My Excluded Middle
March 21st, 2009
In logic, the law of the excluded middle states that the propositional calculus formula “P ∨ ¬P” (”P or not-P”) can be deduced from the calculus under investigation. It is one of the defining properties of classical systems of logic. However, some systems of logic have different but analogous laws, while others reject the law of excluded middle entirely.
Where I seem, to myself, squeamishly non-committal, is how I flee from P or ¬P. I do equivocate, P, but also, you know, from another point of view, ¬P. I have a weakness for reconciliation. It is this, I think. Not-P grows monstrously, refuses to stay the mere negation. P is a single small thing, fragile, and not P is the entire rest of the universe, with its crushing magnitude. P or not-P taunt me, mother or not-mother, writer or not-writer. Non-logically, somehow, there’s conflation and writer is among those things that not-mother includes; not-writer is implied by mother. There’s a fallacy, the artificial dilemma, and I keep getting squeezed into it.
I had this liberating moment with Virginia Postrel’s Substance of Style, which is a lot of pages to mostly make the point that we’re aesthetic creatures, and should make peace with the fact that we find aesthetics appealing instead of trying to always dismiss the frills as contrasting with quality and substance and meaning; that given adequacy of two options, we’re going to then choose the one that has an aesthetic appeal, not because we’re superficial and shallow, but because that’s what aesthetics is. And this may have been obvious to everyone else, but it drove home for me the sort of shame I can feel at liking the pretty, the fact that I have bought, somehow, into this false dilemma “smart versus pretty.”
And of course there was the epiphany about the epiphany: the epi-epiphany? That I have a habit of regularly conflating qualities that are on independent axes. That what intrinsic value or utility something has can land on the X-axis somewhere, and the aesthetic appeal can be somewhere on the Y-axis, and happiness lies in the upper right quadrant. But we do this all the time, with all sorts of things, finding we have to choose between the inexpensive and the environmentally friendly, or between safe/stable and interesting/exciting, writing that is literary or writing that is popular.
I recognize, of course, P is supposed to be a proposition, one to which we can assign definite truth value: Mara is a writer. Mara is a mother. Propositions P and Q where there is no implicit relationship between P’s truth value and Q’s. It’s just that my propositions are prone to conflationary thinking, the sort that used to drive me crazy, where you assume because I am a feminist I am going to have this position on the environment, on labor, on NAFTA. Which, I may in fact, but only as correlation. I have truths that don’t fit into neat propositions and propositions to which I can assign no truth values.
Maybe this is another manifestation of polarizing thinking, an inward version of the interpersonal dance, that we form twos because we are alike, we complement one another, only we inevitably proceed to divide the world between us, the final differences have a weight beyond the preceding million similarities.
The first polarity of my life, the younger sister, so much like me, and yet we were both shaped by all of the years we spent trying to prove how different we are. Only now we understand each other, that sometimes the differences that would appear most crucial seem like superficial ones, different expressions of the same impulse. You step back and look and we have lives with the same elements, the smaller people, the instruments, the books, the husbands.
The polarity that arises in friendship, as if to stem competition: I’ll be the happy homemaker and you be the ambitious and career-minded. Only, it turns out, you have a commitment to your family, and I need more than mine.
The polarity that creates the sparks in the marriage, when gratitude for the things he provides that I couldn’t, a spontaneity, a willingness to live in the moment gives way, splintering, into resentment that I must always worry about the bedtimes, the homework, the practicing, the vegetables, the chores, the character, the punctuality and I cannot find my way back to the whole I was before we divided the world between us.
I think time is the proposition that doesn’t yield a middle, time spent grocery shopping is time not spent reading and writing. I become divided feeling. Time is where I feel squeezed out, wrung out, must make the sacrificial choices, spend the evening regretting the blog entry instead of the violin practice.
New propositions, then, that time has not ended yet, that it is what will be, what has been, what is being in abundance, and that nothing is being sacrificed, that the tension I feel of wanting to be in two places, two roles, two lives at once is merely that of a limited perspective.
March 22nd, 2009 at 9:40 pm
I think you nailed it. Propositional logic doesn’t see in gray, it goes one way or the other. It is one-dimensional.
Project our lives into one dimension: time. Now we can see the exclusion of the middle. Time is our limiting reagent.
March 23rd, 2009 at 10:04 am
What’s that saying? We can have everything, we just can’t have it all at once? Something like that.
There are many reasons why I shouldn’t blog everyday, not the least of which is that I can’t even keep up with my own comments let alone make any comments on other people’s blogs. It feels a little selfish and lopsided.
March 23rd, 2009 at 12:40 pm
What’s all this about a banjo, then?! And a new flavour of kombucha?! I turn my back on you for ONE SECOND missy….
I want to say something smart about this post but find myself feeling extraordinarily dumb. Also nearsighted, suddenly, as I squint at P and not-P. What happened my brain? Why everything blurry?
Well, but I exaggerate (being “pretty” instead of “smart”?). And I come back into sharp focus with the last four paragraphs, especially, laser-like:
“The polarity that arises in friendship, as if to stem competition….” YES! Because there’s some sense of dividing the (as it were) booty, and you actually LIKE the green ones, don’t you? And that way there will be plenty of red and purple ones for me?
(I actually thought lime was my mom’s favorite flavor for, like, decades.)
And even better this:
“…and I cannot find my way back to the whole I was before we divided the world between us.” The Brujo goes spring-break cactus-hunting for five days, and this smites me less than twelve hours into his absence. Look at all these parts of me I forgot about! Still there!
Perhaps one of the ways, then, in which time is (momentarily) merciful. What I refer to, to the End of the World students, as literature’s hungry desire for a “do-over.”
Lately (she remarked irrelevantly, or maybe not) the only poet I can stand to read is Rumi.
March 24th, 2009 at 8:11 pm
Oh my God, this is brilliant. I suddenly got it. I’m sorry I’m so dense.
March 26th, 2009 at 6:09 am
What I like is the idea that P always has some of not-P in it, and, conversely, not-P always has some of P in it. It is the prakriti and the purusha, that which is always changing (prakriti) and that which does not, is eternal, inexpressible, beyond time (purusha). And there is this Sanskrit chant which basically says “All we cannot see is verily the infinite. All that we can see is also the infinite. The whole universe has come from the infinite. Although the finite universe has come from that, it remains infinite.” Basically, both are perfect, and even if we remove a part from that, it still remains perfect.
Does that make any sense in relation to this post?? Or would it suffice to say, the ever-expanding middle is merely a function of age, and is to be accepted as such. Oh, that’s “excluded” middle….Happy Birthday!
April 10th, 2009 at 3:47 pm
And, well, of course I thought of you:
http://therumpus.net/2009/04/i-married-a-novelist/
Still, there are plenty of things about Katharine—and her writing life—that I don’t pretend to understand. For instance: How can she write such beautiful novels while listening to Sonic Youth and My Bloody Valentine? Is such a thing possible without drugs? And why did it take her eight years to write her first novel, when what I hear drifting from her room all day is breakneck typing? What’s she actually writing in there? A hidden masterpiece? All day long, too, I come across enigmatic notes scribbled on Post-its or bookmarks or subscription cards sitting by our bed. ‘A gradual introduction to the sport of boredom’ or ‘F has very small penis!’ I sometimes worry if they were inspired by me…. What does it mean that the one quote she’s chosen to tape to her computer, in distressingly large caps, is “Write as if everyone you know is dead”?