Apologies for being absent. Life has taken a turn toward the even more busy. Nonetheless, earlier this afternoon I was considering the common logical fallacies one sees pointed out in more trafficked blogs with similar content to this one. One common fallacy is the false dichotomy. This actually got me tangled up considering it, because I realized I cannot name a situation in which, to some extent, a dichotomy is not “false.”
I’ll be the first to admit that by and large symbolic logic and other such aspects of philosophy are beyond my ken, so perhaps I’m thinking about this in a way that itself does not make sense, but every practical example of a dichotomy I can conceive of seems wrong somehow. Let me explain. Possibly one of the most ubiquitous dichotomies in our society is that of male and female (masculine and feminine, if you like). Yet, I can ask the question, “How masculine is femininity?” And there could be many different answers to that question. My point is, how true could the dichotomy be if there is some overlap between the two categories.
Even something less subjective and abstract seems to cause problems. The first little thought experiment that popped into my head was this: red and not-red. On the surface, this might seem trivial, but let’s say we’re displaying objects from both categories on a computer display. In this context, at least, one could ask “How red is not-red?” and a legitimate answer could be supplied. Even something that does not appear red at all could have a non-zero R value in its RGB code. Does this invalidate the red vs. not-red dichotomy?
Perhaps I’m being too picky, but to borrow a page from linear algebra, there are plenty of tools that one can use to demonstrate linear independence of vectors. And it seems to me that for all practical purposes, there will always exist a projection of one side of a dichotomy onto the other with a non-zero value. Granted, we can travel to the abstract and see that clearly the vector (1,0) cannot be expressed in terms of the vector (0,1), but I don’t know if such a clear-cut difference could ever be clear on a less abstract, macroscopic scale in terms of a logical discussion.
So I guess my concluding question is really this: are all “useful” dichotomies false? The definition of useful, I guess, being left as a question for another time.