The seminars are held in hybrid format on the Chapman University campus in the Keck Center, home of Schmid College of Science and Technology, in room KC 153 (no. 30 on the Campus map, at the intersection of Walnut Ave. and Center St.), or on Zoom.
Fall 2025
August 29, 2025: Louis Vervoort
Speaker: Louis Vervoort (Higher School of Economics, Moscow)
Time: 4 - 6:50 p.m.
Location: Argyros Forum 209A
Title:
Contextual (Hidden) Variables in Quantum and Fluid Mechanics
Abstract:
One way to escape from Bell’s no-go predicament is the possibility of ‘contextual’
hidden variables, i.e. hypothetical variables correlated with the detector variables
in Bell experiments. Usually such variables are believed to be either nonlocal (involving
superluminal interactions) or superdeterministic or having other unpleasant features.
In this talk I will argue that contextual hidden variables are inevitable and ‘physics
as usual’ if a unification between quantum mechanics and general relativity is possible.
I will make the link with recently discovered ‘hydrodynamic quantum analogs’, namely
droplets walking over a vibrating fluid film. These systems can mimic a surprisingly
long list of quantum effects, including the violation of a static Bell inequality,
and contextuality is here mediated through a pilot-wave that resonates with the droplets
and ‘feels’ the environment. Such experiments are relevant for testing loopholes to
Bell’s theorem, and can inspire new experiments in the quantum realm. I will propose
three of such experiments. I will end with a discussion of the interpretation of Bell’s
theorem.
September 5, 2025: Marco Panza
Speaker: Marco Panza (Chapman University)
Time: 4 - 6:50 p.m.
Location: Argyros Forum 209A
Title:
Zeno, Aristotle and Achilles: Infinity and Continuity
(Joint work with Giovanna Giardina and Chiara Martini)
Abstract:
In his Physics, Aristotle mentions Zeno’s paradox of the Dichotomy and the Achilles four times:
three times the Dichotomy, one time the Achilles. He also replies twice to both of
them at once, by arguing that (despite their difference) they depend in fact on the
same argument, and that this argument is fallacious. This entails that they are in
fact only apparent paradoxes. They are not solved, but dissolved. Aristotle's reply
is, to our mind, unquestionable. In the first part of the talk, we defend the claim
that these are actually not paradoxes. Still, the reason Aristotle mentions them is
not only to confute the Eleatic arguments against motion, but also and overall, since
their setting and his reply involve (and ask for an account for) two fundamental aspects
of his physics: the notion of potential infinity and that of continuity. Both of them
are often misunderstood. In the second part of the talk, we suggest an uncommon (if
not original) account of them.
September 12, 2025: Emily Adlam, Kelvin McQueen, and Cai Waegell
Speakers: Emily Adlam, Kelvin McQueen, and Cai Waegell (Chapman University)
Time: 4 - 6:50 p.m.
Location: Argyros Forum 201
Title:
Agency cannot be a purely quantum phenomenon
Abstract:
What are the physical requirements for agency? In this paper, we investigate whether
a purely quantum system (one that evolves unitarily in a coherent regime without decoherence
or collapse) can satisfy minimal requirements for agential behavior. We adopt a plausible
condition: an agent must possess a world-model and evaluate the consequences of alternative
actions based on that model. This process requires not only storing and transforming
environmental information but also generating multiple internal representations of
that information in order to compare outcomes across different possible actions. We
show that these requirements place a hard physical constraint on quantum agents. The
no-cloning theorem forbids the copying of unknown quantum states, and this restriction
undermines the agent’s ability to construct and evaluate alternative scenarios. We
examine approximate cloning strategies and show that they do not permit sufficient
fidelity or generality for agency to be viable in purely quantum systems. This result
suggests that agency itself is a fundamentally classical phenomenon, or at least one
which requires significant classical elements. The result challenges several quantum
theories of mind.
September 19, 2025: Eddy Keming Chen
Speaker: Eddy Keming Chen (University of California, San Diego)
Time: 4 - 6:50 p.m.
Location: Keck Center 153
Title:
Exchangeability and Algorithmic Randomness: A New Proof of the Principal Principle
Abstract:
We explore the role of algorithmic randomness and exchangeability in defining probabilistic
laws and their implications for chance-credence principles like the Principal Principle.
Building on our previous work on probabilistic constraint laws (arXiv:2303.01411),
we develop a new approach to proving the Principal Principle. This proof avoids circularity
by grounding it in algorithmic randomness, frequency constraints, and exchangeable
priors. Our approach establishes a direct link between long-run frequencies and short-term
credences, clarifying the epistemic foundations of chance, typicality, and probabilistic
laws. (Joint work with Jeffrey A. Barrett.)
September 26, 2025: Alexander Kurz and Michael Robinson (Roundtable starting at 2 p.m.)
Speakers: Alexander Kurz and Michael Robinson (Chapman University)
Time: 2- 4 p.m.
Location: Keck Center 153
Title:
AI and Education: Friends or Foes?
Abstract:
The recent ubiquity of increasingly capable generative AI is causing enormous disruption
in higher education as it threatens to render obsolete modes of instruction and assessment
that college educators have relied on beyond living memory. The questions how best
to respond to this challenge and whether (and how) to incorporate AI into classes
has been at the forefront of many of our minds. The two of us have adopted different
approaches to this question in the various computer science and philosophy classes
we teach. We will share thoughts about our experiences incorporating and excluding
AI and then invite attendees to join us in an open discussion of these issues.
October 17, 2025: Jean-Pierre Marquis
Speaker: Jean-Pierre Marquis (Université de Montréal)
Time: 4 - 6:50 p.m.
Location: Keck Center 153
Title:
What is Mathematical Structuralism? A categorical narrative
Abstract:
In this talk, I will briefly go over the criteria presented by Hellman and Shapiro
in their book on the subject published in 2019, present their analysis of how category
theory fares with respect to these criteria. I will then present an alternative narrative
which leads to different conclusions and a reevaluation of the criteria.
October 24, 2025: Gila Sher
Time: 4 - 6:50 p.m.
Location: Keck Center 153
Title:
On the Connection between Invariance and Structural Necessity in Logic, Mathematics, and Physics
Abstract:
In this talk I will explain the connection between invariance and necessity in logic, mathematics, and physics. The type of invariance I will discuss is property invariance - invariance of properties/relations under all 1-1 and onto replacements of individuals within and across formally/physically-possible domains. The type of necessity connected to this type of invariance is structural necessity. The invariance in question (originated with Mostowski, Lindstrom, and Tarski) has proven very fruitful in meta-logic and the philosophical foundations of logic. Here I will use it to explain: (i) the structural (formal) necessity of logical truths and inferences, (ii) the structural (formal) necessity of mathematical truths, and (iii) the structural (physical) necessity of a certain type of physical truths (universal principles/laws).
October 31, 2025: Jonathan Weinberger
Time: 4 - 6:50 p.m.
Location: Keck Center 153
Title:
Universes and higher algebra in synthetic ∞-category theory
Abstract:
Categories are structures that axiomatize composition of functions. In many settings, however, it is natural to weaken the notion of function composition to be defined only up to homotopy, i.e., a contractible space of data. This idea is familiar from algebraic topology where one studies a topological space by considering its fundamental group, an algebraic structure formed by its loops. But the idea of composition defined up-to-homotopy is even more clearly exemplified in a vast enhancement of this structure, namely the fundamental ∞-groupoid of a space which does not only keep track of the loops or paths, but also paths between paths (aka homotopies), paths between paths between paths (aka 2-homotopies), etc., ad infinitum.
Just like ordinary groupoids naturally form a category, ∞-groupoids form an ∞-category whose morphisms weakly preserve composition. In set-based mathematics, the construction of such universes is not usually done in an extrinsic way, either working non-homotopy invariantly, or switching between various "models" of ∞-categories.
Working in a modal extension of a simplicial homotopy type theory à la Riehl--Shulman, I will present a construction of the synthetic ∞-category of ∞-groupoids and the synthetic ∞-category of ∞-categories. As an application, I will point out some immediate results and future perspectives for doing higher algebra in that setting. The results are joint work with Daniel Gratzer and Ulrik Buchholtz (https://arxiv.org/abs/2407.09146, https://arxiv.org/abs/2501.13229, and further work in preparation).
November 7, 2025: Marta Bílková
Time: 4 - 6:50 p.m.
Location: Keck Center 153
Title:
Epistemic Logic of Crash Failures
Abstract:
Epistemic logic investigates knowledge and belief in multi-agent systems. Epistemic logical semantics is often based on relational structures - Kripke models - that consist of an abstract domain of possible states of the world between which binary relations labelled by agents are defined. The relation captures agents’ uncertainty about the global state of the world. This happens, when the agent considers both states possible which is represented by the agent’s relation connecting these possibilities.
Combinatorial topology on the other hand has been used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed under containment. A vertex of a complex represents the local state of an agent or process. Given a complex, an agent may for example be uncertain about the local state of other agents. This happens when a vertex for this agent is contained in different simplices that contain vertices for the other agents but for different local states of those agents. Simplicial complexes are thus a convenient semantic framework to model synchronous and asynchronous computation in distributed systems, where local states of processes are essential. In synchronous computation, processes may crash, and uncertainty about live processes about what processes have crashed is encoded in so-called impure simplicial complexes. The global state of a distributed system corresponds to a maximal simplex of a simplicial complex, which is called a facet. In an impure simplicial complex not all facets contain information for all processes. The absent processes are assumed to have crashed.
We propose an epistemic logic to reason about such distributed systems with crash failure, that is interpreted in impure simplicial complexes. It naturally has a three-valued semantics, wherein formulas may not only be true or false but also undefined: in particular knowledge of crashed processes and local propositions of crashed processes are undefined. The logic also allows for the live processes to know or be uncertain whether other processes have crashed, which additionally requires the presence of environmental propositional variables. The logic expands a propositional three-valued base that is known as Paraconsistent Weak Kleene logic PWK with a modal epistemic logical base that is derived from the standard epistemic logic S5.
This approach relates to other recent approaches encoding distributed systems with impure complexes, some of which are two-valued, where dead processes are represented as agents knowing the false proposition, and others of which are also three-valued but less expressive; one then cannot have live processes be uncertain whether other processes are dead. A detailed comparison is included in this work. This talk is based on a joint work with Hans van Ditmarsch, Roman Kuznets, and Rojo Randrianomentsoa.
November 14, 2025: Steve Awodey
Speaker: Steve Awodey (Carnegie Mellon University)
Time: 4 - 6:50 p.m.
Location: Keck Center 153
Title:
What is HoTT?
Abstract:
A new branch of logic called Homotopy Type Theory (HoTT) has been developed in the
last 15 years. This talk will survey the historical, philosophical, and mathematical
background leading up to the invention of HoTT, and trace some of the challenges and
advances that have marked its subsequent development. This is a non-technical talk,
intended for a general audience.
November 21, 2025: Double session with Nico Formánek and Teresa Kouri Kissel (3 - 6:45 p.m.)
Double session with Nico Formánek and Teresa Kouri Kissel
Speaker: Nico Formánek (High-Performance Computing Center Stuttgart)
Time: 3 - 4:45 p.m.
Location: Keck Center 153
Title:
Computational power and model selection
Abstract:
Philosophers and scientists alike have worried about the problem of overfitting. The
usual story involves a flexible model and enough computational power for fitting it
to all the idiosyncrasies in one's data. Rather tellingly Kepler's discovery of Mars'
elliptical orbit is often used to illustrate a worrisome scenario: We are asked to
imagine a situation in which Kepler has enough computational power to fit epicycles
to his observations. The suggested conclusion being then that he would have never
come up with the ellipse. Here I will argue that such a scenario, in addition to being
historically inaccurate, is stretching the counterfactuals too far. It ignores all
additional assumptions beyond the data that Kepler made and in turn asks us to ignore
all assumptions beyond the data we could plausibly take. While computational power
surely brings new classes of models into consideration, it is not the only driver
of model selection. I will argue that model selection is actually a rather complex
interplay between data, computational power and background assumptions. Teasing out
the background assumptions involved in specific selective choices is often only possible
with philosophical hindsight and enough computational power to clearly distinguish
between the alternatives. The stories philosophers of science tell about model selection
should thus be taken with a grain of salt.
Speaker: Teresa Kouri Kissel (Old Dominion University)
Time: 5 - 6:45 p.m.
Location: Keck Center 153
Title:
Proof-Theoretic Pluralism and Harmony
Abstract:
Ferrari and Orlandelli (2019) propose that an admissibility condition on a proof-theoretic
logical pluralism be that the logics in question must be harmonious. For them, this
means that they must have connectives which are (a certain brand of) unique and conservative.
This allows them to develop an innovative pluralism where the admissible logics are
both useful and balanced, which shows variance on two levels: the level of validity
and the level of connective meanings.
Here, I will show that we can extend the system one step further, and induce a three-level
logical pluralism, which better fits the criteria of usefulness and balance. The first
and second levels remain as suggested by Ferrari and Orlandelli (2019), but we can
allow for multiple notions of uniqueness in the definition of harmony, or multiple
notions of harmony. Either of these options generates a pluralism at the level of
our admissbility conditions. This generates a pluralism at three levels: validity,
connective meanings, and admissibility conditions. But it still preserves the spirit
of Ferrari and Orlandelli (2019): balance and usefulness remain the admissibility
constraints across the board.
December 5, 2025: Double Session with Sophie d'Espalungue and Alain Yger (3 - 6:45 p.m.)
Speaker: Sophie d'Espalungue (IRIF, Paris)
Time: 3 - 4:45 p.m.
Location: Keck Center 153
Title:
Foundational Aspects of Size and Dimension in Higher Categorical Structures
Abstract:
This talk investigates the structure and role of universes in the formalisation of higher categorical structures, towards a formalisation of the hierarchy of the n+1-category of n-categories. The focus is on motivations and conceptual aspects of ongoing work. I will review notions of smallness in higher categorical structures, bringing together perspectives from homotopy type theory and more classical categorical intuitions. I will then discuss how truncation hierarchies — such as n-truncated types and n-categories — interact with universes under univalence, and use it to outline connections between HoTT and the framework I am developing.
Speaker: Alain Yger (Université de Bordeaux)
Time: 5 - 6:45 p.m.
Location: Keck Center 153
Title:
The Mathematical Concept of Residue and its Ubiquity
Abstract:
Since Cauchy coined the term “residue” in 1825, the concept which lies beyond, and is closely related to that of “trace”, evolved towards a point where seemingly unrelated areas of mathematical research meet together. In this talk, I will present various facets of the so-called residue formula and defend a negative answer to André Weil’s interrogation: does elimination theory need to be eliminated? Henri Poincaré summarized the role of such concept in geometry by saying in 1887 that the integral on a closed surface only depends on the singular curves which lie in the interior of such surface. Then came Jean Leray who had within hands both Georges de Rham’s ideas and analytic duality through Laurent Schwartz’s theory of distributions or currents. The concept of residue, which was originally algebraic or geometric, hence somehow rigid, evolved towards a multivariate analytic object integrating the flexibility of C∞ smoothness besides the rigidity of analyticity, which nevertheless remained central in Alexander Grothendieck’s presentation. Interpolation-division questions in polynomial algebra, as for example Euclid’s division algorithm revisited by Joseph-Louis Lagrange and Leopold Kronecker, David Hilbert’s nullstellensatz or syzygy theorem, or the somehow mysterious Joël Brian¸con and Henri Skoda’s theorem (at the crossing point between analytic geometry and convex geometry) which is not so well known, deserve then to be re-interpreted in terms of multivariate residue calculus and thus profit from such residue concept, which I will humbly try to suggest in this talk. I will deliberately avoid technicity in order to emphasise conceptual facts to the detriment of a detailed mathematical approach.
December 12, 2025: Double session with J. J. P. Veerman and Victor Pambuccian (3 - 6:45 p.m.)
Double session with J. J. P. Veerman and Victor Pambuccian
Speaker: J. J. P. Veerman (Portland State University)
Time: 3 - 4:45 p.m
Location: Killefer Conference Room A
Title:
Birkhoff Sums of Irrational Rotations
Abstract:
We investigate the distribution of a sequence of points in the circle generated by
rotations by a fixed irrational number rho with initial condition x, that is: frac{
x + i \rho} for i from 1 to infinity. The discrepancy as defined by Pisot and Van
Der Corput in the 1930's quantifies how evenly distributed such a sequence is. It
plays a prominent role in numerical analysis, dynamical systems, and ergodic theory.
We associate a measure (the Birkhoff measure) to the distribution of Sum frac{ x +
i \rho } over i in {1,..., n} and show that the graph of the density of that measure
varies strongly with n. Nonetheless, it always tiles \R. We discuss various other
aspects of these measures, including connections with the theory of continued fractions.
Finally, we outline more efficient proofs of two classical results.
Speaker: Victor Pambuccian (Arizona State University)
Time: 5 - 6:45 p.m.
Location: Killefer Conference Room A
Title:
The Fine Structure of the Parallel Postulate
Abstract:
If one believes that continuity (or Archimedeanity) is an essential aspect of geometry,
without which it makes little sense to speak of geometry, then the Euclidean parallel
postulate or its negation are the only axioms that one could add to an absolute geometry
conceived as continuous. If, however, one takes an elementary, i.e. first-order logic,
look at geometry, then Archimedeanity cannot be expressed in an elementary manner
and we find that, with respect to elementary absolute geometry, there are several
weakenings of the Euclidean parallel postulate. These are: (1) the axiom stating the
existence of a rectangle, (2) the axiom, called Lotschnittaxiom, stating that the perpendiculars to the sides of a right angle intersect, (3) Aristotle's
axiom, stating that the perpendiculars dropped from one side of an angle to the other
side grow without bounds. We will study equivalent forms of these axioms, their history,
the languages in which these axioms can (or cannot) be equivalently expressed and
find syntactically simplest forms for them. In particular, both (2) and (3) can be
expressed as incidence-geometric statements, but (1) cannot be expressed without metric
notions. One conclusion of this analysis is that the Euclidean parallel postulate
consists of two completely independent ideas, i.e., is the conjunction of two independent
incidence-geometric statements.
Spring 2025
January 24, 2025: Thomas Seiller
Speaker: Thomas Seiller (CNRS, Laboratoire d'Informatique de Paris-Nord)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
The impressive results obtained by generative language models witness that statistical information about a (large enough) corpus can be used to extract the structure of natural langage. As part of a general effort to investigate how to mathematically understand this process, Bradley, Gastaldi and Terilla have proposed a generalisation of the standard notion of formal concepts to incorporate quantitative information. This approach consists in moving from sets to functions over sets (using presheaves): the generalised formal concepts are thus obtained as so-called nuclei (fixed points) of an adjunction. In this talk I will explain how this generalisation of formal concepts turns out to coincide exactly with a construction of models of (fragments of) linear logic.
February 7, 2025: Silvia De Toffoli (4:45 - 6:15 p.m. PST)
What Mathematical Explanation Need Not Be
(joint work with Elijah Chudnoff)
Speaker: Silvia De Toffoli (School for Advanced Studies IUSS Pavia)
Time: 4:45 - 6:15 p.m. PST
Location: KC 153
Abstract:
Recent works in the philosophy of mathematical practice and mathematical education have challenged orthodox views of mathematical explanation by developing Understanding-first accounts according to which mathematical explanation should be cashed out in terms of understanding. In this article, we explore two arguments that might have motivated this move: (i) the context-sensitivity argument and (ii) the inadequacy of knowing why argument. We show that although these arguments are derived from compelling observations, they ultimately rest on a misunderstanding of what explanation-first accounts are committed to and an underestimation of the resources available to them. By clarifying the terms at play in the debate and distinguishing different objects of evaluation, we show that the insightful observations about practice and education made by challengers to the orthodoxy are in fact best accounted for within the traditional Explanation-first framework.
February 21, 2025: Jacopo Emmenegger
An Introduction to the Theory of Lawvere's Doctrines and its Recent Advances
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
February 28, 2025: Carl Posy (9 - 10:45 a.m. PST)
Infinity, Paradox, and the Fall of Hilbert’s Program
Speaker: Carl Posy (Hebrew University of Jerusalem)
Time: 9 - 10:45 a.m. PST
Location: Hashinger Science Center 205
Abstract:
The tug between infinitary thought and constructivism has been a constant theme throughout
the history of mathematics: Time and again, Platonistic infinitary methods (positing
finitely inaccessible objects, unfulfillable tasks) have proven to be essential to
mathematics; while empiricist thinkers have repeatedly striven to reconcile this fact
with finitary (constructivist) constraints. In modern times, David Hilbert's formalist
program is the most famous reconciliation attempt. Hilbert aimed to secure infinitary
mathematics via finitely graspable formal systems. The program notoriously failed.
Gödel’s theorems did it in.
The first part of my talk concerns that downfall. Using syntactic tools, Saul Kripke
has shown that Hilbert’s program in fact contains the seeds of its own downfall. I
will use different, more semantic tools (though inspired by Kripke) to obtain a similar
conclusion. I will argue that the central notion of a consistent and semantically
adequate formalism already presupposes ways of thinking that unleash infinity and
thus clash with and even block Hilbert’s finitary goal.
But then I’ll point out that infinity itself is not so central a sticking point as
Hilbert made it out to be. Those damning infinitary modes of thinking are in fact
instances of principles that have nothing to do with infinity. Indeed, I will show
that these principles underlie some decidedly finite paradoxes. An interesting observation
on its own.
Having shown this, time permitting, I'll tell you about some consequences of that
observation for understanding the conflict between Platonism and empiricism in particular
and some other issues in the general metaphysics of mathematics.
March 7, 2025: Greg Restall
Modal Logic and Contingent Existence
Speaker: Greg Restall (University of St Andrews)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
Almost all recent work on modal semantics makes essential use of possible worlds models. These models have proved useful for analysing the structural properties of modal logics, but it is less clear that they fix the meaning of our modal vocabulary, given that we have no grasp of what counts as a possible world, independent of our grasp of what counts as possible. In this talk, I describe an inferentialist semantics for modal and quantificational vocabulary, not as a rival to possible worlds models, but as an explanation of how the concepts we do employ can be modelled using possible worlds. I then use this inferentialist semantics to clarify the contingentist’s commitments, and offer answers to necessitist objections.
March 14, 2025: Vincent Jullien
Cavalieri's Indivisibles and its Followers
Speaker: Vincent Jullien (University of Nantes)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
At the beginning of the 17th century, the usefulness, indeed the necessity, of using
objects and methods related to infinity in geometry was strongly felt. Buonaventura
Cavalieri published a Geometria continuorum indivisibilibus... in Bologna in 1635.
The wave spread throughout the European mathematical community: Torricelli, Descartes,
Roberval, Barrow, Pascal, Wallis, Mengoli, Leibniz... I will present this important
episode and try to see how it heralds and prepares the differential and integral algorithms
of the end of the century.
April 4, 2025: Giuseppe Rosolini
Ultracompletions
Speaker: Giuseppe Rosolini (Università degli Studi di Genova)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
The notion of ultracategory was introduced by Michael Makkai in a paper in APAL in
1990 for the characterisation of categories of models of pretoposes, an ample extension
to (intuitionistic) first order theories of Stone duality for Boolean algebras — aka
conceptual completeness. Recently, Jacob Lurie refined that notion in unpublished
notes producing another approach to the duality for pretoposes — the two notions of
ultracategory appear to be different, though no separating example has been produced
yet.
In the talk, we shall give intuitions about Makkai's and Lurie's notions, providing
examples and applications. Then we shall introduce an algebraic notion of structured
category which subsumes the two kinds of ultracategories mentioned above — technically,
the "ultracompletion" 2-functor on the 2-category of small categories, and extend
it to a pseudomonad. Next we show how it can be related to the two existing notions,
using also results recently obtained by Ali Hamad.
This is joint work with Richard Garner.
April 11, 2025: Otávio Bueno
Dispensing with the Grounds of Logical Necessity
Speaker: Otávio Bueno (University of Miami)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
Logical laws are typically conceived as being necessary. But in virtue of what is
this the case? That is, what are the grounds of logical necessity? In this paper,
I examine four different answers to this question in terms of: truth-conditions, invariance
of truth-values under different interpretations, possible worlds, and brute facts.
I ultimately find all of them wanting. I conclude that an alternative conception of
logic that dispenses altogether with grounds of logical necessity provides a less
troublesome alternative. I then indicate some of the central features of this conception.
April 18, 2025: Ahmed Sebbar
Quintics, Platonic Solids and Rogers-Ramanujan Identities
Speaker: Ahmed Sebbar (Chapman University)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
What is the connection between
1) The Quintic
2) Platonic solids and their duality
3) Ramanujan's Letter to Hardy
4) Toric Varieties
5) ADE classification and semi simple Lie Algebras
The aim of this presentation is to provide an overview of these connections, some
of which are explicit and others more subtle, yet all equally mysterious. We will
strive to present the key ideas and their motivations.
April 25, 2025: Jemma Lorenat
Axiomatic collaborations in the foundations of geometry at the University of Chicago,
1900 – 1905
Speaker: Jemma Lorenat (Pitzer College)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
This talk centers around Oswald Veblen’s archival notes taken during a seminar on
the foundations of geometry given in 1901 by E. H. Moore at the University of Chicago.
This seminar would be extremely fruitful for Moore, Veblen, and the study of postulate
systems in twentieth-century American mathematics. From a close-reading of these notes
alongside later publications by Moore and Veblen, I will reconstruct ways in which
American scholars reworked and re-appropriated modern European mathematics. This talk
will focus particularly on graphic notation and the role of independence and categoricity
in Veblen’s Notebook and resulting publications.
This talk is based in joint research with Nicolas Michel (Isaac Newton Institute for
Mathematical Sciences, University of Cambridge) and Emmylou Haffner (Institut des
Textes et Manuscrits Modernes, CNRS).
May 2, 2025: Charles "Chip" T. Sebens
How Do Laws Produce the Future?
Speaker: Charles "Chip" T. Sebens (California Institute of Technology)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
The view that the laws of nature produce later states of the universe from earlier
ones (prominently defended by Maudlin) faces difficult questions as to how the laws
produce the future and whether that production is compatible with special relativity.
This talk will grapple with those questions, arguing that the concerns can be overcome
through a close analysis of the laws of classical mechanics and electromagnetism.
The view that laws produce the future seems to require that the laws of nature take
a certain form, fitting what Adlam has called “the time evolution paradigm.” Making
that paradigm precise, we might demand that there be temporally local dynamical laws
that take properties of the present and the arbitrarily-short past as input, returning
as output changes in such properties into the arbitrarily-short future. In classical
mechanics, Newton’s second law can be fit into this form if we follow a proposal from
Easwaran and understand the acceleration that appears in the law to capture how velocity
(taken to be a property of the present and the arbitrarily-short past) changes into
the arbitrarily-short future. The dynamical laws of electromagnetism can be fit into
this form as well, though because electromagnetism is a special relativistic theory
we might require that the laws meet a higher standard: linking past light-cone to
future light-cone. With some work, the laws governing the evolution of the vector
and scalar potentials in the Lorenz gauge, as well as the evolution of charged matter,
can be put in a form that meets this higher standard.
Links to the recently published paper:
How do Laws Produce the Future? [arXiv]
May 9, 2025: M. Andrew Moshier
Point Set Topology is a Disease from Which the Human Race Will Soon Recover
Speaker: M. Andrew Moshier (Chapman University)
Time: 2 - 4 p.m.
Location: KC 153
Abstract:
Our title is from Poincaré, writing near the beginnings of what we now call algebraic
topology. In this talk, we introduce locale theory, an alternative cure, first due
to Ehresmann, under influences of Wallman, Stone, Tarski, and others. In locale theory,
a space, concretely, is a lattice of parts of the space. A continuous function is
a function on these parts that in a suitable sense preserves their structure. Points
play no role in the general theory.
The talk will begin with an introduction to locales, with attention to the intuitions
behind the definitions. We will then consider some instructive applications of locale
theory that are simply impossible to conceive in a point set framework and will close
with some recent results.
May 16, 2025: Melisa Vivanco
On the Philosophy of Natural Numbers
Speaker: Melisa Vivanco (University of Texas Rio Grande Valley)
Time: 4 - 6:50 p.m.
Location: KC 153
Abstract:
This talk is part of a broader project in which I develop a realist theory of natural
numbers. My research stems from the intuition that mathematical objects exist objectively
and independently of the human mind, yet not all mathematical entities belong to the
same category. Natural numbers serve as a privileged starting point for exploring
mathematical reality due to their foundational role in the discipline and their function
in constructing other numerical systems.
In this presentation, I will outline the core principles of my proposal, according
to which numbers are cardinality properties of pluralities, considered as such rather
than sets or aggregates of individual entities. I will discuss how this perspective
provides a more compelling explanation of arithmetic sentences, their necessity, and
their a priori character, as well as their connection to language and epistemology.
Finally (if there's time enough), I will contrast my proposal with other realist theories
and address the epistemological challenge posed by Benacerraf, suggesting that the
homogeneity between mathematical and non-mathematical knowledge can be preserved if
we adopt a proper conception of numbers as properties.
Fall 2024
August 30, 2024: Marco Panza
Frege's Definition of Real Numbers is Consistent
Speaker: Marco Panza (Chapman University)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
September 6, 2024: Guram Bezhanishvili
The Gödel Translation: History and New Directions
Speaker: Guram Bezhanishvili (New Mexico State University)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
The Gödel translation (1933) interprets the intuitionistic propositional calculus IPC as a fragment of modal logic. In 1940s, McKinsey and Tarski proved that this provides a faithful embedding of IPC into Lewis’ modal system S4. Their result was further generalized to other extensions of IPC. One of the culminations of this line of research is the celebrated Blok-Esakia theorem (1976) which establishes an isomorphism between extensions of IPC and Grz — the well-known extension of S4 introduced by Grzegorczyk (1967).
Things become more complicated when the propositional logics under consideration are replaced by their predicate extensions. As we will see, the Blok-Esakia isomorphism fails already for the one-variable fragments of these logics. This gives rise to a series of problems, which remain open to this day. The aim of this talk is to introduce the audience to this beautiful area of research. Towards the end, I also plan to discuss promising future directions.
September 13, 2024: Carlos Álvarez Jiménez
A Possible Way to Read (and Interpret) Euclid's Elements
Speaker: Carlos Álvarez Jiménez (Universidad Nacional Autónoma de México)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
A classical way to introduce the main problems related to the Philosophy of Mathematics
follows from the (classical) problem of the foundations of mathematics. In this talk,
I do not intend to discuss directly this topic, but to suggest that an interesting
contribution to this classical question may be answered by asking which are, if there
are, the fundamental theorems in mathematics. This very wide question may be focused
in the particular domain of Euclidean geometry and, particularly, concerning Euclid's
reconstruction of plane geometry.
September 20, 2024: Stephen Mackereth
The Philosophical Significance of Gödel’s Dialectica Translation
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
September 27, 2024: Drew Moshier and Alexander Kurz
Interestingness in Mathematics
Speakers: Drew Moshier and Alexander Kurz (Chapman University)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
AI (both symbolic and neural) is changing the way we do mathematics. Already now, cutting edge proofs by leading mathematicians are implemented in programming languages such as Lean and verified by type-checking algorithms. How far are we away from machines doing interesting mathematics independently and without human guidance?
Any answer to this question will depend on understanding what mathematics humans find
interesing. This discussion, led by Alexander Kurz and Drew Moshier, will explore
the question of interestingness in mathematics. In particular, we want to understand
how to define proxies for interestingness based on existing archives of formal proofs.
October 4, 2024: Wesley H. Holliday
From Constructive Mathematics and Quantum Mechanics to Fundamental Logic
Speaker: Wesley H. Holliday (UC Berkeley)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
October 18, 2024: Mateja Jamnik
How can we make trustworthy AI?
Speaker: Mateja Jamnik (University of Cambridge)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
Not too long ago most headlines talked about our fear of AI. Today, AI is ubiquitous,
and the conversation has moved on from whether we should use AI to how we can make
the AI systems that we use in our daily lives trustworthy. In this talk I look at
some key technical ingredients that help us build confidence and trust in using intelligent
technology. I argue that intuitiveness, interaction, explainability and inclusion
of human domain knowledge are essential in building this trust. I present some of
the techniques and methods we are building for making AI systems that think and interact
with humans in more intuitive and personalised ways, enabling humans to better understand
the solutions produced by machines, and enabling machines to incorporate human domain
knowledge in their reasoning and learning processes.
October 25, 2024: Benjamin Faltesek
Can the necessity of mathematics be derived?
Speaker: Benjamin Faltesek (Chapman University)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
Hannes Leitgeb (2020) has offered an argument for the necessity of mathematics. In particular, he gives a derivation using the modal system K of the statement that mathematical theorems are necessarily true. In this talk, I will first motivate the questions of whether mathematics is necessary, and if so, why. I will also defend the strategy of deriving the necessity of mathematics, on the principle that arguments can be explanatory. I will then set out Leitgeb's premises and reasoning. Some key assumptions are that all mathematical theorems are (actually or simply) true and that they can always be translated into ZFC. Although the argument has deficiencies, I will defend Leitgeb's suggestion that the truths of set theory are necessary due to the necessity of identity and the Axiom of Extensionality.
November 1, 2024: Patrick Ryan
A Reassessment of Gödel’s Doctrine: The Necessity of Infinity
Speaker: Patrick Ryan (Chapman University)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
In his landmark 1931 paper, Gödel demonstrated the existence of finitary statements
that required infinitary resources to prove them. This led him to postulate what Solomon Feferman called Gödel’s Doctrine, namely, that “the unlimited transfinite iteration of the powerset operation is necessary to account for finitary mathematics.” This claim garnered further support over the
course of the 20th century because of the production of various other “finitary independence”
results. Nonetheless, proof theoretic work by Feferman and others showed that these
finitary results could be proved using relatively weak systems, e.g., predicatively
justifiable systems, thereby challenging Gödel’s Doctrine. In this talk, I would like
to argue that, though the technical results of Feferman and others are unimpeachable,
their philosophical significance is overstated. That is, even if Gödel’s Doctrine
is dubious when we understand "necessary" to mean "proof theoretically necessary,"
it can be vindicated when we think of other senses in which strong infinitary resources
might be necessary for mathematics. This is done by investigating a fascinating collection
of finitary statements that possess multiple proofs employing both infinitary and
finitary resources. I consider how an analysis of such results can inform debates
in the philosophy of mathematics, especially discussions of purity, content, and explanation.
In particular, if a finitary theorem τ has a perfectly cogent, finitary proof, why
then provide an infinitary proof of τ , a proof involving principles of an ostensibly
different sort? What is gained? Do such infinitary proofs play an explanatory role?
Is there then a sense in which infinity is necessary? I conclude by indicating some
promising directions for future research.
November 8, 2024: Walter Carnielli and Juliana Bueno-Soler
How to Benefit from Uncertainty: An Introduction to Paraconsistent Bayesian Update
Speakers: Walter Carnielli and Juliana Bueno-Soler (CLE/FT- University of Campinas, Brazil,
and Chapman University, USA)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
One of the main questions in Bayesian thinking is how we adjust our beliefs when new
evidence comes along. At the heart of this process are relationships between evidence
E and hypotheses H, which bring up key ideas like plausibility, confirmation, and
acceptability. However, these relationships can get tricky.
In this talk, we’ll show how paraconsistent and paracomplete logics can help solve some of these challenges in Bayesian reasoning. Using a new approach to probability based on the Logic of Evidence and Truth (LET_F), which is designed to handle both evidence for or against a judgement—even when it's incomplete or contradictory—we offer a way to measure how much evidence supports a given statement. We’ll look at some examples showing how paraconsistent and paracomplete Bayesian approaches can effectively handle contradictions in reasoning.
We think these ideas could impact not just the philosophy of science but also fields like Artificial Intelligence, probabilistic networks, and other new models where handling uncertainty and contradictions is crucial.
Reference:
W. A. Carnielli and J. Bueno-Soler
Where the truth lies: a paraconsistent approach to Bayesian epistemology.
Studia Logica, to appear.
Pre-print available Cambridge Open Engage Logica.
https://www.cambridge.org/engage/coe/article-details/6526998c45aaa5fdbbc54fd2
November 15, 2024: Juliet Floyd
The Turing Test as a View From Somewhere:
Hilbert, Wittgenstein and Turing on ‘Surveyability’
Speaker: Juliet Floyd (Boston University)
Time: 4:00 - 6:50pm
Location: KC 153
Abstract:
Recent debates about the philosophical status of formalization and mechanization of proof may be illuminated by considering the mutual impact Wittgenstein and Turing had on one another around issues concerning the evolution of notations in symbolic logic. When Wittgenstein remarked in 1937 that ‘a proof must be surveyable’ he was reworking ideas of Frege, Hilbert and Turing. “Surveyability” for Wittgenstein was neither a verificationist requirement nor a refutation of the claim that all proofs must have corresponding formal proofs, much less a refutation of logicism. Instead, it placed front and center what mathematicians do, i.e., it explores what logicism comes to in an everyday sense. The idea -- consonant with certain trends in so-called “philosophy of mathematical practice”, including recent work by Kennedy on “formalism freeness”, and Floyd’s on “everyday phraseology” -- is not to provide or ask for a “foundation” for mathematics in any ordinary sense, but rather to take a pragmatic and mathematically flexible approach to the very idea of “foundations”.
In 1939 Wittgenstein and Turing discussed these ideas in Wittgenstein’s Cambridge
lectures on the foundations of mathematics, sparking some of Turing’s subsequent work
on types. The relevant ideas here draw out new ways of looking at Turing’s 1936 paper,
as well as his more speculative writings in the late 1940s about “intelligent machinery”
and his 1950 “Turing Test”.