Emily R. Grosholz

philosopher, poet, literary critic

Great Circles: The Transits of Mathematics and Poetry (Mathematics, Culture, and the Arts)

This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge.

The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.

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Starry Reckoning: Reference and Analysis in Mathematics and Cosmology

This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics.

Buy on Amazon: Starry Reckoning: Reference and Analysis in Mathematics and Cosmology (Studies in Applied Philosophy, Epistemology and Rational Ethics Book 30)

The book is enjoyable to read. The broad spectrum of topics and the detail in which they are discussed provide the reader with some interesting insights. In particular, the idea that mathematical analysis not only solves problems, but in the most interesting cases, explains why important problems show up in the first place is well argued and well presented.
Sébastien Gandon, Philosophia Mathematica,September, 2017

The Stars of Earth

Emily Grosholz weaves elements of philosophy, mathematics and the sciences into her experience of the social and natural world, to produce wise and cosmopolitan poetry of high lyricism. The Stars of Earth starts with new poems chronicling the months of a year lived and observed, followed by selections from Grosholz’s previous volumes in chronological order. This rare treasury spans four decades of Grosholz’s acclaimed poetry.

For more on The Stars of Earth, see Word Galaxy Press page and Emily Grosholz's page at Word Galaxy Press.

Buy on Amazon:The Stars of Earth: New and Selected Poems

Representation and Productive Ambiguity in Mathematics and the Sciences

Emily R. Grosholz (Author)

In Representation and Productive Ambiguity in Mathematics and the Sciences, Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian "analysis"--the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience.

Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable fore mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are subtly altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.


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Reviews

  1. French, Steven (2011). Reviewed Work: Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. Grosholz British Journal for the Philosophy of Science. Vol. 62 Issue 4, pp.895-898.
  2. Goethe, Norma B. (2006/2007). Reviewed Work: Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. Grosholz. Studia Leibnitiana, Bd. 38/39, H. 2 , pp. 244-246
  3. Bangu, Sorin. (2009). Representation and Productive Ambiguity in Mathematics and the Sciences. ISIS 100:11, pp. 137-139.

Drafts of Chapters (and Comments)

Earlier versions of each chapter are attached as files (for the most part without plates), but the finished chapters in the book have all been revised, expanded, and corrected a great deal, so you should consult the book for the definitive form of the arguments, case studies, and those very important plates.

Included here are comments written by colleagues in response to some of the arguments or case studies in that chapter, or by myself in response to, or in collaboration with, an interlocutor.

  1. Chapter 1: with the notes but not the plates. The plates can be found in any standard edition of Galileo's Two New Sciences.
    • Comment 1: from Norma Goethe (University of Cordoba, Argentina). Part of a review to appear in Studia Leibnitiana.
    • Comment 2: from Bas van Fraassen (San Francisco State University), a propos the issue of representation in Ch. 1, and in the Introduction and Ch. 1 of his new book on scientific representation.
  2. In chapter 2, I made use of my review of Karine Chemla's and Guo Shuchun's edition and translation of Les Neuf Chapitres: Le Classique mathematique de la Chine ancienne et ses commentaires (Dunod 2004), a text usually refered to as the Chinese analogue of Euclid's Elements. Karine Chemla's commentary argues that the organization of this text is best understood in terms of "generalization" rather than "axiomatization." She, David Rabouin and various members (including myself) of the research group REHSEIS / CNRS / University of Paris Diderot -- Paris 7 are contributing to a volume of essays that will analyze and exemplify the notion of generalization.
    • Comment 1: Here are two commentaries on the issue of generality, apropos a paper by Karine Chemla (commentary 1) on the geometer Michel Chasles, and a paper by Evelyne Barbin on Fermat and Descartes (commentary 2). I wrote them after discussing the papers with Emiliano Ippoliti, a postdoctoral student from the University of Rome, so the comments are ultimately co-authored. These comments take the discussion in Chapter 2 a bit further.
    • Comment 2: When I gave a presentation of this book at the Philosophy of Science Center, University of Pittsburgh, somebody asked me if I were hostile to axiomatization, a question that might occur to someone who read Ch. 2. My answer was, of course not, but I was so surprised that I didn't elaborate much. The following (commentary 3) is a third result of discussions with Emiliano Ippoliti, apropos the interesting remark of Dirk Schlimm that we perhaps need a taxonomy of kinds of axiomatization.
  3. Chapter 3: an early (1998) version of this chapter was co-authored with Roald Hoffmann and published as "How Symbolic and Iconic Languages Bridge the Two Worlds of the Chemist: A Case Study from Contemporary Bioorganic Chemistry," in Of Minds and Molecules: New Philosophical Perspectives on Chemistry, N. Bhushan and S. Rosenfeld, eds., OUP 2000, 230-47 (in French in Les Langages Scientifiques, ed. F. Letoublon, Editions ARASSH, Grenoble.
  4. Chapter 4: an earlier version of this chapter, a paper that I gave in Berlin. To see an earlier version of this chapter, with most of the plates, you can consult "Fedoroff's Translation of McClintock: The Uses of Chemistry in the Reorganization of Genetics," in Tools and Modes of Representation in the Laboratory Sciences, Ursula Klein, ed., Boston Studies Series in the Philosophy of Science (Kluwer 2001), 199-218.
    • Comment 1: on Ch. 4, from September, written by Evelyn Fox Keller.
  5. Chapter 5: without plates. The plates are taken mostly from F. A. Cotton's Chemical Applications of Group Theory (John Wiley and Sons, 1990).
    • Comment 1: from Joseph Mazur (Mathematics, University of Vermont): "One brief observation: I?m very glad you put in the chapter on group theory and representations?it seems to me that what you say there is the kernel; and you say it very well. In fact, beginning group theory students would benefit from your analysis of representation theory. I wish I had had such a view when I was a student and confused about what representations were really about. I understood the mechanics, but not the real purpose."
  6. Chapter 6: Here is an early version of some of the material in this chapter, without plates. All the plates are in a standard edition of Descartes' Geometry.
  7. Chapter 7: an earlier version of this chapter, without plates. The plates can be found in any standard edition of Newton's Principia.
  8. Chapter 8a, Chapter 8b: two earlier papers, which contain much of the content of Chapter 8, without the plates. The plates can be found in the relevant volume of C. I. Gerhardt's editions of Leibniz's mathematical and philosophical writings.
    • Chapter 8: by Norma Goethe (University of Cordoba, Agentina) on this chapter, part of an earlier draft of a review she has written for Studia Leibnitiana.
  9. Chapter 9: an earlier version of a paper that contains much of the content of Chapter 9, which I gave at the University of Rome, without the plates. The plates can be found in Singer & Thorpe, Lecture Notes on Elementary Geometry and Topology.
  10. Chapter 10: an earlier version of Chapter 10.
    • Comment 1: Comments I wrote in 2008 on a paper by John Dawson (Mathematics, Pennsylvania State University) and another by Carlo Cellucci (University of Rome) that seem to me germaine to the issue in Ch. 10. They deal with the role that transferability (similar structures, different objects) and consilience (different structures, same objects) play in the unification of mathematics.

Cartesian Method and the Problem of Reduction

Emily R. Grosholz (Author)

The Cartesian method, construed as a way of organizing domains of knowledge according to the "order of reasons," was a powerful reductive tool. Descartes made significant strides in mathematics, physics, and metaphysics by relating certain complex items and problems back to more simple elements that served as starting points for his inquiries. But his reductive method also impoverished these domains in important ways, for it tended to restrict geometry to the study of straight line segments, physics to the study of ambiguously constituted bits of matter in motion, and metaphysics to the study of the isolated, incorporeal knower. This book examines in detail the negative and positive impact of Descartes's method on his scientific and philosophical enterprises, exemplified by the Geometry, the Principles, the Treatise of Man, and the Meditations.

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Reviews

  1. Ariew, Roger. (Apr., 1992), Reviewed Work: Cartesian Method and the Problem of Reduction by Emily Grosholz. Mind, New Series, Vol. 101, No. 402 , pp. 376-379.
  2. BUROKER, J. V. (1992), Reviewed Work: Cartesian Method and the Problem of Reduction by Emily R. Grosholz. Philosophical Books, 33: 9?11.
  3. Clarke, Desmond M. (1992), Reviewed Work: Cartesian Method and the Problem of Reduction by Emily R. Grosholz. The British Journal for the History of Science, Vol. 25, No. 2 (Jun., 1992), pp. 266-267.
  4. Mahoney, Michael S. (Mar., 1993), Reviewed Works: Cartesian Method and the Problem of Reduction by Emily R. Grosholz; The Magic of Numbers and Motion: The Scientific Career of Rene Descartes by William R. Shea. Isis Vol. 84, No. 1, pp. 146-148.
  5. Gardies, Jean-Louis (JANVIER-MARS 1994), Reviewed Work: Cartesian method and the problem of reduction by Emily R. Grosholz. Revue Philosophique de la France et de l'?tranger, T. 184, pp. 119-121

Studies in History and Philosophy of Modern Philosophy

Emily R. Grosholz (Guest Editor)

Volume 52, Part A, Pages 1-110 (November 2015). Special Issue: Cosmology and Time: Philosophers and Scientists in Dialogue

This collection of essays is based on a Workshop on Cosmology and Time that was held at The Pennsylvania State Univeristy on 16-17 April 2017.

For more on this issue, including a table of contents, see Science Direct.

Beginning and End of the Snow / Début et Fin de la Neige

Yves Bonnefoy (Author). Emily R. Grosholz (Translator).

Yves Bonnefoy's book of poems, Beginning and End of the Snow followed by Where the Arrow Falls, combines two meditations in which the poet?s thoughts and a landscape reflect each other. In the first, the wintry New England landscape he encountered while teaching at Williams College evokes the dance of atoms in the philosophical poem of Lucretius as well as the Christian doctrine of death and resurrection. In the second, Bonnefoy uses the luminous woods of Haute Provence as the setting for a parable of losing one's way.

The poems are prefaced with an essay by Yves Bonnefoy, "Snow in French and English," and followed by an essay I wrote, "Song, Rain, Snow: Translating the Poetry of Yves Bonnefoy," both on the art of translation. The latter essay first appeared, in an extended form, in the Hudson Review (Vol. LXI / 4) pp. 618-642, along with eight poems from the book. One of my translations from this book, along with other, earlier translations, was included in Poets Translate Poets: A Hudson Review Anthology, edited by Paula Deitz (Syracuse University Press, 2013).

Included below are six short poems from the first section, La Grande Neige, of Yves Bonnefoy's Début et fin de la neige (Paris: Mercure de France, 1991). Translation by Emily Grosholz, published as Beginning and End of the Snow (Bucknell University Press, 2011).

For an interview about the translation, see Bucknell University Press Interview.

Buy on Amazon: Beginning and End of the Snow: followed by Where the Arrow Falls

La Grande Neige

[Untitled]

First snowfall, early this morning. Ochre, green
Huddle under the trees.

The second, towards noon. Nothing
Is left of color
But needles from the pines
Falling sometimes thicker than snow.

Then, towards evening,
The light stands poised.
Shadows and dreams balance on the scales.

A faint wind
Writes in the snow a word beyond the world.

[Sans titre]

Première neige tôt ce matin. L’ocre, le vert
Se réfugient sous les arbres.

Seconde, vers midi. Ne demeure
De la couleur
Que les aiguilles de pins
Qui tombent elles aussi plus dru parfois que la neige.

Puis, vers le soir,
Le fléau de la lumière s’immobilise.
Les ombres et les rêves ont même poids.

Un peu de vent
Écrit du bout du pied un mot hors du monde.

The Mirror

Yesterday still
The clouds sailed across
The dark end of the room,
But now the mirror?s empty.

Snow
Disentangles from the sky.

Le Miroir

Hier encore
Les nuages passaient
Au fond noir de la chambre.
Mais à présent le miroir est vide.

Neiger
Se désenchevêtre du ciel.

The Plough

Five o'clock. More snow. I hear some voices
At the edge of the world.

A plough
Like a three-quarter moon
Shines, but then is covered
By the darkness of a fold of snow.

And from now on that child
Has the house all to himself. He goes
From one window to another. He presses
His fingers against the misted pane. He sees
Drops forming where his fingertips stop
Pushing the condensation towards the sky that falls.

La Charrue

Cinq heures. La neige encore. J’entends des voix
À l’avant du monde.

Une charrue
Comme une lune au troisième quartier
Brille, mais la recouvre
La nuit d’un pli de la neige.

Et cet enfant
A toute la maison pour lui, désormais. Il va
D’une fenêtre à l’autre. Il presse
Ses doigts contre la vitre. Il voit
Des gouttes se former là où il cesse
D’en pousser la buée vers le ciel qui tombe.

Spot of Water

To the snowflake
Poised on my hand, I would
Grant eternity,
Understanding my life, my warmth,
My past, these current days,
As simply a moment, this one, limitless.

And yet it melts: already
Only a spot of water, strayed
Into the mist of bodies moving through the snow.

Le Peu d’Eau

À ce flocon
Qui sur ma main se pose, j’ai désir
D’assurer l’éternel
En faisant de ma vie, de ma chaleur,
De mon passé, de ces jours d’à présent,
Un instant simplement: cet instant-ci, sans bornes.

Mais déjà il n’est plus
Qu’un peu d’eau, qui se perd
Dans la brume des corps qui vont dans la neige.

[Untitled]

Snow
Fugitive on the scarf, the glove
Like that illusion, coquelicot,
In the hand that dreamt, last summer
On a path among dry stones,
That the absolute lies within reach of the world.

All the same, what promise
In this drop of water, this brief touch, since it was
Just for a moment, light! No riven cloud
Of a summer sky could open to reveal
A clearer path underneath darker vaults.

Circe
Under her pergola of shadows, the enlightened,
Had no fruits redder than these.

[Sans titre]

Neige
Fugace sur l’écharpe, sur le gant
Comme cette illusion, le coquelicot,
Dans la main qui rêva, l’été passé
Sur le chemin parmi les pierres sèches,
Que l’absolu est à portée du monde.

Pourtant, quelle promesse
Dans cette eau, de contact léger, puisqu’elle fut,
Un instant, la lumière! Le ciel d’été
N’a guère de nuées pour entrouvrir
Plus clair chemin sous des voûtes plus sombres.

Circé
Sous sa pergola d’ombres, l’illuminée,
N’eut pas de fruits plus rouges.

Our Lady of Mercy

Everything, now,
Gathers in warmth
Under your light mantle,
Barely more than mist and knotted lace,
Lady of Mercy of the snow.

Against your body
Creatures and things,
Naked, lie fast asleep, and your fingers
With their clarity veil those closed eyelids

La Vierge de Miséricorde

Tout, maintenant,
Bien au chaud
Sous ton manteau léger,
Presque rien que de brume et de broderie,
Madone de miséricorde de la neige.

Contre ton corps
Dorment, nus,
Les êtres et les choses, et tes doigts
Voilent de leur clarté ces paupières closes.


The last poem in the sequence of six poems given here, "Madone de Miséricorde," was set to music by Thierry Machuel and performed by Música Quántica Voces de Cámara, under the direction of Camilo Santostefano.

My translation of La Grande Neige in Début et fin de la neige is included in the booklet for Mirco De Stefani's Canzoni de La grande neige with Christine Nadal (soprano) and Maria De Stefani (piano) (Rivoalto, 2008). In addition, my translation of Bonnefoy's sequence "L été de nuit," is included in Mirco De Stefani's Canzoni de L été de nuit (Rivoalto, 2010).

Childhood

Emily R. Grosholz (Author), Katerina Stoykova-Klemer (Editor), Lucy Vines (Illustrator).

In this gorgeous, heartwarming collection about childbirth and adopting, children and parents, the poems by accomplished poet Emily R. Grosholz interact with color drawings by gifted Parisian artist Lucy Vines. A fixed percentage from the sale of this book will go to an international organization that works to protect and encourage children worldwide, by providing food and water, medical attention, shelter from violence, and education; this children's humanitarian organization has saved more lives than any other.

Buy on Amazon: Childhood

For more on Childhood, see Interview by Accent Publishing about Childhood, Blurb in the Sewanee Review

Praise for Childhood

These eloquent, edgy poems write of youth and parenting in powerful ways. They also go well beyond that, in addressing childhood as revelation: not just the temporal state we all go through, but the crisis of wonder our own children produce in us. Any reader who picks up this book can draw closer to that wonder and share in it again through this lyrical, moving work.
Eavan Boland
Emily Grosholz is a singular presence in American letters--a poet-philosopher whose brilliant verse on science, mathematics and ideas has been justly praised. But my favorite Grosholz work has always been her tender and arresting poems on motherhood and children. It is a joy to see these luminous and loving poems gathered into one richly expressive volume.
Dana Gioia
These poems lend us wings to fly from Kilimanjaro to Paris and on to the Caribbean with our children, and they make differences of physical size disappear by magnifying molecules and compactifying the universe.
Tadatoshi Akiba

French Translation of Childhood

Telling the Barn Swallow: poets on the poetry of Maxine Kumin

Emily R. Grosholz (Editor)

Buy on Amazon: Telling the Barn Swallow: Poets on the Poetry of Maxine Kumin

  1. Eleanor Wilner. The Wedding of Meaning and Measure: Kumin and the Poetics of Finitude.
  2. Annie Finch. A Rock in the River: Maxine Kumin's Rhythmic Countercurrents.
  3. Henry Taylor. Remembering Where Everything Is: The Poetry of Maxine Kumin.
  4. Emily Grosholz. Mxine Kumin's Poetry of Metamorphosis.
  5. Neal Bowers. Poised in the Galloping Moment: Maxine Kumin's Poetry.
  6. Alicia Ostriker. Making the Connection: The Nature Poetry of Maxine Kumin.
  7. Mark Jarman. The Retrieval System.
  8. Hilda Raz. Maxine Kumin's Sense of Place in Nature.
  9. Wesley McNair. Kumin's Animal Confederates.
  10. Robin Becker. Out of Our Skins: Transformation and the Body in the Poems of Maxine Kumin.
  11. Michael Burns. A Satisfactory Machinery.
  12. Carole Simmons Oles. Max's Garden: For Present and Future Consumption.

POEMS

  1. Robin Becker. Floating Farm.
  2. Robin Becker. A Marriage.
  3. Wendell Berry. Chicory.
  4. Philip Booth. The Dive.
  5. Neal Bowers. Another Language.
  6. Annie Finch. Zaraf's Star.
  7. Emily Grosholz. Sidonie.
  8. Carolyn Kizer. Parents' Pantoum.
  9. Wesley McNair. The Puppy.
  10. Wesley McNair. Why We Need Poetry.
  11. Carole Simmons Oles. Small Poem of Thanks.
  12. Alicia Ostriker. Mid-February.
  13. Hilda Raz. Family.
  14. Eleanor Wilner. Postscript.

Eden

Emily R. Grosholz (Author)

In Eden, Emily Grosholz brings together forty lyric, narrative, and epistolary poems that trace a pilgrimage from the Eden of childhood through alienation and loss to an earthly paradise regained as the poet establishes her own family and a new sense of the purposes of her art.

The route traverses Detroit in the early twenties, Paris and Washington, D.C., in the early seventies, Athens and Toronto in the mid-eighties, yesterday's Thimphu and Cassis. But it always returns to the poet's heartland, Philadelphia and the back country of Pennsylvania and New York. Punctuated by meditations on solitude and death, the poems come full circle to the pleasures of marriage, of friends and children, of creation. To her husband, the poet writes, "However often now our woven/ lives converge and separate, my love,/ today we've come this far." And to her son, "With you fast in my arms,/ I'm back again in the heart's Italy."

Buy on Amazon: Eden (Johns Hopkins: Poetry and Fiction)

It is rare to find poems which offer so much freshness and accessibility of feeling while at the same time hewing to a course of argument charted by a scrupulous intellect.
Robert B. Shaw, Poetry
Emily Grosholz is a poet of light, her luminous poetry arriving from that bright shore where philosophic mediation meets desire. This rare congruence is visible in the radiant reflection that both characterizes her poems and recurs in brilliant images of how things loan each other light.
Eleanor Wilner

The Abacus of Years: Poems

Emily R. Grosholz (Author)

There are two topics that seem largely unexplored by American poets of our time. One is the deep attachment parents (and perhaps most especially working parents) form for their infants and how they perceive their children (perhaps as Blake saw them) with all the wisdom of their innocence. The second is the relationship of science, mathematics and metaphysics to our everyday life. Here is a book that explores, and to some degree attempts to define, the writer's investigations in those two domains, one stemming from her experience as a mother, the other from her profession as a philosopher of science. And it is this juxtaposition of maternal emotion and detached, almost clinical, analysis that provides Grosholz's wonderful new collection with such grace and such power.

Buy on Amazon: The Abacus of Years: Poems

Praise for The Abacus of Years

There is no end to the kinds of poems that Grosholz can write, always with distinction of language and with a great gift for wedding the measures of verse to the rhythms of thought.
Richard Wilbur
Grosholz seems to keep a certain distance from her subjects and to manage this without the ironies one might expect. I take this to be a sign of the writer's intelligence; it is certainly a mark of this poet's admirable apartness from other poets of her time.
Donald Justice

The Growth of Mathematical Knowledge

Emily Grosholz (Editor), Herbert Breger (Editor).

Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone of intelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work of the physicist who provides a quantified account of the machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking of concepts nor the record of perceptual experience. In the Critique of Pure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary laws of Newtonian mechanics.

Buy on Amazon: The Growth of Mathematical Knowledge (Synthese Library)

Part I: The Question of Empiricism. The Role of Scientific Theory and Empirical Fact in the Growth of Mathematical Knowledge. 1. Knowledge of Functions in the Growth of Mathematical Knowledge

  1. J. Hintikka. Knowledge of Functions in the Growth of Mathematical Knowledge
  2. M.S. Mahoney. Huygens and the Pendulum: From Device to Mathematical Relation
  3. D. Gillies. An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics
  4. I. Schneider. The Mathematization of Chance in the Middle of the 17th Century
  5. M. Liston. Mathematical Empiricism and the Mathematization of Chance: Comment on Gillies and Schneider
  6. E. Grosholz. The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge
  7. C. Fraser. Hamilton-Jacobi Methods and Weierstrassian Field Theory in the Calculus of Variations
  8. P. Mancosu. On Mathematical Explanation
  9. F. de Gandt. Mathematics and the Reelaboration of Truths
  10. M. Steiner. Penrose and Platonism
  11. M. Wilson. On the Mathematics of Spilt Milk

Part II: The Question of Formalism. The Role of Abstraction, Analysis, and Axiomatization in the Growth of Mathematical Knowledge.

  1. C. Cellucci. The Growth of Mathematical Knowledge: An Open World View
  2. D. Laugwitz. Controversies about Numbers and Functions
  3. C. Posy.Epistemology, Ontology, and the Continuum
  4. H. Breger. Tacit Knowledge and Mathematical Progress
  5. M.M. Muntersbjorn. The Quadrature of Parabolic Segments 1635-1658: A Response to Herbert Breger
  6. M. Liston. Mathematical Progress: Ariadne's Thread
  7. C. Mclarty. Voir-Dire in the Case of Mathematical Progress
  8. H. Sinaceur. The Nature of Progress in Mathematics: The Significance of Analogy
  9. E. Knobloch. Analogy and the Growth of Mathematical Knowledge
  10. A. Barabashev. Evolution of the Modes of Systematization of Mathematical Knowledge
  11. I. Bashmakova and G.S. Smirnova. Geometry, the First Universal Language of Mathematics

Part III: The Question of Progress. Criteria for and Characterizations of Progress in Mathematical Knowledge.

  1. P. Maddy. Mathematical Progress
  2. M.D. Resnik. Some Remarks on Mathematical Progress from a Structuralist's Perspective
  3. V. Peckhaus. Scientific Progress and Changes in Hierarchies of Scientific Disciplines
  4. S. Demidov. On the Progress of Mathematics
  5. K. Mainzer. Attractors of Mathematical Progress: The Complex Dynamics of Mathematical Research
  6. C. Thiel. On Some Determinants of Mathematical Progress

Shores and Headlands

Emily Grosholz (Author)

"[Grosholz] has a lucid, lyrical voice, a pure, song-like quality. I think many aspire to this sort of effortless music, but few succeed as well as she."
Alice Fulton

Buy on Amazon: Shores and Headlands (Princeton Series of Contemporary Poets)

Logic and Knowledge

Carlo Cellucci (Editor), Emily Grosholz (Editor), Emiliano Ippoliti (Editor)

The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI-VII of Plato's Republic and Aristotle's Prior and Posterior Analytics, to Kant's Critique of Pure Reason and Mill's A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901-1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors.

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The Legacy of Simone de Beauvoir

Emily Grosholz (Editor)

The legacy of Simone de Beauvoir has yet to be properly assessed and explored. The 50th anniversary of the publication of The Second Sex inspired this volume which brings together philosophers and literary critics, some of whom are well known for their books on Beauvoir (Bauer, Le Doeuff, Moi), others new to Beauvoir studies though long familiar with her work (Grosholz, Imbert, James, Stevenson, Wilson). One aim of this collection is to encourage greater recognition of Beauvoir's philosophical writings through systematic reflection on their place in the canon and on her methods. The Second Sex played a central role in the profound shift in philosophy's self-understanding that took place in the latter half of the twentieth century, and today offers new problems for reflection and novel means for appropriating older texts. Its reflective iconoclasm can be compared to that of Descartes' Meditations; its enormous, directly discernible impact on our social world invites comparison with Locke's Two Treatises of Government. The collection also examines the relationship between Beauvoir's literary writing and her philosophical thought. Deeply concerned with the critical and creative powers of reason as well as with the betterment of our suffering world, Simone de Beauvoir wrote in a variety of genres in addition to the philosophical essay: the novel, political journalism, and the memoir. The multiplicity of her voices was closely related to her philosophical project. Since Beauvoir's method (like that of W. E. B. du Bois) proceeded from her own immediate experience, her reflections had to find expression sometimes as narrative, sometimes as autobiography, sometimes as argument. The Legacy of Simone de Beauvoir demonstrates the many ways in which Beauvoir's writings, in particular The Second Sex, can serve as resources for thought, for the life of the mind which is as concerned with the past and future as it is with the present.

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This distinguished volume of essays provides an incisive review of Simone de Beauvoir's legacy, ranging expertly over the historical, philosophical and literary dimensions of a complex and controversial figure...the stature, originality, pragmatism and sheer intelligence of Beauvoir are outstandingly well brought into focus.
Richard Parish, Times Higher Education Supplement

W.E.B. Du Bois on Race and Culture

Bernard W. Bell (Editor), Emily R. Grosholz (Editor), James B. Stewart (Editor)

Interpreting Du Bois' thoughts on race and culture in a broadly philosophical sense, this volume assembles original essays by some of today's leading scholars in a critical dialogue on different important theoretical and practical issues that concerned him throughout his long career: the conundrum of race, the issue of gender equality, and the perplexities of pan-Africanism.

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Leibniz's Science of the Rational

Emily R. Grosholz (Author), Elhanan Yakira (Author)

Interpreting Du Bois' thoughts on race and culture in a broadly philosophical sense, this volume assembles original essays by some of today's leading scholars in a critical dialogue on different important theoretical and practical issues that concerned him throughout his long career: the conundrum of race, the issue of gender equality, and the perplexities of pan-Africanism.

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The River Painter

Emily R. Grosholz (Author)

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Proportions of the Heart: Poems that Play with Mathematics

Emily R. Grosholz (Author), Robert Fathauer (Illustrator)

This volume contains 22 poems by American poet and philosopher Emily Grosholz. The poems in this book blend mathematical topics from fractals to negative curvature with history, classicism, and human emotions. Includes illustrations by Robert Fathauer.

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Praise for Proportions

"Play with mathematics? Emily Grosholz's poems do that and much more. They illuminate its mysteries with alephs flung like a candelabrum, challenge us to study the morphology of the amorphous, and embrace mathematics' aethereal aesthetic. Out of fixed proportions, beauty rises: the elegance, conciseness, and precision of these poems go straight to its heart."
Marjorie Wikler Senechal
"Transfinite and transcendental converge in this delicious medley of verses pulsating with passion and life. Like fractals' captivating patterns, these poems will make you contemplate the infinite possibilities of symmetry, harmony, and love."
Edward Frenkel
"Emily Grosholz's poems respond to streets in Paris, towns in Italy, the body of her husband, the fractals of Benoit Mandelbrot, the transfinite of Georg Cantor. Her linkages of mathematics and poetry can teach both poets and mathematicians. Grosholz's poetic imagination leaps to mathematical depths and heights where discursive reason is left behind."
Reuben Hersh

During National Poetry Month (April 2015) Evelyn Lamb wrote a piece on Proportions of the Heart for Scientific American titled In Praise of Fractals and Poetry.

Leaves/Feuilles, Eight Poems / Huit Poèms

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