“…I can see [symbolic logic] may have value in an academic sense, and I'm an academic, but I'm not sure I trust it: is my distrust a knee-jerk ignorance, a romantic fuzzy-headedness, or something that is worth paying attention to?”
I don’t think there is a simple answer to this question, alas (your name fits so very, very nice in places, mon frere!). Not really knowing you v. well prevents a direct answer, but let me share some thoughts with you.
First, I think that every student everywhere should at least take a first year logic course. It is difficult and requires a high degree of dedication, but teaches rigour and clarity of thought. Personally, I felt that after taking my Logic I course my essay writing skills improved: it is like brain-lego for thought & theory construction. Thus, I feel quite strongly that it is important in an academic sense. I mean, I’ve read some people’s essays where the clarity of thought is v. murky &/v the connection between ideas, while present, doesn’t “flow” or readily present themselves. I feel that knowing a bit of SL teaches a person how to structure paragraphs much better—esp. in developing an argument: state the paragraph’s main point in the opening sentence, link the chain of evidence supporting claim in a clear, precise, and logical manner, conclude the paragraph by restating the now supported point. Begin the next paragraph hot on the heels of the point just argued for previously. I feel a bit of SL provides the skills to write tight, clear, and concise papers. Definitely a plus for today’s busy people: to the point and not superfluous.
Second, logic, to some, has a bad name. I feel that some people tend to look at logic and figure it is for the machines and computers—what’s logic doing in a humanities department?! I mean, for someone either not interested in logic or taking it because hir compsci degree requires it logic likely seems v. much like math did in school: when are we gonna’ use this? This perhaps might generate a “distrust” in logic for some. Here, I would say this is linked directly to the idea that humans are spontaneous and free and that notions of “logic”—in its cold and calculating ways—tie people down and chain them to “contrived” structures. Again, what human endeavour—no matter how profound—doesn’t tie its followers down to contrived notions?
Also related are historical movements—such as “Logical Positivism”—which were based on some sort of “logical” foundation (although, funnily enough perhaps, tenets of “Logical Positivism,” IIRC, are all stated in “natural” language!), and have also fallen into disrepute through their abysmal failures.
Third, I think there can certainly be a “romantic” side to logic; however, this isn’t going to come out in most people. I tend to think of some of the great logicians here and their passion not only for logic as a study, but for life in general. I also tend to think of some of the people in history who made significant contributions to our growth who were, if not learned in formal logics, then were at least close to paradigmatic examples of what it is to think clearly and logically about such-and-such.
Thus, to conclude, regardless of what I’ve said above (if it doesn’t “ring true” to you), I do think that your “distrust” of logic might be something to pay closer attention to, and I also feel that no matter how clear and crisp a thinker you might be, there can be no harm done but only possible improvement to your abilities as a “logical” thinker if you take the time to explore SL. Moreover, learning to think and express yourself in logic needn’t stifle any creativity or spontaneity—it certainly hasn’t made me any less absurd!
I think that Lurid has got it pretty much correct when he says, “…it should be noted that people often use ‘paradoxical’ to mean ‘counter intuitive’, whereas in logic these sorts of terms are much stricter in meaning.” I think that the general or common sense of ‘paradox’ is akin to ‘counter intuitive’. However, on analysis, contradiction, paradox, absurdity, and binary pairs all come out to be the same sorts of things. This is part of the work that I’ve been doing for the last few years.
Looking to the Oxford Dictionary of Current English we find:
paradox n.. 1a seemingly absurd or contradictory though often true statement.
As far as I am aware, logic simply doesn’t deal with paradox; that is, in any logic I am aware of there is neither definition of paradox nor rules or procedures to deal with it. This is likely because in logic a paradox is going to be translated as a strict contradiction—a clear violation of the law of the excluded middle. This is our P & ~P. I mean, look at some of the more common paradoxes:
1) We have the Schrodinger’s Cat Paradox manifesting as the paradigmatic example of the superposition of quantum states: the cat is dead & the cat is alive.
2) We have the classic paradoxes of Zeno. The Arrow shows that a moving object can’t be moving, Achilles and the Tortoise (and its variations) show that Achilles can never catch the tortoise even though he is clearly a faster runner than it; or, Achilles cannot even start the race because there is always half the distance from him to the next step.
Clearly, in these sorts of paradoxes their symbolic representation is going to be our P & ~P.
Thus, it appears more like we call some occurrences of P & ~P paradoxes simply because they seem as necessary contradictions for our very phenomenal existence, whereas if we don’t have to hold a contradiction out of necessity, then we seem somehow happier to call them “absurdities,” or “contradictions,” or “impossibilities.”
“…there is a continual desire to reach an absolute point of clarify and understanding of the world”
For some, yes—anyway, I find the phrasing here particularly poignant to the issue in at least a few ways. Notice the “paradoxical” or if you prefer, “contradictory” nature of the metaphor being employed (also note that this isn’t a criticism towards you, Tom, but merely noting the way that most of us would commonly phrase a similar linguistic structure to convey a similar meaning). ‘Continual’ juxtaposed with ‘point’; that is, continuity with discreteness as a binary pair. We also have, although a little deeper and more implicit, two further pairing: {Self, Other} and {Immanent, Transcendent}. The {S,O} pair is generated when we recognize that this “continual desire” has to be a desire that someone holds—a Self; and, the Other stems from the v. fact the desire is directed towards understanding “the world”—understanding the Other. The {I, T} pair is even more abstract. Since we are looking for an “absolute” we are looking for something unchanging—eternal and fixed. Now, without getting too into it, these are qualities associated with something that must necessarily transcend the changing and fluctuating world. Solutions and understanding regarding the world are formulated within the world, and so, are immanent to it.
“The terrible danger is that we collapse reality down to an unrealistic and absolutist view in a desperate attempt to reconcile contradictions in our thought…”
No doubt! Much of the work that I’ve done in my investigation and analysis of the “contradiction, paradox, duality (binary pairings), and absurdity” connection has been not to resolve, banish, or degrade these things, but to express their apparently central and integral role in the construction/invention of our phenomenal experiences. Embrace not shun! |
