Recapture, Transparency, Negation and a Logic for the Catuṣkoṭi

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps\u27s (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield cannot ground the logic of the catuskoti. The concern is simple: on the one hand, FDE brings with it the failure of classical principles such as modus ponens. On the other hand, we frequently encounter Nāgārjuna using classical principles in other arguments in the MMK. There is a problem of validity. If FDE is Nāgārjuna’s logic of choice, he is facing what is commonly called the classical recapture problem: how to make sense of cases where classical principles like modus pones are valid? One cannot just add principles like modus pones as assumptions, because in the background paraconsistent logic this does not rule out their negations. In this essay, I shall explore and critically evaluate Cotnoir’s proposal. In detail, I shall reveal that his framework suffers collapse of the kotis. Taking Cotnoir’s concerns seriously, I shall suggest a formulation of the catuskoti in classical Boolean Algebra, extended by the notion of an external negation as an illocutionary act. I will focus on purely formal considerations, leaving doctrinal matters to the scholarly discourse – as far as this is possible

Recapture, Transparency, Negation and a Logic for the Catuskoti

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield cannot ground the logic of the catuskoti. The concern is simple: on the one hand, FDE brings with it the failure of classical principles such as modus ponens. On the other hand, we frequently encounter Nāgārjuna using classical principles in other arguments in the MMK. There is a problem of validity. If FDE is Nāgārjuna’s logic of choice, he is facing what is commonly called the classical recapture problem: how to make sense of cases where classical principles like modus pones are valid? One cannot just add principles like modus ponens as assumptions, because in the background paraconsistent logic this does not rule out their negations. In this essay, I shall explore and critically evaluate Cotnoir’s proposal. In detail, I shall reveal that his framework suffers collapse of the kotis. Furthermore, I shall argue that the Collapse Argument has been misguided from the outset. The last chapter suggests a formulation of the catuskoti in classical Boolean Algebra, extended by the notion of an external negation as an illocutionary act. I will focus on purely formal considerations, leaving doctrinal matters to the scholarly discourse – as far as this is possible

On Buddhist logic

This thesis is the attempt to find a logical model for, and trace the history of, the catuṣkoṭi as it developed in the Indo-Tibetan milieu and spread, via China, to Japan. After an introduction to the history and key-concepts of Buddhist philosophy, I will finish the first chapter with some methodological considerations about the general viability of comparative philosophy. Chapter §2 is devoted to a logical analysis of the catuṣkoṭi. Several attempts to model this fascinating piece of Buddhist philosophy with the tools of classical logic shall be debunked. A paraconsistent alternative will be discussed but eventually dismissed. As a rejoinder, I shall propose a model for the catuṣkoṭi with the help of speech-acts. The remainder of this chapter will look at Chinese and Japanese forms of the catuṣkoṭi which I shall model in a quasi-recursive system. The third and final chapter will look at the Kyoto School's soku-hi dialectics which ties together the different threads of this essay. I will criticise an established, classical model of the soku-hi dialectics and offer an alternative with a second-order paraconsistent semantics

Realism and Metanormativity

Political realists have argued that ‘the political’ is an autonomous domain with its own distinctive concepts, distinctive methodology, and distinctive ‘source of normativity’. I here explore the metanormative commitments of realism (of the radical realist branch, in particular) and question the viability of exploring the ontology of the normative altogether. I argue that the escape into the metanormative realm was something of a wrong turn within the realism debates – an intellectual error. My central argument, building on recent metatheoretical work on normativity, is meant to discredit the sheer possibility of metanormative distinctness. If realists can neither prove metanormative, nor traditional, nor methodological distinctness, there is a valid question as to its standing. I speculate, perhaps realism is little more than a new semantic label for ‘continental’ practices of social analysis as they leak into the analytic tradition. But then again it can be argued that most contemporary continental thought, and certainly much of what passes as critical theory these days, is thoroughly moralist, anti-positivist, and postmodern, and those sentiments are not shared by radical realists, who are, or so I’ll argue, far more faithful to the modernist tradition of social theory

How I Learned to Stop Worrying and Love Political Normativity

Do salient normative claims about politics require moral premises? Political moralists think they do, political realists think they do not. We defend the viability of realism in a two-pronged way. First, we show that a number of recent attacks on realism, as well as realist responses to those attacks, unduly conflate distinctively political normativity and non-moral political normativity. Second, we argue that Alex Worsnip and Jonathan Leader-Maynard’s recent attack on realist arguments for a distinctively political normativity depends on assuming moralism as the default view, which places an excessive burden on the viability of realism, and so begs the question. Our discussion, though, does not address the relative merits of realism and moralism, so its upshot is relatively ecumenical: moralism need not be the view that all apt normative political judgments are moral judgments, and realism need not be the view that no apt normative political judgments are moral judgments

PEtab -- interoperable specification of parameter estimation problems in systems biology

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been -- so far -- no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies. Specifications of PEtab, the PEtab Python library, as well as links to examples, and all supporting software tools are available at https://github.com/PEtab-dev/PEtab, a snapshot is available at https://doi.org/10.5281/zenodo.3732958. All original content is available under permissive licenses

Precise interpolar phasing of abrupt climate change during the last ice age

The last glacial period exhibited abrupt Dansgaard–Oeschger climatic oscillations, evidence of which is preserved in a variety of Northern Hemisphere palaeoclimate archives¹. Ice cores show that Antarctica cooled during the warm phases of the Greenland Dansgaard–Oeschger cycle and vice versa[superscript 2,3], suggesting an interhemispheric redistribution of heat through a mechanism called the bipolar seesaw[superscript 4–6]. Variations in the Atlantic meridional overturning circulation (AMOC) strength are thought to have been important, but much uncertainty remains regarding the dynamics and trigger of these abrupt events[superscript 7–9]. Key information is contained in the relative phasing of hemispheric climate variations, yet the large, poorly constrained difference between gas age and ice age and the relatively low resolution of methane records from Antarctic ice cores have so far precluded methane-based synchronization at the required sub-centennial precision[superscript 2,3,10]. Here we use a recently drilled high-accumulation Antarctic ice core to show that, on average, abrupt Greenland warming leads the corresponding Antarctic cooling onset by 218 ± 92 years (2σ) for Dansgaard–Oeschger events, including the Bølling event; Greenland cooling leads the corresponding onset of Antarctic warming by 208 ± 96 years. Our results demonstrate a north-to-south directionality of the abrupt climatic signal, which is propagated to the Southern Hemisphere high latitudes by oceanic rather than atmospheric processes. The similar interpolar phasing of warming and cooling transitions suggests that the transfer time of the climatic signal is independent of the AMOC background state. Our findings confirm a central role for ocean circulation in the bipolar seesaw and provide clear criteria for assessing hypotheses and model simulations of Dansgaard–Oeschger dynamics

Ethics is dead politics: a dissertation on political normativity

This doctoral thesis is prompted by the political realist diagnosis that “ethics is usually dead politics; the hand of a victor in a past conflict reaching out to extend its grip to the present and the future”. While there is already an extensive body of literature on political realism and moralism, my work aims to contribute by exploring various explanations for the realist diagnosis and by assessing the prospects of methodological success for the different realist approaches within contemporary theory. Each chapter offers a distinct perspective on the relationship between political realism and political moralism, and the question of political normativity at large. The central objective is to evaluate existing realist advances and discard those that are methodologically redundant and/or philosophically misled. In short, this thesis deflates ordorealism and contextual realism, challenges extant radical realist proposals, and offers a tentative outline for a more rudimental realist social analysis and critique