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What does it mean to say, x implies y?

It may mean either oftwo of two things: either that x presuppose...,'ypresupposes, in the sense that xrequiresy requires y by a specific and definite necessity;: or that x anticipatesyanticipates y, in the sense that x requiresy by only a generic and indefinite necessity. (Perhaps another way of explaining what is meant by the two things that implication may mean-i.e., presupposition and anticipation-is to say that, whereas the implication rightly distinguished as "presupposition" is unconditional, the implication rightly distinguished as "anticipation" is condi tiona/.) 7 October 2008; rev. 15 August 2009 requires y