| Chapter one is a brief introduction of the contents of the whole paper.In chapter two, we first made a brief review of the philosophical investigations of the presuppositional phenomena conducted by Frege(in Geach and Black[1]) (1892, 1952), Strawson[3] (1952), and Russell[13] (1905), and then tried to indicate that, the examination of presuppositions within a semantic framework is not viable for any truth-conditional approach to meaning. Semantics is concerned with the specification of invariant and stable meanings that can be associated with surface linguistic expressions, while presuppositions, by nature, are not invariant and they are not stable. It soon became clear that apart from specific lexical words or grammatical constructions, contextual and pragmatic factors play an important role in the account of presuppositional phenomena.In chapter 3, we discussed the pragmatic accounts of presuppositions that tried to take speaker's assumptions or mutual knowledge, felicity conditions and conversational implicatures into consideration. They have been proved one by one to be inadequate or improper in some sense, though each of them helped us to broaden our understanding of the nature of presuppositions. Moreover, if a pragmatic framework seemed necessary for such an account, the formalizations of contextual parameters that affect presupposition failure or inheritance are not easy tasks. Although Karttunen and Peters[10] (1979) formulated a number of ad hoc rules for presupposition-triggering words and sentential connectives, the counter-examples where they fail to make the correct predictions are nontrivial and seem to shake their very theoretical foundation. While Gazdar'[11]s Cancellation approach (1979) seems much more powerful and solves K&P's counter-examples effectively, it still leaves its own counter-examples unanswered. What's worse is that both of the two approaches are at most descriptively feasible in some respects, and neither of them is explanatory.In view of the above, in chapter 4, we introduced Fauconnier[12]'s (1994) Mental Spaces theory and his formalization of presupposition projection rules and strategies. Fauconnier's theory is explanatory to presuppositionalphenomena and solves K&P's and Gazdar's counter-examples satisfactorily. One thing extraordinary in his approach is that pragmatic knowledge, contextual factors and interpretation strategies are formalized in his rules and strategies, and this is something that has never been successfully done by any pragmatic approaches. Fauconnier not only specifies under what circumstance presuppositions introduced into "lower" spaces float all the way up to parent space R, but also explains why they can or cannot do so. We have in this paper tried to analyze the various presuppositional projection problems in Fauconnier's mental spaces framework, and concluded that his approach is far more superior to the former two approaches, though it has its own weakness.According to his projection rules and strategies, implicit presuppositions will float up until they are blocked by incompatibility in a higher space (SP2 followed by SP1). This is close in spirit to the principle of cancellation theories in which potential presuppositions are cancelled by stronger implicatures or sentential entailments. But this superficial resemblance is not to cover their theoretical difference. Under the cancellation view, if lower clausal presuppositions are cancelled by the hierarchy of entailments and implicatures, they simply disappear to nowhere, while floating presuppositions from space to space does not change their status: it only changes the number of spaces in which they are satisfied. Presuppositions that do not float all the way up to parent space R still remain as presuppositions in the intermediate spaces to which they may have floated. This is important in reporting speaker's beliefs and assumptions that are not shared by the hearers. What are presupposed in a speaker's belief space may continue to be presuppositions in his belief world...
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