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I left my house this morning to find a truck dumping several tons of dirt @ the end of my street, blocking it entirely. I live on a "cartway" in midcity Philadelphia, and could not get out. That seemed not such a bad image for what I saw Paul dealing w/ a bit later in the morning:  trying to get somewhere as all sorts of obstacles--queries about how going in this direction might be useful--were placed in his way.

I stayed quiet during most of this conversation, in part because I was trying to allow some space-and-time for Paul to lay out "his" proof, and to see what payoff that might give us. But, while silent, I was entertaining obstructionist thoughts quite similar to what was being said by others: of what use value will this be, for me and my discipline? What application can this global claim possibility have for my local particulars? -- particularly since "the inherent limits of formal systems," and the concomitant "need for less constrained approach to inquiry" seem to me exactly the space occupied by humanists (in company with the more qualitatively inclined social scientists). Certainly one payoff might be a better understanding of the use value of formal systems, a better understanding of what they might do, and just where and how they fall short: for things like grading, mentioned this morning; or for the larger structures of assessment in which we all increasingly find ourselves; or for some of the more positivist projects in which both humanists and qualitative social scientists find themselves involved; for my current favorite example, see the open review issue of Shakespeare Quarterly on "Shakespeare and New Media," in particular, an essay on "iterative criticism" that uses multivariate statistics and a text tagging device known as Docuscope to "create a portrait of Shakespearean genre @ the level of the sentence," a process that begins by sorting several million English words (and strings of words)  into grammatical, semantic and rhetorical categories.

Given my own location in the world of academia, and my own particular angle of vision on the world, of particular interest to me in this morning's session was Tim's asking what happens after we name "that," and then name what is "not that." What's next: "'not-not-that'--and so forth, in seriatim? Is this like changing lines in the supermarket, never getting to the cash register? Why check out @ all? Why not reconsider the goal of getting to the checkout counter? Why not change the goal of grocery shopping: you can just go on having interesting conversations (and you never have to pay...)?"

I found myself laughing out loud @ this image: it's such a vivid description of a non-goal-directed sort of teaching-and-learning, such a nice counter to the conventional "check-out counter" model of education that is now largely operative.

But perhaps the most interesting question I heard, while sitting around  in this morning's ever- shifting checkout line (to mix my metaphors a bit), was Alice's great query whether--instead of just noting the difference between "that" (say: Euclidean geometry, or  quantum physics) and "not that" (say non-Euclidean geometry, or non-quantum physics)--we mightn't imagine (or bring into being?) a formal system to put these two different perspectives on the world into dialogue w/ one another. Would you say that that is what Hegelian synthesis did? Or did you (or do others) have other formalisms in mind?