In brief:
I think, therefore I exist (Descartes)
We love, therefore We exist.
In full:
The lyric parallels a key philosophical writing of René Descartes.
A summary is:
1000 Word Philosophy
If you are reading this, then you are probably looking at a screen or a piece of paper. Think to yourself: “I have some paper in my hand,” “I am in front of a computer” or whatever fits.
Is your belief here certain? Is there any way that you could believe this, yet your belief be false? Is there any possibility that you are mistaken about this belief? René Descartes (1596-1650) argues you could: this belief, and almost all other beliefs, are not certain.
Descartes argues that there is one clear exception, however: “I think, therefore I am.” He claims to have discovered a belief that is certain and irrefutable. Perhaps there is no saying more famous in philosophy than this phrase, often known as the “Cogito” after its Latin phrasing, “cogito ergo sum”.
The song lyric may be interpreted as hope of drawing a similar conclusion. A conclusion that “love” (being a belief shared by two people) is certain evidence of a “We”. Just as Descartes argued that thought (a certain activity of one mind) is evidence of existence of an “I”.
The “we” (with object form “us”) is real and of long usage as a pronoun to represent married couples, lovers, parents and so forth.