MCMP Summer School Mathematical Philosophy for Female Students 2019
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Content

Program

Room Arrangement

DateAddress, Room
28.07.2019 Geschwister-Scholl-Platz 1, room A120 (Kleine Aula)
29.07. - 02.08.2019 Richard-Wagner-Straße 10, room numbers in program below
03.08.2019 Professor-Huber-Platz 2, room W401

Sunday, 28 July

TimeTopic
16:00 - 16:45 Registration.
16:45 - 17:00 Welcome.
17:00 - 17:15 Welcoming Remarks (Hannes Leitgeb, MCMP).
17:15 - 19:00 Reception.

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Monday, 29 July

TimeTopic
08:00 - 09:00 Registration.
09:00 - 10:30 Introductory Lecture 1: Semantics for First Order Logic. (Room D105)
10:30 - 11:00 Coffee Break. (Room D016)
11:00 - 12:30 Introductory Lecture 2: Modal Logic. (Room D105)
12:30 - 14:00 Lunch Break.
14:00 - 15:30 Introductory Lecture 3: Probability Theory. (Room D105)
15:30 - 16:00 Coffee Break. (Room D016)
16:00 - 17:30 MCMP Fellows’ Sessions:
1: Martin Fischer: Predicativism and Potentialism (Room D102)
2: Dunja Šešelja: Simulating Science: Can Agent-Based Modeling be of Use to Integrated History and Philosophy of Science? (Room D105)
3: Tom Sterkenburg: The Epistemology of Deep Learning (Room D114)
4: Jo Wolff: Measurement Theory for Philosophers (Room D118)

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Tuesday, 30 July

TimeTopic
09:00 - 10:30 Lecture Stream 1: De se Beliefs (Silvia Milano, Oxford Internet Institute). (Room D105)
10:30 - 11:00 Coffee Break. (Room D016)
11:00 - 12:30 Lecture Stream 2: Barriers to Entailment (Gillian Russell, UNC Chapel Hill). (Room D105)
12:30 - 14:00 Lunch Break.
14:00 - 15:30 Lecture Stream 3: Philosophy of Algorithms and Simulations (Lena Zuchowski, University of Bristol). (Room D105)
15:30 - 16:00 Coffee Break. (Room D016)
16:00 - 17:30 Poster Session.

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Wednesday, 31 July

TimeTopic
09:00 - 10:30 Lecture Stream 1: De se Beliefs (Silvia Milano, Oxford Internet Institute). (Room D105)
10:30 - 11:00 Coffee Break. (Room D016)
11:00 - 12:30 Lecture Stream 2: Barriers to Entailment (Gillian Russell, UNC Chapel Hill). (Room D105)
12:30 - 14:00 Lunch Break.
14:00 - 15:30 Lecture Stream 3: Philosophy of Algorithms and Simulations (Lena Zuchowski, University of Bristol). (Room D105)
15:30 - 16:00 Coffee Break. (Room D016)
16:00 - 17:30 MCMP Fellows’ Sessions:
1: Joe Dewhurst: Physical Computation (Room D102)
2: Bruno Jacinto: Information, Epistemic Normativity and the Normativity of Logic (Room D105)
3: Lavinia Picollo: How Can We (Be Sure We) Talk About Numbers? (Room D114)
4: Rush Stewart: On the Possibility of Testimonial Justice (Room D118)
18:00 - 19:30 Moved to Thursday! Evening Lecture: Justice, Gender Norms, and State Neutrality (Anca Gheaus, University Pompeu Fabra Barcelona) (Room D105)
19:30 - 21:00 Reception.

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Thursday, 1 August

TimeTopic
09:00 - 10:30 Lecture Stream 1: De se Beliefs (Silvia Milano, Oxford Internet Institute). (Room D105)
10:30 - 11:00 Coffee Break. (Room D016)
11:00 - 12:30 Lecture Stream 2: Barriers to Entailment (Gillian Russell, UNC Chapel Hill). (Room D105)
12:30 - 14:00 Lunch Break.
14:00 - 15:30 Lecture Stream 3: Philosophy of Algorithms and Simulations (Lena Zuchowski, University of Bristol). (Room D105)
15:30 - 16:00 Coffee Break. (Room D016)
16:00 - 17:30 MAP Round Table. (Room D105)
18:00 - 19:30 Evening Lecture: Justice, Gender Norms, and State Neutrality (Anca Gheaus, University Pompeu Fabra Barcelona) (Room D105)

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Friday, 2 August

TimeTopic
09:00 - 10:30 Parallel lectures:

Lecture Stream 1: De se Beliefs (Silvia Milano, Oxford Internet Institute). (Room D118)
Lecture Stream 2: Barriers to Entailment (Gillian Russell, UNC Chapel Hill). (Room D114)
Lecture Stream 3: Philosophy of Algorithms and Simulations (Lena Zuchowski, University of Bristol). (Room D102)
10:30 - 11:00 Coffee Break. (Room D016)
11:00 - 12:30 Parallel lectures:

Lecture Stream 1: De se Beliefs (Silvia Milano, Oxford Internet Institute). (Room D118)
Lecture Stream 2: Barriers to Entailment (Gillian Russell, UNC Chapel Hill). (Room D114)
Lecture Stream 3: Philosophy of Algorithms and Simulations (Lena Zuchowski, University of Bristol). (Room D102)
12:30 - 14:00 Lunch Break.
14:00 - 15:30 Parallel lectures:

Lecture Stream 1: De se Beliefs (Silvia Milano, Oxford Internet Institute). (Room D118)
Lecture Stream 2: Barriers to Entailment (Gillian Russell, UNC Chapel Hill). (Room D114)
Lecture Stream 3: Philosophy of Algorithms and Simulations (Lena Zuchowski, University of Bristol). (Room D102)
15:30 - 16:00 Coffee Break. (Room D016)
16:00 - 17:30 Parallel lectures:

Lecture Stream 1: De se Beliefs (Silvia Milano, Oxford Internet Institute). (Room D118)
Lecture Stream 2: Barriers to Entailment (Gillian Russell, UNC Chapel Hill). (Room D114)
Lecture Stream 3: Philosophy of Algorithms and Simulations (Lena Zuchowski, University of Bristol). (Room D102)
19:00 Summer School Dinner.

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Saturday, 3 August

TimeTopic
09:00 - 10:30 Student presentations.
10:30 - 11:00 Coffee Break.
11:00 - 12:30 Student presentations.
12:30 - 12:45 Wrap up and closing.

Abstracts

Anca Gheaus (University Pompeu Fabra): Justice, Gender Norms, and State Neutrality

Women (still) specialise in domestic care-giving, which undermines their competitiveness on the labour market, and are over-represented in caring professions which tend to be under-paid and have little status and power. Men (still) specialise in breadwinning, and tend to be over-represented in positions of economic and social advantage. In other words, the division of labour is (still) gendered, both within the family and within society at large, and the pay-offs of feminised roles generally disadvantage women. Feminists have long identified the gendered division of labour as a cornerstone of gender injustice. This is partly because the gendered division of labour results in women holding less money, power, status and freedom from domination then men. But essential to feminists’ complaint is also the fact that gender norms provide people with incentives to take on different social and economic roles, according to their sex. For many decades now, feminists have sought to dismantle the gendered division of labour and advocated various policies meant to achieve this goal. And yet, there is an ongoing, unresolved debate about the kinds of justification that can support such state policies. Liberal states are supposed to refrain from justifying their policies by appeal to controversial, but reasonable, conceptions of how individuals should lead their private lives; call this “the neutrality constraint”. Gender norms in general, and those mandating a gendered division of labour in particular, are part of a conception of the good life held by numerous individuals. For this reason, it has been argued that, to the extent to which gendered specialisation is voluntary – that is, to the extent to which individuals are morally responsible for following gender norms – unequal outcomes between women and men do not raise a concern of justice. Faced with this challenge, feminists appeal to several reasons why gender norms are objectionable at the bar of justice: First, because they undermine women’s fair equality of opportunity to positions of advantage. Second, because they undermine women’s exercise of citizenship. And third, because they require women to bear the costs of having been socialised, without their consent, into gender norms. In this talk, I formulate a version of each of these arguments that respects the neutrality constraint. I defend the following conclusion: Political liberals may be right that states ought not to try and dissuade adults from leading lives that are informed by gender norms. Yet, they must acknowledge two aims of justice concerning gender norms. The first aim is forward-looking and requires that children be protected from undue influence in the formation of their ambitions and values; in particular, children have a right to be free from adults’ attempts to foist gender norms on them. The second aim is backward-looking and requires that individuals who have been wronged by a failure to implement the first aim are owed reparation; in particular, policies which offset the disadvantage that certain women incur as a result of gender norms are legitimate even if the women in question have internalised, and identified with, the gender norms.top

Silvia Milano (Oxford Internet Institute and Digital Ethics Lab (DELab): De se Beliefs

De se beliefs (that is beliefs about who, when and where you are) are pervasive and play a fundamental role in our epistemic lives. Nevertheless, they raise issues for traditional accounts of epistemic contents, and appear to pose a challenge to Bayesian accounts of diachronic rationality.

In the first part of this lecture stream, we will examine strategies to model the content of de se beliefs using a refinement of possible worlds semantics. In the second part, we will consider how de se beliefs fit within accounts of diachronic rationality, focussing on temporal de se beliefs. In particular, we will examine why they pose a challenge to the Bayesian principle of conditionalization, the relationship between de se beliefs and memory loss, and consider available strategies to solve the challenge. We will finish by examining the prospects for the most promising among these strategies, ur-prior conditionalization.

There are no pre-requisites for this lecture stream as the concepts and formalism will be introduced gradually, but some prior familiarity with the fundamentals of probability theory and formal epistemology would be an advantage.

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Gillian Russell (UNC Chapel Hill): Barriers to Entailment

A barrier to entailment is a thesis that claims that sentences of a certain kind, Y, never follow from premises of another kind, X. A very famous example is Hume's Law: it says that no normative sentences follow from premises that are descriptive. But other barriers to entailment€ - though still well known in philosophy - are much less controversial: claims about the future never follow from claims about the past, claims which say that things must be a certain way don't follow from claims that merely say how they are, general claims don'€t follow from particular claims, context-sensitive sentences never follow from non-context sensitive sentences etc. In this lecture stream we will begin by looking at some influential arguments concerning barriers to entailment - especially proposed counterexamples - and then examine the prospects for formulating and proving them with respect to appropriate logics: e.g. first-order predicate logic for the claim that you can'€t get general claims from particular ones, tense logics for the claim that you can'€t get a claim about the future from claims about the past, modal logics etc. This lecture stream will presuppose that you have taken at least one previous course in logic and have some familiarity with classical sentential and predicate logic, but you will not need to already know about modal, tense or other logics beyond that, as the course will serve as an introduction to a range of logics, brought together around the theme of barriers to entailment.top

Lena Zuchowski (University of Bristol): Philosophy of Algorithms and Simulations

Digital technologies pervade all aspects of our life: for one, they allow us to put this course description into hypertext; save it on a digital network; and have you view it on a handheld digital device! Beyond the ubiquity of its technologies, the digital world is inhabited by a host of strange entities - thinking machines, learning algorithms, virtual lifeforms - whose existences provides philosophy with unique epistemological, metaphysical and ethical challenges.

In this course, we are going to look at how digital language learning differs from how humans learn languages; will analyse the particular epistemological challenges of 'opaque' deep-learning algorithms; and tackle the question of whether there can be algorithmic ethical decision making, focusing on automatic corrections for language biases and the current proposals for algorithms governing the behaviour of self-driving cars.top

MCMP Fellows' Sessions' Abstracts

Joe Dewhurst: Physical Computation

The question of which physical systems perform computations, or which computations they perform, might seem quite trivial, but it is in fact very difficult to answer. If we were only concerned with artifactual computers, i.e. physical computers that we have constructed ourselves, then this might not be such a problem, but the issue becomes more pressing if we are interested in the computational status of natural ystems, such as the human brain. A foundational assumption of much contemporary cognitive science is that the brain is a computer, and that thinking is a kind of computation, and yet it is not always clear what this claim really amounts to, or how we might go about testing it. Philosophers have offered several different accounts of computation in physical systems, each of which suffers from some well known problems.
In this talk I will review the pros and cons of each account, before offering my own thoughts on how we should think about physical computation.top

Martin Fischer: Predicativism and Potentialism

In this talk I want to reconsider parts of Feferman's work on predicativism. Whereas impredicative methods are usually accepted nowadays there are still good reasons for investigating predicative methods. In one of his several presentations Feferman suggests an acceptance only of the natural numbers as an infinite totality. Subsets of the natural numbers are considered to be only potential infinities. An attractive version of potentialism has been proposed by Parson's and Linnebo and I intend to discuss the fruitfulness of capturing the talk of potentialities with possible worlds models and modal theories. The predicativist setting suggest a quite natural version of modalities involved in a version of potentialism given the natural numbers. Here it is also natural to invoke epistemic constraints on the accessibility relation.
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Bruno Jacinto: Information, Epistemic Normativity and the Normativity of Logic

According to the information-theoretic view on belief and intentionality (Stampe 1979, Dretske 1981, Stalnaker 1984), part of what it is for a state of an agent to be a belief state is for it to be a state that tends, under optimal conditions, to carry information about the environment. In this talk the information-theoretic view is shown to support two epistemic norms, to wit, the truth norm of belief (Williamson 2000, Hattiangadi 2010, Sutton 2007), according to which it is epistemically obligatory to have only true beliefs, as well as the answer norm, according to which it is epistemically obligatory to be such that one believes a complete answer to a question if one understands the question (in a suitable sense of "understanding"). The truth and answer norms are shown to yield an interesting theory of the interaction between epistemic obligation, belief and metaphysical necessity. It is also shown that the result of expanding this theory to a theory of the interaction between epistemic obligation, belief and logical consequence, consists of a theory predicting the truth of a number of interesting conditionals relating claims of logical consequence with statements concerning epistemic obligation and belief. This final result is part of a general project of "reducing" the normativity of logic to epistemic normativity by showing that interesting theses closely similar to seemingly plausible bridge principles connecting claims of logical consequence with statements concerning what it is logically obligatory to believe are predictions of a plausible theory of the interaction between epistemic obligation, logical consequence and belief.top

Lavinia Picollo: How Can We (Be Sure We) Talk About Numbers?

How can we make sense of informal talk of 'the natural numbers'? In particular, how can we guarantee that when we talk about the natural numbers we pick out a single structure? How can we guarantee that our arithmetical claims are determinate? With concrete objects, ostention suffices to fix the reference of our terms. In the case of abstract objects, by contrast, this is not a possibility, unless one is happy to invoke some form of mathematical intuition or quasi-perception. A naturalistic approach leaves us with just one way of fixing the reference of our arithmetical vocabulary, that is, via descriptions in our language(s), by means of our (recursive) theories.
Unfortunately, Gödel’s fundamental incompleteness result — which will be discussed in the session — stands in our way. For one thing, it means that in every recursive theory of natural numbers there are claims that are neither provable nor refutable. For another, the incompleteness result implies that there is more than one structure understood in the traditional sense — i.e. model theoretically, as isomorphism types — satisfying the axioms of every recursive first-order arithmetical theory.
In this talk I will discuss two possible responses to the original challenge. Both proposals work with second- instead of first-order arithmetical systems — also to be introduced in the session. One of them, essentially metalinguistic, is formulated in terms of full second-order models and faces serious objections for this reason. The other turns to object-language counterparts of these models and replaces the notion of truth with that of proof. I will argue that this proposal faces similar challenges to the former, leaving us with a semi-sceptical picture.
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Dunja Šešelja: Simulating Science: Can Agent-Based Modeling be of Use to Integrated History and Philosophy of Science?

Computational modeling has in recent years become an increasingly popular method in philosophy of science and social epistemology. In this talk I will discuss the role of simulations of scientific inquiry in the form of agent-based models (ABMs), which are at the heart of this trend. I will start by arguing that a primary function of ABMs of scientific inquiry developed in philosophy of science---in contrast to ABMs in empirical sciences---is to contribute to our understanding of the process of inquiry and factors that may have an effect on it. In view of this, I will defend two specific ways in which ABMs can increase our understanding of science: first, by providing novel insights into socio-epistemic factors that may have a significant impact on the process of inquiry, and second, by providing evidence for or against previously proposed explanations of concrete historical episodes. I will illustrate each of these functions by a set of ABMs, which my collaborators and I have developed. While these models are abstract and highly-idealized, I will show how the results obtained from them can be analyzed in terms of their robustness and empirical validity. The talk is based on joint work with AnneMarie Borg, Daniel Frey and Christian Straßer.top

Tom Sterkenburg: The Epistemology of Deep Learning

Epistemology is the branch of philosophy that is concerned with knowledge. It is concerned, for instance, with the fundamental limitations of automated methods for inferring knowledge from data: methods as developed within machine learning. A central insight, arrived at by philosophers and machine learning researchers alike, is that every
learning algorithm must implement a particular inductive bias, or restrictive inductive assumptions about the learning situation at hand.
Deep learning constitutes perhaps the most successful exponent of modern machine learning. Recently, much discussion within the machine learning community has centered around what has been called an "apparent paradox" of deep learning: the fact that the empirical generalization performance of deep neural networks is astonishingly good, much better than our best mathematical theory can actually explain. To put it differently, we do not understand the inductive biases that deep neural networks implement.
In my lecture I will discuss this debate from a philosophical perspective. Specifically, I will look at the two main lines of proposed explanation: the subtle manifestation of the inductive bias in the "implicit regularization" during the learning process, and the apparent fit of this inductive bias to the particular structure of real-world data.top

Rush Stewart: On the Possibility of Testimonial Justice

Recent impossibility theorems for fair risk assessment extend to the domain of epistemic justice. We translate the relevant model, demonstrating that the problems of fair risk assessment and just credibility assessment are structurally the same. We motivate the fairness criteria involved in the theorems as appropriate in the setting of testimonial justice. Any account of testimonial justice that implies the fairness/justice criteria must be abandoned on pain of triviality.top

Jo Wolff: Measurement Theory for Philosophers

The Representational Theory of Measurement (RTM) provides a powerful and wide ranging formal framework for understanding measurement representations in natural and social sciences. This session will introduce you to the basic principles of RTM and some philosophical applications.