First time asking a question, sorry for any weirdness. The best way for me to illustrate might be with some examples. I believe all 4 of the following are both grammatical and would be commonly used in English.

  1. This is the place I was talking about.
  2. That is the organization I am a part of.
  3. This is the problem I was having trouble with.
  4. That is exactly what I was hoping for.

Are the objects of the preposition place/organization/problem/what? Or this/that/this/that? Is there a good rule of thumb to figure it out? In my experience, you can usually make a question of a prepositional phrase and answer it with the object, like "I went onto the roof" can be "where did I go onto?" "the roof" or "I ran into the store" can be "where did I run into?" "the store". But the answer to "what was I having trouble with?" could be "this" or "(this) problem". And the answer to "what was I hoping for?" is "that". Does the last one even have a prepositional phrase?

  • Within the relative clauses, the object of the preposition is the antecedent, i.e. "place", "organization", "problem" and "what". For example, in 1. the relative clause is "I was talking about __ " where gap is object of "about", and understood as "place".
    – BillJ
    Jan 8, 2022 at 11:46
  • In all the first three examples, optional that hasn't been included, and in principle the last one could be rephrased as That is exactly that which I was hoping for. So they can all feature "relativisers". Jan 8, 2022 at 11:51
  • The fact that the antecedents ("place", "organization" etc.) are predicative complements of "this" and "that" does not affect their status as object of the preposition.
    – BillJ
    Jan 8, 2022 at 11:55
  • Your first three are object relative clauses; the relative pronoun is the object: that I was talking about —> I was talking about that. Your last one is a nominal relative or a fused relative clause; the relative pronoun "lives inside": what I was hoping for —> the thing that I was hoping for —> I was hoping for that. Jan 9, 2022 at 22:36