If we do it this way, then the three premises work together to support the conclusion; an instance of this generalisation would be: 'If PI and P2, then Susan is healthy'. So the argument would be represented as shown in Figure 6.5.
Figure 6.5 Three premises supporting a conclusion jointly
A deductively valid argument is rationally persuasive for you if you have good reason to accept its premises. An inductively forceful argument is rationally persuasive for you provided that you have good reason to accept the premises, and it is not defeated: you do not have some other argument for rejecting the conclusion that is more rationally persuasive for you than the one in question.
Unlike validity, inductive force and soundness, rational persuasiveness is not a feature of arguments in themselves. It is also a matter of a given person's relationship to an argument. An argument may be rationally persuasive for one person but not for another. An argument may be sound but not rationally persuasive for you (for the premises might be true even though you lack good reasons to accept them). Moreover, an argument may be rationally persuasive for you but not sound (for you may have good reasons for accepting a set of premises, even when one of the premises is false). But the question of whether or not an argument is rationally persuasive for you is not simply the question of whether or not you find it persuasive, or whether you are in fact persuaded by it. For unlike the question of whether we are actually persuaded by an argument, we can be mistaken about rational persuasiveness: an argument may be rationally persuasive for you even when you think it isn't, and fail to be when you think it is. The importance of the concept of rational persuasiveness is that it captures what arguments are intended to do: The distinctive aim of persuasion by argument is to persuade people rationally, that is, by actually giving them good reasons to accept a given conclusion, and not just seeming to.
There are various informal methods of logical assessment, and of demonstrating that an argument is not valid or inductively forceful. The principle task is simply to apply the definitions of deductive validity and inductive force, but there are some strategies to facilitate this in more difficult cases. One strategy that is almost always pertinent is to suppose the conclusion of the argument to be false, and then to ask whether it would still be possible for all the premises to be true. Another strategy, where the conclusion of an argument is a conditional, is to suppose that the antecedent of that conditional is true, and then to determine whether the remaining premises force one to conclude that the consequent would also be true. If the conclusion of an argument is a generalisation, an analogous strategy is to suppose that the antecedent of an arbitrary instance of the generalisation is true. Finally, an effective way of demonstrating that an argument is
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