Postclassicism / Postclassical Theory :
Opposed to, and succeeding, classical thought.

Like the other posties (postmodernism, poststructuralism, etc), postclassicism claims, by its very name, to define itself against something: in opposition to, and as a successor of, classicism. Here, that “classicism”, or “classical thought”, refers to some broad philosophical ideas that have dominated European-derived thinking more or less since Plato.

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Mathematics, Science, and Postclassical Theory, edited by Barbara Herrnstein Smith and Arkady Plotnitsky

In 1997, Duke UP published the collection Mathematics, Science, and Postclassical Theory The book advertised itself as “Science Studies”, and came, in part, from a 1993 conference on “Mathematics and Postclassical Theory” at Duke's Center for Interdisciplinary Studies in Science and Cultural Theory.

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Barbara Herrnstein Smith, MSPT co-editor

The director of Duke's Center for Interdisciplinary Studies in Science and Cultural Theory, she was also the primary organizer of the colloquium where many of the essays were originally presented. A key (and formidable) figure in postclassical theory since well before that 1993 event, or the founding of the center.

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Contingencies of Value

In 1988, after a few detours like serving as president of the MLA, Smith wrote a book called Contingencies of Value, which suggested that there weren't a hell of a lot of absolute objective truths to serve as foundations for theory, and people ought to come to grips with contingency. This proved contentious; a number of ethicists and legal scholars accused her of advocating relativist ethics, for example.

Contingencies of Value drew on economics and the American pragmatist philosophical school, particularly the work of Richard Rorty. While it can certainly be considered a work of philosophy, it's generally critical of the European philosophical tradition — a critique that Smith has continued.

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Arkady Plotnitsky

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Brian Rotman, "Thinking Dia-Grams: Mathematics, Writing, and Virtual Reality"

Rotman looks at mathematics as non-alphabetic writing, in the way that we sophisticated comp/rhet theory-head types think of writing. This has some interesting consequences, for example in revealing the agency of mathematical signs in the construction of mathematical knowledge. Rotman also argues that mathematical rigor is a necessary consequence of the rules of mathematical writing.

Note that as far as I'm aware Smith and Plotnitsky don't use the term postclassicism; I'm using it here to mean an orientation toward the “postclassical theory” they describe and include in the collection.

From the introduction to MSPT:
“various critical analyses ... around ...
a cluster of quite general but problematic concepts [such as] knowledge, language, objectivity, truth, proof, reality, and representation

A longer version:

While the term “postclassical theory“ can be given a range of meanings in relation to more or less radical developments in [mathematics, science, theory, and philosophy], its use here is intended primarily to evoke the various critical analyses and efforts at reconceptualization ... that have emerged in the humanities and social sciences around a cluster of quite general but problematic concepts, notably, knowledge, language, objectivity, truth, proof, reality, and representation, and around such related issues as the dynamics of intellectual history, the project of foundationalist epistemology, and the distinctive (if they are distinctive) operations of mathematics and science.

Scandalous Knowledge: Science, Truth, and the Human, Barbara Herrnstein Smith

The scandal in question is the reflexive problem of epistemology: how can we know that we know anything? There are, Smith says, three ways of dealing with this problem: ignore it (as most people do), attempt to refute epistemological scepticism (as the philosophy of science typically does), or mobilize that scepticism to critique the conception of knowledge itself - which of course is what she's doing. Most postclassical theory has been disciplinary and descriptive - analyses of particular practices and so forth - so here Smith is laying out a philosophical (normative) description of postclassical epistemology. It complements Plotnitsky's focus on the postclassical acknowledgment of the limits of epistemology's domain (what we can know about) with a focus on the limits of epistemology's range (what sorts of things we can know about it). And because Smith is interested in arguments over postclassical thought, several of the chapters include extensive rhetorical analysis.

The Knowable and the Unknowable: Modern Science, Nonclassical Thought, and the “Two Cultures”

From quantum physics, Bohr developed a epistemology that challenges pretty much all of Western philosophy from Plato, perhaps Socrates, onwards. Plotnitsky elaborates Bohr's epistemology and in this book connects it to Lacan and Derrida. A significant part of the theory here is rhetorical, as when he discusses Lacan's use of "quasi-mathematics". His engagement with the two cultures and the science wars also provides a platform for further rhetorical inquiry into mathematics and science.

So what about the math? How much is actually involved in this postclassical stuff?

A number of the authors in MSPT do talk about mathematics. Sometimes they're studying mathematics as an epistemological domain (eg Rotman) or an area of intellectual work (eg Pickering). Sometimes they're interested in philosophical claims or common-sense assumptions about mathematics (eg Smith). And sometimes, yes, they're talking about specific mathematical concepts — notably in much of Plotnitsky's work.

Some of this is because MSPT came out of a conference that specifically called for work on mathematics, though. It's quite possible for even the math-phobic to do postclassical work (though learning mathematics builds character and helps prevent tooth decay, kids!). It should be possible to follow most of these arguments without understanding their mathematical claims.

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"Introduction: Networks and Symmetries, Decidable and Undecidable", Smith and Plotnitsky

The editors' introduction offers the expected definition of the book's topic and a brief history. It also discusses some concepts that they see as key to postclassical thought, such as undecidability, networks of practices, and the importance of considering contradictory metaphysical positions.

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"Thinking Dia-Grams: Mathematics, Writing, and Virtual Reality", Rotman

Rotman looks at mathematics as non-alphabetic writing, in the way that we sophisticated comp/rhet theory-head types think of writing. This has some interesting consequences, for example in revealing the agency of mathematical signs in the construction of mathematical knowledge. Rotman also argues that mathematical rigor is a necessary consequence of the rules of mathematical writing.

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"Concepts and the Mangle of Practice: Constructing Quaternions", Pickering

Pickering offers a short example of the method he uses in Constructing Quarks, and the theory he expounds on in The Mangle of Practice. Thus this essay is a quick substitute for reading two entire books — an opportunity that should not be missed.

To make it even shorter: ideas have agency. Pickering is interested in how concepts offer resistance, and how thinking agents (such as mathematicians) working in a field of conceptual agency have to make various moves to maneuver concepts into a form that satisfies some need. Pickering sees cultural practices as mechanical efforts to create conceptual models by producing associations between heterogeneous cultural elements. (This is closely related to Bruno Latour's method of the past decade or so.)

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"The Moment of Truth on Dublin Bridge: A Response to Andrew Pickering", Flanagan

Flanagan takes issue with how Pickering applies his method (originally developed to study the practice of physics) to the "more purely conceptual domain" of mathematics. While he accepts Pickering's overall direction, he raises three issues. He has some worries about Pickering's "mangle of practice" metaphor; and he thinks Pickering overstates the power of disciplinary agency. Finally, he thinks Pickering's final point about metaphysics and mathematics — which is basically that mathematicians sometimes thing about metaphysics, and those thoughts influence what sort of mathematical constructs they arrive at — can be taken even further. Mathematicians, Flanagan suggests, naturally consider metaphysical issues; they're almost unavoidable; and so mathematics has been strongly influenced by people wondering just what it's about.

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"Explanation, Agency, and Metaphysics: A Reply to Owen Flanagan", Pickering

Pickering essentially accepts Flanagan's critique of the mangle metaphor, and suggests that part of the problem is what we traditionally expect explanations to do (which is to present an account of causes and effects). On the other hand, he pushes back on the agency question, where he thinks Flanagan is distracted by flawed humanist notions of agency. (Here he describes his idea of agency as posthumanist, because it's neither founded on a humanist idea of agency as the action of a voluntary human actor, nor an antihumanist conception that sees agency arising from discipline.) He thinks Flanagan might be overestimating the importance of metaphysics, but agrees that it has an important role, whether it's a common concern for mathematicians or just one of the conceptual roads a mathematician might wander down.

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"Agency and the Hybrid Collectif", Callon and Law

Callon and Law are two of the three scholars (the third is Latour) generally credited with creating and promoting Actor-Network Theory (ANT), a linchpin of postclassical thought. Like Latour, they're sociologists and key figures in Science and Technology Studies. This chapter is a conversation between Callon and Law, where they take up topics such as the question of non-human agency, how ANT can degenerate into a sort of liberal extension of the "agency franchise" to non-human actors, the necessity of looking at relations instead of at entities, and of widening the idea of representation to include things like skills.

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"The Accidental Chordate: Contingency in Developmental Systems", Oyama

Oyama is an (emeritus) professor of psychology, but most of her work has been in developmental systems theory, focusing on questions posed by biological theories, such as her famous intervention into the nature/nurture debate in The Ontogeny of Information. Here she riffs off Stephen J Gould's popular writing on the Burgess Shale fossils, arguing that contingency, not some sort of "programming", is the primary constituent of evolutionary development, and of development in general.

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"Complementarity, Idealization and the Limits of Classical Conceptions of Reality", Plotnitsky

Here Plotnitsky offers a short introduction to complementarity and idealization, two of his favorite concepts. He uses complementarity to explain radical alterity, the idea that there are things which are forever outside representation. This is also one of the few chapters to discuss classical thought specifically; Plotnitsky notes how complementarity in effect harkens back to certain pre-Socratic ideas in Western thought, particularly those of Democritus.

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"Is 'Is a Precursor of' a Transitive Relation?", Weintraub

Weintraub's an economist, and here he takes up a very simple question: if you have a pretty convincing argument that idea A led to idea B (ie, that A was a precursor of B), and another one showing that idea B led to idea C, can you put them together to argue that A led to C? No, you can't. The history of ideas may look like a causal progression, but that masks the fact that at any point, we could have gotten to the same place by another route. Every idea has multiple, incommensurate histories.

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"Fraud by Numbers: Quantitative Rhetoric in the Piltdown Forgeries", Ashmore

Ashmore's chapter is a pretty straight-forward rhetorical analysis of quantitative claims in scientific fraud. Good solid stuff, and what's especially interesting is that Ashmore is poking holes in the debunking of the Piltdown claims; he points out that everyone assumes Piltdown is a forgery, without noting how its debunking is itself a rhetorical construct. The essay's also worth reading for Ashmore's critique of his own process in it.

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"A Glance at SunSet: Numerical Fundaments in Frege, Wittgenstein, Shakespeare, Beckett", Smyth

Admit it — you were wondering how Frege's attempts to define mathematics using set theory relate to Shakespeare. Well, read Smyth's chapter, and you'll know. He's trying to show how there are conceptual connections between mathematical philosophers and poets; like a number of postclassical thinkers, he rejects the "two cultures" idea of a split between the sciences and the arts. Smyth's final point is that the arts and sciences remain deeply connected, and no intellectual discipline is privileged over the others.

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"Microdynamics of Incommensurability: Philosophy of Science Meets Science Studies", Smith

To close out the book, Smith weaves some common threads from the chapters with her own critique of classical-derived epistemology into a theoretical program. She starts by criticizing the lack of engagement between the philosophy of science and science studies, and generalizes that into a theory which accepts incommensurability, the idea that there is no final, objective foundation on which competing accounts can be weighed against one another.

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Smith and Plotnitsky are careful to note this is not a new movement

Their short list of relevant figures goes back to early modernity (even Shakespeare is included), and it's possible to argue that some pre- and para-Platonic Classical thinkers, such as the Sophists and Isocrates, could be claimed "postclassical" in this sense.

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But the MSPT collection is animated by a recent historical trend, composed of a handful of related strands.

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the ongoing complication of formal (mathematical) and empirical (scientific) epistemologies

... over the course of the twentieth century, with discoveries such as formal incompleteness (by Cantor, Godel, Turing, etc) and fundamental physical limitations to measurement (by Einstein, Heisenburg, etc). While these did not undermine the Enlightenment project of the pursuit of rational knowledge, they do throw into question many of its underlying philosophical assumptions. (This bothers philosophers much more than it does scientists.)

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the growing critique of science, technology, and the Enlightenment project by critical theory

... this took various forms, some more successful than others, but as the "Science Wars" of the late '80s and early '90s began to cool off (mostly from exhaustion and widespread embarassment), more sophisticated and mature theoretical critiques of science — as philosophy, practice, cultural domain — emerged; today's fields such as Science and Technology Studies (STS) often include collaborations by working scientists and cutural theorists.

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the critique of humanism, particularly human exceptionalism

... which has grown out of, on the one hand, ecology studies and ecofeminism (where non-human organisms are ascribed attributes that were classically reserved for humans); and on the other hand, psychology, neurology, cognitive science, and artificial intelligence (where the nature of concepts such as "consciousness" and "intelligence" has been broadly interrogated).

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