10,845 research outputs found
Ignorance and Blame
Sometimes ignorance is a legitimate excuse for morally wrong behavior, and sometimes it isnât. If someone has secretly replaced my sugar with arsenic, then Iâm 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 donât label them, then Iâm plausibly blameworthy for poisoning you. Why is my ignorance in the first case a legitimate excuse, but my ignorance in the second case isnât? 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 agentâs 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
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