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| paralogisms:illicit_commutation:index [13.04.26, 20:47:03] – created sascha | paralogisms:illicit_commutation:index [13.04.26, 21:17:48] (current) – sascha |
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| > <span conclusio>It follows that: <s invalid "Illicit commutation">Our cat is a dog.</s></span> | > <span conclusio>It follows that: <s invalid "Illicit commutation">Our cat is a dog.</s></span> |
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| The [[glossary:conditional|material conditional]] (“if A, then B”) is //not// a //commutative// operation: if ''A ⟶ B'' is true, it does __not__ follow that ''B ⟶ A'' must also be true. As the example above shows, failing to observe this rule can lead to absurd results. | The [[glossary:conditional|material conditional]] (“if A, then B”) is //not// a //commutative// operation: if ''A ⟶ B'' is true, it does __not__ follow that ''B ⟶ A'' must also be true. As the example above shows, failing to observe this rule can lead to absurd results. |
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| | ===== Other names ===== |
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| | * Illicit conversion |
| | * Invalid commutation |
| | * Non-commutativity violation |
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| | ===== Description ===== |
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| | As in mathematics, the law of commutativity also applies in logic; it determines which operations may be reversed. Just as, e.g. [[wp>Multiplication|multiplication]] allows commutation (''a × b'' is the same as ''b × a''), whereas the same is not permitted for [[wp>Division (mathematics)|division]] (''a ÷ b'' is //not// the same as ''b ÷ a''), there are also rules of commutation (though in this context often called "conversion") for logical operations. For example, swapping the operands is permitted for [[glossary:adjunction|adjunction]], whereas this is not permitted for the [[glossary:conditional|(material) conditional]]. |
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| | The most common form of this fallacy is therefore an erroneous reversal of a conditional statement (“if A, then B”) – as in the example above. This form of an illicit commutation is also known as “[[formal_fallacies:affirming_the_consequent|affirming the consequent]]”. |
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| | #TODO **This article is still a work in progress.** |
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| | ===== See also ===== |
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| | * [[causality:cause-effect|Confusion of cause and effect]] |
| | * [[glossary:commutativity|Commutativity]] |
| | * [[logic:formal_fallacies:index|Formal fallacies]] |
