Must tenses be consistent in a reported speech? For example,
'Isaac told me that he believed(believes) UFO exist(ed).
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As an analytic language English does not mark as clearly tense in reported speech as a language like Latin. As a rule, the reported speech clause is one tense more perfect than its equivalent in direct speech.
Extrapolating, the phrases, 'Isaac told me that he believed that UFOs existed' and 'I believe that UFOs exist' said Isaac are equivalent pairs. Hence, you would use believed and existed.
Yes, tenses must be consistent in reported speech.
Reported speech has many interesting pitfalls, and these include:
1.) How tenses change 2.) How adverbials often change 3.) How modal verbs function in reported speech
Reported speech, or indirect speech, accurately conveys what someone has said. Direct speech, otherwise known as quoted speech, purports to be exactly the same as what was expressed.
When I saw their new kitchen, I thought, “This is amazing!” She said, “The children will be just fine.”
Past tense reported speech is sometimes tricky in English. Reported speech usually starts with a verb such as say, tell, claim, explain, suggest, advise, insist, answer, predict, warn, announce, state, etc. As we have seen, there are many reporting verbs.
When making reported speech, take note of how tenses change (or how they do not), how modal verbs can change, and how adverbials can change. Both direct speech and reported speech can be in the simple present tense. This indicates that the speech or report has just occurred, and that it is important to the present moment.
Some reported speech is about the present.
What was Said Reported Speech in the Simple Present “It is raining.” (said a very short time ago) She says it is raining. “Dinner is cooking.” (said a very short time ago) He says that dinner is cooking. What was Said Reported Speech in the Simple Present “It is raining.” (said a very short time ago) She says it is raining. “Dinner is cooking.” (said a very short time ago) He says that dinner is cooking.
This is similar to how we can say the written word speaks in the simple present:
This poster warns people to watch out for ice on the bridge.
The website says your favorite restaurant is closed because it is being remodeled.
Most reported speech is about the past.
What was Said
Reported Speech not in the Simple Present
“It is raining.” (said some time ago) She said it was raining. “He likes to cook.” He said he liked to cook. “I like spicy food.” He said that he liked spicy food. “I am working a lot.” She insisted she was working a lot. "Are you tired?” He asked if (or whether) I was tired. “They called her.” He said they called her. or He said they had called her. “You can do it.” She predicted you could do it. “I was eating dinner.” Cynthia said she had been eating dinner. “I have not eaten.” He said he had not eaten. "Where did you go last night?" She asked where I had gone the previous evening. “I will eat dinner.” She said she would eat dinner. (will changes to would) "I'm sorry." He apologized. (a short clause can use a verb of warning, apology, thanks, etc.) "Thank you." I thanked him. "Can you come to dinner?" He asked me if/whether I could come to dinner. “I can call you.” He said he could call you. (can changes to could) “I would help if needed.” She said she would help if needed. "It may work." He said it might work. (may changes to might) “I should work.” Lisa said she should work. “I must work.” He said he had to work. or He said he must work. (must as necessity) “I might work.” She said she might work. “They have to go.” He insisted they had to go. "What was the problem?" He asked what the problem was. / He asked what was the problem. "Stop writing, everyone." He told everyone not to write. reporting verb + obj + not + to + infinitive "Get down from the ladder, Lisa!" She told Lisa to get down from the ladder. “Where shall I go?” He asked where he should go. "Have you seen my cat?" He asked if/whether I had seen his cat.