Knowledge of Knowledge

Program

- Daniel Greco (Yale)

- Olivier Roy (Bayreuth)

- Aybüke ?zgün (Amsterdam)

- Jan Constantin (Cologne)

- Luis Rosa (Cologne)

- Eric Pacuit (Maryland)

- Niki Pfeifer (Regensburg)

- Hans Rott (Regensburg)

- Tim Kraft (Regensburg)

Pfeifer

Probabilistic Knowledge of Probabilistic Knowledge

Traditionally, knowledge is conceived as true justified belief. Although we hold many justifiable beliefs in everyday life, we are often uncertain about their truth. Thus, many everyday life beliefs are characterized by (mostly implicit) probabilistic knowledge. In my talk, I will present coherence-based probability logic as a rationality framework for representing and reasoning about probabilistic knowledge. Specifically, I will explain the role of interval-valued probabilities to deal with situations of incomplete probabilistic knowledge. I will critically discuss how to deal rationally with meta-level uncertainty of probabilistic assessments: how to represent and reason about probabilistic knowledge of probabilistic knowledge.

?zgün

Uncertainty About Evidence

We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our models allow the set of possible worlds that a piece of evidence corresponds to to vary from one possible world to another, and therefore itself be the subject of uncertainty. Such structures can be viewed as (epistemically motivated) generalizations of topological spaces. In this context, there arises a natural distinction between what is actually entailed by the evidence and what the agent knows is entailed by the evidence - with the latter, in general, being much weaker. We provide a sound and complete axiomatization of the corresponding bi-modal logic of knowledge and evidence entailment, in which knowledge is both positively nad negatively introspective but evidence entailment is neither. We further investigate some natural extensions of this core system, including the addition of a belief modality and its interaction with evidence interpretation and entailment, as well as the addition of a "knowability" modality interpreted via a (generalized) interior operator.
(This is joint work with Adam Bjorndahl.)

Pacuit

Beliefs, Propositions and Definite Descriptions

In this paper, we introduce a doxastic logic with expressions that are intended to represent definite descriptions for propositions. Using these definite descriptions, we can formalize senences such as:

Ann believes that the strangest proposition that Bob believes is that neutrinos travel at twice the speed of light.

Ann believes that the strangest proposition that Bob believes is false.

The second sentence has both de re and de de dicto readings, which are distinguished in our logic. We motivate our logical system with a novel analysis of the Brandenburger-Keisler paradox. Our analysis of this paradox uncovers an interesting connection between it and the Kaplan-Montague Knower paradox.
(This is joint wirk with Wes Holliday.)

Rosa

As I think about knowledge, it starts to disappear

In this paper I address the following question: Do epistemologists know that subjects have knowledge? The question is targeted at epistemologists who hold that knowledge requires safety, or the elimination of relevant alternatives by the evidence. I will argue that if the epistemologist does not know that the subject's belief that p satisfies those conditions, then the epistemologist does not know that the subject knows that p. I defend this conditional against the objection that the epistemologist might know that the subject knows that p in some other way - other than checking whether the relevant definitions are satisfied. In asserting the target conditional, one does not necessarily commit any kind of intensional fallacy. The final question to be addressed, then, is whether the epistemologist knows that those allegedly necessary conditions for knowledge are satisfied in ordinary cases. Her knowledge that subjects have knowledge is contingent on that.

Constantin

The Rebasing Account of Deafeat

I present an account of defeat that promotes the idea that certain kinds of defeaters, specifically undercutting and higher-order defeaters, lower or remove the justification of a relevant defeated attitude A by rebutting higher-order attitudes about the relationship between A and the epistemic input A is based on. At the same time, such higher-order attitudes are not conceived of as a condition for justification in general, but are only formed, or required to be formed, in response to registering the defeater. Obtaining a defeater creates a doxastic incompatibility in the subject's noetic system, which prompts/requires the re-evaluation of the defeated attitude. A competent re-evaluation features an assessment of the attitude's doxastic base, resulting in newly-formed higher-order attitudes about the base. Thus, a competent re-evaluation of my belief that my wall is orange includes the realization that my belief is based on a visual impression of the wall and that I presume that my visual impression is a good indicator of the wall's colour. Certain types of defeater, such as undercutting defeaters, defeat by rebutting the relevant higher-order attitude: The information that my wall is illuminated by an orange light shows that my visual impression is not a good indicator, after all. I therefore cannot rationally continue to rely on it. I further argue that re-evaluation necessarily includes a rebasing of the re-evaluated attitude from its original doxastic base to the re-evaluation itself. This explains why higher-order rebuttal during re-evaluation also lowers or removes justification for the re-evaluated lower-order attitude. Consistent application of this framework to different kinds fo defeaters can be shown to resolve apparent explanatory problems and illuminates the structural differences between these kinds.

Kraft

Closure, KK and Scepticism

Before we can respond to scepticism we need to understand the sceptical argument. One reconstruction of the sceptical argument is the closure argument (also known as the 'argument from ignorance'): I don't know whether I am a brain in a vat. But I only know that I have hands if I know that I am not a BIV. Hence, I don't know that I have hands. The second premise is supported by closure: Since having hands entails not being a BIV, knowing the former requires knowing the latter. Another reconstruction of the sceptical argument relies on KK or variants of KK, for example, the principle that if knowing P (not just P itself) entails Q, knowing P requires knowing Q. In this talk I defend the KK reading of the sceptical argument. First, I argue that the closure argument has two crucial weaknesses that the KK argument can overcome. Second, I argue that sceptics who accept closure should also accept KK anyway. Thus, understanding scepticism as relying on KK doesn't introduce a new weakness.

Roy

Introspective Groups

I will survey known and new results regarding introspection of different types of group attitudes, ranging from the classical models of shared and common knowledge to models of aggregated attitudes like distributed knowledge and so-called priority merge.

Greco

Knowledge, Common Knowledge, and Granularity

Harvey Lederman (2018) argues that groups can never attain commmon knowledge or any approximation thereof, and that the tradition of appeal to such notions to do explanatory work in philosophy and cognate disciplines is misguided. His challenge is distinctive in that, by contrast with other recent attacks on common knowledge that appeal to the falsity of the KK principle, Lederman explicitly grants this principle. I'll offer a companions in guilt style response: Lederman's challenge is a special case of more general skeptical challenge that threatens regular knowledge for individuals just as much as it threatens common knowledge for groups. While resisting the challenge is difficult and comes with costs, if we're willing to pay those costs to preserve regular knowledge for individuals, common knowledge for groups may come along at no extra charge.