Subjectivity and logic

A friend of mine challenged the system of formal logic claiming that since logic has a subjective nature, trying to formalize it with hard and fast rules will ultimately be problematic. There certainly is some truth to the premise, since logicians will still disagree with one another, which I suppose is evidence of logic's non-mathematical nature. The question I wish to pose asks what element in logical thinking will allow two intelligent and informed individuals to come to two different conclusions?
While some aspects of logic work with mathematical precision, I will contend that the translation of normal sentences into a more purely logical forms add a degree of interpretation. In addition, I think that one's individual values can play a role in determining what constitutes an okay premise or not.

Howdy

Hello. My name is Tyler, and I'm a psych major on my last semester here at MCLA. I'm a multi-instrumentalist and I host poetry open mics at the Parlor (next one thursday 12th). During my time here, I have begun the study of the neuroelectric correlates of meditation, a line of research I also intend to pursue further this semester (in the new awesome building!) . I'm very receptive to meeting new people, so please drop me a line. I've dealt with enough people in my life who are logically challenged, often with disastrous results. Perhaps by honing these skills, I can also improve my ability to help these wretched people learn to reason as well.