A polysyllogism (also called multi-premise syllogism, sorites, climax, or gradatio) is a string of any number of
proposition
In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...
s forming together a sequence of
syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be tru ...
s 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 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 (plural: 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'' comes from , ''heaped up'', from σωρός ''heap'' or ''pile''. Thus a sorites is a heap of propositions chained together. A sorites polysyllogism should not be confused with the
sorites paradox
The sorites paradox (; sometimes known as the paradox of the heap) is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a sin ...
, a.k.a. the fallacy of the heap.
Lewis Carroll
Charles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet and mathematician. His most notable works are '' Alice's Adventures in Wonderland'' (1865) and its sequ ...
uses sorites in his book ''Symbolic Logic'' (1896). For example:
: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
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Anadiplosis
Anadiplosis ( ; el, ἀναδίπλωσις, ''anadíplōsis'', "a doubling, folding up") is the repetition of the last word of a preceding clause. The word is used at the end of a sentence and then used again at the beginning of the next sentence ...
- the rhetorical grounds of polysyllogism.
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Transitive relation
In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive.
Definition
A hom ...
Notes
Bibliography
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Term logic
Syllogism
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