Controversy Over Cantor's Theory
In mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been criticized in several areas by mathematicians and philosophers.
Cantor's theorem is that there are sets having cardinality greater than the (already infinite) cardinality of the set of whole numbers {1,2,3,...}. Cantor's work gave rise to some remarks from Kronecker and others. Logician Wilfrid Hodges (1998) has commented on the energy devoted to refuting this "harmless little argument", asking, "what had it done to anyone to make them angry with it?"
Read more about Controversy Over Cantor's Theory: Cantor's Argument, Reception of The Argument, Objection To The Axiom of Infinity
Famous quotes containing the words controversy and/or theory:
“And therefore, as when there is a controversy in an account, the parties must by their own accord, set up for right Reason, the Reason of some Arbitrator, or Judge, to whose sentence, they will both stand, or their controversy must either come to blows, or be undecided, for want of a right Reason constituted by Nature; so is it also in all debates of what kind soever.”
—Thomas Hobbes (1579–1688)
“Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.”
—Willard Van Orman Quine (b. 1908)