Universal instantiation
Type | Predicate logic |
---|---|
Symbolic statement |
In
quantification theory
.
Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal."
Formally, the rule as an axiom schema is given as
for every formula A and every term t, where is the result of substituting t for each free occurrence of x in A. is an instance of
And as a rule of inference it is
- from infer
Irving Copi noted that universal instantiation "...follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934."[4]
Quine
According to
quantifications and the singular statements that are related to them as instances. Yet it is a principle only by courtesy. It holds only in the case where a term names and, furthermore, occurs referentially.[5]
See also
References
- ISBN 978-0205820375.[page needed]
- ^ Hurley, Patrick. A Concise Introduction to Logic. Wadsworth Pub Co, 2008.
- ^ Moore and Parker[full citation needed]
- ^ Copi, Irving M. (1979). Symbolic Logic, 5th edition, Prentice Hall, Upper Saddle River, NJ
- OCLC 728954096. Here: p. 366.