So far, I have suggested that one can think of the dialectic as a structure, where a system changes as a result of the interaction of opposing tendencies it contains, a structure which, though not universal, is common, and which in particular may be characteristic of capitalism. Here, I'll examine the claim in that last clause and try to remove the hesitant "may be".
Why and how might dialectical forms be characteristic of capitalism?
Let's start with how. There are a number of phenomena in capitalism described by Marxists as "contradictions". Some of the more important:
- Goods and services are produced socially, by the cooperation of vast numbers of people in a complex, organized division of labor, but consumed privately, without any planned allocation and according to no principle of human need. Social production gives society the infrastructure for social consumption but our rulers struggle to ensure that it is not so utilized.
- Everything that is produced has two kinds of value, an exchange value and a use value. Exchange value requires some sort of use value. But things which people desperately need, such as medicine, sometimes do not have a high enough exchange value to be produced, while things with a high exchange value, say oil, may have a negative social use value.
- Capitalism leads to a great increase in humanity's productive capabilities. But this creates the possibility of crises of over-production, where there are too many goods to be sold. This, in turn, halts production, and destroys productive capabilities.
- Capital accumulation is necessary for capitalists to compete, and maintain their profits. But labor is the source of their profits. As they accumulate capital, the proportion of their investment which goes to labor decreases. In the context of competition, this ultimately decreases their profit rate.
- Capitalism increases humanity's control over our environment, with the advancement of technology and the accumulation of resources. This creates the possibility of greater material freedom. But in fact, under capitalism, society itself confronts each person as something external and impersonal, a set of "forces that arise from [our] relations with each other and which have escaped [our] control", and which rule our lives.
- Capitalism creates the modern working class, which has an objective interest in destroying the system which gave it birth; thus Marx calls the proletariat capitalism's "gravediggers".
- The working class has a tendency, according to its own objective interests, and driven by the class struggle, towards socialist ideas and action. But it is also pushed, given the way that its members, if unorganized, compete against one another for jobs, housing, and so on, and given capitalist ownership of the means of communication, towards reactionary ideas.
- In the realm of ideology, by developing science, by destroying feudalism and its mystified social bonds, by giving everything a calculable monetary value, capitalism encourages a materialistic view of the world, albeit a mechanistic one. But at the same time, by creating an independent intelligentsia, by putting ideological production in the hands of a distinct, privileged class, it encourages an idealistic view of the world, which sees ideas operating according to their own independent logic and driving history. (Lukacs describes these tendencies as the "antinomies of bourgeois thought".)
Nor can we say definitively that one of these points is the most fundamental, and the rest derivative. You can't define classes independently of labor and capital, or vice versa. To give any concrete content to the most general assertions about the relationship of humanity to nature, or society to production and consumption, you need to say something more specific about social relations, which means class relations.
But then how do we understand the relationship between these different theses?
The way suggested by the dialectical idea of the "moment", a way which I think is correct, is to see these points as expressing different aspects of a single system, one which can only be fully understood as a whole, and which has a single causal history, but one which can be approached from many different directions, any of which may be necessary in a given context.
From this perspective, it is in a way a mistake to ask why capitalism has a structure which we can call dialectical. There is no answer short of an analysis of its whole history and internal logic as a developing process. But it does.
So. If the Marxist analysis of capitalism is correct, we have at least a minimal validation of dialectics, within a certain field. But it is not yet a complete validation, because from what we have said, we still don't have a reason to use a dialectical method.
Why focus on the dialectical structure of capitalism, rather than other aspects? What's interesting in dialectical forms, abstracted from the context of capitalism? Why should the dialectic be an independent field of study - if it is validated by, and valid only within, its appearance in capitalism? What's the relationship between a commitment to overthrow capitalism and the use of dialectics in analysis?
 That's a very quick sketch. Here's a much longer version.
 Lukacs, History and Class Consciousness, p. 14.