# Circular reasoning

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 Cogito ergo sumLogic and rhetoric Key articles General logic Bad logic v - t - e
Not to be confused with the unrelated expression that something "begs the question" (as in, "invites a follow-up question").
 “”Design must be proven before a designer can be inferred. The matter in controversy is the existence of design in the Universe, and it is not permitted to assume the contested premises and thence infer the matter in dispute. Insidiously to employ the words contrivance, design, and adaptation before these circumstances are made apparent in the Universe, thence justly inferring a contriver, is a popular sophism against which it behoves us to be watchful. —Percy Bysshe Shelley, on the circularity of the argument from design[1]

Circular reasoning (often begging the question) is a logical fallacy that occurs when the conclusion of an argument is used as a premise of that same argument; i.e., the premises would not work if the conclusion weren't already assumed to be true.

The fallacy is an informal fallacy. The phrase "begging the question" comes from a bad translation of the Latin phrase petitio principii, literally a(n) application of/request (or beg) for the premise.

## Alternate names

• assuming the answer
• circulus in probando/demonstrando ("circle in proving/demonstrating")/Self-proving/demonstrating/fulfilling idea
• fallacy of circularity
• circular evidence/justification/logic
• vicious/virtuous circle
• petitio principii (falsi/ficti) ("a[n] application of/request for the [wrong] premise")
• [illicit] question begging

## Form

X is true, because X is true.

Circular reasoning takes the form:

A implies B, which implies A, which …

Begging the question is often considered synonymous, though sometimes is distinguished as following the form:

A implies B; A is only valid because B is assumed; B is only valid …

### Circular explanation

A circular explanation (or "vacuous explanation") occurs when the explanation for an event is essentially the event itself.

For example: "This sedative causes sleep because of its dormitive virtue."

## Explanation

Circular reasoning is fallacious because reasoning and justification must start with the known and then determine the unknown — in the case of circular reasoning, it starts with the known and ends up with the equally known, thus it proves nothing.

## Examples

### God's existence

 “”There's no greater argument for the existence of God than the truth of His existence. —Robert T. Lee of the Society for the Practical Establishment and Perpetuation of the Ten Commandments

We shall prove that God exists:

1. The order and magnificence of the world is evidence of God's Creation.
2. Therefore, we know that God exists.

Here, it is assumed that God exists in order to satisfy the premise that "God's Creation" is evidence of his existence. There is no standalone argument here that connects existence to God's creation except the conclusion, which is that God exists. Note the slight structural differences in the argument to simple circular reasoning — the order of the world isn't implied by God's existence, but trying to use it as evidence of God's existence must assume he exists in the first place.

### Bible is the word of God

A common example of circular reasoning: the Bible.

More God stuff now. This one is so mind-blowingly circular that you'd think it's a straw man. However, most Biblical literalists use the Bible as their main proof of God, and using the Bible as any form of evidence for God must assume the following circular argument.

P1: The Bible tells us that it is the word of God.
P2: The word of God is infallible, according to the Bible.
C1: Therefore the Bible is infallible.
P3: And as such, the Bible must be the word of God.
P4: The word of God is infallible, according to the Bible.
C2: Therefore the Bible is infallible.
P5: And so on, ad infinitum.

This may be a problem for Protestants whose rule of faith is the Bible, though not for Catholics who claim that the infallibility of Sacred Scripture comes from the authority of the Church given by a truthful and good God to a people who need positive revelation as a firm guide in life, though what that claim is based on, bar the Pope said so (itself perilously close to begging the question) is rather hazy.

### Justification of faith

Faith may be defined as belief unsupported by evidence. To justify his religious faith, that world-champion question begger, Paul of Tarsus, offers the following rationale:

 “”Now faith is the substance of things hoped for, the evidence of things not seen. (KJV) —Hebrews 11:1

In other words, the argument boils down to this:

1. There are things we cannot see (God, Heaven, whatever).
2. There is no observable evidence that these things exist.
3. We believe in them anyway.
4. Our faith (unsupported belief) is itself the evidence of these “things not seen.”
5. Therefore these things exist, because we believe they do.

Albeit, in addition to "substance", the Greek word "hypostasis" can be translated as "assurance", "being sure", or "confidence"; also, in addition to "evidence", the Greek word "elenchos" can be translated as "conviction" or "being convinced". This would allow Hebrews 11:1 to be rendered as: "Now faith is the confidence in (or being sure of) things hoped for, the conviction for (or being convinced about) things not seen." Such a translation would be more of a morale boost than an attempt at constructing proof.

### Witnessed miracles

See the main article on this topic: Miracle
1. We know that the Bible is true because there was a miracle witnessed by 500 people.
2. We know that there was a miracle witnessed by 500 people because the Bible says so.

This argument has actually been made by several different people, one of them being Dinesh D'Souza. They tend to try to bolster these types of arguments by saying things like, "How could the Gospel writers have gotten away with claiming this if it didn't happen? Wouldn't someone have called them on it?" Oddly enough, pointing out that these accounts were written generations after the supposed miracles happened, in a time when ready communications weren't reliably available, has little effect on the bullshitter individual putting forth this argument.

### Presuppositionalism

See the main article on this topic: Presuppositionalism

Admittedly, more advanced theologians — well, anyone smart enough to use the word "theologian"[note 1] — aren't this stupid, and some creationists and literalists do try to prove the Bible though other means. However, this usually tends towards Christian Science rather than good scholarship. In a variant used by Jason Lisle — of all creationists, a man who certainly should know better — he states the same thing as:

1. If the Bible were not true, logic would not be meaningful.
2. Logic is meaningful.
3. Therefore, the Bible is true.

Sure, the first premise comes directly from Lisle's special place, but it also assumes that not only is there a connection between logic and the Bible's truthiness, it must assume the Bible is infallibly true to make such a connection in the first place. Remarkably, those premises as stated aren't paraphrased at all. Of course, this isn't the only example of extreme circularity in Lisle's work (and he's only one of a number of creationists). In his proposed anisotropic synchrony convention (a shamelessly plagiarised attempt to circumvent the starlight problem), the actual content of the science becomes meaningless, as his underlying reasoning is that the Earth is 6000 years old because his convention says it is, and the usual speed of light conventions cannot possibly be right because such conventions imply that the world is older than 6000 years. Most flood geology works along similar lines. It first assumes the Earth is 6000 years old in order to reject all established geology, biology, and physics, and then uses new conventions to show that the Earth must be 6000 years old, thus simultaneously validating both their beliefs and methodology.

Why does the Bible get special treatment? The problem with fallacies is that you can also prove a contradiction.

1. a) If the Bible were not true, logic would not be meaningful. b) If the Koran were not true, logic would not be meaningful.
2. Logic is meaningful.
3. a) Therefore, the Bible is true. b) Therefore, the Koran is true.
4. According to the Koran, the Bible is false.
5. Therefore, the Bible is false.
6. a) The Koran and the Bible have common traditions. b) Therefore, the Bible is both true and false.
7. (If part of the Koran is a common tradition with a false scripture, it is false.)
8. (Therefore, the Koran is not entirely true.)
9. (According to the Koran, the Koran should be entirely true.)
10. (Therefore, part of the Koran should be both true and false.)
11. Therefore, 2 + 2 = 5.

### Big Bang

See the main article on this topic: Big Bang
1. Something can't come from nothing.
2. Thus, the Big Bang can't have happened.

The premise 'something can't come from nothing' assumes the Big Bang, being a something that came from nothing, never happened. Therefore, the conclusion is assumed in the premise.

### Intelligent design

See the main article on this topic: Intelligent design
• Joe finds a computer and sees that the computer is irreducibly complex.
• Joe claims that because the computer contains irreducible complexity, it can be inferred that it was designed by intelligent vampires.
• Dan retorts "but wait. How do you know that intelligent vampires will create designs that are irreducibly complex?"

Because observing intelligent vampires making designs is impossible, Joe can only assume what characteristics a vampire design is supposed to have. Thus, it would be begging the question for Joe to find an object bearing those designs and conclude that intelligent vampires made it.

The backbone of the intelligent design arguments claim that designs have certain "characteristics" (e.g. irreducible complexity) that indicate that an intelligent designer made it. At best, this is a half-truth. At best, only intelligent life forms (humans, monkeys, dolphins, etc.) can be observed to make designs containing these "characteristics". Thus, at best, when one finds an object with these "characteristics", it's only logical to conclude that an intelligent life form designed it. Intelligent design, however, isn't concluding an intelligent life form. Doing so would disprove that any god created life or the universe, and also result in an infinite regression.

Intelligent design, thus, must be concluding some "non-life intelligent being." Be it gods, fairies, or vampires, it doesn't matter. One cannot observe these "non-life intelligent beings" make designs. Thus, the "characteristics" of a "non-life intelligent being's" design can only be assumed to contain irreducible complexity etc. Thus, it is begging the question to find these characteristics in the cosmos or life forms, and conclude that a "non-life intelligent being" designed it. Likewise, in the above example, it was illogical for Joe to find these "characteristics" in a computer and claim that vampires designed it.

## By definition

See the main article on this topic: Argumentum ad dictionarium

One of the ways that circularity appears is whenever someone tries to argue a point "by definition". Simply put, if you can define your terms any way you like, then you can conclude anything you like without deriving anything new — hence it's circular. It's very simple to do, and doesn't always require someone running to a dictionary to do it. Consider the cosmological argument for the existence of God, which postulates that there must be a some kind of uncaused cause that brought the Universe into being. While this alone doesn't prove any particular god — Allah, Yahweh, Brahman, and so on — and theologians most likely know this, it can be used as proof if this first cause is God "by definition". However, this makes the logic as follows:

1. We define God as the thing that created the Universe.
2. The Universe exists.
3. Therefore God exists and created the Universe.

Simply substitute "God" for something with fewer religious connotations and it would easily highlight the bizarre circularity. Nothing stops us replacing "God" with the Invisible Pink Unicorn precisely because the argument is constructed almost spherically. In terms of mathematics, the equivalent would be declaring the solution to be X, where X is defined as an operation or series of operations resulting in the correct answer; it is simply placing a name on the unknown.

## Circular definitions versus circular arguments

See the main article on this topic: Tautology

Circularity is fallacious when used in an argument. However, if one wishes to define a word, one must use other words to do so. If one then defines those words in terms of other words, and those words in terms of other words, and so on, one must, since there are a finite number of words, eventually reach a point where there are words that are defined in terms of each other, and thus the definition is in some sense "circular". This phenomenon is inevitable and not necessarily fallacious; the issue is whether definitions are presented as "this is what I mean by these words" or "this is a statement about the world". The latter is fallacious, while the former is not.

So, above, the definition is taken to not merely define the concept of "God", but to speak to God's existence, and is therefore fallacious. On the other hand, consider the following argument made against evolution: "Evolution says that more fit organisms will out-reproduce less fit organisms. However, 'fitness' is defined as the property of being able to out-reproduce other organisms. This is circular." Since evolution is merely presenting the definition of "fitness", and is not asserting that it has proved anything about the actual world, this definition of "fitness" is not fallacious. Every area of study can be presented as making similar statements, for instance "Christianity says that God created the universe. However, 'God' is defined as the creator of the universe." Or "Physics says that acceleration is equal to force divided by mass. But force is defined as mass times acceleration."

## Proving equivalence

A circular argument does not prove that any of the statements involved are true, but it does prove that they are equivalent; that is, all of them have the same truth value (either all are true, or all are false). This in itself can be useful. Consider an n × n matrix A. All of the following statements can be proven:

1. If the column vectors are independent, then A is invertible.
2. If A is invertible, then A has a non-zero determinant.
3. If A has a non-zero determinant, then the dimension of the null space is zero.
4. If the dimension of the null space is zero, then the column space has dimension n.
5. If the column space has dimension n, then the column vectors are independent.

Proving these statements does nothing to establish that A is invertible. It does, however, mean that "the column vectors are independent", "A is invertible", "A has a non-zero determinant", "the dimension of the null space is zero", and "the column space has dimension n" are all basically the same statement, and only one needs be checked for any particular matrix; which is certainly a useful result.

## Psychological causes

Often, people beg the question without being consciously aware that they are doing so. They have so thoroughly internalized a belief that they are not able to rationally evaluate it. When a person has been taking something for granted for a long time, it's difficult to not think that it's "obviously true", and in no need of justification. Trying to remove such a premise from one's thoughts and reason without it can be difficult; take, for instance, many people's attempts to reason in a number system in which A×B is not the same as B×A.

## The denial trap

Often, denying a circular argument can leave one open to accusations that oneself is actually the one engaging in a circular argument. Such an accusation can be the result of one's opponent being devious, or simply being so lost in their own nonsense that they are unable to reason rationally on the subject.

Take the "Bible is the word of God" example given above. One can counter this by saying "The Bible is not the word of God. Therefore, when it says that it is infallible, there's no reason to believe it. Since it's not infallible, there's no reason to believe that it's correct when it says it is the word of God." This counterargument can then be made to look like a circular argument itself.

## Alternative meaning

Breaking: transhumanist madam schools pedantrist scarecrow. (Source)

Many people use the expression "begs the question" to mean "raises the question" — in the sense that they believe an important point is being overlooked in the argument given (i. e. petitio principii veri/recti, which is not fallacious). For example; "If God created the universe, this begs the question of who created God." There are countless examples of this use, which is not incorrect despite what some anal retentive pedants might arbitrarily insist.