Is "so" a pronoun?

Solution 1:

The Cambridge Grammar of the English Language has three pages on anaphoric so. It concludes:

...its properties are unquestionably unique, and we do not believe that anything is gained by forcing it into one or more of our general part-of-speech categories.

Consider that so can stand for a noun (We are doctors. So are they.), an adjective (I’m sleepy. So is she.), a verb (Mine broke. So did hers.), a content clause (I thought that salamanders were amphibians. She thought so too.), a whole sentence or idea (The best things in life are free. I’ve always said so.) etc. Yet it can’t be the subject of a sentence. (In So am I, subject-verb agreement shows that I is subject, not so.)

Solution 2:

In sentences like "I think so", so is an adverb.

This is not surprising if you think that the word yes is also an adverb.

Solution 3:

No. "So" is never a pronoun in English. In the case you cite it is an adverb, modifying "think".

Solution 4:

I believe it is a demonstrative pronoun. See here and here. (Of course, the internet has much more to offer than that, as you should know.)

In these cases, the specific referent must be mentioned previously in the text for 'so' to work in such a way. 'This' and 'that', among other demonstrative pronouns, work in a similar way as well.

Feel free to correct me if I'm wrong since I've only been a student of linguistics for about a year and a half now.

Solution 5:

We need to be careful with the idea of a demonstrative pronoun. Consider if we are standing in a store and I say, "I don't like that." You have no idea what I don't like and the sentence is meaningless unless I point to something. In this case, my communication includes a gesture; the gesture is the noun, and "that" is a demonstrative adjective modifying my gesture.

Generally what we call demonstrative pronouns are really adjectives that would modify a noun, but the noun has been dropped because the sentence is part of a chain of conversation and is understood. This is similar to a one word sentence, "Yes." The main part of the sentence has been dropped. This does not mean that "Yes" is both a subject and verb simultaneously forming a grammatically complete sentence, nor that it is a demonstrative pronoun. It means that in conversation complete sentences are not needed in order to be understood.

Demonstrative pronouns, if they actually exist, should not be used in legal contracts or legislation because it results in ambiguity. In conversation they are fine, but then, a lot of things are.