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. the 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.
Jenkinsis not an experienced person.
gollark: i.e. imagine you have some documents which say "bee" lots, and some which say "apio" lots, and you want to look up ones with "apio" and "bee", *without* just retrieving all the documents for each and computing the intersection.
gollark: So I know approximately how inverted index things work, but HOW the APIO FORM do you efficiently do intersectiony queries on them?
gollark: Does anyone know how I can efficiently search engine?
gollark: HTML rendering.
gollark: I don't believe any existing ones do it.

See also

References
  • B. P. Bairan. An Introduction to Syllogistic Logic. Goodwill Trading. p. 342. ISBN 971-574-094-4.
  1. p.113
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