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The following types of statements are theorems and require some proof.

• Lemma. A lemma is a proven statement used as a stepping-stone toward the proof of another statement.

• Proposition. A proposition is basically a statement with a simple proof.

• Corollary. A corollary is an obvious or reasonable deduction or an easily drawn conclusion that is a natural consequence of a previous supposedly true statement. Pseudo-masters do not like corollaries because they usually expose the illogic of their theories and contentions.

What this means is that, when an instructor or a master makes a statement he or she claims to be true, then others are permitted to make reasonable deductions or conclusions based upon that statement. In other words, if what the person says is true, then it is logical and reasonable to assume that the corollary is also true.

Many times the corollary may be the opposite of the original statement. For example, if a “master” claims to have the best martial art, then a corollary is that all other martial arts must be inferior to the master’s art. If other martial arts are not inferior to the master’s art, then the master’s art must not be the best art.

While a corollary may be the opposite of the original statement, it is not always the case. If I say, a push will move the opponent backward, a corollary may be that a pull will move the opponent forward; however, a push or a pull may also move an opponent sideways, so these could also be corollaries.

• Claim. A claim is a result that may be part of the proof of another statement. Despite its name, a claim must be proved. Pseudo-masters make all kinds of outrageous claims with without offering any proof. They count on no one questioning them since they are “masters.”

Other types of statements are:

• Conjecture. A conjecture or hypothesis is a statement that is believed true but has not been proven true. A master should not state a conjecture as a fact; however, if the statement is prefaced by stating that it is unproven, then it is okay.

• Paradox. A paradox is a statement that has been provably true but it appears to defy simple intuition. The term may also refer to fallacies and other false (but seemingly true) statements. Paradoxes may be confusing, so pseudo-masters use them to support their wild theories. Anyone can walk on hot coals without being burned; this has been proven. However, since it seems impossible, pseudo-masters and other charlatans use hot coal walking as a to support their wild theories.

Hearsay

Hearsay is when someone is stating that something is true, based what they upon what they heard someone else say. Have you ever played the parlor game where a simple statement is whispered to from one person to another in a line with the admonition to repeat the message exactly as it was heard? After only a few people, the message usually does not resemble the original message.

A master may tell a student a fact. Years later, the student becomes an instructor and tells his student what the master said. Years later, that student becomes an instructor and tells her student what the master said. What this final student is told is probably nothing similar to what the master originally said.

Speculation

Speculation is using your logic and reason to make an educated guess about whether something is true or false. If the logic and/or reasoning used in the thought process are flawed, the speculation may be incorrect. Many times instructors and masters will state speculation as being fact, not necessarily to mislead, but because the speculation has been stated so many times that it has taken on the appearance of fact. Sometimes speculation is not based upon any logic or reason, it exists only in the mind of the speculator.

Lies

Lies are purposeful statements of untruths. Some instructors and masters, for whatever reason, such as to hide their ignorance, make themselves seem important, or to take you money, will lie and hope not to be caught in the lie. Even if they are caught in a lie, they will deny it, try to obscure the facts, and change the subject, such as politicians do when they are caught in lies.

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