Ignorance and Blame

Sometimes ignorance is a legitimate excuse for morally wrong behavior, and sometimes it isn’t. If someone has secretly replaced my sugar with arsenic, then I’m blameless for putting arsenic in your tea. But if I put arsenic in your tea because I keep arsenic and sugar jars on the same shelf and don’t label them, then I’m plausibly blameworthy for poisoning you. Why is my ignorance in the first case a legitimate excuse, but my ignorance in the second case isn’t? This essay explores the relationship between ignorance and blameworthiness

BCI-Mediated Behavior, Moral Luck, and Punishment

An ongoing debate in the philosophy of action concerns the prevalence of moral luck: instances in which an agent’s moral responsibility is due, at least in part, to factors beyond his control. I point to a unique problem of moral luck for agents who depend upon Brain Computer Interfaces (BCIs) for bodily movement. BCIs may misrecognize a voluntarily formed distal intention (e.g., a plan to commit some illicit act in the future) as a control command to perform some overt behavior now. If so, then BCI-agents may be deserving of punishment for the unlucky but foreseeable outcomes of their voluntarily formed plans, whereas standard counterparts who abandon their plans are not. However, it seems that the only relevant difference between BCI-agents and their standard counterparts is just a matter of luck. I briefly sketch different solutions that attempt to avoid this type of moral luck, while remaining agnostic on whether any succeeds. If none of these solutions succeeds, then there may be a unique type of moral luck that is unavoidable with respect to deserving punishment for certain BCI-mediated behaviors

Stability under integration of sums of products of real globally subanalytic functions and their logarithms

We study Lebesgue integration of sums of products of globally subanalytic functions and their logarithms, called constructible functions. Our first theorem states that the class of constructible functions is stable under integration. The second theorem treats integrability conditions in Fubini-type settings, and the third result gives decay rates at infinity for constructible functions. Further, we give preparation results for constructible functions related to integrability conditions

Integration of Oscillatory and Subanalytic Functions

We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This paper extends the investigation started in [J.-M. Lion, J.-P. Rolin: "Volumes, feuilles de Rolle de feuilletages analytiques et th\'eor\`eme de Wilkie" Ann. Fac. Sci. Toulouse Math. (6) 7 (1998), no. 1, 93-112] and [R. Cluckers, D. J. Miller: "Stability under integration of sums of products of real globally subanalytic functions and their logarithms" Duke Math. J. 156 (2011), no. 2, 311-348] to an enriched framework including oscillatory functions. It provides a new example of fruitful interaction between analysis and singularity theory.Comment: Final version. Accepted for publication in Duke Math. Journal. Changes in proofs: from Section 6 to the end, we now use the theory of continuously uniformly distributed modulo 1 functions that provides a uniform technical point of view in the proofs of limit statement

Explicit constructions of infinite families of MSTD sets

We explicitly construct infinite families of MSTD (more sums than differences) sets. There are enough of these sets to prove that there exists a constant C such that at least C / r^4 of the 2^r subsets of {1,...,r} are MSTD sets; thus our family is significantly denser than previous constructions (whose densities are at most f(r)/2^{r/2} for some polynomial f(r)). We conclude by generalizing our method to compare linear forms epsilon_1 A + ... + epsilon_n A with epsilon_i in {-1,1}.Comment: Version 2: 14 pages, 1 figure. Includes extensions to ternary forms and a conjecture for general combinations of the form Sum_i epsilon_i A with epsilon_i in {-1,1} (would be a theorem if we could find a set to start the induction in general