Audrey Yap

Dynamic Epistemic Logic and Temporal Modality

Dynamic epistemic logic allows us to model agents who learn new information about the world from events which they observe. In this paper, I add a backward-looking modality to the dynamic language, to allow for our expressing statements about what an agent knew before an event took place. This allows us more completely to model what an agent learns from an event, since we can now talk about the difference in their knowledge before and after its occurrence. It is known that the addition of forward-looking temporal modalities require restrictions, since allowing for infinite forward iteration causes undecidability. However, our product update models have only finite pasts, which makes backward-looking modalities much more manageable. Yet they still allow for a rich increase in expressive power.

Logical structuralism and Benacerraf’s problem

There are two general questions which many views in the philosophy of mathematics can be seen as addressing: what are mathematical objects, and how do we have knowledge of them? Naturally, the answers given to these questions are linked, since whatever account we give of how we have knowledge of mathematical objects surely has to take into account what sorts of things we claim they are; conversely, whatever account we give of the nature of mathematical objects must be accompanied by a corresponding account of how it is that we acquire knowledge of those objects. The connection between these problems results in what is often called “Benacerraf’s Problem”, which is a dilemma that many philosophical views about mathematical objects face. It will be my goal here to present a view, attributed to Richard Dedekind, which approaches the initial questions in a different way than many other philosophical views do, and in doing so, avoids the dilemma given by Benacerraf’s problem.

Idealization, epistemic logic, and epistemology

Many criticisms of epistemic logic have centered around its use of devices such as idealized knowers with logical omniscience and perfect self-knowledge. One possible response to such criticisms is to say that these idealizations are normative devices, and that epistemic logic tells us how agents ought to behave. This paper will take a different approach, treating epistemic logic as descriptive, and drawing the analogy between its formal models and idealized scientific models on that basis. Treating it as descriptive matches the way in which some philosophers, including one of its founders, Jaako Hintikka, have thought about epistemic logic early in its history. Further, the analogy between the two fields will give us a way to defuse criticisms that see epistemic logic as unrealistic. For example, criticizing models of epistemic logic in which agents know all propositional tautologies as being unrealistic would be like criticizing frictionless planes in physics for being unrealistic. Each one would certainly be an unsuitable model for studying some kinds of phenomena, but is entirely appropriate for others. After outlining the analogy between epistemic and scientific models, we will discuss some ways in which idealizations are used by different research programs in epistemic logic.

Logics of temporal-epistemic actions

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic (DEL). Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in DEL.

The History of Algebra’s Impact on the Philosophy of Mathematics

Structuralism in the philosophy of mathematics encompasses a range of views, many of which see structures, such as the natural numbers, as the proper objects of mathematics, rather than objects like individual numbers. This position is relatively recent—many see a paper by Paul Benacerraf in 1965 as one of its earliest articulations, though others have written about Richard Dedekind as an earlier precursor. This paper will consider how Emmy Noether, extending Dedekind’s work and general approach, contributed to a transition in mathematics enabling a fuller range of structuralist positions. Her work in ideal theory is a perfect illustration of the kind of conceptual step that permits seeing structures themselves as objects, which is required for certain contemporary views even to make sense.

Ad Hominem Fallacies and Epistemic Credibility

An ad hominem fallacy is an error in logical reasoning in which an interlocutor attacks the person making the argument rather than the argument itself. There are many different ways in which this can take place, and many different effects this can have on the direction of the argument itself. This paper will consider ways in which an ad hominem fallacy can lead to an interlocutor acquiring less status as a knower, even if the fallacy itself is recognized. The decrease in status can occur in the eyes of the interlocutor herself, as seen in cases of stereotype threat, or in the eyes of others in the epistemic community, as in the case of implicit bias. Both of these will be discussed as ways in which an ad hominem fallacy can constitute an epistemic injustice.