To say that Ted is on St. Catherine’s street is true or false, but it is objectively true or false. It is true (or false) independently of what people believe or perceive (I will agree to define objectivity in just that way: that something is objectively true just in case it is in no way dependent upon either beliefs or perceptions). However, to say that “Ted is there” meaning on St. Catherine’s street, is not objectively true because it is dependent on the speaker’s perceiving a relation of there-ness between herself and the referent Ted and/or St. Catherine’s street. For instance, if I were there with Ted then it would be true to say “Ted is here” instead of saying “Ted is there” (which by contrast would be wrong). There is no objectivity to the terms ‘here‘ or ‘there‘, and in fact I don’t know if I can think of anything more subjective than something’s being here or there. Any sentences involving either ‘here‘ or ‘there‘ are plausibly irreducibly subjective.
Moreover, “Ted is here/there” is, supposing it were true, a truth which may have been false (in another logically possible world, it was false). However, the proposition “I am here” seems to be true is a significant way. It isn’t just the case that it is indubitable, or even indubitably true, or even self-evident. “I-am-appeared-to-Redly” is all of those when true, but there are logically possible worlds in which “I-am-appeared-to-Redly” is not true. For instance the actual world where right now I am not experiencing a perception of ‘red’. Thus, I can utter the sentence “I-am-appeared-to-Redly” and be straightforwardly wrong just in the case that I am not experiencing ‘red’. However, there is no logically possible world in which some subject S utters “I am here” falsely.
Thus the sentence “I am here” is irreducibly subjective, and necessarily true. Maybe this kind of irreducibly subjective necessary truth is analogous to Descartes’ famous Cogito Ergo Sum, where it seems to be an irreducibly subjective and necessary truth which just doesn’t contribute anything of import to Modal Logic. Just because I know that I exist, and that I intuit it to be a necessary truth, does not mean that “that I exist is a necessary truth” in any objective sense. I can imagine logically possible worlds in which I do not exist, and I can imagine them without any confusion on my part (e.g., I could intuit that I am a contingent being).
Moreover, more than just being a necessary and self-evident truth, “I am here” is an analytic truth: one whose truth can be derived solely by understanding the terms and/or connectives in virtue of which it is true.
… Or perhaps it’s only true of a spatially extended being.