Archive for the ‘Logic’ Category
A New Introduction to Modal Logic erratum
Wednesday, April 14th, 2010Just noticed a significant and potentially confusion causing error regarding multiply modal logics in this nonetheless excellent text. On pages 217-218 in my 1996 edition Hughes and Cresswell write:
For instance we might have a necessity operator
, say, which is stronger than
in the sense that
. The canonical model for such a system would obey the restriction that for all
if
then
Now, that should be for all if 
then .
A Question About Belief
Friday, April 9th, 2010If one believes that they believe that p, then do they believe that 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 
. Since they omit this axiom (commonly called the T axiom), 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 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:
A list of doxastic reasoner types can be found here
Transplication as Implication
Wednesday, February 24th, 2010In his contribution on partial logic to the Handbook of Philosophical Logic, Stephen Blamey introduces a ‘value gap introducing’ connective named ‘transplication’ to the standard 3-valued partial logic, the Strong Kleene logic. Blamey suggests the possibility of reading the transplication connective as a type of conditional. I was interested to see how the transplication connective fares as a conditional by testing it against a list of inferences concerning conditionals.
Here is the investigation: Transplication as Implication
I have not come across much material concerning transplication. Does anyone else have any other references or ideas?