In computer programming, there is a concept known as "Garbage In, Garbage Out": if you put in bad information, then even a flawless computer program will give you bad results. Think of it as trying to solve "2+2" on a calculator, but accidentally typing "3+2". The calculator did its job. It didn't know that you made mistake. You entered the wrong number and the calculator correctly gave you the wrong answer. This concept is easily applied to discussions, arguments and debates.
On a web forum I used to frequent, one of the other people on the forum posted about an old church in the UK that was turned into a pub (http://www.falkirkherald.co.uk/news/local-headlines/former_church_turned_into_pub_1_292212). I and some of the other non-religious forum members saw nothing wrong with this. The church was no longer being used by the congregation and the new owner went through all the work to start a pub which created some jobs. To a few of the more religious forum members, this was an outrage. To them, the church was still a church and should be treated with respect. As with all arguments on the Internet, the debate consisted of both sides repeating the same arguments until some new controversy arose.
The reason why the debate went nowhere is because both sides were starting from different fundamental assumptions. The people on my side of the debate assumed that it was just an old building that once was a church. Those disagreeing with us assumed that it was a church and therefore a holy place. Because both sides started from different points, it was not possible for us to find common ground. At one point in the argument, I realized this and suggested that we would just have to agree to disagree. One forum member who disagreed with me then accused me of sticking my fingers in my ears and humming loudly. I pretty much never took him seriously again after that.
The point of this anecdote is to underscore the importance of basic assumptions as foundations for developing thoughts and arguments. Other posts I plan on writing are going to heavily rely on this idea.