RESTRICTED AND UNRESTRICTED MODUS PONENS Draft of September 02, 2020 Matheus Silva In a typical modus ponens the reasoner will (a) assert that a premise materially implies a conclusion in a given world; (b) assert this premise and (c) infer the conclusion. But this restricted modus ponens has little in common with the unrestricted textbook modus ponens, since the latter claims that there are no possible worlds where: (a') a premise materially implies a conclusion, (b') that premise is true and (c') the conclusion is false. It is clear that this textbook modus ponens cannot be a real argumentative form since the same inference cannot be repeated across all possible worlds by one reasoner. Moreover, a reasoner can accept a material implication in some worlds and not in others. So the closest thing to an unrestricted textbook modus ponens would have to require (1) a claim to a formal implication as the main assumption; (2) the assumption that a reasoner would be willing to accept the conclusion from this claim to formal implication in any circumstance where its premise is accepted. The true nature of an unrestricted modus ponens is encapsulated in a disposition to infer a conclusion of a formal implication given the acceptance of its premise. We can use this information and reinterpret the restricted modus ponens as a disposition to infer a conclusion of a material implication in view of the acceptance of its premise. So we have two types of modus ponens and each is most plausibly interpreted as a reasoner's willingness to make inferences in some specified circumstances. Some conditional logics are motivated by the belief that modus ponens inferences (or at least by inferential tests inspired by modus ponens inferences) capture something fundamental about conditionals. But that is only one of the potential inferential uses associated with conditionals. If we make an effort to understand modus tollens, the resulting intuitions will be entirely different. Suppose I say 'If John is an honest guy, I'm a Dutchman'. In such cases the audience is expected to infer that John is not honest from the obvious fact that I'm not a Dutchman. This has nothing to do with hypothetical circumstances where the premise of the conditional is false. Let's say we make a distinction comparable to that of modus ponens between unrestricted and restricted modus tollens. In an unrestricted modus tollens there is a claim to a formal implication as the main assumption and the reasoner's willingness to accept the falsity of its premise in any circumstance where its conclusion is denied. In a restricted modus tollens there is a claim to a material implication as the main assumption and the reasoner's willingness to accept the falsity of its premise in any circumstance where its conclusion is denied. In regards to any given conditional you might (A) accept the corresponding claim to material or formal implication, or both; (B) have a ponens or a tollens inferential disposition in each case, or both; (C) have these inferential dispositions in relation to one specific claim, but not the other (see the Dutchman example mentioned above). But whichever is the combination, you can't (I) arbitrarily separate conditionals from arguments as if they were connectives instead of claims to implication; (II) deposit all our theoretical efforts in ponenscentric intuitions.