Abstracts of the
Talks
You can download the booklet of abstracts here:
fmv2018_abstracts.pdf 
Here is the handout of the talk of Lavinia Picollo

Abstracts of the
Workshops
What we talk about when we talk about neologicism
by Matteo De Benedetto (MCMP, LMU Munich)
The aim of this workshop is to provide the necessary philosophical and technical tools in order to understand the significance of logicism for foundational questions in mathematics. In the first part of the workshop, we will see the conceptual pillars of Frege's logicism, stressing its scope and aims. We will then describe how the different contemporary neologicist proposals try to recover the spirit of Frege's foundational attempt. In the second part of this workshop, we will introduce some important elements of the (neo)logicist toolbox, such as 2nd order logic, Basic Law Five, 2nd order arithmetic, explicit and recursive definitions.
Semantic and Syntactic Approaches to Truth
by Balthasar Grabmayr (HU Berlin, Tel Aviv University)
This workshop aims to provide an introduction to the two prevalent approaches of characterising the notion of truth for formal languages. This will include studying Tarski's notion of truth in a model as well as Kripke's fixedpointed semantics. We will then learn how axiomatic theories of compositional truth can be obtained, which correspond to Tarski's and Kripke's model constructions respectively. Once these formal methods are acquired, we will evaluate and compare the two approaches and conclude the workshop by discussing the relation of the employed methods to philosophical issues regarding the foundations of mathematics.
Canceled Infinitary combinatorics: an introduction by Karl Heuer (University of Hamburg)
Why should philosophers care about the foundations of mathematics?
by Silvia Jonas (MCMP, LMU Munich)
This workshop aims to create an understanding of why philosophers should care at all about the foundations of mathematics. We will start with a quick tour through the history of mathematics. Special attention will be paid to how applied mathematics became pure in the 20th century, thus raising a number of new philosophical questions, such as: if mathematics is no longer applicable to the world, what reason do we have to believe its objectivity? We will then discuss four main approaches to this question, Platonism, Intuitionism, Formalism, and Structuralism, their respective merits and shortcomings. The last part of the workshop will be dedicated to fundamental disagreements in contemporary mathematics. In particular, we will trace some debates about the axioms of set theory, about category theory as an alternative foundation of mathematics, and about corresponding pluralist approaches to mathematical truth. We will conclude the workshop by trying to evaluate the philosophical import of these foundational debates, starting with the following question: if there can indeed be multiple foundations in mathematics, as mathematical pluralists hold, how does this affect the realismantirealism debate about mathematics (and about a priori domains more generally)?
The debate on new axioms in set theory
by Deborah Kant (HU Berlin)
After giving a brief description of the current situation in set theory, we read and discuss passages of important texts in the debate on new axioms in set theory. This includes texts by K. Gödel, P. Maddy, S. Feferman, and J. D. Hamkins.
Proving unprovability  an introduction to forcing
by Regula Krapf (University of KoblenzLandau)
The method of forcing was first used in 1963 by Paul Cohen in order to show that the Continuum Hypothesis (CH) is independent of the axioms of ZermeloFraenkel set theory (ZFC). Since then, forcing has turned out to be a powerful tool for obtaining independence results in set theory. In this workshop I will give a short introduction to forcing and its applications; in particular, I will sketch the proof of the independence of CH.
by Matteo De Benedetto (MCMP, LMU Munich)
The aim of this workshop is to provide the necessary philosophical and technical tools in order to understand the significance of logicism for foundational questions in mathematics. In the first part of the workshop, we will see the conceptual pillars of Frege's logicism, stressing its scope and aims. We will then describe how the different contemporary neologicist proposals try to recover the spirit of Frege's foundational attempt. In the second part of this workshop, we will introduce some important elements of the (neo)logicist toolbox, such as 2nd order logic, Basic Law Five, 2nd order arithmetic, explicit and recursive definitions.
Semantic and Syntactic Approaches to Truth
by Balthasar Grabmayr (HU Berlin, Tel Aviv University)
This workshop aims to provide an introduction to the two prevalent approaches of characterising the notion of truth for formal languages. This will include studying Tarski's notion of truth in a model as well as Kripke's fixedpointed semantics. We will then learn how axiomatic theories of compositional truth can be obtained, which correspond to Tarski's and Kripke's model constructions respectively. Once these formal methods are acquired, we will evaluate and compare the two approaches and conclude the workshop by discussing the relation of the employed methods to philosophical issues regarding the foundations of mathematics.
Canceled Infinitary combinatorics: an introduction by Karl Heuer (University of Hamburg)
Why should philosophers care about the foundations of mathematics?
by Silvia Jonas (MCMP, LMU Munich)
This workshop aims to create an understanding of why philosophers should care at all about the foundations of mathematics. We will start with a quick tour through the history of mathematics. Special attention will be paid to how applied mathematics became pure in the 20th century, thus raising a number of new philosophical questions, such as: if mathematics is no longer applicable to the world, what reason do we have to believe its objectivity? We will then discuss four main approaches to this question, Platonism, Intuitionism, Formalism, and Structuralism, their respective merits and shortcomings. The last part of the workshop will be dedicated to fundamental disagreements in contemporary mathematics. In particular, we will trace some debates about the axioms of set theory, about category theory as an alternative foundation of mathematics, and about corresponding pluralist approaches to mathematical truth. We will conclude the workshop by trying to evaluate the philosophical import of these foundational debates, starting with the following question: if there can indeed be multiple foundations in mathematics, as mathematical pluralists hold, how does this affect the realismantirealism debate about mathematics (and about a priori domains more generally)?
The debate on new axioms in set theory
by Deborah Kant (HU Berlin)
After giving a brief description of the current situation in set theory, we read and discuss passages of important texts in the debate on new axioms in set theory. This includes texts by K. Gödel, P. Maddy, S. Feferman, and J. D. Hamkins.
Proving unprovability  an introduction to forcing
by Regula Krapf (University of KoblenzLandau)
The method of forcing was first used in 1963 by Paul Cohen in order to show that the Continuum Hypothesis (CH) is independent of the axioms of ZermeloFraenkel set theory (ZFC). Since then, forcing has turned out to be a powerful tool for obtaining independence results in set theory. In this workshop I will give a short introduction to forcing and its applications; in particular, I will sketch the proof of the independence of CH.