We have seen self-referential statements such as the following.

And the following.

Logical issues can arise when a self-referential negation is present.

Self-referential statements (or questions) can cause logical problems (i.e., paradoxes).

Is "no" your answer to this question? Answer either "yes" or "no".

Do you see the paradox? Try answering one way, then the other way, thinking each through.

The phrasing of a question is very important. An "ill-posed question" is a question where a "yes" or "no" answer is not sufficient as there may be other implications. Examples:

• Have you stopped beating your wife?
• When will you start studying for the exam?

The general issue here is called "framing" the question.

In the Bible, we often see ill-posed questions involving framing when Jesus is questioned by others. Jesus tends to remove the "framing" so that his statements are more clear.

Note that if only God is "good" but Jesus is also "good" then there is an inconsistency. This paradox can be removed if Jesus is actually God.

Let us get back to logical paradoxes in the form of statements.

A self-referential sentence can be split into two (or more) parts.

No problem here. Whenever sets of logical statements are everywhere reversed from false to true and true to false, the system has no inconsistencies not present in the original, but it can be harder to understand.

Quick! What is the opposite of "not in"? Remember not to forget that! Aside: Flipping logic is one thing that makes concepts such as type 1 and type 2 errors in statistics confusing. If the logic is completely flipped, type 1 errors become type 2 errors and type 2 errors become type 1 errors. False negatives become false positives and false positives become false negatives.

That is why correctly framing or putting context to a statement or claim is important. Statements or claims (or Bible verses) taken out of context can be confusing, misleading, etc. A self-referential paradox can arise, however, in a situation of multiple statements such as the following.

Flipping logic, we have the following, with the same paradox.

However, sometimes a consistent set of statements may not be easily resolvable within the system.

Sometimes the "required" dependency is not easily resolvable within the system. Such a set of statements is sometimes called a "catch-22" situation.

In such cases, one may be required to think "outside the box", which may or may not be easy to do. A "catch-22" situation, from the name of a novel by Joseph Heller (and later movie) refers to a self-referential system where two (or more) parts refer other parts of that group in a way that there is no "fixed point" (i.e., well-defined and consistent) solution. More on "fixed points" later.

How does one get a "job" when all the advertised jobs require "experience", one does not have "experience" and the only way to get experience is to get a job?

This infinite object illustrates a principle known as "infinite regress", but more on that later.

Let us redraw the above diagram to be a finite representation of the above diagram representing an infinite (regress) situation.

The infinite regress situation has been made into a diagram with an infinite cycle (if followed without stopping).

Note: In the 1990's, there were jokes made about companies requiring 5 years of Java programming experience when Java had not been around for 5 years. The same often happens today when new programming languages appear and companies use boilerplate job requirements without checking carefully. A LinkedIn post showed the situation "When employers want 10 years of experience before you turn 20". (as of 2022-05-08)

Which came first, the chicken or the egg?

A CAPTCHA (Completely Automated Public Turing test to Tell Computers and Humans Apart) can be used, say on a web site page, to help determine if the user is a human or a machine (i.e., "bot" for "robot").

Computers can be used to try to recognize/solve a CAPTCHA and have been getting better to the point that they can solve CAPTCHA's that some humans have trouble solving.

The primary CAPTCHA problem is as follows.

• To recognize the CAPTCHA, the image must be segmented into separate symbols.
• The segment the image into separate symbols, the CAPTCHA must be recognized.

This is a catch-22 situation.

There is a Unicode symbol for "Put litter in its place".

• Decimal 128,686 appears as "🚮".
• Hex 1F6AE appears as "🚮".

However, this character is above the 16-bit 0 to 65,535 character range, and may not be supported on the browser you are using to view this page (or any fonts that are loaded, etc.).

At one time, the English word "litter" meant a bed in the sense of a portable couch or straw, etc. Thus, a "litter" of puppies might be on a bed of straw, a "litter" might be used for medical transport for someone in an emergency, etc.

The English word "litter" comes, through French, from the Latin word "lectus" ≈ "couch, bed". This word appears once in the Latin Vulgate.

There are many "viscous cycles". As one set of phrases go:

• Exercises
• Eks-are-cises
• Eggs are sides
• Eggs are sides for bacon, bacon, bacon!

Some ideas, such as Zeno's paradox, lead to an infinite regression.

• If space aliens planted life on earth, then who planted the life for the space aliens.

One example of a "viscous" cycle illusion is the Penrose steps (or stairs).

This page adds more to the page at Catch-22 situations.

The German word "der Teufelskreis" ≈ "devil's circle" is the German equivalent of the English word "catch-22".

This German word is made of two other German words.

• The German word "der Teufel" ≈ "the devil".
• The German word "der Kreis" ≈ "the circle".

The word "cycle" is sometimes substituted for "circle".

The German word "Teufelskreis" has the connotation of a hopeless situation created by a series of inter-dependent events.

Interestingly, the two words that make up this one word appear together in only one verse in the Luther German.

The Latin word "totius terrae" ≈ "total world".

The Wycliffe follows the Latin and combines "earth" and "whole world".

The next verse refers to the battle of Armageddon.

More: Armageddon

Let us return to the catch-22 viscous circle from the Latin perspective.