When two college kids in a coffee shop begin discussing philosophy, you know it’s going to be a long night. I remember doing this, but it wasn’t over coffee; our conversations always took place over pizza at 2 am. Everything is fair game to amateur philosophers, and one simple question could take them down long, winding, scary-looking roads. One thing you might want to see them do is set up ground rules for their discussion. However, today, the likelihood of postmodernists setting up rules for discussion is pretty distant. Postmodernists are absolutely certain that there are no absolutes.
Our postmodern debaters might instead toss logic aside for the purpose of wide-ranging debate. They evade moral boundaries with “that’s your truth, not mine.” Comfortable with opposing presuppositions, the two decide that what’s true for one may not be true for the other, but that’s okay.
What they don’t realize, while coffee cools and conversation continues, is by setting aside basic truth, they have lost the means by which to build a real discussion. What follows is nonsense. Essentially, they’ve washed away the very foundations of logic in pursuit of erudite, meaningless philosophical dialogue.
Considered the father of logic, Aristotle recorded what he observed in the world. He is renowned for his laws of thought, one of which is called the Law of Non-Contradiction. This law seems so simple, yet its application threatens postmodern thought. Thus the reason that many teachers and scholars today depart from (or ignore) Logic: the Law of Non-Contradiction is an inconvenient truth that wreaks havoc on their pseudo-intellectual debate.
This law states that a thing cannot be both true and false at the same time. In other words, something cannot be both A and non-A. That seems like a no-brainer. However, most likely our postmodern coffee-house debaters have abandoned this basic law of thought. “What’s true for you may not be true for me” cannot exist as a basic truth in light of Aristotle’s law, because two conflicting or contradictory statements cannot both be true.
Take for example something a blogger recently posted. He made a seemingly innocuous statement about religions: “True religions encourage good behavior.” (I won’t copy the entire sentence, because what follows that statement is a fallacy I may choose to take apart another time.)
Let’s unravel the phrase “true religions.” That in itself is a contradiction. Every religion claims to be a true religion. (Honestly, why would you not claim to follow a true religion? Put it another way: why would you follow a religion you knew to be false?)
Most religions claim that their god is the one true god (or, in some cases, the many gods who reign and rule). If they don’t hold to a deity, they do follow certain paths to holiness or heavenly existence. So if religion A claims its god is the one true god, and religion B makes the same claim, each religion has just vowed the same, yet conflicting, statement.
By saying “mine is the one true god,” you have implied that all other gods are not-true. If that is so, you cannot say that religion B’s god is also true without abandoning logic. Thus only one religion’s truth claim can be true, according to the Law of Non-Contradiction.
Go ahead and try to believe that all truth claims—even contrasting ones—are valid. Believe that your coffee is both cold and not-cold. Just realize that you have kicked the foundation out from under your discussion, and it’s going nowhere.
Writing Rhetorically 
Your logic is logical to you, but what if it’s not logical to me?
I reject your reality and substitute my own!
I think the postmodernist thought of “what’s true for one person may not be true for another” stems from the fact that our discussions are never truly based on reality. Reality is something we never truly experience. We only experience what our senses tell us and then only the information our mind filters through and says “this is important” based on our predisposed beliefs and constructs about life. So in a way it seems more that it’s a perceived truth or falsity that is “true for one but false for another” rather than actually claiming that one thing is both true and false at the same time.
Also I think there is a place for throwing out logic simply for the sake of throwing out the boundaries of our thinking for sake of reaching a higher level of mental creativity. But you’re right, to through out logic is to destroy the common understanding of a discussion which is to find the truth, but if the purpose is to individually find truth, then there isn’t much need for logic (necessarily) since the discussion could simply be meant to stimulate ideas between individuals.
Unfortunately you beg the question here. Do you need to throw out logic in order to reach a higher level of mental creativity? Is logic separate from creativity? You answered yourself in your next sentences by acknowledging that logic is the foundation of all thought. We cannot reason without it. We cannot solve problems without it. And who are we, all day long, but problem-solvers?
Are we problem-solvers? Or can we have a discussion which has a purpose other than solving a problem? Can’t a discussion be about stimulating each individual’s personal thoughts rather than having to solve everything all the time? Life would be pretty bland if our entire purpose was to solve problems.