I met Emily Grosholz, professor of philosopy at Penn State University and a distinguished poet and essayist, at the Sewanee Writers’ Conference, where I was in her poetry workshop in 1991 and 1992. In the first year, the inaugural of the writers’ conference, she read my fledgling poems, and I was grateful for her kindness and instructive suggestions. Along with her deep learning in philosophy, poetry and matematics, I was delighted to discover that she is also well-versed in baseball, and if I remember correctly, tennis. We also shared anecdotes, stories and information about our then young families. I remember as well her calm, quiet presence in the workshops, which she conducted along with two roaring lions of American poetry, Howard Nemerov the first year, and John Hollander the second.
Over the years, I’ve followed Emily’s work in The Hudson Review, where she is an advisory editor. Her work in the the journal displays an astonishing versatility, including poetry, essays, criticism and travel pieces. The autumn 2009 issue includes Emily’s probing essay on the poet Anne Stevenson. The issue also includes a poignant poem by Stevenson about teaching her sons to swim at Walden Pond. I particularly enjoyed the poem because I in the summer of 2008 visited the site of Thoreau's cabin on Walden Pond, amused and impressed to discover that the pond is a public swimming beach, as Stevenson evokes.
With my warm memories of Emily, I asked her to participate in a
One other thought: In the spirit of Emily's allusions to different texts, her citation of Aristotle’s comment that “a swallow does not a summer make” reminded me of Robert Lowell’s reference to this in his poem “Fall 1961,” which can be found in his “For the Union Dead.” Looking back at
Part 1: On Philosophy and Poetry, and Walks Through Fields
Part 1: On Philosophy and Poetry, and Walks Through Fields
1. As a philosopher and poet, what do you feel is the relationship between philosophy and poetry?
2. To follow up on the first question, you are also an accomplished editor, essayist and critic. Such varied interests are said to be rare in our age of specialization. What is the source and inspiration for your versatility?
3. Your comments in your essay on the poet Anne Stevenson in the current
4. After Sept. 11, 2001, many in the
Barnes & Noble has a new series of modestly priced hardcover books they call, “Rediscovers,” which “brings back into print books of special merit in history, literature, philosophy, religion, the arts and science.” One of them, no doubt included because of
The reason I mention this series is because it includes George Santayana's “Three Philosophical Poets: Lucretius, Dante, Goethe," which also inspired me in high school, though I have since lost my dog-eared paperback copy, and so was glad to pick up a new one at Barnes & Noble, where I went to buy Garrison Keillor’s latest book for my eldest son Benjamin, who is studying classics and mathematics at the University of Chicago. He wasn't home for Thanksgiving, so I sent him a book instead of a turkey, as well as two packages of hawthorn-berry tea. The only place in town where I can get that kind of tea is The Granary, a health food store run by Lena Scholton, a friend of mine who is Finnish and grew up in
Finally, apropos this morning’s errands, a review of a new biography of Cassirer that Paula Deitz and Managing Editor Ron Koury persuaded me to write is coming out shortly in The Hudson Review, and so is a poem about walking in the fields at night with my other children, directly inspired by Loren Eiseley: it evokes the last ice age, and ends with a large tree completely covered in fireflies. Note that my prose style here echoes Garrison Keillor. It is after all Saturday (“Prairie Home Companion” day) and I've recently returned from the
However, following Keillor, I have wandered away from George Santayana. Over the years at
another sense they are off the Line). Because a Platonic dialogue does not end in a conclusion, you have to somehow connect the top of the line with the bottom and start all over, and what connects the top and the bottom is… myths! The Platonic myths are the most gorgeously poetic parts of the dialogues, and the most important. So go figure. Also, Platonic dialogues are sprinkled with quotes from Homer.
Most of this I learned from my fellow
Aristotle is another matter. I read the “Nichomachean Ethics” together with the "Rhetoric” and the “Politics" on the one hand, and the "Poetics" on the other. Another of my former teachers, Eugene Garver, has written a number of distinguished books on Aristotle, and in a recent e-mail wondered how I see connection between the "Nichomachean Ethics" and "the Poetics." The connection I see is only the obvious: poetry is (according to Aristotle) the imitation of human action, and he gives us the schema for narrative: beginning, middle, end, as he gives us the schema for argument: premise, premise, conclusion. And ethics is the study of how human action can be virtuous, which requires us to focus on character, the second most important term in “The Poetics,” after plot. (I wrote an essay about this in Midwest Studies in Philosophy, whose latest issue is devoted to poetry and philosophy, and begins with a poem by John Ashbery!)
Aristotle shows that when tragedy arises, the deed is either done or not done, and, done in ignorance or done knowingly; the main issue in “The Ethics” is the question of the relation between knowing and doing. Socrates claims that if I could only know what is right, I would do it; vice is ignorance. Aristotle shows at length that character is built up over a long period of time by repeated actions, taken in the midst of the repetitive patterns of social life, and changes just as slowly, so that though I may know the good, I may be unwilling to do it if my character is ill-formed. He also observes that happiness depends not only on virtue but also on good luck; tragic heroes are doomed not only by flawed character but also by misfortune. So for Aristotle, there’s not much tension between philosophy and poetry, though oddly he himself never writes poetically (and the textual basis for his philosophy is lecture notes), except occasionally: “One swallow doth not a summer make.” That reminds me of a philosophical poem I just wrote, and a good philosophical joke that I sometimes tell my undergraduates (usually I am the only one who laughs at it) because it is not off color; however, there is not enough room in the margin to write it here.
Part 2: On Poetry and Mathematics, Empson and Housman
5. According to your
When I applied to the
My apprenticeship has been three monographs and an edited collection of essays on the history and philosophy of mathematics, and four books of poetry and more than 50 items of literary criticism —essays and essay-reviews. A couple of years ago, I wrote what will become one of the proposed book’s initial chapters, “The Uses of Periodicity in English Verse,” published in The Hudson Review, which like the “Letter from Helsinki,” can be found on FindArticles. One chapter may address texts written by Leibniz and Goethe (apropos the Italienische Reise that changed the life and work of each); another may be about the way in which abstract form brings the finite and the infinite into relation in the work of Rilke and Hilbert; another might be about temporality, and the way it both resists and lends itself to representation by mathematical form and by narrative.
In any case, the book “Mathematics and Poetry” must have two dimensions. One is epistemological. Human understanding hovers between the timeless realm of concepts, propositions, and arguments that stand in inferential relations tracked by logic and rhetoric, and the historical realm in which discoveries are made and projects framed on the basis of earlier results and in light of as-yet-unsolved problems. A name or concept pulls something that exists out of the flux of time, and by imposing the universal on the particular gives it a kind of local immortality. (This happens quite a bit in Dante’s “Divine Comedy.”)
Arguments organize thoughts so that they can be rehearsed and examined; narratives organize human actions so that they can be revisited and their meaning reconsidered. A scientific experiment on the one hand and a theatrical drama on the other deliberately represent situations both as having happened once — physically or dramatically real — and as meant to be repeated — universally true. In mathematics and poetry, the tension on this duality is especially strong. The study of mathematical knowledge and poetic knowledge is therefore central to philosophical epistemology; the dialogues of Plato testify to this. My work in the philosophy of mathematics take its inspiration from the 20th century European tradition that begins with Poincaré, Hilbert, and early Husserl, and tries to explain mathematical rationality as an interplay between logical necessity and historical contingency. My literary work locates human action and utterance at the crossroads between the constraints of moral law and the fatal accomplishments of history, and the free play of artistic form and anarchic will, always imagining”what if...?”
The other dimension is aesthetic. Art (including poetic art) and mathematics characteristically generate beautiful forms that express human action on the one hand, and on the other hand the stable systems and dynamic processes of nature. In my book “Representation and Productive Ambiguity in Mathematics and the Sciences” (directly influenced by William Empson’s “Seven Types of Ambiguity”), I examine how demonstrations proceed when they occur, as they so often do, at the intersection of heterogeneous domains. When one domain is brought in to augment the resources of another, each with its own tradition of representation, the result is the combination, superposition and metamorphosis of a variety of modes of representation that often produce new mathematical entities. I call into question standard accounts of theory reduction (because I argue that reductive strategies do not reduce the number of idioms that express a problem situation, but rather multiply them, and that is why they work well), and moreover present striking examples of constructive ambiguity. What Empson shows so brilliantly, how poets exploit the semantic field of dictionary definitions or a given spectrum of cultural associations, also holds true for the mathematician.
So, for example, the ellipse in Proposition XI of Newton’s “Principia” must be read as a trajectory, as a figure derived from Euclid and Apollonius, as a dynamic nexus determined by a central force and (after the work of Leibniz inspired by
In poetry, the line embedded in stanzas and organized by rules of meter and rhyme (or studied violations of them) creates a formal counterpoint of superimposed periodicities that deepens and complicates what it means. Thus in a poem a thought is suspended at the end of a line even if it is also continued, by enjambment and grammar, on to the next line, or by the logical structure of an argument to the next stanza. This formal construction of ambiguity, which exploits aural patterns of repeated sound and beat, grammatical structure, poetic lineation, metrical structure and logical structure, shows that a poem is not just a string of words but a two-dimensional, planar array which composes a rich plurality of modes of representation.
In the essay on Housman mentioned above, “The Uses of Periodicity in English Verse,” I show that this formal ambiguity mirrors the ambiguity of human intention: whenever we act, we are aware of what we might have chosen but in fact did not choose, and those unrealized possibilities remain with us as part of the meaning of what we did. We act at the crossroads of necessity and freedom, and of the visible and the invisible. And poor Housman: his whole life was lived among the unrealized possibles that Spinoza denied and Leibniz multiplied, making them infinitely infinite in all those possible worlds that are not the best, like ours. This reminds me of a poem I wrote when I was in