1)His dream is to have a big house.
2)His dream is having a big house
Are both the sentences correct? If yes, What is the difference in meaning between these two sentences?
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I thought they are objects for verb dream.
Is is the verb, not dream.
Possessive determiners such as my, our, his, her, their, X's, like any other determiner, make the following word a noun, not a verb.
And usually English non-question sentences start with a noun, and the verb follows the noun, because of "Subject-Verb-Object" order.
His dream is actually the subject of the verb is, which is a form of be.
The verb be is in a category with a couple of verbs--such as seem, like, become and a few others--called copular verbs.
Copular verbs don't take objects; in the place that looks like an object for other verbs is what's called a predicate nominatives or subject complements.
Predicate nominatives tell you the name of something. I am John - John is a PN.
Subject complements - in X is Y, if Y is a SC, Y tells you one or more attributes of X. The water is hot - hot is a SC.
This is different than an object. An object is the "target" of a verb, but words like be are more like "equal signs" than actions.
Here's an example of a verb that requires an object.
I hit the wall
The wall is the object of hit. You can't substitute an adjective for the wall, such as hot, because hit wants objects, not PNs or SCs.