Affirmative conclusion from a negative premise

From RationalWiki
Jump to: navigation, search
Part of the series on

Logic and rhetoric

Icon logic.svg
Key articles
General logic
Bad logic
Not to be confused with negative proof.

An affirmative conclusion from a negative premise (also illicit negative) occurs when a categorical syllogism has a positive conclusion, but one or two negative premises.

It is a syllogistical fallacy and a formal fallacy.

Contents

[edit] Forms

An affirmative conclusion from a negative premise can take three forms:

First form: (single "not", second premise)
P1: Some A are B.
P2: Some B are not C.
C1: Some A are C.

Second form: (single "not", first premise)
P1: Some A are not B.
P2: Some B are C.
C1: Some A are C.

Third form: (double "not")
P1: Some A are not B.
P2: Some B are not C.
C1: Some A are C.

The third form is also a fallacy of exclusive premises.

[edit] Non-fallacious form

It is acceptable to have an affirmative premise and a negative premise as long as the conclusion is negative. The only problem is when the conclusion is positive. Two examples make this clear:

Negative conclusion:[1]
P1: All farmers produce excess food.
P2: All city dwellers do not produce excess food.
C1: All city dwellers are not farmers.

Positive conclusion:[1]
P1: Some city dwellers are not hungry.
P2: Some hungry people are farmers.
C1: Some city dwellers are farmers.

[edit] Problem

The fallacy is invalid because any valid categorical syllogism with a negative premise must have a negative conclusion.

When both premises are negative, the syllogism is also a fallacy of exclusive premises.

[edit] Examples

P1: No cats are marsupials.
P2: Some mammals are not cats.
C1: Some mammals are marsupials.[2]

P1: No people under the age of 66 are senior citizens.
P2: No senior citizens are children.
C1: All people under the age of 66 are children.[3]

  • All birds are reptiles, and humans aren't birds, therefore humans are reptiles.
    The exclusion of 'humans' from the 'birds' category gives no reason to include humans in the 'reptile' category. It is easily proven false by finding an example that disproves the conclusion, but doesn't invalidate the premises, such as finding a human that isn't a reptile.
  • Atheists are not good. Christians are not atheists. Thus, Christians are good.[4]
  • Evolution is not true. Intelligent design is not evolution. Therefore, intelligent design is true.[4]
  • No fish are dogs, and no dogs can fly, therefore all fish can fly.[5][6]
  • We don't read that trash. People who read that trash don't appreciate real literature. Therefore, we appreciate real literature.[5][6]
  • All mice are animals, and some animals are not dangerous, therefore some mice are dangerous.[7]
  • No honest people steal, and all honest people pay taxes, so some people who steal pay taxes.[7]

[edit] See also

[edit] External links

[edit] Footnotes

Personal tools
Namespaces

Variants
Actions
Navigation
Community
Tools
support