The basepoint-freeness threshold of a very general abelian surface

For abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepoint-freeness threshold. Our main tool is the relation between cohomological rank functions and Bridgeland stability. In virtue of recent results of Caucci and Ito, these computations provide new information on the syzygies of polarized abelian surfaces.

What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achillesand the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox thereforenaturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

Indian Ocean Listening Stations: Governmental Ears, Surveillance Acoustemologies, and the Maritime Silk Road

In this article, I examine the discourse surrounding “listening stations” (surveillance outposts) that the Indian government has built to counter Chinese infrastructural projects in the Indian Ocean. As surveillance technologies are placed on out-of-the-way islands and deep underwater, the ocean is discursively situated in the press and diplomatic circles as a site where the geopolitical and sonic ‘noise’ of the metropole is evaded in virtue of the seeming fidelity of the sea, thus garnering potential for the listening stations to reveal China’s true geopolitical intentions. Drawing on classic securitization theory, as well as writings in the anthropology of security and sound studies, I argue that the positioning of listening stations as sites defined by listening and protection from Chinese encroachment obfuscates how they function as geopolitical speech and an expansion of Indian power. I coin the term “surveillance acoustemology” to refer to the ways that India’s listening stations spatialize India’s projected influence and its ability to hear its Chinese rival across the Indian Ocean.

Dogmatism and Ampliative Inference

The evidential role of experience in justifying beliefs has been at the center of debate in philosophy in recent years. One view is that experience, or seeming, can confer immediate (defeasible) justification on belief in virtue of its representational phenomenology. Call this view “representational dogmatism.” Another view is that experience confers immediate justification on belief in virtue of its relational phenomenology. Call this view “relational dogmatism.” The goal of this paper is to pit these two versions of dogmatism against each other in terms of their ability to account for ampliative, or non-deductive, inferential justification. I will argue that only the representational view can provide a plausible account of this type of justification.

The Ethical Value of the Inhumanity in Art A Levinasian Reading

Reality and its Shadow, a brief yet powerful essay written in 1948, is the only text where Emmanuel Levinas (1906-1995) deals solely with the ontology of art. Already in this early text, we can see how his understanding that ethics is the ground of philosophy drives his discussion. The nature of art is therefore treated in relation to what it does, ethically, to the subject, the maker, and the viewer. Art is the “inhumanity” and “inversion” of ethics. Only philosophical criticism reintegrates its “inhumanity” in the ethical relation. The strength of Levinas’s philosophy issues from a pre-cognitive commitment to the “other”, epitomised in the “face to face” relation. Any philosophy emphasising the primacy of the subject over and above the “other” crumbles under his reading. Yet this same strength implies that those domains where the “face to face” relation is obscured lead to irresponsibility. One such domain is art. In this essay I argue that by applying his mature work to the criticism he advances in Reality and its Shadow we can find ethical value in art in virtue of its “inhumanity” and “inversion”. That is, we can agree with Levinas that art leads to irresponsibility, and yet ascribe to it positive ethical value in Levinas's own terms. This can help concretise the tension between the ethical and unethical aspects of art within a Levinasian framework.

Duties of Corrective Justice and Historical Emissions

This paper addresses the question of whether agents have incurred duties of corrective justice to bear the costs of climate change in virtue of having produced historical emissions, or emissions produced when it was still reasonable to be ignorant of the causes and harmful consequences of climate change. It argues that it is likely that agents have incurred duties of corrective justice in virtue of having produced some of their historical emissions, given that it is likely that they would have produced these emissions had they known, when they produced them, that the emissions would contribute to harmful climate change.

The Relevance of Motivations to Wrongdoing for Contributing to Climate Change

This paper makes progress towards an account of moral wrongdoing for individual contributions to collectively-caused harms and substantial risks of harm, like the harms and risks stemming from climate change. To do so, this paper argues that an agent’s motivations can be relevant to whether an agent’s contribution to a collectively-caused harm or risk is morally wrong. Specifically, this paper argues that an agent’s contribution to a collectively caused harm or risk can be wrong in virtue of her motivations even when she does not intend to contribute to the harm or risk, but rather contributes to the harm or risk as a foreseeable but unintended side-effect of her otherwise good end.

Persson’s Merely Possible Persons

In many cases, it seems, one possible outcome is worse than another in virtue of the well-being of people who do not exist in both. For example, it seems, creating a very unhappy person makes the world worse, other things being equal. And some would say that we make the world better, other things being equal, by creating a very happy person. It would be easy to justify such claims if it can be better, or worse, for a person to exist than not to exist. But that seems to require that things can be better, or worse, for a person even in a world in which she does not exist, which sounds paradoxical. This paradoxical sounding claim has been defended by Ingmar Person. He argues that in a world in which a person does not exist, she is a merely possible being – a being that has never existed and never will – and that for such beings it is worse not to exist than to exist with a good life. Furthermore, he argues for this claim from what he claims are “incontestable” premises. We argue that the premises are far from incontestable. The argument, as stated by Persson, has false premises and is invalid. We can reconstruct the argument to make it valid, but this still leaves us with some clearly contestable premises. Finally, we will argue that it is possible to make sense of our obligations to future generations without letting merely possible beings into the moral club.

Nudging Well

Cleaning up the epistemic environment, in the way advocated in the last chapter, is or entails nudging beliefs, and nudging is very controversial. A central reason why nudging is controversial is that nudges are believed to bypass rational cognition. This chapter describes this concern, and argues it’s misplaced. Typically (at least) nudges provide higher-order evidence in favor of the options nudged. Nudges recommend options, and agents respond to nudges as recommendations. Our responses to nudges are (usually, at least) rational responses to evidence. Once we see how nudges work through the provision of higher-order evidence, we are in a position to recognize that the cues to expertise and to reliability we examined in previous chapters work in precisely the same way: they provide genuine evidence and we respond to them in virtue of that fact.