An important type of statements are counterfactual statements, that is statements about what would be the case if a fact of the matter were different than it actually is. “If a massive meteor had not hit the Earth at around the KT-boundary, birds would not be the only extant dinosaurs” is a counterfactual statement, since the antecedent is false. Counterfactual statements are important, since they allow us to reason about causal relations and thus to make predictions and interventions. But there is, allegedly, a fly in the ointment: we cannot apply truth-functional logics to counterfactuals, and thus we will remain, as a point of logic, unable to evaluate whether any given counterfactual statement is true or false. If you are familiar with our other posts, you might already see where I will be going – I will claim that this is sheer nonsense.
So, what is the supposed problem? The problem, we are told, stems from the properties of material implication. To see this, let us take a look at a piece of counterfactual reasoning: “If instead of A, which is in fact the case, B would be the case THEN also C would be the case.” Even more formally:
A ⇔ ¬B
B ⇒ C
Here the problem rises: if the antecedent of a material implication is false, the implication will turn out true! So, all counterfactuals would turn out true. But clearly they all cannot be true, at least if causal explanations rely on getting our counterfactual reasoning right. William Starr pulls no punches in drawing a grim conclusion:
Truth-functional logic is inadequate for counterfactuals not just because the material conditional [⇒] does not capture the fact that some counterfactuals with false antecedents […] are false. It is inadequate because there is, by definition, no truth-functional connective whatsoever that simultaneously combines two false sentences to make a true one […] and combines two false ones to make a false one[.]Starr 2019
Starr goes on to point out that this is presently taken to show the inadequacy of classical logic, or alternatively to show that one should not assign truth values to counterfactual statements (ibid.).
But what is really going on here? Why did we insist on the counterfactual nature of the antecedent? After all when formalising an argument, we usually pay no heed to whether our premises are true. We only care about the truth of premises when evaluating whether an argument is sound in addition to being valid. If one took the attitude taken above with regards to merely valid arguments, then (at least in those cases where a false premise is the antecedent of a material implication) one should reach an equally grim conclusion: truth-functional logic is inadequate for such purposes. We can only use truth-functional logics, it appears, when all the premises are true. This would be a curious result indeed.
Am I mixing syntactics and semantics here? Perhaps, but only insofar as they are inexorably mixed (at least) in all cases to do with scientific reasoning. If we cannot take provisional claims as our starting position and then apply deductive reasoning of a truth-functional type, most theoretical science will be lost. After all, all scientific facts are held only provisionally – they may end up having been false. Can we then not look at the (material) implications of such claims?
So, how to deal with counterfactuals? Simply by taking for the purpose of reasoning the (counterfactual) antecedent to be true! Just keep in mind for you meta-level considerations that it actually was false. (Also when dealing with several counterfactuals at a time, one must take care not to take as true a set of statements that would lead to a contradiction.) This simple trick allows us to do what we have already been doing: evaluate the truth-values of counterfactual statements. That is, after all, what most exercise problems in physics are…
Again, logic is a tool. Like all tools it can be used well or used poorly. It is not the fault of the tool, if it is used improperly. Of course one may take the problem more seriously and develop non-standard connectives and logics & other tools. But, the thing is, one need not.
Starr, William (2019). Counterfactuals, The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2019/entries/counterfactuals/>.