Formal Logic Flaws

Confusing Sufficiency for Necessity

When the necessary condition is mistakenly thought to trigger the sufficient condition, and the sufficient condition is mistakenly taken as a requirement for the necessary condition.

Example:

A → B

—-

B → A

Remember:

• The necessary condition doesn’t trigger the sufficient condition.

• The necessary condition can occur whether or not the sufficient condition occurs.

Denying the Sufficient Conditoin

Happens when the sufficient condition is mistakenly taken as a requirement for the necessary condition.

Example:

A → B

X^/A

—

X^/B

In general, denying the sufficient condition yields no information about the necessary condition. If the sufficient condition is failed, it yields no information about the necessary condition. The necessary condition could be true or could be false.

Affirming the Necessary Condition

Happens when the necessary condition is mistakenly thought to trigger the sufficient condition.

Example:

A → B

X^B

—

X^A

Affirming or satisfying the necessary condition yields no information about the sufficient condition.The sufficient condition could be true or could be false.

Most Statements are NOT Reversible

Happens when Most relationship between two sets is interpreted in the wrong direction.

Lawgic:

A -m→ B

—

B -m→ A

This is an invalid argument. The truth of the premise does not guarantee the truth of the conclusion. Don’t read unidirectional arrows backwards.

A -m→ B does NOT imply B -m→ A because the A set could be tiny in comparison to the B set.

All before Most

Happens when “all A are B” and “most B are C” is mistakenly thought tot imply that “some A are C.”

Example:

A → B -m→ C

—

A ←s→ C

This WRONG!!

Correct way to draw a valid conclusion: In a logic chain, the most arrow MUST precede the all arrow. Then, we can draw a valid conclusion using some.

A -m→ B → C yields a valid conclusion via the chain.

A → B -m→ C yields NO valid conclusion via the chain.

All before Some

Happens when “all A are B” and “some B are C” is mistakenly thought to imply that “some A are C.”

When you see an all arrow before a some arrow, there are no valid conclusions to be drawn.

Lawgic:

A → B ←s→ C

—

A ←s→ C

This is WRONG!!

Think about how strong your premises need to be to support a conclusion. B -m→ C is stronger than B ←s→ C. If the stronger premise can’t even support the conclusion, then of course the weaker premise cannot either.

Correct way: A ←s→ B → C yields A ←s→ C (valid).

A ←s→ B → C yields a valid conclusion via the chain.

A → B ←s→ C yields NO valid conclusion via the chain.

Most before Most

Happens when “most A are B” and “most B are C” is mistakenly thought to imply that “some A are C.”

Lawgic:

A -m→ B -m→ C

—

A ←s→ C

This is WRONG!!

When two most arrows are chained together, there are no valid conclusions to draw via the chain.

Remember: Two most arrows can yield a valid conclusion only if they both come from the same set (same sufficient condition).

A -m→ B -m→ C yields NO valid conclusions via the chain.

A -m→ B and A -m→ C yields a valid conclusion.

Some before Some

Happens when “some A are B” and “some B are C” is mistakenly thought to imply that “some A are C.”

Lawgic:

A ←s→ B ←s→ C

—

A ←s→ C

This is WRONG!!

When you see a logic chain with two some arrows, there are no valid conclusions to be drawn.

A ←s→ B ←s→ yields NO valid conclusions via the chain.