I am going to bring the discussion in the comments section of what is now an old post: "Why Traditional Logic Does Not Employ Truth Tables" back out to the main blog. The interest in my posts on logic, which tend to get a little technical, continues to astound me. Part of the interest in this last one is clearly the fact that the philosopher Ed Feser linked to it. My Sitemeter stats show that clearly. But even before that, my previous post, "The Difference between Traditional and Modern Logic," which just had its three year anniversary, continues to consistently attract more hits than almost any other post on this blog.
The term "logic" rivals only "science" (about which anything I say seems to invite comment and criticism) and "zombies" as the most popular topics. If I could only devise a post which dealt with all three--imagine what my Google page rating would be!
So here is my response to one of the comments on the "Why Traditional Logic Does Not Employ Truth Tables" post, which will be the first of several.
Thanks for your post. Let me take up your comments (and others here) in several posts. Here is the first of these. You say:
"M]uch of logic is usually unnecessary to see basic validity, as many arguments can be seen to be valid or invalid without any conscious analysis. Bringing the entire heft of Aristotle's Logic down an argument like, "My house is painted red, therefore the west wall of my house is painted red," is clearly overkill. All logic is about the more complex arguments. However, truth tables are very useful in proving theorems like "P V Q === Q V P" (where "===" is used as the symbol for L-equivalence).
I don't know that "all" logic is about more complex arguments. From someone in the academic world, that may be close to being so, especially in modern academic philosophy. Then again, most instances of the use of logic are outside that context and are not even close to being as complicated as that context would require.
I'm sure there are contexts that require a more quantitative treatment, as your example of L-Equivalence illustrates. But, again, this particular illustration seems to me to be required only because L-Equivalence is a concept of equivalence in the field of mathematics. I may need to understand these more quantitative concepts in mathematical logic when I am dealing with modern specialists who are dealing with qualitative concepts in mathematical logic, but in the vast majority of philosophical writings outside this field of specialty it will have no value at all.
I would go further and say that, although I studied mathematical logic in school (and have taught it at the introductory level), the fact is that there is no single instance in all the philosophical writings I have read (or any other writings for that matter), in school and without, that required a knowledge of mathematical logic. A knowledge of traditional logic, on the other hand, was indispensable.
I'm sure that will sound heretical to someone inside the academy, and I admit, as someone who does not operate in that world, to having more than a little impatience with unnecessary academic subtleties. In a world of specialists, any generalist must seem a little primitive.
I hate to sound like such a pragmatist here, but even the vast majority of complex arguments don't require the kind of symbolization that modern logic employs, and my evidence for that is the whole history of philosophical writing, the great majority of which was accomplished, not only without the employment of any kind of modern symbolic calculus, but without the least knowledge of it.
I would also assert that there is a tendency among many modern philosophers to employ symbolism in a way that not only does not clarify anything, but actually obfuscates it. I have no proof of this other than my own experience, but I can think of more than one occasion--in a lecture or some academic article--on which the speaker or author has begun some point by saying "Let P equal ...," a few minutes into which it becomes very evident that, not only did we not need anything to "equal P" in order to understand the point, but that letting something "equal P" actually obfuscated what was not a terribly complex point.
In other words, I think most of the time we just need to let P equal P and go on with our philosophical lives. But I am starting to belly-ache here. I hope you see my point, and you are welcome to try to dispel my ignorance on these points on which I am, far from being an expert, simply an interested observer.