The sentence “Why did everyone’s father think that Tom said that you were fired?” is supposedly ambiguous in three different ways. However, I can’t seem to get any ambiguous reading from it. I have one thought that it has to do with ‘’everyone’s father’’ where you could say that it’s either (1) every different father of every single different individual or (2) that every different individual has the same father. Please correct me if I am wrong. What about the third reading though? It doesn’t make sense to me. Is there a way which I can use to find out if sentences are ambiguous?
There are two sources of ambiguity in the sentence: the scope of every- and the base position of the causal interrogative pronoun Why. The first of these sources is mentioned in the question: either everyone present has the same one father (the referential reading of everyone's father) or the father varies for each person present (the bound variable reading of everyone's father).
The second source of ambiguity is more difficult to discern. A fronted adjunct can lead to ambiguity based upon the base position of the adjunct, that is, whether the base position is in the matrix clause or in the embedded clause. This source of ambiguity becomes evident when a related example is used:
(1a) Why did Tom say you were fired? ('You weren't actually fired; it's just that Tom said you were.')
(1b) Why did Tom say you were fired? ('You were indeed fired and I want to know why you were fired.')
The paraphrases in parentheses draw attention to the distinct readings based upon the base position of the adjunct Why. If Why is interpreted as originating in the matrix clause associated with say, then the first reading obtains, but if it is interpreted as originating in the embedded clause associated with fired, then the second reading obtains.
Returning to the sentence from the question, getting the various readings is difficult for me. But if the second source of ambiguity is acknowledged, then the sentence should in fact be six-way ambiguous (three clauses times two readings of everyone's father). My guess is that whoever has produced the sentence and the claim that it is three-way ambiguous is acknowledging only the second source of ambiguity. Without the first source, the sentence would be three-way ambiguous based solely on the base position of the fronted adjunct Why, that is, whether it is construed with think, said, or fired.