Foundations Of Statistics

Scholars of culture, humanities and social sciences have increasingly come to an appreciation of the importance of the legal domain in social life, while critically engaged socio-legal scholars around the world have taken up the task of understanding "Law's Empire" in all of its cultural, political, and economic dimensions. The questions arising from these intersections, and addressing imperialisms past and present forms the subject matter of a special symposium issue of Social Identities under the editorship of Griffith University's Rob McQueen, and UBC's Wes Pue and with contributions from McQueen, Ian Duncanson, Renisa Mawani, David Williams, Emma Cunliffe, Chidi Oguamanam, W. Wesley Pue, Fatou Camara, and Dianne Kirkby. This paper introduces the volume, forthcoming in late 2007. The central problematique of this issue has previously been explored through the 2005 Law's Empire conference, an informal but vibrant postcolonial legal studies network.

Law's Empire

Two people, 1 and 2, are said to have common knowledge of an event E if both know it, 1 knows that 2 knows it, 2 knows that 1 knows it, 1 knows that 2 knows that 1 knows it, and so on.

Agreeing to disagree.

Logical Foundations of Probability By Rudolf Carnap Pp xvii + 607 (London: Routledge and Kegan Paul, Ltd, 1951) 42s net

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Logical Foundations of Probability

Frances Mei Hardin, MD, MSMA member since 2017, is in the Department of Otolaryngology, University of Missouri, Columbia, Missouri. Above, she is shown as MSMA Physician of the Day at the Missouri Capitol in 2018.

Contact: ude.iruossim.htlaeh@fnidrah






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This article was not sponsored by Easton bats, Headspace, Calm, Sycamore Creek Farms, Pilot, or Casamigos, but if any of these institutions would like to reach out, I’ll be available.

What We Owe To Each Other.

I advocate Time-Slice Rationality, the thesis that the relationship between two time-slices of the same person is not importantly different, for purposes of rational evaluation, from the relationship between time-slices of distinct persons. The locus of rationality, so to speak, is the time-slice rather than the temporally extended agent. This claim is motivated by consideration of puzzle cases for personal identity over time and by a very moderate form of internalism about rationality. Time-Slice Rationality conflicts with two proposed principles of rationality, Conditionalization and Reflection. Conditionalization is a diachronic norm saying how your current degrees of belief should fit with your old ones, while Reflection is a norm enjoining you to defer to the degrees of belief that you expect to have in the future. But they are independently problematic and should be replaced by improved, time-slice-centric principles. Conditionalization should be replaced by a synchronic norm saying what degrees of belief you ought to have given your current evidence and Reflection should be replaced by a norm which instructs you to defer to the degrees of belief of agents you take to be experts. These replacement principles do all the work that the old principles were supposed to do while avoiding their problems. In this way, Time-Slice Rationality puts the theory of rationality on firmer foundations and yields better norms than alternative, non-time-slice-centric approaches.

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Time-Slice Rationality

How slack are requirements of rationality? Given a body of evidence, is there just one perfectly rational doxastic state to be in given that evidence? Defenders of Uniqueness answer ‘yes’ while defenders of Permissivism answer ‘no.’ For Permissivists, rationality gives you a certain amount of leeway in what to believe, with the result that rational people with the same evidence can nonetheless disagree with each other. By contrast, Uniqueness theorists hold that if two agents share the same total evidence and are rational in evaluating that evidence, they must have the same beliefs in response to that evidence. The debate over Uniqueness and Permissivism is important in its own right, but it also has implications for a number of other epistemological disputes. First, it has taken on a central role in debates about the epistemology of disagreement and the role of higher-order evidence. Second, it bears on whether requirements of rationality are diachronic, concerning how your beliefs at different times ought to be related to each other, or only synchronic, concerning only how your beliefs are at particular times, and Uniqueness and Permissivism are compatible with any number of views about how to conceive of rational doxastic states they could be sets of binary (on/off) beliefs, or credence functions, or pairs consisting of a credence function and a set of binary beliefs, or all manner of other possibilities. What Uniqueness says is that given a body of total evidence, there’s a unique doxastic state (whatever structure that might have) that it’s rational to be in, while Permissivism denies this. See Matheson (2009), Christensen (2010), Ballantyne and Coffman (2011, 2012), and Schoenfield (2014).

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Uniqueness and Metaepistemology

Predictive algorithms are playing an increasingly prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm’s predictions and the actual outcomes, for instance requiring that the rate of false positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results shows that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except for a calibration criterion, are necessary conditions for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness.

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On statistical criteria of algorithmic fairness

Determing what you ought to do can be broken down into two stages. The first stage is determining what your options are, and the second stage is ranking those options. While the second stage has been widely explored by philosophers of all stripes, from ethicists to decision theorists to epistemologists to action theorists, the first stage has gone largely unaddressed. And yet, without a theory of how to conceive of your options, the theory of practical rationality of how you ought to act will be incomplete. I will argue that the fact that what you ought to do depends on your uncertainty about the world ultimately forces us to conceive of your options as consisting of all and only the decisions you are presently able to make. In this way, oughts apply only to decisions, and not to the non-mental acts that we ordinarily evaluate for moral and rational permissibility. This change in our conception of your options is not of mere bookkeeping interest; it has substantive implications for first-order normative theorizing. First, it directly takes into account the potential costs and benefits of the decision itself in determining what you ought to do. Second, it provides a principled solution to Chisholm’s Paradox, in which your doubts about your own self-control seem to give rise to conflicting claims

Options and the subjective ought

We are not omniscient agents. Therefore, it is our lot in life to have to make decisions without being apprised of all of the relevant facts. We have to act under conditions of uncertainty. This uncertainty comes in at least two kinds. First, there is ignorance of descriptive facts; you might be ignorant of the potential causal impacts of the various actions available to you. For instance, you might be unsure whether to give the pills to your headache-suffering friend because you are uncertain whether they are painkillers or rat poison. Second, there is ignorance of normative facts, or facts about whether a certain action or outcome is good or bad, permissible or impermissible, blameworthy or praiseworthy, etc. For instance, you might know exactly what would happen (descriptively speaking) if you (or your partner) had an abortion and what would happen if you didn’t, and yet still be uncertain about whether having an abortion is a morally permissible thing to do. Due to the ubiquity of normative, and not just descriptive, uncertainty, we might want a theory that provides some guidance about how to take this normative uncertainty into account in deciding what to do. While I will be concerned with specifically moral uncertainty, much of what I say will carry over to other cases of normative uncertainty, such as uncertainty about what would be instrumentally rational to do or what it would be epistemically rational to believe. At this stage-setting phase, some terminology will be helpful. Let us say that what you objectively ought to do depends only on how the world in fact is, and not on how you believe the world to be. For Utilitarians, what you objectively ought to do is whatever will in fact maximize happiness, irrespective of your beliefs about what will maximize happiness. For non-consequentialists, what you objectively ought to do might depend, for instance, on facts about whether

Does MITE Make Right? Decision-Making Under Normative Uncertainty

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