Over at Culture Watch, Douglas Groothuis has written on "Basic Logical Principles Required for Apologetics". I certainly wouldn't want to encourage illogical principles of apologetics. But I reviewed my bookshelves and noticed that a number of apologetics books begin with -- or are completely occupied with -- simple, basic logic. And I've lost count of the number of "how to do logic" articles I've seen around the net from time to time. For all the emphasis on logic, these books typically don't really review the limits of logic in more than the most passing and basic of ways. Now if all the work I'd seen had ignored logic, I'd be obliged to write the part about logic; but since it's the other way around, here are some comments on not being too impressed with definitions and syllogisms:
Principle (or law) of identity That is to say, A = A. Problem? Most things in the real world aren't "A". The more interesting the thing you consider, the more difficult it is to define. The less adequate our definitions, the less certain we can be of our results. Arguments tend to gather around the outer margins of our definitions, where the definitions (and therefore the results) are less certain. Much interesting work remains to be done in exploring our definitions: learning what, exactly, is the nature of the world around us.
Principle (or law) of excluded middle That is to say, a meaningful proposition must be true or false, not somewhere in between. Problem? That's a popular formulation for a popular forum, but the popular formulation is often enough false. For example, take the statement "My mother is half Welsh." That's 100% true. So if my mother is half Welsh, what do we say about the statement "My mother is Welsh"? Seems like that statement is 50% true and 50% false. Why? Because the categories don't fit neatly. For any time that "excluded middle" is invoked, "mismatched definitions and categories" is a logically possible answer; the thing theoretically might be part one thing and part something else. In this case, Welsh and non-Welsh don't completely exclude each other; though being *fully* Welsh and *fully* non-Welsh would exclude each other. Every person or object in the real world does not always fit neatly into every category that can be imagined. The more interesting arguments tend to gather around the boundaries between categories, which in certain instances may overlap.
Logic has other shortfalls. Our assumptions are limited by the boundaries of our perception. Logic itself assumes that things are best understood as propositions and best evaluated with reference to truth. Things can be evaluated in terms of truth -- or love, or joy, or usefulness, or a number of other things. In the real world, it's possible to formulate propositions about my neighbor's cat to evaluate on a scale of propositional truth. But if you did that, you'd miss almost everything interesting about my neighbor's cat. Logic can tell you that the cat's softness is true; but it can't pet the cat or enjoy its company. If you managed to understand the cat at all with a logical method, it would have been far more work than required and risks losing the majority of what was worth knowing along the way.
Of course the case is much more pronounced with what we've done with God. We've turned Him into a logical construct, tried to define him -- questionable if we have the mental faculties for that really -- tried to relate to him as Truth. As far as that goes, it's a valid approach; if nobody were taking that path, I'd be obliged to say so and encourage people to evaluate in terms of knowledge and truth. But these days, God's most profound attributes are more often the subject of debates about their implications than they are the occasion for admiration. After all you don't admire a proposition, you evaluate it. Logic is a valuable tool in our toolbox, but it is not the only one, and neither is it always the best one. If logic becomes the only tool that we use in evaluating the world, we lose much of the more interesting content along the way.
I'd think that "loving God with all your mind" would tend to see God's profound attributes and relate to them not only with analysis but also with awe and reverence.
It seems, from real-life examples, that the formulation "All meaningful propositions are either true or false" is not itself an entirely true poposition. It does not pay enough respect to ambiguity, to the unclearness of definitions -- or to incomplete knowledge, which is an inescapable part of our human experience. A statement can be partially meaningful or partially clear, therefore partially true, partially false, or partially both. This is a common situation that plays a very real role in everyday discussions. The absolutist ideal of logic in some ways assumes that our knowledge and clarity are enough to warrant it; real-world situations show that often this is not the case. None of this is intended to diminish the right place of logic, only to show the realistic limits of logic based on limited understanding and limited precision.