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Willard Quine presents a historical synopsis of the origin of the theory of types and the " ramified " theory of types : after considering abandoning the theory of types ( 1905 ) , Russell proposed in turn three theories : the zigzag theory theory of limitation of size , the no-class theory ( 1905 – 1906 ) and then , readopting the theory of types ( 1908ff ) Quine observes that Russell 's introduction of the notion of " apparent variable " had the following result : the distinction between ' all ' and ' any ' : ' all ' is expressed by the bound ( ' apparent ' ) variable of universal quantification , which ranges over a type , and ' any ' is expressed by the free ( ' real ' ) variable which refers schematically to any unspecified thing irrespective of type .
 Willard Quine, Quine
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 Willard Quine, Quine