Two proof-systems P and P* are said to be complementary when one proves exactly the non-theorems of the other. Complementary systems come as a particular kind of refutation calculi whose patterns of inference always work by inferring unprovable conclusions form unprovable premises. In the first part of my talk, I will focus on LK*, the sequent system complementing Gentzen’s system LK for classical logic. I will show, then, how to enrich LK* with two admissible (unary) cut rules, which allow for a simple and efficient cut-elimination algorithm. In particular, two facts will be highlighted: 1) for any given provable sequent, complementary cut-elimination always returns one of its simplest proofs, and 2) provable LK* sequents turn out to be “deductively polarized” by the empty sequent. In the second part, I will observe how an alternative complementary sequent system can be obtained by slightly modifying the Gentzen-Schütte system G3. I will finally show how this move could pave the way for a novel approach to multi-valuedness and proof-theoretic semantics for classical logic.
This event will feature a thought-provoking panel discussion with sexual and reproductive justice experts on the value of the sexual and reproductive justice framework and how it can be applied to diverse stakeholders, settings, and contexts. Panelists will also highlight examples from around the world of momentum towards sexual and reproductive justice.
Event Information
Free and open to the public; registration is required for both in-person and online attendance. For additional information, please visit the event webpage. Please email Malia Maier at mm5352@cumc.columbia.edu with any questions. All in-person attendees must follow Columbia’s COVID-19 policies.
Hosted by the Global Health Justice and Governance Program at Columbia University.
A conference hosted by the Motherhood and Technology Working Group at the Center for the Study of Social Difference on the theme of “Conception and Its Discontents.”
Medical technologies have radically transformed the biological and social experience of motherhood. Advances in genomic and reproductive care, the circulation of novel kinship structures, the entrenchment of existing global networks of power and privilege, and the politics of contested bodily sites mark this emerging constellation.
Technological advancements have in particular impacted not just the understanding of conception, but the very process by which a human embryo is created, implanted, and matured. Egg freezing, embryo storage, IVF, and surrogacy afford women new freedoms in choosing when and how to become mothers, while also raising troubling questions about the pressures of capitalism and the extension of worklife, as well as the global inequalities present in the experience of motherhood. In addition, technologies have arisen allowing for unprecedented control over not just who becomes a mother, but what kind of embryo is allowed to be implanted and to grow. Technologies such as CRISPR and NIPT have re-introduced the question of eugenics, radically shifting the very epistemology of motherhood and what it means to be “expecting.” And contemporary abortion debates draw on technology in order to make arguments both for and against access, with imaging technologies being instrumentalized in the building of a sympathetic case for the unborn, and the very notion of a “heartbeat bill” reliant on the misreading of technologies for measuring fetal activity.
While these problems are urgent today, questions of conception and technology are by no means recent developments. The 18th century saw a flourishing of philosophical and scientific theories regarding the start of human life and its formation within the womb. Such theories relied on modern technologies, such as autopsy, to atomize and visualize the body. In the 19th and 20th centuries, eugenic medical science produced theories of reproductive difference between differing racial and social groups, leading to forced sterilization laws in both the US and in Germany. This long history of racializing the rhetoric of fertility and motherhood continues to influence political debates on immigration and demographic changes in the present.
Full conference details and schedule to come.
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