Formal Logic Flaws

Confusing Sufficiency for Necessity

NOT LAWGIC:

A → B

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B → A

• truth of premises does not guarantee the strength of the conclusion

• the sufficient is not a requirement for the necessity

Denying the Sufficient Condition

NOT LAWGIC:

A → B

_X/A

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_X/B

• denying the suficient yield no information about the necessary nor a valid conclusion

Affirming the Necessary Condition

NOT LAWGIC:

A → B

_xB

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_xA

the necessary is mistakenly thought to tigger the sufficient

“Most” Statements Are Not Reversible

NOT LAWGIC:

A —m→ B

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B —m→ A

the “most relationship between 2 sets is interpreted in the wrong direction

“All” Before “Most”

NOT LAWGIC:

All A are B : A→B—m→C

Most B are C

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Some A are C : A←s→C

• no valid conlcusion can be drawn, because set “A” could be tiny (in comp) tto B and C sets

“All” Before “Some”

NOT LAWGIC:

All A are B : A→B←s→C

Some B are C

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Some A are C : A←s→C

• when you see an “all” arrow before a “some” arrow no valid conclusion can be drawn. Set A could be very tiny (in comparison) to B and C sets.

“Most” Before “Most”

NOT LAWGIC:

Most A are B : A—m→B—m→C

Most B are C

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Some A are C : A←s→C

• when 2 “most'“ statements are chained together, there are no valid conclusion

“Some” Before “Some”

NOT LAWGIC

some A are B : A←s→B←s→C

some B are C

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some A are C : A←s→C

• a logic chain with 2 “some” arrows has no valid conclusion, because no overlap is guaranteed.