(Edit) My comment is probably a little more aggressive than I would have preferred. I figured I would give a fair warning.

The connection is obvious to me.

But you are not important when trying to persuade someone else of a point.

I believe they do prove a point. The fact that Paul, who invented Christian theology, just once in his life said, "See to it that no one takes you captive through hollow and deceptive philosophy, which depends on human tradition and the basic principles of this world rather than on Christ," shows that Paul had deeply flawed epistemology.

And what, according to Paul, are the basic principles of the world? Do you know? I highly doubt he is talking about science or math or the roots of meta-physics. The second half of the sentence can make a valid point in the sense that philosophy should not be dependent on Christ and if there is a collision between Science and Christ this passage is telling you to go with Christ. But without specifically studying what "the principles of this world" means, the Christian skeptic will probably choose to interpret "this world" as "ungodly nations" and unless you can back the argument up with something more than how the NIV translated that particular sentence you are dead in the water.

Futhermore, Christians are not making a mistake when they do that; the mistake lies prior to that in their reasoning.

Actually, they are. Context is extremely important when studying the Bible. Context is important when studying anything. Throwing out the context is like watching the end of a movie and deciding the character is the antagonist because it killed someone.

They are operating under the assumption that you don't need to check the context of the verse. God said it, that settles it. Contextual criticism is of the devil; it assumes that the world is not full of simple objective moral truths. So turnabout is fair play.

In all of my conversations with Christians, and having attended classes that specifically teach how Christians are supposed to study the Bible, the overwhelming majority believe that context is key to understanding a passage of scripture. If you want me to find specific people who say this I can, but I flatly claim that your statement is wrong .

Noted. Usually I pick whichever I can find first, or whichever sounds the most well-written. The KJV sounds grander, but the NIV is the clearest, with NASB intermediate on both measures.

The KJV has been rejected in most Christian apologetic circles as a fatally flawed translation. Personally, I would not use it all when talking to apologetics unless they specifically state that it is a valid and unerring translation. Again, if you are curious about why this is I can elaborate.