T4.3 5 of 6

To recapitulate:

We have seen examples from English of sentences which appear to be material conditionals.

This is important because there are many cases of English counterfactual conditionals which are not material conditionals. These conditionals are about what would have been. E.g.,

(3) If Frank were to attend graduate school, then it would be the case that he needs to take out a loan.

You may recall that counterfactual conditionals are not even truth functional. So (3) cannot be well symbolized with a horseshoe. The idea of these "subjunctive mood" conditionals is a concern with the hypothetical, with what might have been the case, rather than with what is in fact the case. This is beyond truth functional analysis. (Though as we noticed in chapter 2, we cannot do any better than the horseshoe for symbolizing in SL – in practice we will use the horseshoe as an imperfect symbol for counterfactual and all other conditionals.)

But conditionals of English in the indicative mood (typically without the "were" and "would") may be material conditionals. The examples about passing the course and IRS filing are meant as evidence for this.

Still even this limited claim about symbolizing with the horseshoe is controversial. There's one final problem we might consider.