The greatest changes of all come not as a thief in the night, as the oak-tree from the acorn. The most radical of thinkers is soaked in tradition; he spends a lifetime bending ancient ideas to a slightly different use, and his followers soon revert to the familiar pattern while still mumbling the novel terms. And it is so: men can work only upon what they have inherited. Fresh experience and novel problems they must understand with instruments they have learned from those who came before them. New ideas they must grasp in the concepts they already know, for they have no others; new habits they must work slowly into the accustomed pattern of their lives.
— J. H. Randall, The Career of Philosophy, quoted in Kostas Kalimtzis, Aristotle on Political Enmity and Disease
Some thoughts:
1. We cannot think in a vacuum. We never start from scratch. Even to reject a tradition is to be rooted in it.
2. A sentence is a vehicle of thought, a carrier of meaning, but the meaning of a string of written or spoken words is never confined to those words. Words neither initiate nor complete the meanings that they summon. Words have both histories and destinies, both of which are part of what the words “mean.”
3. Like any doxa, a tradition has both its satisfaction and dissatisfaction. The traditionalist is one who would remain comfortably ensconced in the satisfaction, against which the dissatisfaction is seen as threatening to his repose. The rebel would view the positive accomplishments of the tradition as excuses against participation in the energetic demands created by dissatisfaction. Both the satisfaction and dissatisfaction, affirmation and denial, are partial glimpses into the truth that tradition makes possible.
4. Fidelity to a tradition demands that we remain attentive to the dissatisfaction to which it gives rise. Every valid rejection is grounded in an affirmation that we have (perhaps unknowingly) inherited from our tradition.
5. We don’t reach truth by either simply rejecting or accepting doxa, but by thinking through it and by it.
shared ignorance 
A structuralist would say that even to speak a language means to be ensconced within tradition. Like you say, even in countering tradition we have our feet planted firmly in it.
Thanks for the comment. I can’t speak to what structuralists would say, but your second sentence is a good example of what I’m talking about, at least on the level of meaning.
“Speech always implies both an established system and an evolution; at every moment it is an existing institution and a product of the past.” That’s from a really good essay by Ferdinand de Saussure called “The Linguistic Sign.”
Thanks for the quote. One of the examples that I had in my head was Arthur Danto’s critique of history conceived as a record of what has happened in the past by as recorded by a hypothetical Ideal Chronicler. The gist of the critique is that a contemporary chronicler of an event cannot always determine whether or not the event is significant. Such significance can usually only be determined after the event, as measured by its casual impact on the things that follow it. So the historical meaning of an event is only partially available to its contemporaries, but never fully, and only at the end of some epoch. As Hegel writes, ‘The Owl of Minerva only takes flight at the coming of the dusk.” The same would apply to personal biographies, etc.
“You can’t improvise on nothing, man.” Charles Mingus to Timothy Leary
Love it. That reminds me of Schoenberg, who was in practice a musical revolutionary, but in his pedagogy insisted that his students master the classical canon before attempting to depart from it.
In a similar vein, I think it is an error to start out breaking the rules of the tradition before appreciating them from the inside. Much experimental fiction or art seems like a lazy attempt to outflank the need for the discipline essential to any craft. Avant-garde-anything has to prove to me that it understands fully the rules of the craft it is supposed to be overcoming before I will take it very seriously. I am all for experimentation, rule-bending, etc. as long as such efforts extend what the tradition can do without abandoning the hard-won fruit of the past. Gratitude and piety are eternal virtues — even/especially for revolutionaries.