## Confirmation Measures and Transmitted Information

The following Bayesian confirmation measure is associated with John Maynard Keynes, having appeared in his A Treatise on Probability (1921). The degree to which evidence e confirms hypothesis h is given as:

$R(h,e) = \text{ln}(\frac{p(h | e)}{p(h)})$

Interestingly, this is strongly reminiscent of a subsequent measure found in Shannon information theory. In philosophy literature, this formula can be found in Dretske’s formulation of information transmission derived from Shannon’s work as well as a measure of transmitted information given by Hintikka.

## A Gettierised (Russellised) Historical Fact?

I finally dug up my copy of Russell’s Human Knowledge: Its Scope and Limits and located the passage in which he gives the Gettier-like broken clock example (15 years before Gettier’s paper):

It is very easy to give examples of true beliefs that are not knowledge. There is the man who looks at a clock which is not going, though he thinks it is, and who happens to look at it at the moment when it is right; this man acquires a true belief as to the time of day, but cannot be said to have knowledge.

This passage is found in Section ‘D. Knowledge’, at the end of the Chapter ‘Fact, Belief, Truth, and Knowledge’.

Most would agree that this is not a case of knowledge. But how far can we carry this? Take the following example: A famous historical figure (X) dies and a medical staff member in attendance records X‘s exact time of death using a clock hanging on the wall. This clock is also broken but happens to be stuck on the actual time, say, 6pm. Now, although the staff member records a fact (a true proposition), they do not actually know that X died at 6pm. Furthermore, by standard Dretskean information-theoretic epistemology, neither are they informed by the clock that X died at 6pm.

If the staff member does not have knowledge of nor are they informed of the time of death, is what they record a piece of information? Can a recorded fact be information or knowledge if the source of that record neither was informed of nor knew the proposition in question? If their record is used in a biographical book on X, can someone who reads this book 100 years later come to know that X died at 6pm?

## Quantifying Information to Quantifying Beliefs

In the previous post, I showed how a truthlikeness semantic information measure could be applied in order to get a basic way in which knowledge can be quantitatively measured. This advantage set the truthlikeness approach apart from inverse probabilistic approaches to quantifying semantic information.

In looking at a way to work out something similar for quantitatively measuring beliefs, it occurred to me that things are the other way around; it is the inverse probabilistic approach instead which is to be applied.

## Quantifying Information to Quantifying Knowledge

Part of my current research has focused on the quantification of semantic information, on ways to measure the semantic information yield of logical statements. Instead of the somewhat standard Bar-Hillel/Carnap/Hintikka inverse probabilistic approach, I have opted to quantify semantic information using the notion of truthlikeness. The former is associated with a Theory of Weakly Semantic Information (TWSI), `weakly’ because truth values play no role in it. The latter is associated with a Theory of Strongly Semantic Information (TSSI), according to which information encapsulates truth. TSSI is associated more generally with the veridicality thesis, that semantic information is meaningful, well-formed data that is also true. See On Quantifying Semantic Information for more on this.

## Talk on Knowledge and Information

Details for an upcoming talk I am giving. Date and time TBA:

Title: Knowledge and Information

Abstract: Information and knowledge are commonly associated with each other; colloquially, in dictionaries, the two terms are often treated as synonymous. Within philosophy however, information-theoretic epistemology goes beyond this casual, colloquial association. It involves the development of specialised accounts of information and furthermore attempts to develop an explication of knowledge with such accounts, to show how information causes or leads to knowledge. In this presentation I outline and discuss a theory of information and how it is used to develop an information-theoretic epistemology. Information is treated as a fundamental precursor to knowledge, with knowledge encapsulating truth because it encapsulates information, which itself is also veridical by definition.

## Epistemology and the Value of Knowledge

The Value of Knowledge and the Pursuit of Survival, a paper I have just looked at which impressively supports the view that knowledge is more valuable than mere true belief, a view which I support.

A copy of the draft from the author’s website can be found here.

Being a proponent of informational epistemology, one of the things that interests me is how informational accounts of knowledge and general informational notions applied to epistemology can address the Value Problem in epistemology.