An arbitrarily long series of premises consisting of concatenated universal quantifications (or conditionals) that can be replaced by a new universal quantification, constructed from the antecedent of the first premise and the consequent of the last.
This can be represented as a formula as follows:
All A are B.
All B are C.
…
All M are N.
Therefore, All A are N.
A variant of the Sorites that is based on conditional statements (instead of 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 A, then B.
If B, then C.
…
If M, then N.
Therefore, If A, then N.
The name “sorites” comes from σωρός [sorós], the Ancient Greek word for a “pile” or “heap”. It is used as a shorter form for the latinized term “soriticus syllogismus” and should not be confused with the Sorites fallacy.
All squares are rectangles.
All rectangles are parallelograms.
All parallelograms are trapezoids.
All trapezoids are quadrilaterals.
All quadrilaterals are polygons.
All polygons can be drawn in a continuous sequence of lines.
Therefore: All squares can be drawn in a continuous sequence of lines.