The concept of truth is ambiguous in the philosophical jargon. Since Tarski showed how we can avail ourselves of the truth predicate by his theory of truth, the concept of truth has been understood in two different ways. On the one hand, the truth predicate involved in the T-sentences can be interpreted as truth for (or relative to) a particular language. On the other hand, the truth predicate can also be interpreted as truth for all languages. Quine has made use of Tarski's theory of truth and developed his own disquotational view regarding the concept of truth. However, Quine recognizes that the disquotational feature of truth has to be immanent: to call a sentence true is just to include it in our language, in our own theory of world, or in our science. But neither our language nor our science can fix truth. Quine knows very well that truth should hinge on reality but not language, and that our theory of world can be proved wrong. It seems to be this concern that leads Quine to puzzle over a transcendent sense of truth, and allows the kind of truth to be something that scientists are always in quest of, or something that ”looms as a heaven that we keep steering for and correcting to”. It will be shown that Quine's immanent concept of truth should be understood as ”truth-in-L1” in Tarski's theory, and that the transcendent concept of truth can be identified as the general concept of truth which is supposed to be applied to all languages. I will argue that both of Quine's immanent and transcendent concepts should be accommodated at the linguistic level or in the semantic project, rather than being defined and explained from a metaphysical point of view.