In a material implication the relation of logical consequence is restricted to a world parameter, whereas in a formal implication the relation of logical consequence extends over many worlds. One could infer from this pattern that the material implication should be reduced to formal implication since it is just a restricted version of it, or, inversely, that formal implication should be reduced to material implication since it is an unrestricted version of it. But both reductionist claims would betray a superficial understanding of this connection. The obvious kinship between material and formal implication just means that they are versions of the same type of implication. The only difference is that in each case the same type of implication is presented in two degrees.
Keywords material implication  formal implication  deduction  possible world
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