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Can counterfactuals in premises make an argument sound and valid?

I understand that soundness requires both validity and true premises whilst validity requires the premises to follow to the conclusion.

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    Your second sentence already answers your first. If a premise is counter to fact it isn't true by definition, so there is no point discussing soundness for counterfactuals, only validity. – Conifold Jul 8 at 4:19
  • Some basic terminology regarding deductive and inductive argumentation can be found here. – J D Aug 4 at 16:26
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Counterfactual conditionals do appear in arguments, and we tend to treat them as contributing to validity and soundness, but their logic is much more problematic than other conditionals. Consider, for example:

  1. If Caesar had not crossed the Rubicon, the Roman Republic would have survived for another hundred years;
  2. If the Roman Republic had survived for another hundred years, Caligula would never have become emperor;

Therefore,

  1. if Caesar had not crossed the Rubicon, Caligula would never have become emperor.

This argument appears to be a case of hypothetical syllogism, but it is not quite so straightforward. For one thing, you have to consider whether counterfactuals are the kind of thing that are capable of being true or false. Historians may like to discuss the plausibility of premise 1, but it is contentious to say that it is definitely either true or false. Some hold that it lacks a truth value, but it can be assessed on the basis of some other criterion, such as assertability or probability. Others hold that it has a truth value, but it is unknown to us. Maybe Jupiter knows what would have happened to the Roman Republic but he is not sharing.

Another issue is that arguments of this form are not always valid. When we form a counterfactual, some background assumptions carry over from what is actually true into the hypothetical case of the antecedent, but others do not, and sometimes these assumptions conflict. For example, suppose President Smooch of the Free Hugs for All Party was up for re-election last year and won. We might accept the counterfactual,

  1. If the Free Hugs for All Party had lost the election President Smooch would have resigned after the election.

But if we also believe that President Smooch was his party's greatest electoral asset, we might also accept the counterfactual,

  1. If President Smooch had died the day before the election then the Free Hugs for All Party would have lost the election.

But we cannot combine these to draw the conclusion,

  1. If President Smooch had died the day before the election, he would have resigned after the election.

Other familiar logical rules, such as contraposition and strengthening of the antecedent, also do not always work for counterfactuals.

Some influential accounts of counterfactuals, such as those of David Lewis and Robert Stalnaker, make use of possible world semantics and hold that the truth of a counterfactual depends on what is true in the closest possible world to the actual world. David Lewis worked out a logic for counterfactuals on this basis (Counterfactuals, Blackwell, 1973). Other accounts appeal to probabilities and make use of the probability calculus.

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