Distribution (logic)

from Wikipedia, the free encyclopedia

Distribution in syllogistics

Within syllogistics , one speaks of the fact that a term in a syllogistic statement ( called categorical judgment in the tradition ), for example in the sentence “All philosophers are human,” appears distributed or not distributed .

  • Distributes a term occurs in a statement when each statement follows from this statement that is created by replacing the term affected by a real sub term. For example, in the sentence “All philosophers are people”, the term “philosopher” appears in a distributed manner, because this statement implies that all language philosophers (a sub-concept of “philosopher”) are people, that all existential philosophers (another sub-concept of “philosopher ") People are etc.
  • The occurrence of a term in a statement is not distributed if the statement does not allow such a conclusion. In the example mentioned, “All philosophers are human,” the term “human” does not appear in a distributed manner: the sub-term “European” is a counterexample, because the fact that all philosophers are human does not mean that all philosophers are Europeans .
Distribution (hatched) is given if the set can be replaced by any subset of itself without the statement becoming untrue.

The distribution of a term in a syllogism depends on its quantity and quality ; for general syllogisms ("All A are B", "No A are B") the subject is distributed, for negative syllogisms ("No A are B", "Some A are not B") the predicate :

  • In generally affirmative (“All A are B”) propositions, the subject (A) is distributed.
Example: All philosophers (A) are people (B). The statement remains true in any case, even if A ("philosophers") is replaced by any sub-term (language philosophers, ancient philosophers, PhD philosophers). If, on the other hand, B ("people") is replaced by any sub-term (men, children, Greeks), there may be cases in which the statement becomes untrue.
  • In generally negative (“No A are B”) propositions, the subject (A) and the predicate (B) are distributed.
  • In particular affirmative (“Some A are B”) propositions neither subject nor predicate are distributed.
  • In particular negative (“Some A are not B”) propositions the predicate is distributed.

In the tradition, formal rules for the validity of syllogisms were established, some of which fall back on the distribution of the terms that occur. Among other things, because, depending on the specific interpretation, a different number of syllogistic modes are valid, there are also different sets of rules in the tradition.

This is what Salmon says:

  • The middle term must be distributed exactly once .
  • If a term appears distributed in the conclusion, it must also appear distributed in a premise.

while Bird and Copi demand:

  • The middle term must be distributed at least once .
  • If a term appears distributed in the conclusion, it must also appear distributed in a premise.

False conclusions that arise from the fact that a term appears distributed in the conclusion but not in the premise are referred to as an illicit major .

Deontic distribution

In deontic logic , i.e. H. In logical systems that deal with normative statements ("It is permitted that ..." or "It is necessary that ..."), distribution is understood to be a syntactic decision-making process by Georg Henrik von Wright .

See also

Individual evidence

  1. ↑ Salmon 1983, p. 110
  2. ^ Bird 1964, p. 21, Rules 1 and 2
  3. ↑ Copi 1998, rule 2 on page 112 and rule 3 on page 113

literature

  • Otto Bird: Syllogistic and Its Extensions. Englewood Cliffs: Prentice-Hall 1964
  • Elmar Bund : Legal Logic and Argumentation. Rombach, 1982, ISBN 3-7930-9028-0
  • Irving M. Copi: Introduction to Logic. UTB Stuttgart, 1998, ISBN 3-8252-2031-1
  • Wesley C. Salmon: Logic. Reclam, 1983, ISBN 3-15-007996-9
  • Georg Henrik von Wright: “Deontic Logic,” Mind 60 (1951), pages 1-15

Web link