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Since Pollock (1976), there has been much debate on the so-called consequent-entailment problem of even if P, Q (eP > Q). Researchers such as Bennett (1982, 2003), Lycan (1991), Barker (1991, 1994), and Guerzoni & Lim (2007) tried to offer explanations about this linguistic phenomenon. However, in most cases, eP > Q generates a factive implicature rather than an entailment, which this paper endeavors to explain. The present study also presents conditions for pragmatically factive implication (PFI) of the consequent of eP > Q. For eP > Q to be felicitous, P should be at a point on a given scale low enough to make eP > Q sufficiently informative. The consequent of eP > Q has PFI iff P is at the lowest point on a given scale or alternative conditions at lower points than P are pragmatically excluded either for their pragmatic irrelevance or pragmatic impossibility. Their pragmatic relevance is determined by mutual knowledge between the speaker and the hearer(s), and their pragmatic possibility is by world knowledge.