the fallacy of the linguistic paradox, or “this post is true”

In the fifth century BCE, a pagan mystic named Epimenides famously assessed that “All Cretans are liars.” This statement later became the basis of a so-called logical paradox known as “the liar paradox.” The supposed paradox is as follows:

“If Epimenides, himself a Cretan, states that ‘all Cretans are liars,’ then how can his statement be true, since he himself must be a liar as well? If we say it’s true, then it is false that all Cretans are liars, since Epimenides (a Cretan) has told the truth, and if we say that it is false, then the statement itself must be true.”

Setting aside for now the obvious problems with viewing this “paradox” as anything other than a contextual quirk of language, it took on various forms throughout history and was discussed by various thinkers.

In a modern philosphical context, the “liar paradox” is commonly illustrated with a statement similar to:

“This sentence is false.”

For certain reasons (mostly having to do with the development of Western analytical philosophy), this and similar statements have managed to bewilder philosophers and have received an inordinate amount of attention from logicians as well. As a result, entire edifices of supposedly “logical” structures have been constructed in attempt to solve the apparent conundrum.

Before presenting the solution to the above “paradox,” it is essential to review the basic principles of logic – often called the “canons of logic” – and how they are substantiated as such. The basic principles of logic are three:

1. Identity, i.e. A is A

2. Non-contradiction, i.e. A is not ~A (not-A)

3. Excluded Middle, i.e. Either A or ~A

These principles led Ayn Rand to describe logic as “the art of non-contradictory identification.”

The Law of Identity (#1), viz. that every thing “is what it is,” is a fundamental principle of metaphysics, and is based in objective reality. A rock is a rock and is not an egg. That is an objective fact of reality. No matter how much one may wish, hope, or will that a rock be an egg, it will never be possible to crack open a geode and make an omelette. This means that the validity of logic depends on its correspondence with reality. It also means that “A” (and any other variable or symbol of logical analysis) is void and meaningless without being properly representative of reality. Conversely, one cannot extrapolate facts of reality from an unrelated juxtaposition of logical symbols or variables, even if they happen to be arranged in a technically or syntactically correct fashion.

“This sentence is false” is not paradoxical precisely because it neither corresponds with nor references anything in reality. If we were, for example, to state the converse, i.e. “This sentence is true,” then we would immediately be faced with questions such as “How is it true?” and “What makes it true?” and “What is true about it?” There are no answers to these questions because simply stating something about a sentence which has no referent (i.e. no correspondence to reality) is meaningless. The same is true of “This sentence is false.” The fact that we jump to a seemingly paradoxical conclusion is simply an error of logic based on our being led astray by the word “false” contained in the phrase itself.

The only way in which “This sentence is false” could be meaningful is if it were actually referring to a sentence other than itself such as, “Dogs are a type of cat. This sentence (i.e. the preceding assertion) is false.” “Dogs are a type of cat” conveys meaning on “this sentence is false” because it references a sentence that is invalid due to its discontinuity with the facts of reality.

Those who conclude in favor of a real paradox make the mistake of constricting meaning to a simple accordance with grammatical rules. Sentences which are both grammatically correct and meaningless are abundant. For example, “These submarines are hominids” is completely meaningless yet grammatically correct.

I have only scratched the surface here, but I think the general schema of the issues as presented is clear. Perhaps I will expound on this further in another post, but suffice it to say, “This sentence is false” presents no paradox.

the end of theism

In the early 18th century, Leibniz wrote Théodicée in response to the contentions of Pierre Bayle, a French religious skeptic who, among other things, maintained that reason ultimately led one astray and that a “proof” of the insufficiency of human reason was that compelling philosophical proofs could be offered which undermined the tenets of Christianity entirely – including the persistent presence of evil.

Bayle averred that no rational defense could be made for the existence of evil vis-à-vis a Christian conception of god. Leibniz, however, disagreed and offered a defense of god’s existence, goodness, providence, and absolute perfection despite his seeming toleration of evil. In doing so, Leibniz introduced and coined the term theodicy, which has since referred to any philosophical attempt to vindicate god qua god in relation to evil and [innocent] suffering.

I have written elsewhere regarding the origins and development of religious belief from animism to monotheism, and there I stated:

“…removing the possibility of multiple deities in conflict multiplied the already existing problems for monotheism. As we have touched on previously, a singular god is either deficient or immoral (or both).”

This, in a sense, is what I refer to as the “brick wall” of monotheism, i.e. that god cannot be either all-powerful or morally good – to maintain one, one must logically give up the other.

One common attempt to get around this logical impediment (viz. the “brick wall”) is to try and conceive of god as an impersonal force (much like gravity). However, this route presents its own philosophical problems since implicit in the identification of god with such a force is the admission that it cannot be moral (otherwise there would be no need to reduce god to a force). If god is not morally good in any sense that is relevant to humans, then he cannot represent our highest ideal(s), which necessarily negates any worship of or devotion to him. In fact, if god is neither moral nor all-powerful, and represents no human ideal, then it begs the question: “What good is god?”

Other attempts to sidestep such brutal moral atrocities as the Holocaust – or any intensely gruesome event marked by human brutality – include appeals to the divine will as “mysterious.” However, if the divine will is mysterious regarding the most violent and horrendous (i.e. the most obviously immoral) of human actions, then how are we:

(a) able to claim that we understand the divine will regarding any other act, since there seems to be no prime value to anchor a moral system based on theistic beliefs, or

(b) able to look to the divine will for moral guidance in any meaningful way? If no moral guidance may be inferred from god or a belief in his existence, then what purpose can religious belief possibly serve?

This seems to be the end of theism. Any path taken in effort to solve the logical conundrums presented by monotheism only leads to contradictions, begged questions, and conclusions which directly undermine the discussion of god in the first place.

morality without god, or testing god’s goodness

In Euthyphro, one of Plato’s Five Dialogues, Socrates presents a classic dilemma concerning the nature of morality:

“Is piety loved by the gods because it is pious, or is it considered the pious because it is loved by the gods?”

The word translated as “the pious” is the Greek phrase τὸ ὅσιον, which, despite its pagan and polytheistic etymology, may easily and properly be translated for modern discussion as “the moral.” Additionally, the number of deities is not important to either the strength or nature of the question being posed by Socrates, so it, too – again, for the sake of modern discussion – may reasonably be replaced by the singular “god.”

As such, a modern restatement of the Euthyphro Dilemma might be:

If we assume that morality is inextricably linked to the existence of god or is a result of his will as expressed in religious texts, then is moral behavior loved by god because it is moral, or is it considered moral because it is loved by god?

In other words, when someone does something that is considered morally good, how does a religionist assess why it is good? Is the action taken by said person a moral action because it is considered desirable to god? Or does god desire such action because it is morally good?

The entire dilemma is focused on whether morality is something intrinsic to a divine will or extrinsic. If it is intrinsic, as many maintain (viz. “if god commands it, then it is categorically good”), does this mean that rape, genocide, slavery, or theft can be good if it is entailed by divine will? If it is extrinsic, a position which most religionists would reject, does it not imply that what is morally good should obligate god as well? And if what is morally good for human beings does not also obligate god, then how can he be said to be categorically good?

Of course, the veracity of this dilemma has been challenged throughout history by religious philosophers and theologians alike. Most, if not all, of their arguments, however, are based on an a priori belief in god and a simultaneous imputation to him of various attributes which either excuse him from the dilemma or excuse him from acting morally from a human perspective. The existence of god on its own is an untenable proposition in the light of a proper metaphysics and epistemology, and attempts to rationally defend such a belief can be made only if both are subverted to accommodate it. In fact, such subversion stems from the medieval Christian tradition of philosophy serving as the “handmaiden” of theology (i.e. the latter is subverted for the sake of the former).

What the dilemma very strongly implies is that morality is not – and cannot – be contingent on the will or existence of god. This means that despite the faith claims of, in the words of Nietzsche in Ecce Homo, “Christians and other nihilists,” it is not only possible to be moral apart from a belief in god, it is necessary to be so. The fact is, most reasonable people – even religionists – in our post-Enlightenment era regularly separate moral goodness from their belief in god, and do so almost as if from a sort of cultural instinct. Even attempts by religious believers to justify or contextualize, for example, the genocide routinely commanded by god in the Bible, is a tacit admittance that genocide is morally objectionable to the enlightened mind and its presence in the Bible is thus problematic.

I have written elsewhere about “giving god a pass” – a common (and potentially dangerous) reflex of psycho-epistemological disconnect on the part of religionists. A proper logical test for whether one should accept a particular behavior as morally good when attributed to god, is to simply replace god in the scenario with a human being. If one would not accept a given behavior or expressed moral sentiment from even the best human, then there is no basis on which to accept it from god either. Unless, of course, one is willing to admit that god is immoral (an admission that no theist can make while remaining a theist). In this way, god’s goodness may be tested for any given case and evaluated in light of ethics and moral philosophy with religious believers.

The next question is: since morality is necessarily separate from either the existence of god or religious faith, how is moral good determined or derived? And, prior to this question is: why does humanity need systems of morality or ethics in the first place? I will leave these for another time.

the origins of god, or what does belief in god do?

One of the questions posed by atheist philosophers is: “Did god create man, or did man create god?” I affirm the latter, of course, but the reason for this affirmation is due mostly to an argument from historical progression and historical context. Just to be clear, I am not referring to an argumentum ad antiquitatem (an “appeal to antiquity” or “tradition”), a common logical fallacy, but a recognition that we do know the occasion of certain ideas – including the idea of the divine.

Originally, the concept of “gods” or “spirits” were postulated by primitive man in effort to make sense of the forces of nature (viz. sunrise, sunset, wind, rain, et al) and the events which took place throughout the course of life, e.g. death, birth, illness, etc. Monotheism – belief in only one god – is actually the latest development in the human conception of the divine. The anthropological progression was as follows:

  • animism – ascribing “souls” or spiritual forces to everything, including inanimate objects.
  • polytheism – a belief in multiple gods or goddesses, usually as representatives of natural forces, animals, realms, or objects.
  • henotheism – a belief in polytheism, but a devotion or fealty to a single deity.
  • monotheism – a disbelief in polytheism; a belief in only one god.

As science and philosophy progressed, humanity began to discover the workings of nature and to highlight the logical contradictions posed by animism, polytheism, and henotheism. For a period in human history, monotheism has been the clear logical winner among the theisms, but monotheism poses its own serious logical problems. In fact, removing the possibility of multiple deities in conflict multiplied the already existing problems for monotheism. As we have touched on previously, a singular god is either deficient or immoral (or both).

Scientifically, we have attained to the knowledge that matter and energy are never created or destroyed, but merely change form (i.e. Einstein’s Conservation of Energy Principle; E = mc2). This was essentially Einstein’s mathematical confirmation of Aristotle’s original conception of the indestructible nature of the “four elements” (viz. earth, air, fire, water). Put very simply, despite the constant insistence of a “beginning,” this principle implies that the universe (i.e. the sum total of existents) is eternal. No, I am not outright denying the “Big Bang,” but I do question its exact nature in light of this absolute principle. Even Quantum Physics, which is far from sorted out, although once thought to possibly conflict with E = mc2, has now been shown to be in strict accordance with it.

Only by positing a mystical being which is capable of the absolutely impossible (i.e. creating something from “nothing”; creating and destroying energy) can one retain a belief in a god. So where did the universe “come from”? As Ayn Rand once said, just because we may not know something does not permit us to begin making things up. The ultimate origin of our eternal universe we may never be able to know (if such a concept exists in reality), but until then we can be sure that the basic metaphysical axiom which is at the the base of all else is “existence exists, and only existence exists” – excluding gods, spirits, souls, and all other supposedly supernatural entities. In the words of Victor Stenger: god is a “failed hypothesis” – i.e. to propose the existence of god is of no use whatever and serves to explain nothing.

This leads me to my next point: what does “belief” in a god do, exactly? I have met many people, usually former religionists, who are hesitant to outright deny the existence of a god. “What if he does exist?” they ask. My response is always, “Who cares if he does? What difference is your profession or denial of his existence going to make? Where did you get the idea that simply ‘believing in god’ is what connects you to him and ensures that you will not face some sort of divine reprisal? From religion, that’s where!” The proposition that disbelieving in a god which might actually exist can get you punished is an unproved and baseless claim. If we are going to believe baseless claims, there is no end to the abject nonsense we could obsess over.

But herein, I believe (pun intended), lies the key: since the idea god is a psychological projection into the dark void of human ignorance, ‘believing’ is the only tool available to keep god ‘real’ in their minds. This is why so many atheists hold onto a ‘maybe,’ however slight in their estimation.

god and proving a negative

When they can muster no positive evidence for the existence of a god, religious people will often not cede the point, but will say something like, “Okay, so it isn’t possible to prove that god exists, but you can’t prove he doesn’t exist either.” That announcement is supposed to be the magical moment where the atheist admits defeat, or is forced to concede that his “belief” in atheism is, at the very least, in equal standing with that of the religious believer. However, what such religious people don’t know is that they have just engaged in a common logical error which relies on an even more common logical fallacy.

The logical error has to do with a principle, known in Latin as onus probandi (“burden of proof”), which states that the one making a claim bears the burden for proving that claim, it is not the responsibility of the one denying the claim to disprove it. In fact, claims of “there isn’t any evidence for it, but you can’t disprove it either” are logically impossible to disprove, which is why religious people often use them in effort to keep their faith “safe” from crticism or standards of evidence. However, neglecting one’s burden of proof – or attempting to shift it to the other party – is usually the result of a logical fallacy known as argumentum ad ignorantiam (“an argument from ignorance”), in which someone holds that a claim is proven true because it has not [yet] been proven false or that a claim is false because it has not [yet] been proven true.

However, when confronted with more obvious examples of this fallacy, even religious people will readily deny wild claims for which there is no evidence, but have not been disproved. Consider the following conversation:

A. I believe that god exists.

B. What is the evidence for such a belief?

A. Well, there isn’t any direct evidence, but I feel that it must be true. Besides, you can’t prove that god doesn’t exist, so how can you say that you don’t believe that there is a god?

B. True. It is impossible to prove a negative. Do you know what I believe?

A. What?

B. I believe that beneath the atmosphere of Venus, there are unicorns mating and binge-watching episodes of “Cheers.” It’s just that the atmosphere is opaque and we can’t see them.

A. That is ridiculous.

B. Why?

A. Because there is no evidence for that at all.

B. Yes, but you can’t prove that those unicorns aren’t on Venus watching Hulu, can you?


Even the most religious person will readily object to such a claim, but in the same instance will exempt their belief in god from the same standard of proof and logical tenability.

trusting your own mind.

The following is a paraphrastic version of a conversation that I have had several times with various types of religious people.

A: It’s so obvious that god exists.

B: I disagree. I’m an atheist and I don’t believe in a god.

A: You don’t believe in a god? Why?

B: I don’t see any logical or philosophical reason to believe in the existence of a god. There’s no evidence, and I don’t operate on faith, only by the proper use of reason.

A: What? No faith? So you think you are the smartest person who ever lived? Your problem is that you trust your mind too much. How can you trust your intellect so implicitly as to come to such a narrow conclusion?

B: Okay, I’ll tell you what. You explain to me your reasoning for belief in the existence of god and when you are all finished, I will ask you one simple question.

A: Which question is that?

B: “How can you trust your intellect so implicitly as to come to such a narrow conclusion?”

A: Oh, you!

Fact is, everyone trusts their own mind. They have no choice. It is impossible to make reference to any conclusion one reaches without assuming it or making reference to it. The “technology” discovered to test the conclusions of the mind is logic, which according to Ayn Rand is “the art of non-contradictory identification.” Once logic shows the conclusion of the mind to be in full accordance with reality, it not only can be trusted, but if the human species is to perpetuate, it must be trusted.


faith claims: a war between the devil and god?

Over the years, I have found that religious people, Christians in particular, will readily and enthusiastically affirm the idea that the forces of good and evil (usually personified in “god” and “the devil,” and/or “angels” and “demons”) are locked in a constant cosmic battle with one another. Those who espouse this idea will often say that the goal and prize of such a battle is the human soul. Imagining such a battle between invisible forces is a classic religious attempt to explain the presence of evil in the world. This idea is not new, however, and represents the adoption of a central tenet of Zoroastrianism by Christianity.

My response to this contention has always been that it inevitably results in an intractable dilemma: either god is not almighty or he is immoral. The reasons for this dilemma are as follows:

If we assume that such a cosmic battle truly does take place, then we have one of two choices:

A. god is really fighting, or

B. god is merely pretending to fight.

If he is really fighting, then he cannot be almighty or all-powerful since the battle is continuous and does not always win (this, of course, is the occasion for this explanatory device in the first place). If god were all-powerful in this case, then the devil would never be able to best him, for even a single moment. For this reason, most Christians reject this option and opt to defend the second option, i.e. that god is only staging a battle at present.

If god isn’t really fighting, but only feigning a battle – allowing the devil to run amok among humanity – then he is decidedly immoral. Why immoral? Because it means that he is playing games at the expense of human suffering and loss of life.

This comes back to a common problem that keeps true believers under the sway of faith claims: getting god “off the hook.” Intellectually, most people give god a set of special privileges to act in a way that one would not tolerate from even the greatest human being. If god exists and is perfect, then he must be at least as smart as we are, at least as compassionate as we are, at least as righteous as we are. To explain away all standards of decency and wise action from god is to essentially conceive of god in the same way that members of cults view their leaders: as categorically good. Such a view of any being, real or imagined, is dangerous.