Rescuing Logic From the Abuse of Bayes’ Theorem: Validity, Soundness, and Probability

By R.N. Carmona

In recent years, there has been a surge in the use of Bayes’ Theorem with the intention of bolstering this or that argument. This has resulted in an abject misuse or abuse of Bayes’ Theorem as a tool. It has also resulted in an incapacity to filter out bias in the context of some debates, e.g. theism and naturalism. Participants in these debates, on all sides, betray a tendency to inflate their prior probabilities in accordance with their unmerited epistemic certainty in either a presupposition or key premise of one of their arguments. The prophylactic, to my mind, is found in a retreat to the basics of logic and reasoning.

An Overview on Validity

Validity, for instance, is more involved than some people realize. It is not enough for an argument to appear to have logical form. An analysis of whether it, in fact, has logical form is a task that is seldom undertaken. When people think of validity, something like the following comes to mind: “A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid” (NA. Validity and Soundness. Internet Encyclopedia of Philosophy. ND. Web.).

Kelley, however, gives us rules to go by:

1. In a valid syllogism, the middle term must be distributed in at least one of the premises
2. If either of the terms in the conclusion is distributed, it must be distributed in the premise in which it occurs
3. No valid syllogism can have two negative premises
4. If either premise of a valid syllogism is negative, the conclusion must be negative; and if the conclusion is negative, one premise must be negative
5. If the conclusion is particular, one premise must be particular (Kelley, D.. The Art of Reasoning. WW Norton & Co. 2013. Print. 243-249)

With respect to the first rule, any argument that does not adhere to it commits the fallacy of undistributed middle. Logically, if we take Modus Ponens to be a substitute for a hypothetical syllogism, then undistributed middle is akin to affirming the consequent. Consider the following invalid form:

All P are Q.

All R are P.

∴ All R are Q.

When affirming the consequent, one is saying Q ⊃ P. It is not surprising that these two fallacies are so closely related because both are illegitimate transformations of valid argument forms. We want to say that since all P are Q and all R are P, therefore all R are Q in much the same way we want to infer that P ⊃ Q. Consider the well-known Kalam Cosmological Argument. No one on both sides questions the validity of the argument because validity, for many of us, is met when the conclusion follows from the premises. However, one can ask whether the argument adheres to Kelley’s rules. If one were to analyze the argument closely enough, it is very arguable that the argument violates Kelley’s fourth rule. The issue is that it takes transposing from the fifth rule to fourth rule because the argument does not violate the fifth and therefore, appears valid. However, when restated under the fourth rule, the problem becomes obvious. In other words, the universe is a particular in both Craig’s conclusion and in the second premise of his argument. Let’s consider the KCA restated under the fourth rule:

There are no things that are uncaused.

There is no universe that is uncaused.

∴ All universes have a cause.

Restating it this way appears controversial only because the argument seems to presuppose that there is more than one universe. Two negatives must have properties in common. Put another way, since there are many of all things, then the universe cannot be the only thing of its kind, if we even agree that the universe is like ordinary entities at all. Craig, perhaps unintentionally, attempts to get a universal from a particular, as his argument restated under the fourth rule shows. Given this, we come to the startling conclusion that Craig’s KCA is invalid. Analyses of this kind are extremely rare in debates because most participants do not know or have forgotten the rules of validity. No amount of complexity hides a violation of basic principles. The advent of analytic philosophy with Bertrand and Moore led to an increasing complexity in arguments and for the most part, validity is respected. As shown here, this is not always the case, so a cursory analysis should always be done at the start.

Validity is necessary but not sufficient for an argument to prove effective and persuasive. This is why arguments themselves cannot substitute for or amount to evidence. Soundness is determined by taking a full account of the evidence with respect to the argument. The soundness of an argument is established given that the pertinent evidence supports it; otherwise, the argument is unsound. Let us turn to some simple examples to start.

An Overview of Soundness

“A deductive argument is sound if and only if it is both valid, and all of its premises are actually true. Otherwise, a deductive argument is unsound” (Ibid.).

All ducks are birds.

Larry is a duck.

∴ Larry is a bird.

This argument is stated under Kelley’s fifth rule and is no doubt valid. Now, whether or not the argument is sound will have us looking for external verification. We might say that, a priori, we know that there are no ducks that are not birds. By definition, a duck is a kind of bird. All well and good. There is still the question of whether there is a duck named Larry. This is also setting aside the legitimacy of a priori knowledge because, to my mind, normal cognitive function is necessary to apprehend human languages and to comprehend the litany of predicates that follow from these languages. We know that ducks are birds a posteriori, but on this point I digress. Consider, instead, the following argument.

All ducks are mammals.

Larry is a duck.

∴ Larry is a mammal.

This argument, like the previous one, is valid and in accordance with Kelley’s fifth rule. However, it is unsound. This harkens back to the notion that ducks belonging to the domain of birds is not a piece of a priori knowledge. Despite knowing that all ducks are birds, the differences between birds and mammals are not at all obvious. That is perhaps the underlying issue, a question of how identity is arrived at, in particular the failure of the essentialist program to capture what a thing is. The differentialist program would have us identify a thing by pinning down what it is not. It follows that we know ducks are birds because anatomically and genetically, ducks do not have the signatures of mammals or any other phylum for that matter. A deeper knowledge of taxonomy is required to firmly establish that ducks are, in fact, birds.

An exploration of soundness is much more challenging when analyzing metaphysically laden premises. Consider, for example, the second premise of the KCA: “The universe began to exist.” What exactly does it mean for anything to begin to exist? This question has posed more problems than solutions in the literature; for our purposes, it is not necessary to summarize that here. We can say of a Vizio 50-inch plasma screen television that it began to exist in some warehouse; in other words, there is a given point in time where a functioning television was manufactured and sold to someone. The start of a living organism’s life is also relatively easy to identify. However, mapping these intuitions onto the universe gets us nowhere because as I alluded to earlier, the universe is unlike ordinary entities. This is why the KCA has not been able to escape the charge of fallacy of composition. All ordinary entities we know of, from chairs to cars to elephants to human beings exist within the universe. They are, as it were, the parts that comprise the universe. It does not follow that because it is probable that all ordinary things begin to exist that the universe must have begun to exist.

This is a perfect segue into probability. Again, since Bayes’ Theorem is admittedly complex and not something that is easily handled even by skilled analytic philosophers, a return to the basics is in order. I will assume that the rule of distribution applies to basic arguments; this will turn out to be fairer to all arguments because treating premises as distinct events greatly reduces the chances of a given argument being true. I will demonstrate how this filters out bias in our arguments and imposes on us the need to strictly analyze arguments.

Using Basic Probability to Assess Arguments

Let us state the KCA plainly:

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

The universe began to exist.

∴ The universe has a cause for its existence.

As aforementioned, the first premise of the KCA is metaphysically laden. It is, at best, indeterminable because it is an inductive premise; all it takes is just one entity within the universe to throw the entire argument into the fire. To be fair, we can only assign a probability of .5 for this argument being true. We can then use distribution to get the probability of the argument being sound, so since we have a .5 probability of the first premise being sound, and given that we accept that the argument is not in violation of Kelley’s rules, we can therefore distribute this probability across one other premise and arrive at the conclusion that the argument has a 50% chance of being true.

This is preferable to treating each premise as an isolated event; I am being charitable to all arguers by assuming they have properly distributed their middles. Despite this, a slightly different convention might have to be adopted to assess the initial probability of an argument with multiple premises. An argument with six individual premises has a 1.56% chance of being true, i.e. .5^6. This convention would be adopted because we want a probability between 0 and 100. If we use the same convention used for simpler arguments with less premises, then an argument with six premises would have a 300% chance of being true. An arguer can then arbitrarily increase the amount of premises in his argument to boost the probability of his argument being true. Intuitively, an argument with multiple premises has a greater chance of being false; the second convention, at least, shows this while the first clearly does not. The jury is still out on whether the second convention is fair enough to more complex arguments. There is still the option of following standard practice and isolating an individual premise to see if it holds up to scrutiny. Probabilities do not need to be used uniformly; they should be used to make clear our collective epistemic uncertainty about something, i.e., to filter out dogma.

Let us recall my negation strategy and offer the anti-Kalam:

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

The universe did not begin to exist.

∴ The universe does not have a cause.

Despite my naturalistic/atheistic leanings, the probability of my argument is also .5 because Craig and I share premise 1. The distribution of that probability into the next premise does not change because my second premise is a negation of his second premise. In one simple demonstration, it should become obvious why using basic probabilities is preferable over the use of Bayes’ Theorem. No matter one’s motivations or biases, one cannot grossly overstate priors or assign a probability much higher than .5 for metaphysically laden premises that are not easily established. We cannot even begin to apply the notion of a priori knowledge to the first premise of the KCA. We can take Larry being a bird as obvious, but we cannot take as obvious that the universe, like all things within it, began to exist and therefore, has a cause.

Now, a final question remains: how exactly does the probability of an argument being sound increase? Probability increases in accordance with the evidence. For the KCA to prove sound, a full exploration of evidence from cosmology is needed. A proponent of the KCA cannot dismiss four-dimensional black holes, white holes, a cyclic universe, eternal inflation, and any theory not in keeping with his predilections. That being the case, his argument becomes one based on presupposition and is therefore, circular. A full account of the evidence available in cosmology actually cuts sharply against the arteries of the KCA and therefore, greatly reduces the probability of it being sound. Conversely, it increases the probability of an argument like the Anti-Kalam being true. The use of basic probability is so parsimonious that the percentage decrease of the Kalam being sound mirrors the percentage increase of the Anti-Kalam being sound. In other words, the percentage decrease of any argument proving sound mirrors the percentage increase of its alternative(s) proving true. So if a full account of cosmological evidence lowers the probability of the Kalam being sound by 60%, the Anti-Kalam’s probability of being true increases by 60%. In other words, the Kalam would now have a 20% probability of being true while its opposite would now have an 80% of being true.

Then, if a Bayesian theorist is not yet satisfied, he can keep all priors neutral and plug in probabilities that were fairly assessed to compare a target argument to its alternatives. Even more to the point regarding fairness, rather than making a favored argument the target of analysis, the Bayesian theorist can make an opponent’s argument the target of analysis. It would follow that their opponent’s favored argument has a low probability of being true, given a more basic analysis that filters out bias and a systematic heuristic like the one I have offered. It is free of human emotion or more accurately, devotion to any given dogma. It also further qualifies the significance of taking evidence seriously. This also lends much credence to the conclusion that arguments themselves are not evidence. If that were the case, logically valid and unsound arguments would be admissible as evidence. How would we be able to determine whether one argument or another is true if the arguments themselves serve as evidence? We would essentially regard arguments as self-evident or tautologous. They would be presuppositionalist in nature and viciously circular. All beliefs would be equal. This, thankfully, is not the case.

Ultimately, my interest here has been a brief exploration into a fairer way to assess competing arguments. All of this stems from a deep disappointment in the abuse of Bayes’ Theorem; everyone is inflating their priors and no progress will be made if that continues to be permitted. A more detailed overview of Bayes’ Theorem is not necessary for such purposes and would likely scare away even some readers versed in analytic philosophy and more advanced logic. My interest, as always, is in communicating philosophy to the uninitiated in a way that is approachable and intelligible. At any rate, a return to the basics should be in order. Arguments should continue to be assessed; validity and soundness must be met. Where soundness proves difficult to come by, a fair initial probability must be applied to all arguments. Then, all pertinent evidence must be accounted for and the consequences the evidence presents for a given argument must be absorbed and accepted. Where amending of the argument is possible, the argument should be restructured, to the best of the arguer’s ability, in a way that demonstrates recognition of what the evidence entails. This may sound like a lot to ask, but the pursuit of truth is an arduous journey, not an easy endeavor by any stretch. Anyone who takes the pursuit seriously would go to great lengths to increase the epistemic certainty of his views. All else is folly.

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 that begins to exist has a cause.

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 is 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.” In any case, 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.

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:

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.

A Refutation of Weaver’s “An Objection to Naturalism and Atheism from Logic”

By R.N. Carmona

Weaver’s argument, although robust, commits what I think is a cardinal sin in philosophy: “An objection from logical considerations against atheism is one which attempts to show that some deliverance of logic is at odds with atheism or something strictly implied by atheism” (Weaver, C.G. (2019). Logical Objections to Atheism. In A Companion to Atheism and Philosophy, G. Oppy (Ed.). https://doi.org/10.1002/9781119119302.ch30). One should not get in the habit of drawing ontological conclusions on the basis of logical considerations and though Weaver makes a good attempt to justify his conclusion, there are too many areas in his composite argument that are vulnerable to attack. There are parts of his composite argument that are clearly stated in his own words, but other parts have to be sifted out from his discussions, specifically on logical monism and classical logical consequence (CLC). Also, the conclusion that atheism is false has to be gathered from his discussion following his claim that ontological naturalism is false.

A general note, prior to proceeding, is in order. Weaver’s paper is quite technical and not at all easy for the untrained eye to read, let alone understand, so I will endeavor to avoid technicality wherever necessary; I will only permit pursuing one technical element because I disagree with Weaver’s treatment of supervenience, how he conveniently begs the question regarding reductionist materialism (if only to ensure that his argument is not met with immediate difficulty), and the conclusion he believes follows. More importantly, I think that the domestication of philosophy within the ivory towers of academia was a critical misstep that needs to be rectified. While analytic philosophy has its use, its abuse makes philosophy the slave of academic elites and therefore, keeps it well out of the reach of ordinary people. Philosophy, therefore, if it is to be understood by laypeople, needs to be communicated in ordinary, relatable language. Since my interest is to, first and foremost, communicate philosophy in an approachable way, I tend to avoid technicalities as much as possible. With that said, it is not at all necessary to quibble with Weaver’s logical proofs of validity (especially because validity matters much less than soundness) or Williamson’s notion that contingentist statements can be mapped onto necessitist ones and vice versa, but that “The asymmetry favours necessitism. Every distinction contingentists can draw has a working equivalent in neutral terms, but the extra commitments of necessitism allow one to draw genuine distinctions which have no working equivalents in neutral terms. If one wants to draw those distinctions, one may have to be a necessitist” (Williamson, T.. “Necessitism, Contingentism, and Plural Quantification.” Mind 119 (2010): 657-748. 86. Web.).

Williamson and Weaver, following his cue, are both guilty of ignoring logical atomism, so ultimately, it does not matter if the validity of logical statements suggests that necessitism about mere propositions is probably true because ultimately, we are not talking about mere propositions but rather Sachverhalte, “conglomerations of objects combined with a definite structure” (Klement, Kevin, “Russell’s Logical Atomism”The Stanford Encyclopedia of Philosophy (Spring 2020 Edition), Edward N. Zalta (ed.)). This is perhaps Weaver’s motivation for dismissing Carnap who was anti-metaphysical. It can be argued, therefore, that reinstating metaphysics or overstating its importance is necessary for any argument against naturalism and/or atheism or conversely, for Theism, to get any traction. The fact remains, however, that propositions comprising a sound logical argument are dependent on real world experiences via the senses. The proposition “there is a cat” may speak to the fact that either i) one believes they have seen a cat in whatever space they find themselves in ii) one knows and can confirm that there is a cat in their vicinity iii) there is presently a cat within ones field of vision. While I grant that propositions can speak to entirely imaginary or, at least, hypothetical entities, all propositions rely on entities we have identified in our common tongue. Therefore, statements like “there is a cat” will always rely on content not necessarily entailed within a given proposition. There is still a question as to the context of such propositions and the preciseness of what one is trying to say.

Weaver’s Composite Argument Against Naturalism and Atheism, and Its Problems

With these preliminary concerns in our rearview, I can now turn to Weaver’s composite argument and provide a few avenues for the atheist to refute his argument.

W1 Since situationspf do not exist (“I will therefore be entitled to reject…the existence of situationsPF” (Weaver, 6).), situationsC exist.

W2 Given situationsC , classical logical consequence (CLC) is the case.

W3 From W2, necessitism is true.

W4 “If necessitism is true, then ontological naturalism is false.”

W5 “Necessitism is true.”

W6 “Therefore, ontological naturalism is false” (Weaver, 15).

W7 From W6, “Necessitism is true and modal properties are indispensable to our best physical theories.”

W8 If W7, “then there is a new phenomenon of coordination (NPC).”

W9 “Necessarily, (if there is an NPC, it has an explanation).”

W10 “Necessarily, [if possibly both (atheism is true and there is an NPC), then it is not possible that the NPC has an explanation]”

C “Therefore, atheism is false” (Weaver, 18).

Setting aside that Weaver assumes that suitably precisified situations (situationspf) cannot exist and the problems he would face if just one instance of such a situation does exist, there is a way to show that even on the assumption that just classically precisified situations (situationsC) exist, it doesn’t follow that CLC holds. Weaver seems to think that CLC follows from a schema concerning mere validity: “A deductive argument is valid, just in case, there is no situation in which the premises are true and the conclusion false” (Weaver, 4). I think it is straightforwardly obvious that a typical non sequitur already violates this schema. Consider the following:

P1 If it is cloudy outside, there is a chance of precipitation.

P2 It is cloudy outside.

C Therefore, the Yankee game will be postponed.

The first two premises are true perspectively. In New York City, at this present hour, it is partly cloudy outside and there is thus, a chance of precipitation. However, the conclusion is false because the New York Yankees are not even in Spring training and it is out of the norm for them to have a regular season home game in late January. The above argument can prove true given not only at least one extra premise, but also the fact that it is not winter but spring, and that the MLB regular season is underway. This goes a long way in showing that propositions are usually missing crucial content and are true given specified context. Perhaps, then, Weaver should provide a different schema to ground CLC.

Weaver, unfortunately, does not give an adequate account of what he means by situationspf and what such situations would look like. It is enough to reiterate that the existence of even one such situation takes him back to square one. This is aside from the fact that a rejection of pluralism entails a rejection of arguments operating outside of classical logic, e.g., Plantinga’s Modal Ontological Argument, which rests of the axioms of S5 modal logic. A thorough rejection of free logical systems would limit Theists to the domain of classical logic, which will prove unforgiving since nothing like God seems operative in the real world.

Weaver’s dependence on situationsC and CLC proves problematic and is one place for an atheist to focus on. Another avenue for an atheist to take is W4 and W5. Is the notion that ontological naturalism is false conditional on necessitism being true? I do not think Weaver established that this premise is true. Furthermore, aside from exploring whether these clauses have a conditional relationship, one can simply ask whether necessitism is true. The jury is still out on whether necessitism or contingentism is the case, and there may yet be a synthesis or a handful of alternative positions that challenge both. Given the current state of the debate, I am uncommitted to either position, but I am suspicious of anyone siding with one for sake of attempting to disprove a position they already assume is false, which, in Weaver’s case, are naturalism and atheism.

In plain language, the perspective of necessitists falls flat or appears to be saying something nonsensical. Williamson outlines where disagreement lies:

For instance, a contingentist typically holds that it is contingent that there is the Thames: there could have been no such river, and in those circumstances there would have been no Thames. By contrast, a necessitist typically holds that it is necessary that there is the Thames: there could have been no such river, but in those circumstances there would still have been the Thames, a non-river located nowhere that could have been a river located in England. Thus the contingentist will insist that necessarily if there is the Thames it is a river, while the necessitist allows at most that necessarily if the Thames is located somewhere it is a river.

Williamson, T.. “Necessitism, Contingentism, and Plural Quantification.” Mind 119 (2010): 657-748. 9. Web.

Contingentists deny the necessity of the Thames, whether river or not. These identity discussions extend further when one considers people. Manuel Pérez Otero explores this and tries to synthesize these two opposing point of views (see Otero, Manuel Pérez. “Contingentism about Individuals and Higher-Order Necessitism.” Theoria: An International Journal for Theory, History and Foundations of Science, vol. 28, no. 3(78), 2013, pp. 393–406. JSTOR, http://www.jstor.org/stable/23926328. Accessed 25 Jan. 2021.). Though Otero’s synthesis is tangential for our purposes, it shows that this binary Weaver thinks exists is one of his own making, essentially a false dichotomy. Given the issues necessitism presents for ordinary language, and the likelihood of one of its alternatives being true, it follows that necessitism is probably false. An exhaustive defense of a position I am not committed to is not at all required to show where Weaver has gone wrong.

This takes us to Weaver’s treatment of supervenience and his New Phenomenon of Coordination (NPC), which states:

Why is it that modal properties and notions enter the verisimilitudinous fundamental dynamical laws of our best and most empirically successful physical theories given that modal properties do not weakly supervene upon the physical or material? (or) How is it that the material world came to be ordered in such a way that it evolves in a manner that is best captured by modally laden physical theorizing or dynamical laws given that modal properties do not even weakly supervene upon the material and non-modal? (Weaver, 17)

If necessitism is probably false, then ontological naturalism still has a chance of being true. This is despite the fact that Weaver failed to show that the falsity of ontological naturalism is conditional on necessitism being true. A stronger route for him to have took is to argue that ontological naturalism is false iff necessitism is true because even if turns out that necessitism is true, ontological naturalism can also be true. Weaver has not established that they are mutually exclusive. Therefore, an atheist can feel no pressure at all when confronted with NPC. This is setting aside that Weaver appears to be undisturbed by the incongruity of our scientific and manifest images. One would think a reconciliation is required before proclaiming that the material world is organized via modally laden physical theories and dynamic laws that supervene, whether strongly or weakly, on the material world.

The primary issue with Weaver’s assessment is the assumption that all atheists must be committed to reductionist materialism or physicalism to be a consistent ontological naturalist. There are alternative naturalisms that easily circumvent Weaver’s NPC because such a naturalist would not be committed to any version of supervenience. As an example, this naturalist can hold, to put it as simply as possible, that scientific theories and models are merely representations. Therefore, the modality of scientific theories need not supervene on the material world at all. Given a representationalist account of scientific theories, perhaps something like a reverse supervenience is the case.

∎∀𝑥∀𝑦(∀𝐹 𝐹𝑥 ≡ 𝐹𝑦 ⟶ ∎∀R R𝑥 ≡ R𝑦 )

Necessarily for any entity and for any entity y, [(if for any material property F, (has F, just in case, has F), then necessarily, for any representational property M, (has M, just in case, has M)].

Scientific theories and models are, in other words, more akin to impressionist paintings than a group of modally laden propositions. This is a more commonsense view in that a scientific model is a portrait of the real world. While there is a feedback between the model and the material world, in that theories have to be tested against reality, theories and models are not conceived in a vacuum. Real world observations impose the postulates of a theory or render a portrait that we call a model. Ptolemy misconstrued planetary orbits and attributed their motions to invisible spheres rather than the ellipses we are familiar with. He was not far off the mark, especially given that there is an intangible involved, namely gravity, but his impression was inexact. This is what a representationalist account of scientific theories would look like and whether something like reverse supervenience is necessary does no real harm to the account.

The last route atheists can take is in Weaver’s conflation of atheism and naturalism. Though I am sympathetic to the conflation, like Nielsen, who stated, “Naturalism, where consistent, is an atheism” (Nielsen, Kai. Naturalism and Religion. Amherst, N.Y.: Prometheus, 2001. 30. Print.), the same need not apply in vice versa. In other words, the following statement need not be the case: “atheism, where consistent, is a naturalism.” While I am also partial to that statement, even going as far as defending it in Philosophical Atheism: Counter Apologetics and Arguments For Atheism, that gods do not exist does not entail that no immaterial beings can exist. It could be the case that no iteration of god exists, but that ghosts do. Weaver’s conflation seems to rest on the assumption that naturalism is the antithesis of supernaturalism. Naturalism is also opposed to paranormal phenomena, so there can be defeaters of naturalism that are not also defeaters of atheism. In other words, a definitive proof of the paranormal does not debase the thesis that gods do not exist. A definitive proof of one’s great grandma roaming the estate does not imply that God or any other god undeniably exists. Nielsen’s statement implies only that a disproof of atheism is also a disproof of naturalism, but this does not work in the other direction.

Ultimately, in light of the composite argument above, one that I think is true to Weaver’s overall argument, fails to disprove ontological naturalism and atheism. There is far too much controversy in a number of places throughout his argument to regard it as convincing. The argument needs to be critically amended or entirely abandoned because in its present form, it does not meet its end. My rebuttal provides fertile ground for further exploration with respect to necessitism, contigentism, and any possible syntheses or alternatives, in addition to what is required to contradict naturalism and atheism. God, whether the idea Theist philosophers defend, or a more common concept tied to a particular religion, is still resolutely resigned to silence, hiddenness, and outright indifference. Therefore, Theists have their own onus that must go beyond even a successful argument against naturalism and/or atheism.

Problems With Pruss’ Argument For An Omniscient Being

By R.N. Carmona

What follows is Alexander Pruss’ Argument For An Omniscient Being. While he does not exactly give his argument a ringing endorsement, admitting that he is skeptical of the first two premises, there are other problems that elude him and any theist who believes that omniscience is possible. Pruss formulates the argument as follows:

1. The analytic/synthetic distinction between truths is the same as the a priori / a posteriori distinction.

2. The analytic/synthetic distinction between truths makes sense.

3. If 1 and 2, then every truth is knowable.

4. So, every truth is knowable. (1–3)

5. If every truth is knowable, then every truth is known.

6. So, every truth is known. (4–5)

7. If every truth is known, there is an omniscient being.

8. So, there is an omniscient being. (6–7)

Pruss, Alexander. “An odd argument for an omniscient being”. Alexander Pruss Blog. 2 Nov 2020. Web.

In my new book “The Definitive Case Against Christianity: Life After The Death Of God,” I state the following:

God’s belief in propositions has to change in accordance with migrating facts. While it is true that the Sun is currently one astronomical unit away, that will not always be the case. At every moment when the Sun begins to expand during its Red Giant phase, the distance between the Earth and the Sun will gradually decrease until the Sun ultimately ends all life on our planet, if not disintegrating it entirely. At each moment, it will be incumbent on God to update his knowledge by changing his prior beliefs concerning the distance between these two bodies. It is prerequisite for facts to be fixed in order for God to be immutable. Since facts are not fixed, his beliefs and corresponding propositions about any given state of affairs have to change — otherwise he fails to be omniscient. (193)

A Christian might assert that there is a simple solution to the issue I have raised: God is also omnipresent. The issue with this objection is that God’s perspectives would be in direct contradiction with one another and so, from the perspective of other sentient beings, he would regard two logically contradictory propositions as true. From our perspective, he would believe in a truth and a lie, namely that from Earth, there is a supernova two million lightyears away, but in Andromeda, there is no longer a supernova to speak of. In other words, since the light from this event took two million years to reach humans on Earth, humans are just now learning of this supernova in Andromeda whereas an intelligent species on a planet relatively near to the event in Andromeda would report no supernova at that location. Perhaps it happened long before they emerged or before they were advanced enough to observe, record, and describe such an event. The fact remains that their present does not feature this supernova event while ours does.

Another fun example from theoretical physics involves watching someone falling into a black hole. The following is a summary of the relativistic experiences the observer and the faller would have:

1. The light coming from the person gets redshifted; they’ll start to take on a redder hue and then, eventually, will require infrared, microwave, and then radio “vision” to see.

2. The speed at which they appear to fall in will get asymptotically slow; they will appear to fall in towards the event horizon at a slower and slower speed, never quite reaching it.

3. The amount of light coming from them gets less and less. In addition to getting redder, they also will appear dimmer, even if they emit their own source of light!

4. The person falling in notices no difference in how time passes or how light appears to them. They would continue to fall in to the black hole and cross the event horizon as though nothing happened.

“Falling Into a Black Hole Sucks!”. ScienceBlogs. 20 Nov 2009. Web.

God’s omnipresence, therefore, fails to solve the issue because in order for him to have all possible perspectives, he would have to hold contradictory propositions on pretty much any and all events in our universe. He would have our perspective in the Milky Way as well as the point of view of the Andromeda galaxy’s civilization. He would also have the perspectives of the observer and the faller in our black hole example. The glaring issue is that he would have these perspectives at the same time and in the same respect, thus resulting in contradictions. Perhaps one can still find a way to try and circumvent these issues.

Given the idea that a day is as a thousand years and vice versa for God (2 Peter 3:8), if he, for sake of argument, experiences time-laden events in God-days (equivalent to one human millennium) or even all at once, God would make entirely different claims from the ones we believe to be knowable. In other words, while we are discussing here and now, before and after, duration, and the such, God would state something like the following: “all of the people, places, events, etc. that existed from the first century through the tenth century CE existed simultaneously.” For us, this is unlike propositions we believe are knowable, indeed nonsensical. God, therefore, being a timeless being cannot know anything about time-laden truths. It would be incumbent on him to not be timeless, but then, he is immediately confronted with the relativity of experience in the physical universe.

More importantly, 5 is debatable despite Fitch’s Knowability Paradox. Pruss states: “The argument for 5 is the famous knowability paradox: If p is an unknown truth, then that p is an unknown truth is a truth that cannot be known (for if someone know that p is an unknown truth, then they would thereby know that p is a truth, and then it wouldn’t be an unknown truth, and no one can’t know what isn’t so)” (Ibid.). The tendency, however, to leap from the possibility of knowing every truth to someone knowing every truth is dubious. It is similar to the leap rooted in Anselm: conceivability implies possibility. Worse still is that Pruss leaps from possibility to actuality. One should not draw ontological conclusions on the basis of logical considerations.

Pruss would appreciate an example from mathematics, namely that mathematicians work with infinity in their equations and even think of it as a real, tangible object in the universe. Unfortunately, there does not seem to be a physical correlate to infinity. Pradeep Mutalik, writing for Quanta Magazine, explains:

While “most physicists and mathematicians have become so enamored with infinity that they rarely question it,” Tegmark writes, infinity is just “an extremely convenient approximation for which we haven’t discovered convenient alternatives.” Tegmark believes that we need to discover the infinity-free equations describing the true laws of physics.

Mutalik, Pradeep. “The Infinity Puzzle”. Quanta Magazine. 16 Jun 2016. Web.

With this in mind, one can see that though mathematicians logically consider and defend the concept of infinity, one should proceed with caution in terms of stipulating that reality features anything like this concept. It follows then, that just because all truths are potentially knowable, there does not already exist a being that knows all things. Aside from the problem resulting from the relativity of truth, stemming from the relativity of space-time especially as one approaches the speed of light, there is this unjustified assumption that possibility implies actuality. In the main, possibility does not necessarily entail probability, the latter of which having to be established before concluding that something exists. Given these brief objections, one should maintain that there is no omniscient being.

Ultimately, a lot more can be said. All humans can really say about knowledge is what they experience with respect to acquiring it. As such, we would be wise to recall that we acquire knowledge first by way of awareness and conscious focus on what it is we are inquiring about. A truly omniscient being, which would be difficult to distinguish from a being who knows all things except how to play billiards or count to infinity (the conclusion of my Argument From Vagueness (see The Definitive Case Against Christianity, 194), would first and foremost have to be perfectly aware and focused for all of eternity. If this being loses focus at any point, myriad truths would have changed, progressing toward inevitable obsolescence, and new truths, that are not all related to the old truths, would have emerged. This being would therefore, have lost its claim to omniscience. This is setting aside that humans can apprehend truths intuitively, without having dedicated concentrated inquiry into a matter. Other sentient beings could have this capacity as well. In any case, the likelihood that an omniscient being exists is practically zero.

A Solution to The Infinite Regress Problem

By R.N. Carmona

The problem, as commonly framed, is that the truth of P1 is substantiated by a P2, which is then substantiated by a P3. The thought is that this goes on forever. The Infinite Regress problem resulted in foundationalism, which was motivated by the pursuit of certainty. Ross Cameron frames the problem as follows:

An infinite regress is a series of appropriately related elements with a first member but no last member, where each element leads to or generates the next in some sense. An infinite regress argument is an argument that makes appeal to an infinite regress. Usually such arguments take the form of objections to a theory, with the fact that the theory implies an infinite regress being taken to be objectionable.

Cameron, Ross. “Infinite Regress Arguments”. Stanford Encyclopedia of Philosophy. 2018. Web.

The Infinite Regress Problem is therefore, not much of a problem unless a given interlocutor decides that it is. Such an interlocutor usually makes that decision due to prejudice, an unabashed bias for their own conclusion or perspective while in other cases, the individual disagrees with an alternative explanation so much that they go out of their way to express skepticism toward this explanation to an extent that they never applied to their own. In other words, someone who is skeptical of Correspondence Theory will go as far as questioning reality, e.g. Descartes’ Evil Demon, or questioning the very existence of the person they are debating, e.g., “how do you know you’re not a brain in a vat?” This is all while ignoring that if such an evil demon is distorting reality on a whim, they too are subject to its deception and that if the person they are debating is a brain in a vat, it is far likelier that they themselves are in the same predicament.

The issue with any Infinite Regress argument is that the radical skeptic has glossed over basics in philosophy. For the skeptic’s argument to work, the onus is on him to find a premise containing necessary and sufficient conditions in relation to the premise he is skeptical of. Put another way, if I say that Correspondence Theory says nothing other than the fact that the proposition “it is snowing” holds true if, in fact, it is snowing, the interlocutor is tasked with finding a premise on which the truth of the proposition “it is snowing” rests. The fact that it is snowing is a distinct reality from my proposition, especially because I can make that claim, for whatever reason, even when it is not the case that it is snowing. I could either be off my rocker or lying, but any proposition can be proposed even when what informs the proposition is not the case. Andrew Brennan puts it this way:

The standard theory makes use of the fact that in classical logic, the truth-function “p ⊃ q” (“If pq”) is false only when p is true and q is false. The relation between “p” and “q” in this case is often referred to as material implication. On this account of “if pq”, if the conditional “p ⊃ q” is true, and p holds, then q also holds; likewise if q fails to be true, then p must also fail of truth (if the conditional as a whole is to be true). The standard theory thus claims that when the conditional “p ⊃ q” is true the truth of the consequent, “q”, is necessary for the truth of the antecedent, “p”, and the truth of the antecedent is in turn sufficient for the truth of the consequent

Brennan, Andrew. “Necessary and Sufficient Conditions”. Stanford Encyclopedia of Philosophy. 2017. Web.

If Brennan is correct, then an Infinite Regress is not, in fact, an issue no matter how much a disingenuous interlocutor says it is. An Infinite Regress is nothing more than a rebranded Slippery Slope, the termination of which is decided by a premise containing either a viable truth maker or that corresponds to reality in a noncontroversial way. Furthermore, it would be a premise that has no conditional relationship to some other premise. This premise q would not require a premise r on which the necessity of its truth is grounded. It is simply one proposition that is established by some external reality or lines of evidence that make its truth more likelier than not. This is what is meant by propositions like “evolution is true.” This conclusion is supported by lines of scientific evidence strongly suggesting that the proposition is probable. Given the advent of fallibism, what epistemologists look for are propositions that are highly probably true. They are no longer in the business of certainty. So while any true proposition has a small, usually negligible, chance of being false, one could achieve a high degree of certainty in exactly those propositions that are highly likely to be true.

Recall that to terminate a Slippery Slope, it is necessary to show that a proposed consequence will not end up being the case if a given action is taken. Opponents of same-sex unions would often say things like, “what’s next!? people marrying their dogs!?” It was easily shown that their concerns were non sequitur and thus, in similar fashion, one could do away with an Infinite Regress argument by establishing that the interlocutor has failed to find a premise r on which the truth of q rests. The onus is heavy because he is tasked with finding a premise that is necessary and sufficient in relation to the truth of q. If he cannot do so, he has admitted that the regress terminates at q and accepts justification, however begrudgingly, for why this is the case.

In general, the issue at the heart of any Infinite Regress argument is the fact that people, especially non-philosophers, tend to be disingenuous. They will concoct some ridiculous standard for any point of view that disagrees with theirs while failing to scrutinize their own views in accordance with that standard. There is no Infinite Regress. In the end, what remains is disagreement, to some degree of strength, with the justification(s) underlying certain beliefs. If, for example, someone claims that they know we are all brains in vats because a being outside of our reality told them this, then it is within my right for me to inquire about this being. Moreover, it is within my right to question this person’s sanity or at the very least, their sobriety. If this revelation was received while this person was drunk or high on a hallucinogen, then it is far likelier that their account is false. The same applies if this person has been diagnosed with a mental illness that makes hallucinations a frequent occurrence for him.

Ultimately, the nature of dialogue, especially on social media, has revealed the basest human fault: the propensity to be disingenuous. Everyone who has a bias distorts facts, omits evidence to the contrary, employs radical skepticism, and sets up an Infinite Regress problem as the standard for the opposition to reach. With respect to the latter, it is a standard that their own views have not met, despite the disingenuous interlocutor’s assertions. The Infinite Regress Problem is not a problem, but rather an argument offered by someone bent on remaining obstinately unconvinced by a position or conclusion that rubs them the wrong way. These arguments are no different from Slippery Slope arguments and terminate at the point in where you locate a proposition that is not contingent on another. This issue no longer concerns epistemologists and should be of no concern to any student of philosophy.

Arguments From Vagueness Against the So-Called God of Monotheism

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.

The Logical Failure of Divine Command Theory

I wrote the following in response to a Muslim on a New York Times opinion piece on Facebook. Everyone who discusses the actions of the Judeo-Christian and/or Muslim gods focuses far too much on the moral and legal ramifications of said actions. No one realizes that, per the theist, their god is perfectly logical. As such, the logical dimension of an action attributed to this god has to be captured. With that in mind, I offered the following.

Even if punishing children for the crimes of their parents is either moral or legal, though we haven’t apprehended that as of yet, there’s still the issue that it isn’t logical. Logic is a priori and therefore, logic for humans is logic for the god of monotheism. Just as we can’t make a round square or sided circle, neither can god. Per the philosophically inclined theist, the laws of logic, as an extension of his creative power, are part of him and as such, he can’t violate his own nature. As such, god would be perfectly logical and would thus reason perfectly, which means he wouldn’t commit logical fallacies. Given that, he wouldn’t commit an act that’s based in the fallacy of guilt by association. To punish a child for their parents crimes is exactly that! God would be finding someone guilty do to their association or more specifically, their relation to a sinner.

To my mind, this is the ultimate defeater because it should be clear that the Judeo-Christian and Muslim gods have acted on the basis of fallacious logic. It would make more sense that such actions are the actions of people who wished to attribute said actions to a god, perhaps for sake of justifying their actions and attempting to spare themselves any guilt they might have felt. Clearly, however, a perfectly logical god wouldn’t base any of its actions on fallacious logic. The doctrine of original sin, for instance, is itself based on guilt by association. So even if a Christian fails to see the moral failing in such a doctrine, they would have to concede that there’s certainly a logical failing.

As is commonplace when discussing religion, there’s always someone who will disagree, either because they’re religious or are agnostics who favor belief over non-belief. This individual contended that the soundness of informal fallacies is established a posteriori rather than a priori. He also stated that god might have written guilt into our DNA and that therefore, it is heritable. I found that both of these contentions neither change my argument nor succeed at defeating it.

The reason for this is because I don’t think that every informal fallacy’s soundness is determined a posteriori. If soundness is reached via reason, and I see no reason to add an empirical dimension to determine the soundness of an informal fallacy, then that is also a priori. Even still, however, a perfectly logical being wouldn’t reason fallaciously, let alone base his actions on fallacious reasoning. Even if inherited guilt was built into our DNA, which no empirical research has shown, there’s still a logical issue with making a child pay for their parents sins. So even if I somehow inherit the guilt of my mother’s marital infedility, that doesn’t mean that I should pay the price for her adultery.

Collective guilt, for example, is a thing. I am, for instance, ashamed of my country’s actions. I am American and at the moment and for practically my whole life, I haven’t been proud to be one. I feel guilty being a citizen of a country that murdered millions of Native Americans and stripped them of their lands, allowed slavery, incarcerated Japanese citizens in internment camps, and incarcerates rates Blacks and Latinos disproportionately in comparison to other ethnic groups — aside from the many other human rights infractions this country has committed. That, however, does not mean that I should pay the price for American crimes. While some people may be perfectly content to make me pay on the basis of guilt by association (i.e. well, he’s an American, so his arrest or death is good enough for me!), a perfectly logical being simply should not and would not be content with passing such a sentence. It isn’t logical, just, or moral, but alas, the Judeo-Christian and Muslim gods are said to behave accordingly. If a theist or an agnostic who favors theism is reluctant to admit that there are moral or legal failings in the actions of these theistic gods, they must admit that there are clear logical failings in their actions. That poses yet another problem in a long list of problems for theism.

On Challenging the Laws of Logic

R.N. Carmona

In the past, I’ve argued that the laws of logic can be challenged or even violated. A response to my post on procedural realism and the Moral Argument mentioned that the laws of excluded middle and non-contradiction have been challenged by analytic philosophers. I found it curious that there was no mention of a challenge to the law of identity, since I think it’s the most easily challenged.

In order to challenge the law of identity, one need only challenge its underlying assumption, namely essentialist ontology. “The essentialist tradition, in contrast to the tradition of differential ontology, attempts to locate the identity of any given thing in some essential properties or self-contained identities” (see here). According to modern physics, as it now stands, all objects are atoms in flux and empty space. Where then is the atomic glue that holds a table or chair together and how does one differentiate between two chairs that look precisely alike without presupposing the essentialist tradition?

The essentialist tradition begs the question when concerning identity, since there’s no way to prove that any one object has essential properties. Interestingly, the reason for presupposing the essentialist tradition might have everything to do with personal identity. People are animate objects, but objects nonetheless. Without essentialism, we can no longer assume that we have a distinct identity. Physically, we are atoms in flux and empty space as well and thus, what we’re left with are second order grounds for personal identity. In other words, we can avoid talk of atoms and empty space and instead look to DNA, neurons, brain anatomy, and so on. In this way we retain our uniqueness without first order grounds.

That aside, if we instead argue from the basis of differential ontology, the law of identity is no longer as unassailable as it appeared. As stated, we would rely on second order grounds. “Differential ontology…understands the identity of any given thing as constituted on the basis of the ever-changing nexus of relations in which it is found, and thus, identity is a secondary determination, while difference, or the constitutive relations that make up identities, is primary.” We would therefore ignore notions of a stable identity and instead look to differences between objects.

Given this, the law of identity (A = A) will be replaced with the law of distinction, i.e., something like A =/= B or C or D and so on. Since A is not B or C or D, then we identify A because it is contrasted with objects in relation to it. We are no longer assuming that there are essential properties that make A, A. This is, after all, what we say of ourselves. We do not say I am me because I have essential characteristics. Instead we contrast ourselves with others; we factor in physical appearance, ethnicity, gender, personality, and so on. We then add other factors like level of income and education, personal tastes, and so on. Clearly none of these characteristics are essential.

Ultimately, the law of identity is not unassailable and can be challenged by uprooting its essentialist assumption. One way of doing so is by positing differential ontology. One can, however, do so by positing human consciousness. In other words, another traditional philosophical assumption (contra-pragmatism) is that there’s a deeper reality that goes beyond our everyday experience; perhaps quantum mechanics hints at this. On the basis of this, we cannot draw ontological conclusions on the basis of our faculties. In other words, the four chairs and dining room table in my living room look distinct because my faculties see them as such. In reality, however, there’s nothing but atomic flux and empty space. This is in no way an attempt to undermine the usefulness of our faculties, but if there’s a deeper layer to reality that we cannot capture, then there’s no way we can argue for essential properties. Furthermore, we wouldn’t be able to argue from difference either. We would, in other words, have to assume the accuracy of our faculties in order to argue for a law of identity.