Polysyllogism

Not to be confused with Polylogism.

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. For example:

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.

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 "the fallacy of the heap", from σωρός "heap" or "pile". In other words, a sorites is a heap of propositions chained together.

Lewis Carroll uses sorites in his book Symbolic Logic. 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.

References