I was wondering if you could explain what you mean by archaeology being biased?

In terms of what portion of historical information we have in the record, out of all possible information--very little. I won't put a number to it. But think of all the multitudes that exist, or have existed, and how much of their lives is actively recorded. Project that mentality into the past and think about how much of peoples lives, actions, thoughts, beliefs, etc, was recorded in the first place, and how much of that record survived, and how much of that has been adequately mined for all its potential information...let's just say it's probably a minority share. That's not to say historians don't have much to go on or that they don't make good use of it. But if people were hoping for an eventual unified catalog of everything ever, it ain't gonna happen.

Now on to the more interesting part of your question, which is how much historians can know. Well, history is not a science. It has experts who employ rational, deductive interrogations of their sources. Through both individual effort and peer review (historiography), historians are often able to construct sophisticated reflections of that past that may come close to truth, but at the end of the day interpretation of sources is essential to historical scholarship. History is interpretive, and therefore it is human. There is no such thing in history as absolute truth or objective knowledge. The "objectivity question" is something historians regularly revisit among themselves. While objective truth used to be something historians believed they could achieve, that idea has been debunked for a long time now (the objectivity question could be a whole post on its own, forgive me for moving on).

It's also clear that the reigning interpretations held by historians are heavily dependent on the social conditions of the time in which they are made. I've read works discussing the revolutions of 1848 which viewed those conflicts through the lens of Wilsonian self-determination. It's not a coincidence that those works were written shortly after World War 1. It's also not a coincidence that histories of the American Civil War did not incorporate heavy racial themes or widely acknowledge the centrality of slavery prior to the Civil Rights Movement. These concurrences, to me, reflect on the very purpose of history in the first place.

It's also where my opinions become solely my own. I'm only speaking for myself here, but I've increasingly come to view history as a largely personal endeavor at its heart. Historians, as professionals, perform an important function in treating sources on the past seriously and with care. Their work is neither trivial nor random just because they and their process are interpretive. But their efforts are also bound to the larger contexts in which they work, and this helps shape their resulting scholarship. This sounds like a weakness, as though historians' work is tainted by worldly forces they can't escape, or as though the goal of objectivity is continually denied. But objectivity and detachment from contemporary forces that define all our lives might not be the point after all. If the goal of studying the past is self-reflection, to better understand who we collectively are by examining who others were, then to wrench history from its relation to the present would be to render it inert.

Instead, the history that historians produce through their interpretive research is meant to be reacted to--by you, by me, by each individual classroom student, book reader, or museum goer, etc. Just as your life's progression is guided by your experiences and the choices you base upon them, so perhaps should society's progress be based on its collective experience. I, as the historian, am responsible for presenting to you the best image of the past that I can, one based on rational, expert interpretation of sources. But the real value is not in my presentation of it but in your internalization of it and in what you think and do about it. When you use the past to personally reflect on yourself and the world you live in, that's when our purpose for remembering the past has been fulfilled.

History will never be exact or objective. That isn't changing. But viewing history this way means that our interpretive lens doesn't taint history but rather gives it its purpose.