Speechless

A puzzle from the Middle Ages, adapted by A.N. Prior:

Four people, on a certain occasion, say one thing each.

A says that 1 + 1 = 2.

B says that 2 + 2 = 4.

C says that 2 + 2 = 5.

Can D now say that exactly as many truths as falsehoods are uttered on this occasion?

“If what D says is true,” Prior writes, “that makes 3 truths to 1 falsehood, so that it is false; while if it is false, that makes two truths and two falsehoods, and it is true.”