Increasing Levels of Rationality
- Type 1 reasoner: A type 1 reasoner has a complete knowledge of propositional logic i.e., he or she sooner or later believes every tautology (any proposition provable by truth tables). Also, his or her set of beliefs (past, present and future) is logically closed under modus ponens. If he or she ever believes p and believes p → q (p implies q) then he or she will (sooner or later) believe q .
- Type 1* reasoner: A type 1* reasoner believes all tautologies; his or her set of beliefs (past, present and future) is logically closed under modus ponens, and for any propositions p and q, if he or she believes p→q, then he or she will believe that if he or she believes p then he or she will believe q. The type 1* reasoner has "a shade more" self awareness than a type 1 reasoner.
- Type 2 reasoner: A reasoner is of type 2 if he or she is of type 1, and if for every p and q he or she (correctly) believes: "If I should ever believe both p and p→q, then I will believe q." Being of type 1, he or she also believes the logically equivalent proposition: B(p→q)→(Bp→Bq). A type 2 reasoner knows his or her beliefs are closed under modus ponens.
- Type 3 reasoner: A reasoner is of type 3 if he or she is a normal reasoner of type 2.
- Type 4 reasoner: A reasoner is of type 4 if he or she is of type 3 and also believes he or she is normal.
- Type G reasoner: A reasoner of type 4 who believes he or she is modest.
Read more about this topic: Doxastic Logic
Famous quotes containing the words increasing and/or levels:
“A point has been reached where the peoples of the Americas must take cognizance of growing ill-will, of marked trends toward aggression, of increasing armaments, of shortening tempers—a situation which has in it many of the elements that lead to the tragedy of general war.... Peace is threatened by those who seek selfish power.”
—Franklin D. Roosevelt (1882–1945)
“Pushkin’s composition is first of all and above all a phenomenon of style, and it is from this flowered rim that I have surveyed its seep of Arcadian country, the serpentine gleam of its imported brooks, the miniature blizzards imprisoned in round crystal, and the many-hued levels of literary parody blending in the melting distance.”
—Vladimir Nabokov (1899–1977)