TILPS

Program

Professor Hacking will deliver his Descartes Lectures in the first morning session of each day (9.00-10.30). The second session (11.00-12.30) contains the two commentaries and gives further room for discussion. The afternoon sessions consist of contributed papers and graduate student presentations from the Bochum-Lausanne-Tilburg Graduate School. They take place from 14.00 to 15.30 and from 16.00 to 17.30.

Note that the conference is preceded by the Workshop "Objectivity and the Practice of Science", click here for more information about the workshop.

Day 1: Wednesday 6 October

	Morning session (Room: DZ1)
8:30 - 9:00	Registration
9:00 - 10:30	Ian Hacking
	Why Is There "Philosophy of Mathematics"?
10:30 - 11:00	Coffee break
11:00 - 12:30	Hannes Leitgeb and Mary Leng
	Commentary and discussion
12:30 - 14:00	Lunch break (CZ111)
	Parallel sessions
	Room: CZ111	Room: CZ113
14:00 - 14:45	Davide Rizza	Kathy Puddifoot
	Mathematical Practices and Philosophical Views: The Case of Applicability	Contexts, Reflection and Norms of Reasoning
14:45 - 15:30	Holger Leuz	Tomoo Ueda
	A Priori / A Posteriori Within Mathematics	Communicating Beliefs: A Communicational Theory of Propositional Attitude Reports
15:30 - 16:00	Coffee break
16:00 - 16:45	Elijah Chudnoff	Martin Kusch
	A Cartesian Theory of Intuitive Knowledge	Mini-tutorial: Hacking on Styles of Reasoning (takes two blocks)
16:45 - 17:30	Jennifer Mulnix
	A Reliabilist Account of Mathematical Intuition and A Priori Knowledge
18:00 - 19:30	Get together in Cafe Esplanada

Day 2: Thursday 7 October

	Morning session (Room: CZ9)
9:00 - 10:30	Ian Hacking
	Meaning and Necessity - and Proof
10:30 - 11:00	Coffee break
11:00 - 12:30	James Conant and Martin Kusch
	Commentary and discussion
12:30 - 14:00	Lunch break (Dante Foyer)
	Parallel sessions
	Room: CZ111	Room: CZ113
14:00 - 14:45	Fabrizio Cariani	Julie Jebeile
	Mathematical Induction and Explanatory Value in Mathematics	Numerical Calculations Versus Certainty
14:45 - 15:30	Susan Vineberg	Juan Duran
	Explanation and Proof	The Materiality Problem in the Dilemma of Computer Simulations
15:30 - 16:00	Coffee break
16:00 - 16:45	Ole Hjortland	James Conant
	Proof-Theoretic Semantics in the Substructural Era	Mini-tutorial: Hacking on Logic, Mathematics, and Proof (takes two blocks)
16:45 - 17:30	Stefan Wintein
	Calculating With Sentences Which Are A Priori in Virtue of Our Intuitive Notion of Truth
17:30 - 18:15	Anna Ciaunica
	A Priori Physicalism ‘Naturalized’?
20:00	Conference dinner

Day 3: Friday 8 October

	Morning session (Room: CZ7)
9:00 - 10:30	Ian Hacking
	Roots of Mathematical Reasoning
10:30 - 11:00	Coffee break
11:00 - 12:30	Marcus Giaquinto and Pierre Jacob
	Commentary and discussion
12:30 - 14:00	Lunch break (CZ186)
	Parallel sessions
	Room: C186	Room: C127
14:00 - 14:45	Madeline Muntersbjorn	Oran Magal
	Kinds of Minds and the Unity of Mathematics	A Kantian Reading of Hilbert's Programme: Formalism for the 21st Century
14:45 - 15:30	Catarina Dutilh Novaes	Katherina Kinzel
	Demonstration as Discourse, Calculation as Mental Process	Stability and Dynamics in the Laboratory Sciences: A Comment on Hacking and Rheinberger
15:30 - 16:00	Coffee break
16:00 - 16:45	Tim Storer	Kim-Erik Berts
	Dummettian 'Logicism', Intuitive Models, and A Priori Knowledge	The Certainty of Mathematics
16:45 - 17:30	Bence Nanay	Vincent Ardourel
	Singularist Semirealism	How Does Physical Analogy Help Solve Pure Mathematical Problems?
17:30	Closing reception

Mathematical Practices and Philosophical Views: The Case of Applicability
Davide Rizza, University of East Anglia

In this talk I explore the idea that philosophy of mathematics is constituted by a constellation of local views, each of which is constrained by the type of practice out of which it grew. To substantiate this point, I show how one can reach very different and even contrasting pictures of applied mathematics by working philosophically with correspondingly different types of practices. This shows the centrality of mathematical content to the articulation of philosophical ideas. Because content may be strongly dependent on a certain way of doing or using mathematics, philosophical reflection based on content is correspondingly localized.

Contexts, Reflection and Norms of Reasoning
Kathy Puddifoot, University of Sheffield

Kornblith has presented a challenge to the trend of placing high value on reflection. He argues that empirical data about reasoning shows that reflection should not be treated as a unique or special source of normativity or epistemic value because it only sometimes improves reliability. Kornblith targets Sosa’s view that there are two forms of knowledge: animal knowledge and reflective knowledge. In this talk I shall defend a distinction similar to Sosa’s, challenging the view that empirical data undermines the normativity of reflection by developing a contextualist approach to reasoning influenced by evolutionary psychology and strategic reliabilism.

A Priori / A Posteriori Within Mathematics
Holger Leuz, University of Regensburg

Mathematical proofs frequently proceed by mapping the problem to be solved into another problem in a different branch of mathematics, where it can be solved and the solution mapped back into the original background. In the light of this method we can discern a priori results and a posteriori results within mathematics – which is not to say that mathematics is an a posteriori, or empirical, discipline as a whole. However, this observation has consequences for the analysis of the notion of mathematical provability and the Fregean view that mathematics is analytic. The latter is highly problematic, if not untenable, in the light of the former.

Communicating Beliefs: A Communicational Theory of Propositional Attitude Reports
Tomoo Ueda, Ruhr-Universität Bochum

Reports of propositional attitudes have been said to support following apparently conlicting intuitions, namely the semantic innocence on the one hand and the intuitive truth-value evaluations after substituting coreferring genuine singular terms on the other. In this talk, I shall try to propose a pragmatic theory for reports of propositional attitude, which I call “communicational theory of ascription” (CoTA). This is based on the criticism against the semantic theory of Recanati, especially against his thesis about the opacity and it should resolve some apparently con?icting intuitions concerning the truth-value evaluations of attitude reports, or so I shall argue.

A Cartesian Theory of Intuitive Knowledge
Elijah Chudnoff, University of Miami

By a theory of intuitive knowledge I mean a theory about what it is in virtue of which our beliefs formed on the basis of intuition amount to knowledge, when they do so. By a Cartesian theory of intuitive knowledge I mean—to a first approximation—a theory of intuitive knowledge that plays up the similarities between intuition and perception. One aim of this paper is to explain more fully what makes a theory of intuitive knowledge Cartesian. Another aim of this paper is to promote Cartesian theories of intuitive knowledge by pinpointing the main challenges facing them and explaining how those challenges might be met.

Mini-tutorial: Hacking on Styles of Reasoning
Martin Kusch, University of Vienna

This mini-tutorial will be devoted to a critical discussion of Hacking's important work on styles of reasoning. In the first 45 minutes, I shall give a summary of my paper "Hacking's Historical Epistemology: A Critique of Styles of Reasoning". In the second 45 minutes we shall discuss Hacking's views (and whether my criticism is on target).

A Reliabilist Account of Mathematical Intuition and A Priori Knowledge
Jennifer Mulnix, University of Massachusetts at Dartmouth

This paper proposes a reliabilist account of mathematical a priori knowledge utilizing a naturalistically acceptable account of ‘intuition’. On this view, mathematical intuition consists in a non-inferential belief-forming process where the entertaining of propositions or certain contemplations result in true beliefs; the inputs are not abstract numbers, but rather, contemplations of abstract numbers. Thus, this view is free of any causal conditions incompatible with abstract objects, for the reason that it is not necessary that S stand in some causal relation to the entities in virtue of which p is true. This paper concludes by responding to certain key objections.

Mathematical Induction and Explanatory Value in Mathematics
Fabrizio Cariani, Northwestern University

Marc Lange recently argued that almost all proofs by mathematical induction fail to provide explanations of their conclusions. His arguments turn on showing that for each argument by mathematical induction X, there is another argument Y, for the same conclusion such that (i) X and Y have the same claim to be considered the explanation of the conclusion and (ii) X and Y cannot both explain the conclusion. I argue that Lange's argument turns on ignoring several ways in which arguments can come to have different explanatory values. Once those are appreciated, (i) fails in a number of interesting cases. However, I do not take the moral to be that mathematical inductions are explanatory. Rather, I conclude by sketching a view on which there is no uniform answer to the question whether mathematical inductions explain their conclusions.

Numerical Calculations Versus Certainty
Julie Jebeile, University of Paris

The epistemic opacity of computers simulations (CSs) hinders the application of what I shall call “the Cartesian approach” for ensuring theaccuracy of CSs. According tothis approach, numerical calculations have to be checked step by step from stem to stern. I illustrate an alternative procedure to the Cartesian approach that physicists follow to ensure the accuracy of computer simulations: the Verification and Validation approach (V&V). I contend that V&V is not only an alternative to the Cartesian approach, but also a more efficient way to ensure the accuracy of CSs. Finally, I claim that V&V implies a slightly modified conception of what is counted today as certainty.

Explanation and Proof
Susan Vineberg, Wayne State University

Drawing from work on scientific explanation, this paper argues that while generality and unification are features of some explanatory work in mathematics, other mathematical explanations center on displaying a form of logical or structural dependence. After sketching this idea, it is then used to argue that constructive proofs, those centering on calculation, and even some computer proofs, can be explanatory in an important sense, contrary to common intuition. Such explanation extends beyond individual proofs, and illuminates foundational studies on weak theories. Other examples are drawn from Mancosu’s study of Pringsheim’s development of complex function theory and recent work of Hales involving computer proofs.

The Materiality Problem in the Dilemma of Computer Simulations
Juan Duran, Universität Stuttgart

The dilemma of computer simulations centers on the question whether the epistemological payoff of a traditional experiment has greater (or less) confidence than a computer simulation. The “materiality problem” is in the basis of this dilemma. In this work I show that the epistemic reliability of computer simulations is philosophically detached from the materiality problem. I will show that materiality only restricts computer simulation from “accessing” certain aspects of the world which require a causal story. I will also show that computer simulations provide ways of inference that do not depend on its materiality but on its capacity for representing empirical as well as non-empirical systems.

Proof-Theoretic Semantics in the Substructural Era
Ole Hjortland, University of St Andrews

We develop a proof-theoretic semantics in the spirit of Hacking (1979) which is sensitive to substructural distinctions. In particular, we formulate a notion of proof-theoretic harmony that differentiates between additive and multiplicative connectives. This is achieved by following work on so-called generalised elimination rules in Schroeder-Heister (1984) and Read (2000). We then compare the requirement to definitional reflection in sequent calculus to isolate structural features in a natural deduction framework.

Mini-tutorial: Hacking on Logic, Mathematics, and Proof
James Conant, University of Chicago

This mini-tutorial will be devoted to a critical discussion of Hacking's work in the philosophy of logic and mathematics. In the first 45 minutes, we shall discuss some of Hacking's early work on this topic, and in the second 45 minutes we will concentrate on his most recent work on these topics.

Calculating With Sentences Which Are A Priori in Virtue of Our Intuitive Notion of Truth
Stefan Wintein, University of Tilburg

By an *a priori sentence* we mean a sentence whose semantic value is knowable independent of experience. Sentences such as the Liar and the Truthteller qualify as a priori in virtue of our intuitive notion of truth which is, we will argue, captured by the valuation function V of *Assertoric Alethic Semantics* (Wintein, 2010). Defining the a priori in terms of V, we show that certain query problems can be solved *more efficiently* by exploiting a priori sentences. In short, we will show how to *calculate* with sentences which are *a priori* in virtue of our intuitive notion of truth.

A Priori Physicalism ‘Naturalized’?
Anna Ciaunica, University Of Burgundy

Recently, D. Stoljar (2006) appealed to the metaphor of “slugs-on-the-mosaic” in order to defend what he called “the epistemic view” and proposed shifting focus from the contrast between the mental and the physical to the contrast between experiential and non-experiential truths. He consequently argues that if the ignorance hypothesis (IH hereafter) is true (i.e. we are ignorant of a type of experience-relevant non-experiential truth) then the problem of experience is solved. According to Stoljar, once we shift focus, the traditional mind-body problem might be replaced by a logical one. My aim in this paper is to discuss some consequences of Stoljar’s viewpoint on a priori physicalism.

Kinds of Minds and the Unity of Mathematics
Madeline Muntersbjorn, University of Toledo

The growth of mathematics over time suggests that while mathematical content is neither inert nor eternal the unity of mathematics as a discipline is not a dispensable illusion. This essay presents Poincaré’s interrelated hypotheses that mathematicians come in different kinds and that mathematical discovery occurs in stages. The cultural and cognitive diversity of the mathematical community makes the evolution of mathematics possible. But while there are good reasons to understand mathematical objects from the perspective of dynamic nominalism, mathematical relations, especially the relations between arbitrary symbols and imagined referents, are better understood from the perspective of an emergent realism.

A Kantian Reading of Hilbert's Programme: Formalism for the 21st Century
Oran Magal, McGill University

Two crucial, connected trends shaped modern mathematics: the liberation of mathematics from necessary connection to intuition (Cantor: the essence of mathematics is its ‘freedom’), and the increasing centrality of the axiomatic method. Hilbert was a central figure in both; moreover, he is generally regarded as the standard-bearer of ‘formalism’. I wish to challenge the more-or-less standard reading of Hilbert’s formalism as a kind of instrumentalist anti-realism, by looking closely at the role of intuition in Hilbert’s Programme, stressing its continuity with his earlier foundational work. The upshot is a reconception of formalism which makes it a more viable contemporary contender.

Demonstration as Discourse, Calculation as Mental Process
Catarina Dutilh Novaes, University of Amsterdam

The paper explores the fundamental dissimilarities between two crucial mathematical practices – demonstration and calculation – from a historical and cognitive point of view; it is an attempt at what Netz (1999) has termed ‘cognitive history’. I argue that a promising way to start thinking about the differences between the two is the following: a demonstration is best seen as corresponding to a multi-agent discursive situation, while a calculation is best seen as corresponding to a mono-agent mental process. Based on historical and psychological-cognitive observations, I also argue that the demonstrative technique is rather contrived, whereas calculation is a practice particularly compatible with our natural cognitive apparatus.

Stability and Dynamics in the Laboratory Sciences: A Comment on Hacking and Rheinberger
Katherina Kinzel, Univie

This paper compares Ian Hacking's analysis of the "self-vindication" of the "laboratory style of reasoning" with Hans-Jörg Rheinberger's account of "experimental systems". The main difference between the two views of experimentation is that Hacking focuses primarily on stability whereas Rheinberger emphasizes first and foremost dynamics and instability. I shall aim for a third proposal that avoids the shortcomings and one-sided perspectives of these two authors. My ultimate goal is to work towards a better understanding of how the two aspects – the stability and the dynamics of experimental work – are intertwined.

Dummettian 'Logicism', Intuitive Models, and A Priori Knowledge
Tim Storer, Cambridge University

Dummett's "new" argument for antirealism in mathematics turns on the difference between mathematics and the natural sciences. What makes mathematical statements true is the conception we have of the objects concerned. This means that for a generalization over mathematical objects to have a determinate meaning, our conception must settle what objects of the appropriate sort there are. In the case of quantification over physical objects, by contrast, this is settled for us by empirical reality. I examine what it means to have such a conception of mathematical objects; and I argue that our conception can settle what natural numbers exist, but not what real numbers or infinite sets there are.

The Certainty of Mathematics
Kim-Erik Berts, Åbo Akademi University

Mathematics is often taken to give us certain knowledge. There is, however, no clear-cut way of understanding what this amounts to. This paper discusses different ways of understanding the certainty of mathematics. It is concluded that some of these are not meaningful suggestions, while others do not seem to be what one could mean by the certainty of mathematics. It is concluded that we must rather look at the status of mathematical propositions as they are used in different kinds of discourse in order to understand what one is trying to capture by labelling mathematics "certain."

Singularist Semirealism
Bence Nanay, University of Antwerp

This paper proposes to carve out a new position in the scientific realism/antirealism debate and argue that it captures some of the most important realist and some of the most important antirealist considerations. The view, briefly stated, is that science aims to give us literally true singular statements about the world, but it does not aim to give us literally true non-singular statements. I call this view singularist semirealism. Singularist semirealism sides with scientific realism with regards to singular statements but it is an antirealist view with regards to non-singular statements. I compare and contrast this view with Ian Hacking's entity realism, which it is supposed to be the closest descendent of.

How Does Physical Analogy Help Solve Pure Mathematical Problems?
Vincent Ardourel, University of Paris

The paper focuses on the heuristic function of physics in mathematics. More precisely, I shall discuss to what extent physical analogy can be used to solve pure mathematical problems. I will begin my discussion with H. Poincaré’s claim according to which physical analogy helps solve pure mathematical problems because it enables mathematicians to visualize a physical situation relied to the pure mathematical problem. In this paper, I will argue that visualizing physical images does not suffice to justify the heuristic function of physical analogy in mathematics. In order to fulfil this goal, I will discuss two examples of pure mathematical problems solved with physical analogies.