Some thoughts on logic

Posted by shonk at 11:57 AM in Geek Talk | TrackBack

Over at mock savvy, Neil begins his investigation of logic with an attempt to categorize exactly what logic is:

By nature, logic tends to escape exact definition; it is, vaguely put, the study of thought; and while one of the most intrinsic qualities of humanity, it does not lend itself to an intuitive characterization. This definition of logic, “the study of thought,” is equivalent to “thought about thought,” and although circular and nondescript, it is not wildly insufficient, as the reader by this point in his or her life has undoubtedly experienced the phenomenon of thought. For the purpose at hand, this simple definition provides an initial locus for the investigation of logic: the qualification of human thought.

I have to admit, I don’t particularly like this definition of logic. Neil is saying that “logic” is functionally equivalent to “metathought”. Maybe I should hold back from jumping into the fray until he fleshes the idea out a little further, but I’m not at all convinced, at this point, that metathought is necessarily logical. When I think about my thoughts, I can just as easily find myself being reflective, nostalgic, arational and even irrational as logical. For example, if I think about my thoughts and beliefs from my high school years, I often do so with a mixture of fascination and contempt. I don’t necessarily subject my thoughts from those days to a rigorous analysis, though often, of course, I do.

My point is this: as I see it, logic is a mode of thought that can be applied to virtually any subject matter, rather than a particular category of thought that can only be applied to particular subjects (other thoughts, in Neil’s contstruction). In fact, I would go further and say that logic, in the rigorous sense, is an idealized mode of thought, a structural goal which we often strive for, but, as an ideal, one which we cannot consistently achieve. In this sense, logic is strikingly similar to art; with art, too, we aspire to an artistic way of thinking, but, as even the greatest artists could probably tell you, we fall short of that ideal more often than we succeed.

In fact, this similarity between logic and art is one that has been extensively commented on by a lot of brilliant people. The most famous example I can think of is G.H. Hardy’s A Mathematician’s Apology. As W.W. Sawyer says :

Hardy is very anxious to show that the value of mathematics lies in its beauty, not in its practical consequences. Real mathematics is that “which has permanent aesthetic value”.

In other words, Hardy is saying that, although advances in mathematics have helped spawn orbital mechanics, computers and countless other advances, those applications do not justify the study of mathematics in and of itself. Rather, mathematics is justified by its beauty, by its aesthetic appeal. This may seem a bit strange to those who cannot or will not appreciate the full beauty of mathematics, but I would just note that Hardy’s justification is one that we take for granted in the case of art. That is, although art may be used to advance political causes (propaganda), to introduce people to new products and experiences (advertising) or to make a gathering more comfortable (background music), we don’t justify art on these practical terms. We view art as valuable and worthy of our attention and our effort because it is beautiful.

With those similarities in mind, I think my definition of logic, as an idealized mode of thought, makes some sense. This, perhaps, roughens some of the lustre of logic, as it does not grant logic the more generalized position of being “thought about thought” or metathought, but I think it’s clear that thoughts about thought can be artistic as easily as they can be logical.

One other important consideration is the following: if logic is, as Neil suggests, the “qualification of human thought”, then what is the “qualification of logic”? That is to ask, is logic capable of qualifying itself? Certainly not completely so, but perhaps incompletely? I guess I would have to argue that it is not. I admit this is a bit more epistemological than I like to get, but I’m not at all convinced that we can achieve a rich understanding of logic and logical thought entirely through logic. I think a broader, perhaps intuitive, context is necessary in order to understand both the power of logic and its limitations. I touched on this issue, albeit obliquely, in my critique of Austrian economics, but I have to admit that I’m not really ready yet to fully flesh the topic out. Nonetheless, I think it’s something to think about.

That all having been said, I’m really glad Neil is doing this and am looking forward to his development.