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Validity of weak crossover effects?

Dear linguists,

I am wondering in what way weak crossover effects can count as a test for movement. If I understand correctly, in the sentence (1) *The boy[i] that his[i] father hit t[i] the reading where "boy" and "his" are coreferent is impossible, due to the fact that the operator, being coreferent with the antecedent, leaves a trace behind that cannot be bound be the possessive (Principle C of Binding Theory). So far, so good.

However, isn't the sentence (2) *His[i] father> hits him[i] also impossible with the coreferential meaning? If so, how can we say then that it's the movement that renders (1) ungrammatical, if the pre-movement derivation is ungrammatical as well? Or, the other way around: how can we conclude that the ungrammaticality is evidence for there to be movement, if the ungrammaticality has always been there? As far as I can see, this is not the case for strong crossover effect<s, e.g.="" (3)="" *the="" man[i]="" that="" he[i]="" thinks="" &gt;you="" saw="" t[i].="" in="" (3),="" coreference="" with="" "man"="" and="" "he"="" is="" impossible="" again,="" and="" in="" this="" case,="" it="" is="" more="" clear="" to="" me="" how="" this="" could="" be="" interpreted="" as="" evidence="" for="" movement:="" the="" unmoved="" version="" is="" perfectly="" possible,="" i.e.="" (4)="" he[i]="" thinks="" you="" saw="" him[i].="" so,="" movement="" applied="" to="" sentence="" (4)="" equals="" ungrammaticality.="" <="" p="">

I hope you see my problem and can help me out. Thanks a lot