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.)
“We rail at trade, but the historian of the world will see that it was the principle of liberty; that it settled America, and destroyed feudalism, and made peace and keeps peace; that it will abolish slavery.”
—Ralph Waldo Emerson (1803–1882)