In support of ‘if A then B’, you could argue that because the natural language conditional is harder to satisfy then the logical construct, it means that any proposition that is logically valid is automatically true in natural language. This does not work the other way around though. If something is true in natural language, it might not necessarily be true in logic. However given that the focus of our attention is logic, we should start with the logical statement. When this is true, we can be confident that the natural language sentence is equivalent to the proposition.
Philosophers have also argued that the classical reading of ‘if A then B’ keeps things simple, and works in most mathematical situations. However, we do strike oddities when we consider the classical interpretation in comparison to natural language, and perhaps all we can do here is recognise and work-around these problems as best we can. Again, this is where probability theory might help to make the logic conditional closer to natural language.
Up until this point, I have been mainly talking about ‘indicative conditions’, which refer to actual states of affairs where the speaker is expressing his/her belief on what will happen if one of the possible options is satisfied. However, a second type of ‘if A then B’ scenario occurs with subjunctive conditionals. This occurs, most obviously, when the speaker considers the ‘what if’ scenario, something that is not true, but the speaker wants us to assume that it is true in order to investigate an argument further. I used an example earlier of ‘if Germany won the war…’. This is an example of a subjunctive conditional, or ‘counterfactual’, a statement that deliberately runs contrary to known facts.
A subjunctive can also be used to express a proposition that is likely to be true: ‘if it were to rain tomorrow, I’ll be very upset in having to cancel the picnic’. Although the subjective tends to use the ‘were to’ construction, it is possible that a statement expressed in present tense could also be considered a subjunctive: ‘if it rains tomorrow…’. This shows that the difference between indicative and subjunctive conditionals is sometimes a very fine one, and we could go either way. As a result, when we speak of subjunctives, we tend to only refer to those statements that are obviously counterfactual, such as ‘if Germany had won the war…’.
David Lewis provided the following definition of a subjunctive conditional: we are speaking of a world in which A is true, and B is also true, and this world is more similar to the actual world than any other world in which A is true but B is not true. To support this argument, Lewis used the famous example: if kangaroos had no tails, they would fall over. We are asked to imagine a possible world in which kangaroos don’t have tails, and what would be the likely result, closest to the actual world. Lewis believes that in such a world, nobody would come to the kangaroo’s rescue and they would simply fall over. But you could also argue that because there are a lot of people interested in animal welfare, they would find some way to ensure that the kangaroos stayed upright. So it is debatable whether the kangaroo proposition is an example of a persuasive subjunctive argument.
This example demonstrates that it is not easy to determine which of the possible worlds is most similar to the actual world. Is it the world where the kangaroos fall over or is the world where the animal lovers come to the rescue? Lewis himself admits that the process of finding similarity between two worlds is ‘extremely vague’. However he also thinks that this is ‘par for the course’ as far as subjunctives are concerned. Because they are hypothetical to begin with, they always contain an element of uncertainty, so there is no getting around the fact that any argument based on ‘if A then B’ will be difficult to draw any logical conclusion from.
Lewis uses another example to highlight that subjunctives are not easy to assess:
- If Verdi and Bizet had been compatriots, Verdi would have been French
- If Verdi and Bizet had been compatriots, Bizet would have been Italian
It is unclear which version we should prefer. Lewis concedes that we have to rely on our intuitions here as he cannot see any objective ‘formula’ that can be used to provide guidance on the similarity-of-worlds question. However, you could argue that some subjunctives are not so vague, and it is easy to agree with the conditional: ‘if the Moon landings were faked, there would be no American flag standing on the Moon’. Lewis’s theories do not really cover this kind of scenario, although perhaps Lewis himself would argue that this is a case of relying on one’s intuitions and agreeing the statement is likely true.