Sorites

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.

• Polysyllogism
• Multi-premise syllogism
• Modus BarbaraShow in Syllogism-Finder App – a specific form of the sorites with exactly three terms.
• Acervus

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.

• (Material) Conditional
• Enthymeme
• Hypothetical syllogism § chain argument
• Modus Barbara

• Polysyllogism on Wikipedia