Is there an English language example where modus tollens is valid but contraposition is not valid?

Question

I was reading an answer by Bumble where the topic of modus tollens being valid but contraposition being not valid came up: https://philosophy.stackexchange.com/a/43004/29944

More importantly, there are logics in which contraposition is not valid at all. For example, in David Lewis' logic of counterfactual conditionals, A ◻→ B does not entail ¬B ◻→ ¬A. Also, in Ernest Adams' probability logic it may be highly probable that B given A, but not highly probable that ¬A given ¬B. So in general, when speaking of ordinary English conditionals, one cannot always expect contraposition to be safe. A noteworthy corollary is that in both the Lewis and Adams logics, while contraposition is not valid, modus tollens is valid. Some accounts of logic incorrectly run together contraposition with modus tollens and treat them as the same thing. While both are classically valid, they do not agree across all logics.

I don't doubt this, but I was trying to think of an English language example to illustrate this without success.

Hence the question: Is there an English language example, the simpler the better, where modus tollens is valid but contraposition is not valid?

An example where contraposition is valid but modus tollens is not valid would be nice as well, but I don't want this question to become too broad.

Answer 1

Here's the example from David Lewis's Counterfactuals (1973):

If Boris had gone to the party, Olga would have gone.

Now suppose that Boris wants to go, but not if Olga goes, because he wants to avoid her. Olga, on the other hand, wants to see Boris, and wants to go if he does. Given this supposition, the contrapositive of the above is false:

If Olga hadn't gone to the party, Boris wouldn't have gone.

As for modus tollens, this is valid:

1. If Boris had gone to the party, Olga would have gone.
2. Olga didn't go to the party.
3. Therefore, Boris didn't go to the party.

The conclusion follows from the premises: we know that Boris didn't go, because Olga didn't -- she would have if he had.

Answer 2

As well as the counterfactual example given by Eliran, there are an abundance of examples where the conditionals are uncertain. For example, given the poor record of the Norwegian soccer team, I might believe strongly that if Norway reach the final of the next world cup then they won't win. The contrapositive of this is that if Norway win then they won't reach the final, which is impossible. More generally, it may be highly probable that B given A, but not highly probable that not A given not B. Conditional probabilities do not follow the same rules as classical material implications, but many real world uses of conditionals behave like claims of conditional probabilities being high.