If one believes that they believe that p, then do they believe that p ($\text{B} \text{B} p \supset \text{B} p$)?

I was recently thinking about this property and its absence from standard systems of doxastic logic. Systems of doxastic logic rightly do not validate the property $\text{B} p \supset p$. Since they omit this axiom (commonly called the T axiom), $\text{B} \text{B} p \supset \text{B} p$ cannot be simply derived. But although the T axiom should not be valid in a doxastic logic, it is fair to say that the axiom $\text{B} \text{B} p \supset \text{B} p$ should be valid; if one believes that they believe that p, then they do believe that p.

This type of agent is apparently termed a stable reasoner by Raymond Smullyan:

Stable reasoner: A stable reasoner is not unstable. That is, for every p, if it believes Bp then it believes p.

A list of doxastic reasoner types can be found here

## Knowledge and Its Value: Some Suggestions as To Why Knowledge Is More Valuable Than True Belief

Now for something with an epistemological and value theoretical flavour, a paper I have been working on titled ‘Knowledge and Its Value: Some Suggestions as To Why Knowledge Is More Valuable Than True Belief’

I have just come across a paper by Christian Piller titled ‘Valuing Knowledge: A Deontological Approach’, which explores my last idea in depth.

## Dretske’s Account of Knowledge Against Some Epistemological Cases

Knowledge and luck do not mix. Our intuitions and definitions of knowledge suggest and require the absence of luck in cases of knowledge. Edmund Gettier’s landmark 1963 paper ‘Is Justified True Belief Knowledge?’ not only prompted a revision in epistemological theorising, but gave us the terms Gettier-examples and the related Gettier-luck. Gettier provided his examples in order to refute the account of knowledge which defines it as justified true belief (JTB). Here is one of the two examples he provided. It is supposed that Smith has strong evidence for the following proposition:

Jones owns a Ford (A)

Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith randomly selects the names of three cities and uses them to construct the following three propositions:

• Either Jones owns a Ford, or Brown is in Boston. (B)
• Either Jones owns a Ford, or Brown is in Barcelona. (C)
• Either Jones owns a Ford, or Brown is in Brest-Litovsk. (D)

now, each of B, C and D is entailed by A so Smith comes to accept them. Smith therefore has correctly inferred B, C, and D from a proposition A for which he has strong justification. Hence Smith is justified in having the true beliefs of B, C and D. Now imagine in the scenario that firstly Jones does not own a Ford, but is instead at present driving a rented car. Secondly, by sheer coincidence and unknown to Smith, Barcelona happens to be where Brown is. So even though Smith clearly does not know that C is true, it is true, he believes it and he is justified in believing it.

This example along with the other example in the paper sufficed to show that truth, belief and justification were not sufficient conditions for knowledge. In both of Gettier’s actual examples, the justified true belief came about as the result of entailment from justified false beliefs; in the given example the justified false belief that “Jones owns a Ford”. This led some early responses to Gettier to conclude that the definition of knowledge could be easily adjusted, so that knowledge was justified true belief that depends on no false premises. This “no false premises” solution did not settle the matter however, as more general Gettier-style problems were then constructed or contrived, in which the justified true belief does not result using a chain of reasoning from a justified false belief.

## Some Offhand Commentary on Fred Dretske’s Knowledge and the Flow of Information

Fred Dretske’s Knowledge and the Flow of Information is ultimately an attempt to use the notion of information to explicate knowledge. As part of this enterprise, several philosophically interesting issues are tackled. The first of these is the development of a semantic theory of information. After establishing a connection between information and knowledge, Dretske goes on to apply his ideas to key philosophical areas such as perception and intentional content or meaning. Here I take a look at his account of information.