Consequently, he should estimate the number of black ravens at 25, the number of black non-ravens at 25 and the number of non-black non-ravens at 50. According to this argument, since the two people disagree about their estimates after they have accepted the different hypotheses, accepting "All ravens are black" is not equivalent to accepting "All non-black things are non-ravens"; accepting the former means estimating more things to be black, while accepting the latter involves estimating more things to be non-ravens. Correspondingly, the argument goes, the former requires as evidence ravens that turn out to be black and the latter requires non-black things that turn out to be non-ravens. Existential presuppositions A number of authors have argued that propositions of the form "All are " presuppose that there are objects that are . This analysis has been applied to the raven paradox: ... : "All ravens are black" and : "All nonblack things are nonravens" are not strictly equivalent'' ... due to their different existential presuppositions. Moreover, although and describe the same regularity – the nonexistence of nonblack ravens – they have different logical forms. The two hypotheses have different senses and incorporate different procedures for testing the regularity they describe. A modified logic can take account of existential presuppositions using the presuppositional operator, '*'. For example, can denote "All ravens are black" while indicating that it is ravens and not non-black objects which are presupposed to exist in this example. ... the logical form of each hypothesis distinguishes it with respect to its recommended type of supporting evidence: the possibly true substitution instances of each hypothesis relate to different types of objects. The fact that the two hypotheses incorporate different kinds of testing procedures is expressed in the formal language by prefixing the operator '*' to a different predicate. The presuppositional operator thus serves as a relevance operator as well. It is prefixed to the predicate ' is a raven' in because the objects relevant to the testing procedure incorporated in "All raven are black" include only ravens; it is prefixed to the predicate ' is nonblack', in , because the objects relevant to the testing procedure incorporated in "All nonblack things are nonravens" include only nonblack things. ... Using Fregean terms: whenever their presuppositions hold, the two hypotheses have the same referent (truth-value), but different senses; that is, they express two different ways to determine that truth-value. See