"This one is" OR "This is"

Solution 1:

Using "this one" instead of "this" places increased emphasis on the phrase, and draws the listener's attention to the specific "one" instead of generically to the rest of the sentence.

This is Daddy's.

It is assumed that the listener already knows what is being talked about. Whatever "this" is, it's taken for granted. The semantically important point is "Daddy's" -- the rest of the sentence is just lead-in for the important point that it belongs to a certain person.

This one is Daddy's.

In this sentence, the emphasis shifts (slightly, subtly) to the subject. Here, the focus is on the object, and the specific "one" that the speaker is referencing. (Likely, the speaker is also holding or pointing to the object in question.) Thus, the emphasis is on distinguishing this particular item as belonging to Daddy.

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Another way to look at it is whether the question is "what" or "which." For example:

What do I feed the cat?

This is for the cat. (Holds up a bag of cat food)

Contrast with:

Which one do I feed the cat? (Points to a bunch of bags of cat food)

This one is for the cat. (Holds up a specific bag of cat food)

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Another example might help. Imagine you are at a friend's house watching TV and want to adjust the volume. You look down at the coffee table and see five remote controls. You look to your friend and plead, "I just need to adjust the volume!" Your friend helpfully points to a specific remote control and says, "This one control the TV." The use of "one" draws attention to the specific one. The listener already knows that there is a remote control among the pile there that has the capacity to control the TV volume. So if the friend had picked one up and said, "This controls the TV," the emphasis would be (incorrectly) on the ability of the remote to control the TV. Instead, the emphasis needs to be on which one controls the TV. Thus, "This one" would be the correct way to lead this sentence.

In reality, both example sentences in the original question are semantically nearly identical, and it is hard (impossible?) to definitively state that any time the speaker uses "one" in this manner, he/she is attempting to shift emphasis as I've described. Counter examples can and will be found. But in aggregate, using "this one" has such an effect.