What is so special about analogue simulations?

Contra Dardashti, Th\'ebault, and Winsberg (2017), this paper defends an analysis of arguments from analogue simulations as instances of a familiar kind of inductive inference in science: arguments from material analogy (Hesse, Models and Analogies in Science, Univ Notre Dame Press, 1963). When understood in this way, the capacity of analogue simulations to confirm hypotheses about black holes can be deduced from a general account - fully consistent with a Bayesian standpoint - of how ordinary arguments from material analogy confirm. The proposed analysis makes recommendations about what analogue experiments are worth pursuing that are more credible than Dardashti, Hartmann, Th\'ebault, and Winsberg's (2019). It also offers a more solid basis for addressing the concerns by Crowther, Linneman, and W\"utrich (2019), according to which analogue simulations are incapable of sustaining hypotheses concerning black hole radiation.Comment: 26 pages, 1 figur

Reasoning by Analogy in Mathematical Practice

The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of analogical reasoning in mathematics, stating general conditions under which an analogy may provide genuine inductive support to a mathematical conjecture (over and above fulfilling the merely heuristic role of 'suggesting' a conjecture in the psychological sense). The proposed conditions generalize the criteria put forward by Hesse (1963) in her influential work on analogical reasoning in the empirical sciences. By reference to several case-studies, we argue that the account proposed in this paper does a better job in vindicating the use of analogical inference in mathematics than the prominent alternative defended by Bartha (2009). Moreover, our proposal offers novel insights into the practice of extending to the infinite case mathematical properties known to hold in finite domains.Comment: 35 pages, 4 figures. Forthcoming in Philosophia Mathematic

Light curves and spectra from off-axis gamma-ray bursts

If gamma-ray burst prompt emission originates at a typical radius, and if material producing the emission moves at relativistic speed, then the variability of the resulting light curve depends on the viewing angle. This is due to the fact that the pulse evolution time scale is Doppler contracted, while the pulse separation is not. For off-axis viewing angles $\theta_{\rm view} \gtrsim \theta_{\rm jet} + \Gamma^{-1}$, the pulse broadening significantly smears out the light curve variability. This is largely independent of geometry and emission processes. To explore a specific case, we set up a simple model of a single pulse under the assumption that the pulse rise and decay are dominated by the shell curvature effect. We show that such a pulse observed off-axis is (i) broader, (ii) softer and (iii) displays a different hardness-intensity correlation with respect to the same pulse seen on-axis. For each of these effects, we provide an intuitive physical explanation. We then show how a synthetic light curve made by a superposition of pulses changes with increasing viewing angle. We find that a highly variable light curve, (as seen on-axis) becomes smooth and apparently single-pulsed (when seen off-axis) because of pulse overlap. To test the relevance of this fact, we estimate the fraction of off-axis gamma-ray bursts detectable by \textit{Swift} as a function of redshift, finding that a sizable fraction (between 10\% and 80\%) of nearby ($z<0.1$) bursts are observed with $\theta_{\rm view} \gtrsim \theta_{\rm jet} + \Gamma^{-1}$. Based on these results, we argue that low luminosity gamma-ray bursts are consistent with being ordinary bursts seen off-axis.Comment: 13 pages, 17 figures, submitted to MNRAS main journal; updated estimate of the fraction of off-axis grbs seen by Swif

Causal Models and Default

This paper criticizes some recent arguments by Halpern (2008) and others to the effect that the structural equations framework used for modeling relations of singular causation ought to be supplemented with some function, a normality ordering, reflecting the distinction between default or normal states of things and deviant or abnormal ones. A central contention of this paper is that these proposals are insufficient to solve the problem they are intended to solve. This raises the question whether we should search for a replacement for the structural equations approach or instead think of the failure of the Halpern proposal as due to a deeper problem with the project. In the conclusion, I provide an argument in favor of the latter thesis.Master of Art

How I Would have been Differently Treated: Discrimination Through the Lens of Counterfactual Fairness

The widespread use of algorithms for prediction-based decisions urges us to consider the question of what it means for a given act or practice to be discriminatory. Building upon work by Kusner and colleagues in the field of machine learning, we propose a counterfactual condition as a necessary requirement on discrimination. To demonstrate the philosophical relevance of the proposed condition, we consider two prominent accounts of discrimination in the recent literature, by Lippert-Rasmussen and Hellman respectively, that do not logically imply our condition and show that they face important objections. Specifically, Lippert-Rasmussen’s definition proves to be over-inclusive, as it classifies some acts or practices as discriminatory when they are not, whereas Hellman’s account turns out to lack explanatory power precisely insofar as it does not countenance a counterfactual condition on discrimination. By defending the necessity of our counterfactual condition, we set the conceptual limits for justified claims about the occurrence of discriminatory acts or practices in society, with immediate applications to the ethics of algorithmic decision-making

'The Most Beautiful of All Bonds': Analogy in Scientific Inquiry

Combining philosophical analysis with historical perspective, my dissertation aims to dispel what is, in my view, a harmful prejudice about the work accomplished by analogies in empirical investigations. This prejudice has drawn philosophers and scientists alike to a picture of scientific rationality that is not only unfaithful to the methods by which empirical knowledge is produced, but also isolates the scientific endeavor from all other human endeavors of knowledge-production employing analogy and comparison. Against the idea that analogies can only serve as ‘food for thought’, I defend the claim that there exists an inductive use of analogy in science: i.e., that analogies can sometimes be sources of defeasible support for hypotheses about the yet unknown. I propose to vindicate the inductive use of analogy in science by appeal to an expectation (which can be more or less reasonable depending on the context of investigation) of simplicity in the description of natural and social reality: i.e., with the idea that the same explanatory patterns employed in the analogy’s source are ‘on the right track’ to providing us with an understanding of a target system.Doctor of Philosoph

Foundational issues in the metaphysics of David Lewis

Few contributions in the field of metaphysics can be compared, for their depth and impact, to the work of the American philosopher David K. Lewis. A feature of this work, which partly explain its great appeal, is its systematicity. Lewis’s views on intrinsicality, naturalness, supervenience, mind and modality, to mention just a few themes, constitute a unified and connected body of doctrines. As Lewis himself acknowledged in the introduction to the first volume of collected papers: “I should have liked to be a piecemeal, unsystematic philosopher, offering independent proposals on a variety of topics. It was not to be” (Lewis 1983, p. XI). Surely there is an element of beauty in this systematicity. But there is also an element of precariousness. For a body of doctrines has some vital organs: claims or assumptions that are so central to the life of the system that, if one were to reject them, the system as a whole would likely collapse. This seems to be true, in particular, of Lewis’s metaphysical system. What I present here are two investigations concerning, respectively, the problem of ontic vagueness and the existence of a fundamental level. I believe that the evaluation of these two issues is of vital importance for assessing the tenability of Lewis’s systematic metaphysics. There is a general worry lurking behind my discussion, which it’s worth making explicit here. The worry is that, if the justification for Lewis’s claims on ontic vagueness and fundamentality turned out to be wanting or otherwise unsatisfactory, and if I am right to think that these theses are part of a number of central claims constituting the basis of his metaphysical system, then it seems we should start being suspicious of the very tenability of the Lewisian metaphysics as a whole. What I will be arguing for in the two main chapters of this dissertation provides, in my view, enough material for a modest defense of Lewis’s views on ontic vagueness and fundamentality. I will clarify the content of this modest defense, and explain its significance for the development of the contemporary debate in metaphysics, as well as for a redefinition of a kind of Lewisian metaphysics, in a brief note at the end of the introduction