Quantification (logic)
Quantification (also: quantification ) is in formal logic , in set theory (and in linguistics ) a term used to denote the binding of a variable in an expression by a quantifier .
The quantification by a universal quantifier is called Allquantifikation that by existential as existential quantification .
Only when all variables are linked by quantifiers does an expression turn into a sentence that can be true or false. An "open sentence" becomes a truthful sentence.
If you use a quantifier, you implicitly presuppose a basic area ( universe of discource , discourse universe ). This is the object area that is defined or required when using quantifiers. If the basic area is the entire universe, one also speaks of an unrestricted quantification , otherwise of a restricted quantification . Object areas can also be (all) possible worlds . Then there is a quantification over (all) possible worlds.
See also
Individual evidence
- ↑ See Tarski , Introduction to Mathematical Logic, 5th ed. (1977), p. 23
- ↑ Detel, Basic Course Philosophy I: Logic (2007), p. 73
- ↑ Brands / Kann, Logic, in: Honnefelder / Krieger, Philosophische Propädeutik I (1994), ISBN 3-8252-1822-8 , p. 104
- ↑ a b Bußmann, Lexikon der Sprachwissenschaft, 3rd edition (2002): Quantification