An interesting take on this is in Nicholas Rescher’s Cognitive Systematization where he says that basically you need a hermeneutic circle among the axioms of a formal system and that process is the foundation.
But to your deeper question, at the level of Pure Being there is static meaning, but at the level of Process Being there must be a dynamic uncovering of meaning. Deconstruction is a method invented by Heidegger and picked up by Derrida. But of course they meant different things by it.
“We understand this task as one in which by taking the question of Being as our clue, we are to destroy the traditional content of ancient ontology until we arrive at those primordial experiences in which we achieved our first ways of determining the nature of Being- the ways which have guided us ever since. (Heidegger, 1962:44)”
“There is no sense in doing without the concepts of metaphysics in order to shake metaphysics. We have no language – no syntax or lexicon- which is foreign to this history; we can pronounce not a single destructive proposition which has not already had to slip into the form, the logic, and the implicit postulations of precisely what it seeks to contest.” (Derrida, 1980: 354)”
Thus for Derrida Deconstruction is decentering within language while for Heidegger it is getting back to primordial experiences that motivate philosophy.
Hermeneutics on the other hand is to attempt to produce a story concerning the meaning of things. Notice that Derrida and Heidegger both are trying to create strategies that will allow them to unlock meanings. For both I think there is something more like a Hermeneutic Spiral going on. For Derrida it feeds back on itself, but for Heidegger it keeps on going deeper as we keep coming back to the same place again seeing it differently because the experience is different each time. We get deeper and deeper into the primordial phenomena as we interpret the texts anew, coming back to them again and again as he did with Aristotle.
Thus both Heidegger and Derrida are practicing Hermeneutics. For Heidegger it is a way to access what is absent and buried under our history of interpretations that we take for granted and do not question inherited from the tradition. Gadamer goes on to expand on Heidegger’s idea of Hermeneutics. For Derrida we are trapped in our language and there is no outside primordial phenomena to get at, there are merely different language games (to use a phrase form Wittgenstein).
So Hermeneutics is the purpose behind the Deconstruction of both Philosophers.
But the primary difference between them is that they are operating on two very different levels of Being. Heidegger is doing his hermeneutics at the level of Process Being where there is uncovering of truth going on (http://en.wikipedia.org/wiki/Ale…). This is the nature of truth beyond mere static verification at the Process meta-level of Being where the ready-to-hand shows up along with semiotics. Heidegger said we were trapped in OntoTheological Metaphysics (http://en.wikipedia.org/wiki/Ont…) that caused us to interpret our experience wrong due to the forgetfulness of Being. Heidegger later discovered the third kind of Being which he called Being crossed out and put a line through it.
Derrida picked this up and defined Differance (differing and deferring) which he investigated by the contrast of writing to speaking. Writing had the nature of differance while speaking was a process trapped in time. You could rearrange writing after the fact, but you could not do that with speech. He focused on the trace level of things, i.e. the fact that writing leaves traces, like the cuneiform we found in the desert that the rosetta stone allowed us to translate and discover the world of the Sumerians (http://en.wikipedia.org/wiki/Cun…). On the other hand there are mute traces such as those found in Indus civilization (http://www.harappa.com/har/indus…). Derrida said our tradition was Logocentric in that we valorized speech over writing in spite of the fact that our civilization itself was based on writing. (http://en.wikipedia.org/wiki/Log…). The argument over whether there was such a thing as what Merleau-Ponty called the “hyper-dialectic between Process Being (of Heidegger) and Nothingness (of Sartre) in The Visible and the Invisible (not a direct quote) was put to rest by the fact that it was discovered that Plato had also identified a “third kind of being” in the Timaeus. See The Third Kind in Plato’s Timaeus (Hypomnemata) by Dana Miller. See also John Sallis’ Chorology: Beginning in Plato’s Timaeus.
If even Plato knew there was a third kind of Being then it must exist. And somehow that fact had been lost in the history of philosophy as the commentaries did not pick upon it. Thus Heidegger and then Derrida elaborating on the basic idea rediscovered, brought back from oblivion something forgotten in the tradition, that could be seen as a form of primordial experience thus closing the gap with Heidegger somewhat.
So how does going up a meta-level of Being effect the Hermeneutic Circle. Well one thing we know is that the aspects of Being change at every meta-level. So truth, reality, presence and identity are different at these different levels. Whereas at process being being level there is a straight forward becoming that goes forward and does not turn back on itself. But at the Hyper Being level there is a “slip-sliding away” (Paul Simon) or an undecidability (Heisenberg), or an incompleteness (Godel) that cannot be escaped. What is interesting is that Plato in the Timaeus associated that with the generation of the world. It is like the poet in the Mahabharata that actually fathers his characters in the story. So while the hermeneutic spiral of Heidegger goes forward, the spiral of Derrida feeds back on itself and is more like a mobius strip that is locally decidable but globally undecidable.
So the Hermeneutic circle must become a spiral in Heidegger as the process in time does not allow for closure but remains open, while the spiral becomes closed again with a twist in Derrida to form a mobius strip. Deconstruction at the Process Being and Hyper Being levels are fundamentally different, because the concept is transformed by being taken to the next meta-level of Being.