Seminar Question: Phenomenological Immortality and the Lived-Body

I should say that I am having a blast in the Husserl seminar I'm auditing. With that said, today's seminar conversation really got me thinking.

Today, we read Section 24 in Analysis Concerning Passive and Active Synthesis, and Appendix 8. Husserl concludes that the self-becoming of self-consitutions appears in experience without beginning or end. This can be called phenomenological immortality, and so it is not a conclusion about immortality as a property of the soul or endorsing anything metaphysical. It is simply a thesis about how the self is given before the self. I am given eternally as self-giving. I took issue with the fact that self-constitution is given in this way as phenomenologically immortal and consequently, I went the other direction of the whole seminar.

For me, to talk of self-givenness in this way reifies the process as it appears. There is no lived-body here. As I walked with the Professor of the seminar, I repeated my frustration and urged that the self-temporalization of becoming may appear to us as given as phenomenologically immortal fashion, but that doesn't remove the fact that self-temporalization takes place in a lived-body. It is the lived-body that also impinges and makes me aware of how I am given before myself. In this way, I urged that the constraints of the lived-body imply a phenomenological mortality.

The seminar ended with me conceding that I understood what Husserl had meant, but there is still a lingering suspicion that, like Descartes, we have reified the process of self-temporalization and implied the manner of givenness we think reveals itself as phenomenologically immortal. The Professor urged me that even if we conducted the same level of description at the level of the lived-body, we would arrive at the same conclusion. This leaves us with the question I wanted to quickly write it down here: Would phenomenological immortality of the givenness of self-constitution remain immortal if the same analysis described self-constitution of the lived-body?