proof is often done by a false notion that only claims of existence suffer from burden of proof. But again, this issue has already been addressed in the prelims.

Probably and Unlikely

The words “probably” and “unlikely” are both used to deflect burden of proof. “There probably is a god” or “gods are unlikely” are still claims. All claims suffer from burden of proof. Claims cannot be shown false through a simple lack of evidence. And absence of evidence does not make something unlikely. Yet that is often the exact idea used. Can we go around saying that someone “probably beats his wife” or that he “probably doesn’t have an education?” That would be absurd. It is the same in this situation. A statement of probability requires information about the probability space in question, and that comes either from construction, or evidence.

Proof by Obvious

This “methodology” is used in many contexts. Theists sometimes use it to argue that god obviously exists because the universe exists. Sometimes “obvious” is not explicit but is still there, for instance when there is a direct leap in logic from “the universe exists” to “there is a god.”

Further Reading

• The Profile of the American Religious Rejectionist
• What Would an Eternal Afterlife Feel Like?
• Flawed Argument Against an Afterlife
• The Problem of Evil: A Few Analogies to Bring Perspective