A Semantics for Belief in Simplicial Complexes
Published:
Joint work with Adam Bjorndahl, though he could not attend the conference.
Talks and Presentations
A list of all the talks I have given, both contributed and invited. Click on each for details about venue and topic!
Contributed Talks
Description Fitting and Alan Turing
Published:
Joint talk with Stephen Perry.
One classic question of 20th century philosophy, inspired by Wigner’s classic 1960 paper, is “Why is mathematics, something abstract, so applicable to the sciences, something empirical?” A new analytical tool, description fitting, seeks to ease our mind about such questions. There is no one, singular way that applied mathematics works. Rather, the particular goals relative to each project inform how each piece of applied mathematics “works”. Applied mathematicians will massage, or “fit” their description of the natural world, sometimes in very idealized or even false ways, in order to make that description amenable to formalization.
Invited Talks
An Implementation of Belief Revision in Simplicial Models for Dynamic Epistemic Logic
Published:
In this talk we set out to show how to connect belief revision to dynamic epistemic logic by leveraging tools given by the setting of simplicial semantics. We start by modifying some of the existing models for DEL in simplicial semantics (“Knowledge and Simplicial Complexes”, “A Simplicial Complex Model for Dynamic Epistemic Logic”). In particular, we will show how to modify these models for DEL so that they work in a setting for belief, rather than knowledge, using tools from the upcoming paper “Belief In Simplicial Complexes”. With this in hand, we will then motivate an endogenous notion of “nearness” between facets, where two facets sharing more perspectives in common is interpreted as the two facets being more similar. We exploit this notion of “nearness” to give a model for belief revision ala Lewis’ “Probabilities of Conditionals and Conditional Probabilities”, and ultimately we use this notion of nearness to give a model of DEL where agents update via revision, rather than classically. We will conclude with a discussion of some existing and future work which attempts to exploit this notion of nearness to give new tools for fault tolerance.
Description Fitting and Alan Turing
Published:
Joint talk with Stephen Perry.
Philosophy Then and Now: A Re-Evaluation of Rorty’s Philosophical Pessimism
Published:
This was a talk I was invited to give at a special session of the Richard Rorty Society by Dr. David Rondel. The main goal of the talk was to compare and contrast the metaphilosphies of Richard Rorty and Philip Kitcher, with the ultimate goal of showing that each has something to inform the other. In particular, each misses something of value the other catches. Rorty is ultimately overly skeptical of both formal philosophy, and both are overly skeptical of various politically motivated philosophical projects. However, Rorty’s views on this latter topic notably evolved in complex ways over time.
Modal Logic Without Possible Worlds
Published:
Joint talk with Brittany Gelb. We presented a semantics for modal logic based on simplicial complexes that instead of possible worlds uses an “Agent Perspective”. Philip explained the details of the formalism, including a novel soundness and completeness proof. Brittany followed up with some applications of these models to a distributed setting. Additionally, she showed how we can use tools from algebraic topology to show a variety of things including the nonexistence of bisimulations.
Modal Logic Without Possible Worlds
Published:
Joint talk with Brittany Gelb. We presented a semantics for modal logic based on simplicial complexes that instead of possible worlds uses an “Agent Perspective”. Philip explained the details of the formalism, including a novel soundness and completeness proof. Brittany followed up with some applications of these models to a distributed setting. Additionally, she showed how we can use tools from algebraic topology to show a variety of things including the nonexistence of bisimulations.
A Logical Model of Pluralistic Ignorance
Published:
Much of the existing literature on pluralistic ignorance suggests that agents who find themselves in such a situation must consider themselves “special” in one way or another (Grosz 2018, Bjerring et al. 2014). Agents have to recognize their own dishonesty, but believe everyone around them is perfectly honest. This argument is taken to show that pluralistic ignorance is irrational. Modifying work from Christoff 2016, we use a simple logical model to show that these arguments for the irrationality of pluralistic ignorance depend on various introspection assumptions. We will finish by putting forth various scenarios where agents can be honest, headstrong, or something similar (generally taken to be impossible under pluralistic ignorance) but are nonetheless consistent if one relaxes introspection assumptions. This shows that agents can see themselves as no different from their friends and still be in a situation of pluralistic ignorance with sufficiently weak introspection assumptions.