In set theory, a branch of mathematics, a reflection principle says that it is possible to find sets that resemble the class of all sets. There are several different forms of the reflection principle depending on exactly what is meant by "resemble". Weak forms of the reflection principle are theorems of ZF set theory due to Montague (1961), while stronger forms can be new and very powerful axioms for set theory.
The name "reflection principle" comes from the fact that properties of the universe of all sets are "reflected" down to a smaller set.
Read more about Reflection Principle: Motivation For Reflection Principles, The Reflection Principle As A Theorem of ZFC, Reflection Principles As New Axioms
Famous quotes containing the words reflection and/or principle:
“Men should pledge themselves to nothing; for reflection makes a liar of their resolution.”
—Sophocles (497–406/5 B.C.)
“The principle of the brotherhood of man is ... narcissistic ... for the grounds for that love have always been the assumption that we ought to realize that we are the same the whole world over.”
—Germaine Greer (b. 1939)