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This type-III conditional sentence,

“I could not have played volleyball when I was an elementary school student if I had been short.”

should be (I think) changed to:

“I would not have been able to play volleyball when I was an elementary school student if I had been short.”

But why?

Following some of the advice from the ‘was able to’ vs ‘could’ question I can see that ‘could’ and ‘could not’ can be used to talk about a general ability, in the past. And the two sentences gleaned from the conditionals,

“In elementary school I could play volleyball [because I was tall enough].”

“In elementary school I couldn’t play volleyball [because I was too short].”

seem perfectly fine.

Then, the opposite, counterfactual of that first type-III conditional using ‘could’ seems to work:

“I could have played volleyball when I was an elementary school student if I had been taller.”

It doesn’t seem like ‘could have played’ needs to be replaced with ‘would have been able to play’, because, following the rule of talking about a general ability (and not a single past occasion), ‘could’ works well enough. However, with the original sentence, why do I have the intuition that ‘could not have played’ has to be ‘would not have been able to play’?

User ‘Arun’ quotes, in that 'was able to' vs 'could' thread, from Practical English Grammar by AJ Thomson et al, that

“the one difference between could and be able to in the past affirmative is that could just implies that you had the general freedom or permission to do something, but may not have actually done or achieved it, where as be able to implies that you actually went ahead and did it."

I feel this is an important addition to the ‘could’ vs. ‘was able to’ usage criteria, but how does this ‘actually went ahead and did it’ feature of be able to apply in a type-III conditional when it’s inherently hypothetical and counterfactual?

Or is there something to the single past occasion usage of 'was able to' that applies in a type-III conditional?

“I wouldn’t have been able to understand the usage of ‘could’ and ‘was able to’ in a type-III conditional if I hadn’t come to english.stackexchange.com.” is something I hope I can soon say...

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