What is the difference between using ている、ていた、た in relative clauses?

I remember seeing in the thread before that there was no difference between ている and た. So then what would be the difference between the usage of them in these sentences below?

• 最後に立っていたものが勝者だ


• 最後に立っているものが勝者だ


• 最後に立ったものが勝者だ

All the above are from using google search with the first two being the most common and the third being the least with only two hits with the words 最後に立ったものが.

Answer

Well, as with any sentences that don't have a large number of adjuncts or context limiting their meaning, there are many interpretations.

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最後に立っていたものが勝者だ

1. 
   

   Matrix time: present
   Subordinate time: past

   
   

   
   

   ("Who is the winner?")
   
   "The last person who was standing is the winner."

   
   

   
   

   That is, the person who was (before time of speech) standing up last (and may or may not be standing at time of speech) is the winner.

   
   


2. 
   

   Matrix time: future
   Subordinate time: past or relative past

   
   

   
   

   "The last person who was standing (will be / is) the winner."

   
   

   
   
   

   That is, either:

   
   
   
   
   • "was" = past: the person who was (before the time of speech) standing up last (and may or may not be standing at the time of speech) will be the winner.
   
   
   • "was" = relative past: the person who was (before the reference time) standing up last (and may or may not be standing at the reference time) will be the winner.
   
   
   
   

   (As for the English gloss, this sentence suggests the past interpretation as opposed to the relative past interpretation at first glance, I think. But, with enough context: "In this game, people sit up and down in order, and then a bell randomly rings. When that happens, the person who was standing up last will be the winner.", the relative past interpretation works fine in English as well.)

   
   

For both interpretations, in Japanese and the English glosses, whether the person is still standing up or not is not specified, though there is probably a slight suggestion of "no longer standing" (since you would use 「立っている」/"is standing" otherwise, after all).

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最後に立っているものが勝者だ

1. 
   

   Matrix time: present
   Subordinate time: present

   
   

   
   

   ("Who is the winner?")
   "The last person who is standing is the winner."

   
   
   

   
   

   That is, the person who is (at time of speech) standing is the winner.

   
   

   Honestly, interpreting this sentence as occurring in present time is slightly weird, since you'd probably just say 「立っている人が勝者だ」 "The standing person is the winner.".

   
   


2. 
   

   Matrix time: future
   Subordinate time: present or relative present

   
   

   
   

   "The last person who is standing (will be / is) the winner."

   
   

   
   
   

   That is, either:

   
   
   
   
   • "is" = present: the person who is (at time of speech) standing up last is the winner.
   
   
   • "is" = relative present: the person who is (at reference time) standing up last is the winner.
   
   
   
   

   Again, the present is somewhat pragmatically weird, since you would normally not use 「最後に」 "last" -- that means this sentence would probably have the subordinate clause interpreted in the relative present.

   
   

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最後に立ったものが勝者だ

1. 
   

   Matrix time: present
   Subordinate time: past

   
   

   
   

   ("Who is the winner?")
   "The last person who stood up is the winner."

   
   

   
   
   

   That is, the person who (before the time of speech) stood up last (and may or may not be standing at time of speech) is the winner.

   
   


2. 
   

   Matrix time: future
   Subordinate time: past or relative past

   
   

   
   

   "The last person who stood up (will be / is) the winner."

   
   

   
   

   That is, either:

   
   
   
   
   
   • "stood up" = past: The person who (before the time of speech) stood up last (and may or may not be standing at the time of speech) will be the winner.
   
   
   • "stood up" = relative past: The person who (before the reference time) stood up last (and may or may not be standing at the reference time) will be the winner.
   
   
   
   

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Finally, to address the core of your confusion, 「た」 cannot be interpreted as 「ている」 here (which is hopefully clear due to the different glosses provided).

The reason for this is because (as further explained in the thread I linked in the comments), the actor (namely, the person who stood up) is explicitly mentioned in the sentence, which prevents the stative reading of 「た」. With a different head, like 「立った状態」, 「立った」 can be interpreted as 「立っている」.