# 2014-2015 Lectures & Colloquia

## Fall

**Thursday, September 25, 2014,** *Philosophy Colloquium*

**Patrick Forber, **Tufts University**A spiteful wrench in the works: rethinking the evolution of (human) cooperation***Reception:* 4:10 DH 4301, *Talk:* 4:45-6:00 BH A53

The evolution of cooperation presents a puzzle: why pay a cost to help another when I do better by looking after my own interests? This puzzle has a number of solutions—group selection, conditional strategies, punishment, and so on—and philosophers of science have played some role in the development and refinement of these solutions. In part, because of the complexity of the controversy surrounding group selection, but also because of the importance of cooperation to understanding the evolution of human social behavior, even human morality. However, many explanations of cooperation overlook the role spite can play in the evolution of social behavior. In this talk I will present some results on the evolution of spite developed with my collaborator, Rory Smead, and discuss the philosophical consequences of these results. In particular, I will focus on how we measure the fitness of social behavior, and the connection, if any, to human evolution and morality.

**Thursday, October 2, 2014,** *Philosophy Colloquium*

**Sherri Roush**, King's College London**Rational Self-Doubt: The Re-calibrating Bayesian***Reception:* 4:10 DH 4301, *Talk:* 4:45-6:00 BH A53

If one is highly confident that #3 in the line-up is the murderer from having witnessed the crime, and then learns of the substantial experimental psychology evidence that human beings are unreliable and overconfident at eyewitness testimony, is one thereby obligated to reduce one’s confidence about #3? How far, and why? This question corresponds to a challenge posed in 1980 to the effect that a Bayesian cannot coherently re-calibrate on the basis of feedback about his prior performance. I represent the feedback as second-order evidence, and generalize 1st-order Bayesian rationality constraints away from idealizations in a principled way, to give a rule for proportionally revising 1st order beliefs on the basis of 2nd-order evidence about one’s reliability. It is a conditionalization rule that re-calibrates the subject and sidesteps standard objections to calibration. It shows why taking doubt about one’s own judgment seriously does not need to end up in incoherence or runaway skepticism, and what the added value of this kind of evidence is.

**Thursday, October 16, 2014,** *Philosophy Colloquium*

**Louis Narens,** UC Irvine**Context and Probability***Reception:* 4:10 DH 4301, *Talk:* 4:45-6:00 BH A53

Standard probability theory has been enormously productive in science. But there are instances where it fails to provide adequate concepts and mathematical methods. Decision theory and quantum mechanics are examples. In these cases, context can interact with the phenomena of interest in ways that standard probability theory does not productively capture-that is, in ways that standard probability theory does not provide insights and methods for useful modeling and apparently fails to capture key concepts. This talk will present alternatives to standard probability theory by changing the logical structure of event space from boolean algebras to other algebras in order to accommodate context, and will apply some of the results involving the new algebras to rationality issues in philosophy and the behavioral sciences.

**Thursday, November 6 2014,** *Philosophy Colloquium*

**Harvey Lederman,** University of Oxford**Uncommon Knowledge***Reception:* 4:10 DH 4301, *Talk:* 4:45-6:00 BH A53

A group commonly knows a proposition if all know it, all know that all know it, and so on (and similarly for common belief). An important argument for the possibility of achieving common knowledge and belief is an abductive one: these states provide the best explanation of human behavior, and in particular coordination behavior. This paper argues that the abductive argument for common knowledge and belief fails.

**Friday, November 7 2014,** *Philosophy Colloquium*

**Harvey Lederman,** University of Oxford**Prospects for a Naive Theory of Classes (with Hartry Field and Tore Fjetland Øgaard)**

12pm-1:30pm, Doherty Hall 4303

We examine the prospects for a naïve theory of classes, in which full “naïve” comprehension and an extensionality rule are maintained by weakening the background logic. Without extensionality, proving naïve comprehension consistent is formally analogous to proving naïve truth consistent, and in recent years much progress has been made on the latter question. But there is no natural analog for extensionality in the case of truth, so the question arises whether these logics for reasoning about truth can also be shown consistent with a form of extensionality. In a series of papers, and in his 2006 book, Ross Brady has presented various theories of naïve classes. We begin by providing a simpler, more accessible version of Brady’s proof of the consistency of these theories. Our new presentation of Brady then makes it easy to see how Brady’s result can be generalized to apply to certain logics which have a modal-like semantics given using four-valued, as opposed to three-valued worlds. But we argue that even these improved Brady-like logics are too weak for reasoning about classes. Worse yet, we conclude with an impossibility result which shows fairly decisively that one cannot hope to do significantly better.

**Thursday, November 13 2014,** *Philosophy Colloquium*

**Wilfried Sieg,** Carnegie Mellon University**What is the concept of computation?***Reception:* 4:10 DH 4301, *Talk:* 4:45-6:00 BH A53

The Church-Turing Thesis asserts that particular mathematical notions are adequate to represent informal notions of effective calculability or mechanical decidability. I first sketch contexts that called for such adequate mathematical notions, namely, problems in mathematics (e.g., Hilbert’s 10th problem), decision problems in logic (e.g., the Entscheidungsproblem for firstorder logic), and the precise characterization of formality (for the general formulation of Gödel’s incompleteness theorems).

The classical approach to the effective calculability of number theoretic functions led, through Gödel and Church, to a notion of computability in logical calculi and metamathematical absoluteness theorems. The classical approach to the mechanical decidability of problems concerning syntactic configurations led, through Turing and Post, to a notion of computability in formal calculi (canonical systems) and metamathematical representation theorems.

Particular features of formal calculi motivate the formulation of an abstract concept of acomputable dynamical system. This concept articulates finiteness and locality conditions that are satisfied by the standard concrete notions of computation. In addition, a representation theorem can be established: Turing machines can simulate the computations of any concrete system falling under the abstract concept. I sketch a generalization of this approach to obtain computable parallel dynamical systems. Some applications will conclude my discussion.

**Thursday, November 20, 2014,** *Philosophy Colloquium*

**Philip Ehrlich,** Ohio University**Cantorian and non-Cantorian Theories of Finite, Infinite and Infinitesimal Numbers and the Unification Thereof***Reception:* 4:10 DH 4301, *Talk:* 4:45-6:00 BH A53

In addition to Cantor’s well-known systems of infinite cardinals and ordinals, there was a variety of other important though less well-known systems of actual infinite numbers that emerged in the decades bracketing the turn of the twentieth-century. Some grew out of work on the rates of growth of real functions, and others emerged from the pioneering investigations of non-Archimedean ordered algebraic and geometric systems. Unlike Cantor’s number systems, which were designed to answer questions such as

or

What position is occupied by a member of an infinite well-ordered set?

and

In recent decades, theses number systems have been enjoying a robust resurgence in interest as part of a more general interest in non-Archimedean ordered fields and relational expansions thereof. Unlike Cantor’s number systems, which solely embrace finite numbers alongside his well-known infinite numbers, the just-said non-Cantorian number systems, like the better-known hyperreal number systems associated with Abraham Robinson’s nonstandard approach to analysis, embody finite and infinite as well as infinitesimal numbers.

In [Ehrlich 2012], we show how the above-mentioned Cantorian and non-Cantorian number systems admit a striking unification in the author’s [Ehrlich 2001] algebraico-tree-theoretic approach to J. H. Conway’s system of surreal numbers. Building on the above, in this paper we will provide introductions to the aforementioned non-Cantorian theories of the finite, infinite and infinitesimal that emerged in the decades bracketing the turn of the twentieth-century, explain the motivation for their introduction, outline the roles these and related theories play in contemporary mathematics and discuss the relations between these theories and the better-known theories of Cantor and Robinson that emerge from the just-said unification. It is the author’s hope that by drawing attention to the spectrum of theories of the infinite and the infinitesimal that have emerged from non-Archimedean mathematics since the latter decades of the 19th century, it will become clear that the standard 20th-century histories and philosophies of the actual infinite and the infinitesimal that are motivated largely by Cantor’s theory of the infinite and by non-standard analysis are not only limited in scope but are inspired by an account of late 19th- and early 20th-century mathematics that is as mathematically myopic as it is historically flawed.

Philip Ehrlich, Number Systems with Simplicity Hierarchies: A Generalization of Conway’s Theory of Surreal Numbers, The Journal of Symbolic Logic 66 (2001), pp. 1231-1258.

Philip Ehrlich, The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small, The Bulletin of Symbolic Logic 18 (2012), pp. 1-45.

## Spring

**Monday, January 12, 2015,** *Philosophy Colloquium*

**Ilya Shpitser**, University of Southampton

*Mediation: From Intuition to Data Analysis*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

Abstract: Modern causal inference links the "top-down" representation of causal intuitions and "bottom-up" data analysis with the aim of choosing policy. Two innovations that proved key for this synthesis were a formalization of Hume's counterfactual account of causation using potential outcomes (due to Jerzy Neyman), and viewing cause effect relationships via directed acyclic graphs (due to Sewall Wright). I will briefly review how a synthesis of these two ideas was instrumental in formally representing the notion of "causal effect" as a parameter in the language of potential outcomes, and discuss a complete identification theory linking these types of causal parameters and observed data, as well as approaches to estimation of the resulting statistical parameters.

I will then describe, in more detail, how my collaborators and I are applying the same approach to mediation, the study of effects along particular causal pathways. I consider mediated effects at their most general: I allow arbitrary models, the presence of hidden variables, multiple outcomes, longitudinal treatments, and effects along arbitrary sets of causal pathways. As was the case with causal effects, there are three distinct but related problems to solve -- a representation problem (what sort of potential outcome does an effect along a set of pathways correspond to), an identification problem (can a causal parameter of interest be expressed as a functional of observed data), and an estimation problem (what are good ways of estimating the resulting statistical parameter). I report a complete solution to the first two problems, and progress on the third. In particular, my collaborators and I show that for some parameters that arise in mediation settings, triply robust estimators exist, which rely on an outcome model, a mediator model, and a treatment model, and which remain consistent if any two of these three models are correct.

Some of the reported results are a joint work with Eric Tchetgen Tchetgen, Caleb Miles, Phyllis Kanki, and Seema Meloni.

**Thursday, January 15, 2015,**

*Philosophy Colloquium*

**Robin Zheng**, University of Michigan

*Moral Responsibility for Implicit Bias: Attributability, Accountability, and Appraisal*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Monday, January 19, 2015,** *Philosophy Colloquium*

**Paolo Santorio**, University of Leeds

*Alternative Counterfactuals*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Thursday, January 22, 2015,** *Philosophy Colloquium*

**Gina Schouten**, Illinois State University

*Is the Gendered Division of Labor a Problem of Distribution?*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

Abstract: Despite women’s increased labor force participation, household divisions of labor remain highly unequal, with women in every industrialized country continuing to perform the vast majority of unpaid housework and childcare. This persistent gendered division of labor is remediable. Properly implemented, “gender egalitarian” political interventions such as work time regulation, subsidized dependent care provisions, and paid family leave initiatives can induce families to share paid work, unpaid work, and leisure time more equally than they currently do. In the long run, these interventions can effectively reform the norms and institutions that currently sustain the gendered division of labor.

Gender egalitarian political interventions face a formidable justificatory hurdle, however. By subsidizing gender egalitarian lifestyles, these interventions appear to violate a basic liberal requirement for legitimacy: that political interventions be publicly defensible within the justificatory community of reasonable citizens. In order for interventions to be defensible in this way, the reasons justifying intervention must be neutral among the conceptions of the good that citizens may reasonably embrace. By this standard, interventions aimed at influencing families’ allocations of work appear illegitimate. They apparently fail to abide by the neutrality constraint on legitimate exercises of political power, because many citizens consciously enact and even celebrate gender inegalitarian domestic arrangements. Thus, the value of gender egalitarianism seems not to be a value that can be recognized as such by all reasonable citizens; it therefore cannot be invoked to justify exercises of political power like gender egalitarian interventions without violating the constraint of neutrality. Some proponents of gender egalitarian interventions have devised elegant arguments for the conclusion that these interventions can be defended without violating the constraint of neutrality, and are thus legitimate after all. My project in this paper is to critique one widely-deployed strategy for defending gender egalitarian political interventions. According to this strategy, the gendered division of labor constitutes or causes unjust distributions of goods, and gender egalitarian interventions can be neutrally justified as necessary means to remedy those injustices. Whether or not such interventions can ultimately be shown to be legitimate, I raise doubts that the strategy I consider meets this burden. But the problems that beset this strategy are illuminating, and point the way toward a more promising approach. In closing, I briefly sketch my own positive view regarding how gender egalitarian interventions can be defended as legitimate exercises of political power that abide fully by the constraint of neutrality.

**Monday, January 26, 2015,** *Philosophy Colloquium*

**Danielle Wenner**, Carnegie Mellon University

*The Social Value of Research-Generated Knowledge: Re-Imagining the Responsiveness Requirement for International Clinical Research *

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

*responsive*to host community health needs.

Although responsiveness is an oft-repeated ethical requirement for international research, there exists ongoing disagreement about both the content of responsiveness as well as its usefulness as a guideline governing international clinical research. In this paper, I propose a framework intended to clarify the responsiveness requirement. I begin by motivating the paper with a couple of examples and presenting some of the shortcomings of existing interpretations of responsiveness. I suggest that one helpful way of characterizing the normative content of the requirement is as a demand that the knowledge sought in clinical research be socially valuable to those populations within which, and upon whom, such research is conducted. I then borrow from decision theory a framework for the assessment of the value of information, and go on to outline how this approach can be utilized in the prospective assessment of a clinical trial’s responsiveness to host community needs. I consider what data would be necessary as inputs to fully operationalize this framework, in the process demonstrating how it avoids each of the objections raised to competing conceptions of responsiveness. Next, I discuss some of the hurdles to the full operationalization of the framework, and indicate how it can nevertheless operate as a threshold condition for the ethical permissibility of research conducted in LMICs. Finally, I conclude by briefly indicating some other issues in research ethics upon which this approach may shed light.

**Thursday, January 29, 2015,** *Philosophy Colloquium*

Kun Zhang, Max Planck Institute for Intelligent Systems

*Hunting Causal Asymmetry and Using It: Some Methodological Developments and Their Foundations*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Monday, February 2, 2015,** *Philosophy Colloquium*

**Ariella Binik**, Oxford University

*The Ethics of Risk in Research with Children*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

Various thresholds have been proposed to constrain research risks that do not offer children the prospect of direct medical benefit. These proposals include limiting research risks to (1) the risks of routine medical examinations (CIOMS 2002; Kopelman 2004), (2) the risks of participation in charitable activities (Wendler 2010), (3) the risks of family life (Ackerman 1980; Nelson and Ross 2005), and (4) the risks-of-daily-life (Freedman, Fuks, and Weijer 1993; McMillan and Hope 2004). I examine which, if any, of these thresholds is defensible. I argue that the risks-of-daily-life threshold is defensible, but not for the reasons currently offered. I raise a problem with the current justification of the risks-of-daily-life threshold, and I propose a new justification. I argue that the risks of daily life are justifiable because they are part of a reasonable trade-off between personal safety and our ability to pursue meaningful lives.

**Thursday, February 5, 2015,** *Philosophy Colloquium*

**Igor Yanovich**, Univeristy of Tubingen

*New frontiers in modality*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Thursday, February 12, 2015,** *Philosophy Colloquium*

**Nina Gierasimczuk**, ILLC, University of Amsterdam

*On topological logic for learning*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Thursday, February 19, 2015,** *Pure and Applied Logic Colloquium*

**Ryota Akiyoshi,**, Kyoto University

*Brouwer’s Argument of the Bar Induction Revisited*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

Let us formulate the bar induction. Let

*B*be the set of “barred” nodes. Roughly speaking,

*B*is the set of nodes in the tree at which the tree is well-founded. Suppose that

*P*is a property (or a predicate).

**Bar Induction (BI):**Assume that

A1 ∀

*α*∃

*x*(

*x*) ∈

*B*),

A2 ∀

*n*∀

*y*(

*n*∈

*B*→

*n*∗ 〈y〉 ∈

*B*),

A3 ∀

*n*(

*n*∈

*B*→

*n*∈

*P*),

A4 ∀

*n*(∀

*y*(

*n*∗ 〈

*y*〉 ∈

*P*) →

*n*∈

*P*).

Then 〈 〉 ∈

*P*.

Brouwer’s argument in 1927 aimed to give a constructive justification of this theorem. His argument was based on the BHK-reading of the statement of BI. Brouwer’s argument has been controversial and received different evaluations because it depends on an assumption saying that any proof of (A1) consists of only few elementary inference rules. For example, van Atten and Sundholm regard this assumption as a transcendental requirement in the sense of Kant. Another researchers, especially logicians (van Dalen, Kleene, Troelstra), have believed that the assumption is not mathematical, hence Brouwer’s argument is not justifiable mathematically. In this tradition, BI is not proved but postulated as an axiom.

In this talk, we present an approach to understanding Brouwer’s argument via a tool called the Ω-rule in infinitary proof theory. The Ω-rule was introduced by Buchholz in 1970’s for ordinal analysis of iterated inductive definitions and subsystems of second-order arithmetic. We compare Buchholz’s embedding of the induction axiom in

*ID*

_{1}with Brouwer’s argument for BI and claim that the embedding via the Ω-rule is really close to Brouwer’s argument. According to this interpretation, Brouwer’s assumption is a quite natural mathematical restriction on proofs for the quantification over proofs to work. This implies that Brouwer’s argument should be a mathematically well-motivated argument. As in the Ω-rule, his argument would contain a vicious circle without the assumption.

**Thursday, February 26, 2015,** *Philosophy Colloquium*

**Tamar Lando**, Columbia University

*Modal logic, measure semantics, and pointless space*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

*S4*, each formula is evaluated to a subset of a fixed topological space. I develop a closely related, probabilistic (or measure-based) semantics for modal logics, in which modal formulas are interpreted in the Lebesgue measure algebra. I'll discuss some completeness results I've obtained for this semantics, and show how I think we can use the formal structures involved to understand what physical space might be like, if space is devoid of 'points.'

**Monday, March 2, 2015,** *Center for Ethics and Policy Lecture*

**Michelle Meyer**, Union Graduate College-Icahn School of Medicine, Mount Sinai Bioethics

*Two Cheers for (Some) Nonconsensual Corporate Experimentation*

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 Wean Hall 5415

**Tuesday, March 3, Thursday, March 5 & Friday, March 6, 2015**

Ernest Nagel Lectures in Philosophy and Science

**Thursday, March 26, 2015,** *Philosophy Colloquium*

**Carole Lee**, University of Washington

**Commensuration Bias in Peer Review**

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Thursday, April 2, 2015,** *Pure and Applied Logic Colloquium*

**Michael Rathjen**, University of Leeds

**Strong type theories: their set and proof-theoretic sides**

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

Aczel's sets-as-types interpretation into these type theories gives rise to rather unusual set-theoretic axioms: negative power set and negative separation. But it is not known how to determine the proof-theoretic strengths of intuitionistic set theories with such axioms via familiar classical set theories (though it is not difficult to see that ZFC plus infinitely many inaccessibles provides an upper bound). The first part of the talk will be a survey of known results from this area. The second part will be concerned with the rather special proof-theoretic behavior of such theories.

**Thursday, April 9, 2015,** *Philosophy Colloquium*

**Jean-Pierre Marquis**, University of Montreal

**What is abstract about abstract homotopy theory?**

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Wednesday, April 15, 2015,** *Philosophy Colloquium*

**Mark Addis**, Birmingham City University

**Automatically Generating Scientific Theories**

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Thursday, April 23, 2015,** *Philosophy Colloquium*

**Ofra Magidor**, University of Oxford

**Conditional Acceptance**

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 BH A53

**Monday, May 4, 2015,** *Philosophy Colloquium*

**Juan Dubra**, Universidad de Montevideo and NYU

**A Theory of Rational Attitude Polarization**

*Reception:* 4:00 DH 4301, *Talk: *4:30-6:00 Location BH A53