Research Seminar in Logic and Philosophy of Mathematics (FTY-911) 2017/2018

General information

The seminar is directed by Sara Negri and Jan von Plato. Time and place: Friday 10-12. University Main Building, Unioninkatu 34, Auditorium III (old side).

The announcements are posted to a seminar mailing list. All people interested in the seminar and not belonging yet to the list can send an e-mail to "sara dot negri at helsinki dot fi" to be included among the recipients.

For students

Postgraduate and advanced undergraduate students will get an occasion to learn about recent research on logic and philosophy of mathematics, and a training for presentation skills and for participation in scientific discussion in such a context.

The research seminar in logic is primarily intended for the presentation of original research in logic and philosophy of mathematics by junior and senior researchers and by international guests. The detailed schedule of the seminar, with titles and abstracts of the presentations will be posted on this web page (see below).

Credits are acquired through regular attendance, active participation in the discussions and, when possible, a presentation at the seminar. The presentation can be based either on existing literature, to be agreed with the docent, or on original research.

Please cf. Web Oodi for the registration and a description of the learning goals in Finnish.

Forthcoming seminars

1.12.2017: Marianna Girlando (Univ. of Aix-Marseille and Univ. of Helsinki) "A proof theoretical approach to conditionals".

Abstract: Conditional logics are extensions of classical propositional logic: they display an additional operator suited to represent conditional sentences - such as counterfactuals - that cannot be captured by material implication. These logics were introduced after 1960 by Stalnaker and Lewis, and have been widely studied since then: other than counterfactual reasoning, they can be used to capture forms of non-monotonic inference and belief change. We are interested in defining deductive calculi (in particular: sequent calculi) for the widest possible family of conditional logics. In this seminar we will present labelled sequent calculi, that is to say, calculi that import part of the semantic information into the rules. To this aim, after a survey of the principal systems of possible world semantics devised for conditional logics, we shall focus on neighbourhood semantics. Neighbourhood models a generalization of Lewis' sphere models, and associate to each world a set of sets of worlds. This semantics allows for the definition of a sequent calculus with strong proof theoretical properties for a large number of conditional logics, including Lewis' logics. We will detail the method to construct the rules out of neighbourhood models, and present the main properties of the resulting calculi. (Joint work with Sara Negri and Nicola Olivetti)

Past seminars

17.11.2017: Mirja Hartimo ''On Husserl's Structuralist Philosophy of Mathematics''

Abstract: The paper discusses Husserl's view of mathematics by means of two theses, namely the Incompleteness Claim and the Dependence Claim, with which Øystein Linnebo (2008) has characterized non-eliminative structuralism as opposed to the more traditional Platonist view of mathematics. According to the Incompleteness Claim, mathematical objects are incomplete in the sense that they have no non-structural properties. The Dependence Claim holds that the mathematical objects are dependent on each other and/or structure to which they belong. Husserl's view is shown to be a combination view: It is generally a species of non-eliminative structuralism, of which the two claims hold. However, in addition the Incompleteness Claim motivates constructivism about the mathematical objects. Moreover, due to the ''thinness'' of his ''mathematics-first'' approach, he is ultimately also open to the more traditionally Platonist approaches.

Reference:

Linnebo, Ø (2008) Structuralism and the Notion of Dependence, Philosophical Quarterly, 58: 59-79.

3.11.2017: Markus Pantsar "Cognitive complexity and mathematical problem solving"

Abstract: The prevalent paradigm in modelling human cognitive capacities focuses on computational explanations. When it comes to mathematical problem solving, this approach appears to imply that the complexity of a problem can be equated with the complexity of the cognitive task of solving the problem. But in the computational approach we are concerned only with the optimal algorithms for solving problems, whereas human cognizers use many heuristic tools (e.g. diagrams) that make their solutions computationally unoptimal. In this talk, I propose a contrast between optimal and humanly optimal algorithms, which gives us a wider framework in which to study cognitive complexity.

13.10.2016: Andreas Fjellstad (U. of Helsinki & U. of Bergen) "Imitating revision-theoretic limit rules for truth and validity"

Abstract: This paper develops a labelled sequent calculus to represent limit rules in transfinite revision sequences for (self-referential) truth- and validity-predicates. Following the presentation of the calculus, we highlight some features of the resulting logic regarding the extent to which the defined predicates can be said to capture truth and validity with respect to classical logic. It is argued that, whereas the truth-predicate fails to capture truth in classical logic, the validity-predicate seems to adequately describe classical logic.

6.10. 2017: Hanoch Ben-Yami (CEU, Budapest) "The Quantified Argument Calculus"

Abstract: I present a logic I and others have recently developed, in which the quantifier attaches to a unary predicate and together they form a quantified argument, occurring at the argument positions of predicates. That is, if the Natural Language sentence "Alice is polite" is formalised P(a), the sentence "Some students are polite" shall be formalised P(∃S). In several ways, this logic -the Quantified Argument Calculus (Quarc)- is closer to Natural Language more than is any version of Frege's Predicate Calculus (PC), which will become clear as I proceed to discuss further of its features. For instance, Quarc incorporates, like Natural Language and unlike PC, both sentential negation and predication negation, as well as converse relation-terms. It also sheds light on the necessity for the expressive power of Natural Language of these devices. The use of anaphors vis-a-vis variables is also discussed. I next describe the system's semantics and proof systems, and its meta-logical properties. I then extend Quarc to modal logic and show how its version of the Barcan formulas and of their converses come out straightforwardly invalid, which is apparently an advantage of modal Quarc over modal PC. Finally, I shall mention other work which has been done on the system, among other things extending Quarc in various ways, and directions for further research, some currently pursued. Arguably, Quarc might be preferable over PC as a tool to the study of the logic and semantics of Natural Language.

22.9.2017: Gabriel Sandu: "The genesis of modal logic in Northern Europe"

Abstract: I will be concerned with the beginnings of modal logic in the fifties\ and early sixties as reflected in the work of G. H. von Wright, Jaakko Hintikk\ a, and Stig Kanger, making some comparisons to the work of Saul Kripke.

8.9.2017: Jan von Plato "Gödel's reading of Gentzen's first consistency proof for arithmetic".

Abstract: A shorthand notebook of Gödel's from late 1935 shows that he read Gentzen's original, unpublished consistency proof for arithmetic. By 1941, many such notebooks were filled with various formulations of the result, one with explicit use of choice sequences, and a generalization based on an induction principle for functionals of finite type over Baire space. Gödel's main aim was to extend Gentzen's result into a consistency proof for analysis. In the lecture, an overview of these so far unknown results about consistency proofs for arithmetic will be presented. Last updated September 2019