====== Sorites ======

An arbitrarily long series of premises consisting of concatenated [[glossary:universal_quantification|universal quantifications]] (or [[glossary:conditional|conditionals]]) that can be replaced by a new //universal quantification//, constructed from the [[glossary:antecedent|antecedent]] of the first premise and the [[glossary:consequent|consequent]] of the last.

This can be represented as a formula as follows:

> All <var>A</var> are <var>B</var>.
> All <var>B</var> are <var>C</var>.
> ...
> All <var>M</var> are <var>N</var>.
> <span conclusio>Therefore, All <var>A</var> are <var>N</var>.</span>

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

A variant of the Sorites that is based on [[glossary:conditional|conditional statements]] (instead of [[glossary:universal_quantification|universal quantifications]]) is sometimes called a “chain argument”.

Since //conditional statements// can always be converted into universal ones, the following form is //logically equivalent// to the one listed above:

> If <var>A</var>, then <var>B</var>.
> If <var>B</var>, then <var>C</var>.
> ...
> If <var>M</var>, then <var>N</var>.
> <span conclusio>Therefore, If <var>A</var>, then <var>N</var>.</span>
===== Name =====

The name “sorites” comes from <span :grc>σωρός</span> [<i :grc-Latn>sorós</i>], the Ancient Greek word for a "pile" or "heap". It is used as a shorter form for the latinized term “<span "Lat.: piled syllogism"><i :la>soriticus syllogismus</i></span>” and should not be confused with the [[logic:emergence:sorites|Sorites fallacy]].

==== Other names ====

  * Polysyllogism
  * Multi-premise syllogism
  * [[logic:inferences:modus_barbara:index|Modus Barbara]]<span noprint>[[app>#barbara|Show in Syllogism-Finder App]]</span> – a specific form of the //sorites// with exactly three terms.
  * <i :la>Acervus</i>

===== Example =====

> All **[[wp>Square|squares]]** are [[wp>Rectangle|rectangles]].
> All //rectangles// are [[wp>Parallelogram|parallelograms]].
> All //parallelograms// are [[wp>Trapezoid|trapezoids]].
> All //trapezoids// are [[wp>Quadrilateral|quadrilaterals]].
> All //quadrilaterals// are [[wp>Polygon|polygons]].
> All //polygons// can be **drawn in a continuous sequence of lines**.
> <span conclusio>Therefore: All **squares** can be **drawn in a continuous sequence of lines**.</span>

===== See also =====

  * [[glossary:conditional|(Material) Conditional]]
  * [[glossary:enthymeme|Enthymeme]]
  * [[logic/inferences/hypothetical_syllogism#chain_argument|Hypothetical syllogism § chain argument]]
  * [[logic:inferences:modus_barbara:index|Modus Barbara]]

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

  * [[wp>Polysyllogism]] on //Wikipedia//