# Polysyllogism

A **polysyllogism** (also called **multi-premise syllogism**, **sorites**, **climax**, or **gradatio**) is a string of any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on. Each constituent syllogism is called a **prosyllogism** except the very last, because the conclusion of the last syllogism is not a premise for another syllogism.

## Example

An example for a polysyllogism is:

- It is raining.
- If we go out while it is raining we will get wet.
- If we get wet, we will get cold.
- Therefore, if we go out we will get cold.

Examination of the structure of the argument reveals the following sequence of constituent (pro)syllogisms:

- It is raining.
- If we go out while it is raining we will get wet.
- Therefore, if we go out we will get wet.

- If we go out we will get wet.
- If we get wet, we will get cold.
- Therefore, if we go out we will get cold.

## Sorites

A **sorites** is a specific kind of polysyllogism in which the predicate of each proposition is the subject of the next premise. Example:

- All lions are big cats.
- All big cats are predators.
- All predators are carnivores.
- Therefore, all lions are carnivores.

The word "sorites" /sɒˈraɪtiːz/ comes from Ancient Greek: σωρίτης, "heaped up", from σωρός "heap" or "pile". In other words, a sorites is a heap of propositions chained together. A sorites polysyllogism should not be confused with the sorites paradox, a.k.a. fallacy of the heap.

Lewis Carroll uses sorites in his book *Symbolic Logic* (1896). Here is an example:[1]

- No experienced person is incompetent;
- Jenkins is always blundering;
- No competent person is always blundering.
- ∴ Jenkins is inexperienced.

Carroll's example may be translated thus

- All experienced persons are competent persons.
- No competent persons are blunderers.
- Jenkins is a blunderer.
- ∴ Jenkins is not an experienced person.

## See also

- Anadiplosis - the rhetorical grounds of polysyllogism.
- Transitive relation

## References

- B. P. Bairan.
*An Introduction to Syllogistic Logic*. Goodwill Trading. p. 342. ISBN 971-574-094-4.

- p.113