Unlike Kant, says Houlgate, who attempted to show that through the use of analytic judgments we "do not proceed to a new and different determination, we simply gain greater clarity about what we began with" (whereas with synthetic judgments we really do discover new determinations), Hegel seems to think that new determinations CAN be found analytically -- that is, "the concepts of becoming and determinate being are derived by Hegel simply by considering what is involved in thinking pure being... by 'analysing' that initial determinate concept." (p. 37)
So, in contrast to Kantian thinking, which concerns itself with developing the relations of identity or equivalence between things and/or ideas, Houlgate explains that "Hegelian logic is 'analytic' to the extent that it merely renders explicit what is implicit or unthought in an initial category. However, by explicating the indeterminate category of being, we do not merely restate in different words what is obviously 'contained' in it; we watch a new category emerge." (p. 38, emphasis in original) Thus, "we are required by Hegel's method of 'analysis' to undertake constant and subtle revisions of the way we think." (p. 38) It is this approach, I think, which is a great strength of Hegelian logic. But it also contains an inherent weakness since, to the extent that it is wedded to an historical or material ontology, it results in an inevitable incompleteness that can never be resolved. (I think this is something of what Derrida tries to say vis-a-vis Hegelian thought.)
Houlgate explains that "The dialectical principle, for Hegel, is the principle whereby apparently stable thoughts reveal their inherent instability by turning into their opposites and then into new, more complex thoughts." (p. 38) Hegel believes that a system built upon this principle creates freedom for thought, as thought is no longer forced into the mold cast for it by certain logical necessities that have been dictated by various philosophers. Rather, the only 'necessity' is the logic of thought itself, which is such that there is vast dialectical space for freedom. The question, however, is whether such 'freedom' will truly make one free. It is perhaps instead the case that such openness will leave one actually trapped by the very dialectic that promised to make one free; after all, to have endless possibility for development and the inability to achieve it can very easily become a kind of existential bondage.