Both modernism and postmodernism doubt that a text harbors a single authentic truth. But one big difference between them is that one-modernism-presumes a single truth that human beings cannot find out, and adheres to the concept of a unified self who can endures the world of lost order between reality and fictions while the other-postmodernism-distrusts any such unknown single truth, as well as distrusting unified self. Joyce criticism to date tends to apply an extreme postmodernist conception of the decetered text and framented subject an indefinite accumulation of meanings or search for the one authentic meaning but to stage the mechanisms of its infinite productivity. They seem to go to extremes in emphasizing only the deconstruction of text and characters. But Julia Kristeva`s theory, emphasizing the "process" of deconstruction and construction, regards fixed meanings and a fixed subject as one important phase of the process. Such fixities are as important as their deconstruction. If we apply her theory to Joyce, Ulysses can be seen as a text in process and Bloom as a subject in process. While Stephen Dedalus, a hero according to the modernist notion, is afraid of his self being fragmented and therefore stands by his unifed self, Leopold Bloom, a hero according to the postmodernsit notion, is not confined to a fixed self and rather shows the heterogeneousness of his position as subject. This exiling of a fixed self, however, does not necessarily mean a fragmentation leading to madness. Bloom shows a moving balance between Kristeva`s "semiotic" and "symbolic."