NON-THEISTIC ARGUMENTS
With “Non-theistic arguments” I mean arguments that do not support atheism per-se, but instead tries to evade the necessity for argumentation altogether. Often these are arguments for the low prior-probability of the existence of GOD, or arguments rooted in a certain (often misguided) philosophical standpoint. These are, one could say, arguments to evade arguments. A non-theist, by the way, is someone who says “I do not know if GOD exists, but I will simply assume GOD does not exist until I find evidence for the contrary”. An atheist, on the other hand, firmly states that “there is (probably) no GOD”. This is also my general comment for non-theistic arguments: they are not truly arguments for atheism; rather these arguments try to protect the person from the necessity for giving arguments. But, of course, the burden of proof lies with both the theist and the atheist. Only a practical agnostic is free of any burden of proof.
By the way: I agree with non-theists that the prior-probability of GOD's existence is lower that the probability of HIS non-existence, when not looking at the arguments for GOD's existence.
What follows are the non-theistic arguments that I have heard most often, with their refutations.
THE NULL-HYPOTHESIS ARGUMENT / “ATHEISM IS TRUE BY DEFAULT”
There are various "popular" variations of this, like: "atheism is true by default". These are all essentially the same statement, and it's based on how statistics is used in empirical science when testing hypothesis: in empirical science, you cannot proof a negative; i.e. you cannot proof that black swans do not exists, for to do so you need to be truly everywhere throughout all time, which is physically impossible. Therefore, one ASSUMES the Null Hypothesis. But in this argument, the non-theist goes even further and says that thus GOD does not exist. There are 2 problems with this argument:
1) FAILING to DISPROVE the Null Hypothesis, in the empirical application of statistical science, does not equal to PROOFING the Null Hypothesis. Rather, one simply REFRAINS from making a statement. In this context, the Null Hypothesis is "GOD does not exist", and the Alternative Hypothesis is "GOD exists". Thus, failing to disprove "GOD does not exist" does not proof that GOD does not exist; it merely leaves us from refraining to make a statement. All one is left, when failing to disprove GODs non-existence, is agnosticism, or at the very best non-theism. However, this is not the biggest problem; the biggest problem is the next point:
2) The usage of the Null Hypothesis is not a matter of true epistemology, but a matter of methodological limitations in empirical science. The problem, however, is that GOD is not a question of empirical science, and therefore investigating GOD's existence does not have the same methodological limitations as empirical science. GOD's existence is, in my opinion, a more formal question, a philosophical question, and here you can proof a negative. You can, for example, proof that in a certain mathematical equation X does not equal 3. Thus, since GOD 's existence, in my opiion, is a question in formal inquiry, you can give proof of GOD's non-existence. Thus, the argument that atheism is the default position is, I think, false.
FALSIFICATIONISM
The argument here is that GOD's existence cannot be falsified, and is therefore false. This is based on the belief that only falsifiable statements are meaningful statements. But this is false: for example, it is metaphysically impossible to falsify your own existence, yet to say “I exist” is a meaningful statement. Moreover, GOD's existence is, apparently, falsifiable, since many arguments have been proposed for atheism, as is evident from this blog.
VERIFICATION-ISM
The argument in question goes something like this: GOD’s existence cannot by verified using empirical science, therefore stating GOD exists is meaningless. This is rooted in verification-ism, which is the view that all truth claims need to verified by empirical science in order to be accepted and believed. However, one cannot verify using empirical science that all truth claims need to be verified by empirical science, since verification-ism is itself not an empirical statement, but a philosophical statement. Verification-ism therefore is a self-defeating concept and thus false. Moreover, empirical sciences a-priori require formal sciences (like mathematics) and analytical deductions (analytical philosophy). But since verification-ism does not accept non-empirical evidence, like mathematical proofs, empirical science itself cannot operate while holding to verification-ism. Furthermore, even if it were true, you cannot verify the non-existence of GOD either, since empirical science cannot deal with that which is beyond the physical world.
HARDCORE EMPIRICISM
"Empirical science can account for everything, and thus GOD is unnecessary." This is a classic example of hardcore Empiricism. The problem with this statement is that empirical science cannot account for everything.
First and foremost, empirical science cannot account for the formal sciences (like mathematics) nor for analytical philosophy, since empirical science presupposes formal science and analytical philosophy. Using empirical science to proof logic, even though empirical science pre-supposes logic, is a painfully obvious example of circular reasoning.
Secondly, empirical science cannot account for the truth of rational intuition (i.e. "there are other minds besides my own", or "my life is real and not an illusion brought about an experiment with my brain in a laboratory", etc.).
Thirdly, empirical science cannot account for extrapolated scientific assumptions – like: ALL mass attracts each other, or light ALWAYS travels in a constant speed of light in vacuum – since that requires one to be everywhere in the known and unknown universe, and all the time throughout history and the future.
Finally, as a bonus, empirical science also cannot account for moral truths, so clearly, empirical science cannot accont for everything.
NO PREDICTIONS
The argument goes that the existence of GOD does not lead to any empirical predictions, therefore it is useless to even consider GOD's existence. This argument makes multiple fundamental mistakes.
First, GOD is not part of the physical world, and so there is no reason to expect that GOD would leave any "traces" of HIS existence in the physical world. Of course, GOD can choose to interact with the world, but there is no strict expectation for HIM to do so, and so no predictions.
Second, there are many things whose existence can be pondered seriously without having an real predictions attached to them. Historical figures, and abstract objects, are 2 examples of things whose existence does not contribute to predictive power in empirical science.
Third, one can, to a certain extend, make predictions in light of GOD's existence. For example, one would predict that GOD, at least as described in the Judeo-Christian worldview, would have performed at least one miracle. And we have in fact historical evidence that increases the likelihood that miracle: the historicity of the post-mortem experiences of Jesus of Nazareth by a variety of witnesses, both enemies and followers of Christ.
Fourth, there are, for some natural phenomenon, multiple empirical theories which are all equivalent in terms of their predictive power, so making decisions purely on the basis of predictability clearly isn't the right way. For example, there are many theories in physics on the correct interpretation of quantum mechanics. But these theories all give the same predictions, so clearly predictions on themselves don't tell you everything.
Finally, as is the case with most arguments on this list, saying that GOD does not give us predictions does not mean GOD does not exist.
MATERIALISM
Materialism is true, therefore purely non-physical entities (like GOD) do not exist. This is not really an argument, but a statement, which itself needs arguments. Nonetheless, materialism or naturalism cannot be affirmed rationally. This is so because if naturalism is true, our cognitive faculties are created by random mutation and natural selection (evolution), and therefore aimed at survival, not truth or real logic. Therefore, one cannot truly trust our reasoning, and a naturalist cannot reason that naturalism is true because naturalism itself discredits reason in the first place.
LOGICAL POSITIVISM
Logical positivism cannot lead one to conclude that GOD exists, therefore GOD does not exist. Logical positivism is the view that only that the only statements that are meaningful and worthy to be taken seriously, are statements that can be (potentially) investigated using empirical science. Notice that this is based on falsifiable-ism, verification-ism, empiricism, and materialism. I have given my opinion on falsifiable-ism, verification-ism, empiricism, and materialism here above, and find that sufficient.
CULTURAISM
Belief in GOD is associated with one's environment (i.e. culture, parents, friends, etc.), therefore GOD probably does not exist. There are several problems with this objection. First, "belief" in GOD is not relevant; what is relevant is whether GOD actually exists. Second, belief in atheism is also associated with one's environment, and therefore, this reasoning would also conclude one that atheism is probably false. Finally, and most importantly, showing how one comes to belief in something, does not proof nor disproof that belief, since that would be the genetic fallacy.
MANY GODS ARGUMENT
The main argument
The main argument goes as follows. There is an extraordinaire long list of gods, mostly polytheistic gods. If one accepts one religion, one often has to deny many other religions. But the prior probability of the existence of one particular God, in light of, or rather conditioned upon, the non-existence of all (or at least most) other Gods, is of course very low. After all, if consistently Gods are either assumed or proven to be non-existing, than probably the next and last God is also going to be assumed or proven to be non-existing. In other words: he probability of all gods being non-existent, but this one GOD being the one exception, is a-priori incredibly low. Or so the argument goes.
There are several problems with this argument.
Problem 1 - Polytheistic "Gods" are hardly comparable to any monotheistic God:
The first (and by far the most obvious) problem with this argument is that the vast majority of Gods in the list of all Gods in history, are mostly polytheistic "Gods", not monotheistic. These are not the same – in fact, the very word “GOD” means something entirely different in polytheism than in monotheism. Here are some very, very obvious differences between "God" in monotheism VS polytheism:
1) In monotheism, GOD is the supreme perfect being, and therefore (by logical necessity) unchanging. Polytheism is in essence a belief in a mythological system. I am using “mythology” here in the historical sense of the word: essentially the the tales of the "lives" of these polytheistic "Gods". Thus in polytheism, gods are intrinsically changing, and have very human-like interactions with each other.
2) In monotheism, GOD is unique and everlasting (neither born nor kill-able). Therefore, Apotheosis (= a human becoming a true Polytheistic God) and Theogony (=tales of the births of Gods) are both logically incoherent concepts in monotheism. In Polytheistic religions, however, Theogony and Apotheosis are both fairly common.
3) In monotheism, GOD cannot truly die, as that is logically incoherent (yes, I'm looking at you Christians). In polytheism, "Gods" actually dying or even being murdered is actually quite common in polytheistic religions.
4) In monotheism, GOD is, in essence, "unlimited" and as such cannot be hurt, subjugated, raped, or anything like it, as these things are (again) strictly logically incoherent for a Monotheistic God. In polytheism, however, "Gods" ARE limited, and therefore polytheistic "Gods" being hurt, raped (yes, rape as in sexual abuse) and so on is actually quite common in polytheistic religions. I hope the extreme difference here between monotheism and polytheism isn't lost to the reader.
5) In monotheism, GOD, at least in its most fundamental essence, is defined as the greatest possible being. As a consequence, one often argues, that means that any superior rules, like the Laws of Logic, and the Laws of Ethics, are by necessity equal to GOD Himself (or Itself, whatever one might prefer). In polytheism, on the other hand, the "Gods"are not the greatest, as they are almost always subject to (what the historian of religion Yehezqel Kaufman called) "Meta-Divine Realm" (or "Primordial Realm"). Sometimes this subjugation is explicit sometimes it is more subtle and implicit. This Meta-Divine Realm is (usually) both prior and superior to the polytheistic "Gods", and constitutes both the realm in and the rules by which the polytheistic "Gods" live by and interact with each other. But the polytheistic Gods are always inferior to this Realm, never equatable with the Meta-Divine Realm.
6) In monotheism, GOD is consistent (or at least claimed to be consistent) in all of His (or "Its") ways. Polytheistic religion have no problem with Gods being explicitly opposites to one another.: morally good, morally evil, and morally ambiguous "Gods", all contradictory forces ruling the same universe.
7) In Monotheism, GOD is a single supreme God of ALL. By logical necessity, polytheistic Gods are NOT supremen entities. To understand this, consider the following. Suppose 2 polytheistic "supreme" Gods, lets call them God A and God B, have a disagreement about how the universe should be. What happens if they have a disagreement? If A gets its way, than A is apparently (at least sometimes) superior. If B gets its way, than B is apparently (at least sometimes) superior. If a comprise is made between the wishes between A and B (so far as that is possible), than neither are superior. If neither A nor B gets their way, than neither are clearly superior. Finally, if A and B necessarily always want, act, and think the same way, and thus never have a disagreement, than A and B are essentially one entity (kind of like the weird "trinity" concept in Christianity), which forces A and B to merge as a single monotheistic GOD, and all the logically necessary constraints that come with it. Thus, at least (somewhar) internally consistent polytheisytic religions, these polytheistic "Gods" are generally personifications of natural forces/elements (i.e. the storm, the sea, the woods, etc.) and/or social constructs (i.e. war, love, deception, etc.). Even polytheistic religion that has some kind of "superior God", is itself a personification of one or a few particular natural forces/elements and/or social constructs, but not a GOD of all.
So, considering the above 7 points, clearly, the very core philosophical worldview is fundamentally different between polytheism and monotheism. Notice, however, that there are indeed great practical and historical overlaps in polytheism in monotheism: many polytheistic religions have similar stories (i.e. about creation, life after death, even a flood, and so on), and similar practices (animal sacrifices, praying, keeping idles, etc.). But practical similarity does not equal philosophical similarity, and it is the philosophical that is relevant here.
So what's the point? Well, since polytheistic "Gods" are so very appreciably different from monotheistic Gods, they cannot be compared with each other so lazily. Saying that a monotheistic God does not exist because all polytheistic "Gods" probably do not exist, is like saying that all sightings of a new particular species of insects are probably fallacious because all sightings of post-mortem Elvis Presley are probably false. After all, these Elvis sightings may be improperly founded, but what do Elvis sightings have got to do with sightings of a species of insects?? Exactly: they are incomparable.
PS: Yale University has an excellent Introductory course of Old Testament history which also goes into the details on monotheism VS polytheism in the history of Judaism. You might want to check it out.
Problem 2 - there is a serious limitation to the variations of logically consistent monotheistic Gods one can make:
Let’s suppose, for the sake of the argument, that there would be many, many monotheistic religions. Would that matter? Barely: the monotheistic concept of GOD brings with it some philosophical necessary properties, or limitations, of what kind of GOD this would be. Religions that deny these necessities are inherently contradictory. So even with many monotheistic religions, the variations of its monotheistic Gods are quite limited. And if that's the case, the statistical correlation between all of these monotheistic Gods would be high, and thus one cannot simply make the simple prior probability for one specific God to be equal to 1/N (with N being the number of monotheistic religions).
Conclusion:
Thus, the problem with this non-theistic (or semi- atheistic) argument is that it treats monotheistic and polytheistic GODs equally, even though they are different. If, however, one accepts contemporary mainstream history of religion, only the GOD of the monotheistic religions remain. Of those monotheistic religions only those that are inherently logically consistent remain. And monotheistic religions that are logically consistent, will be philosophically almost equivalent (even if the rituals, traditions, and history differ greatly) And so the number of clearly different monotheistic Gods becomes a very, very low number (1 or 2, perhaps).
Therefore, the prior-probability of the existent of a monotheistic GOD VS the non-existence of a monotheistic GOD, although possibly low, is not lowered even more by the disproval of many polytheistic gods.