====== Hypothetical syllogism ======

A valid logical [[logic:inferences:index|inference]] consisting of the concatenation of two or more [[glossary:conditional|conditional]] statements.

 For example:

> When it rains, the road gets wet.
> When the road is wet, it is slippery.
> <span conclusio>Therefore, when it rains, the road gets slippery.</span>

or as a formula:

> <span "if A, then B.">''A ⟶ B''</span>   – //if// A, //then// B.
> <span "if B, then C.">''B ⟶ C''</span>   – //if// B, //then// C.
> <span conclusio "therefore: if A, then C>''∴'' ''A ⟶ C''</span> – //therefore: if// A, //then// C.

The name refers to the principle that //conditionals// can also be formulated as [[glossary:categorical_statement|categorical statements]] and therefore these inferences could also be expressed as [[glossary:syllogism|syllogisms]].

The example above could also be formulated as a [[logic:inferences:modus_barbara:index|Modus Barbara]]<span noprint> [[app>#AA1A|Show in Syllogism-Finder App]]</span>, for example as follows:

> For //all// situations where it is raining, it is //true// that the road will get wet.
> For //all// situations in which the road is wet, it is //true// that road will get slippery.
> <span conclusio>Therefore, for //all// situations in which it is raining, it is //true// that the road will get slippery.</span>

Obviously, the formulation as an “if … then”-statement is much easier to understand; logically, however, they are //equivalent//.

For more information, see: <span maniculus "go to:">[[glossary:syllogism|Syllogism]]</span>.

===== Chain argument =====

A variant of the //hypothetical syllogism// that combines multiple //conditionals// (typically more than two) is also sometimes called a “chain argument”. This can be seen as a variation of the [[logic:inferences:sorites|Sorites]] based on //conditionals//. Alternatively, the //hypothetical syllogism// can be seen as a special case of the chain argument with exactly two premisses, similar to how the [[logic:inferences:modus_barbara:index|Modus Barbara]] can be seen as a special form of the //Sorites// with exactly two [[glossary:universal_quantification|universal quantifications]].
===== See also =====

  * [[glossary:conditional|Conditional]]
  * [[logic:inferences:sorites|Sorites]]
  * [[glossary:syllogism|Syllogism]]

===== More information =====

  * [[wp>Hypothetical syllogism|Hypothetical syllogism]] on //Wikipedia//