In Irish, the basic word order is VSO in tensed clauses, and SOV in infinitival clauses. McCloskey (2001), among others, argues that the underlying word order of clauses is SVO, and the SOV order in infinitival clauses surfaces as a result of object shift based on examples with floating quantifiers (FQs). In this paper, we investigate in detail the distribution of FQs in Irish, and argue (1) that in infinitival clauses, not only object shift but also subject shift and verb raising take place, (2) that FQs move to their host NPs at LF, (3) that LF movement of FQs is subject to Minimality, and (4) that the underlying word order of Irish clauses cannot be solely determined as SVO.