The Surprise Examination Paradox in Dynamic Epistemic Logic
Alexandru Marcoci
Abstract:
The surprise examination paradox has been the topic of many
philosophical papers. However, despite its long history, no
long-lasting solution emerged. The debates related to the surprise
examination paradox go deeper than what the correct solution is. One
highly debated issue that I directly address in this thesis is the
following: is there a solution to be given or should we embrace the
surprise examination paradox as a true paradox and look for an
inconsistency in our conceptions on knowledge, belief, etc. Kaplan and
Montague (1960) argue that the surprise examination paradox is indeed
a paradox, while Gerbrandy (2007) and Baltag and Smets (2010) believe
that a solution could be given but not if the teacher’s announcement
is meant to be fulfilled (Gerbrandy), or if the students are to trust
the teacher (Baltag and Smets). Of course, such approaches have a lot
of merit and all authors manage to use their (negative) conclusions to
argue for deep philosophical conceptions regarding knowledge and the
way in which agents revise their beliefs in face of new
information. However, these approaches fail to meet widely accepted
criteria that philosophers expect a solution to the surprise
examination paradox to meet. They have been explicitly set up by
Wright and Sudbury (1977) and contain the idea that the students
should be surprised even after the teacher’s announcement (which
neither Kaplan and Montague, nor Gerbrandy can accommodate) and that a
surprise examination is indeed possible (which Baltag and Smets cannot
accept).
In this thesis I show that dynamic epistemic logic (DEL) can guide us
towards a philosophically informed solution to the surprise
examination paradox. The question that drives the analysis is: is
there a way of coming up with an intuitive solution to the surprise
examination paradox that meets the criteria of Wright and Sudbury? I
argue that there is indeed such a solution. I show that DEL can
provide a way of distinguishing between various possible definitions
of surprise, considerably more than have been addressed in the
literature so far. I investigate how (some of) these definitions
inﬂuence the outcome of the teacher’s announcement on the
students. The result is that one of the new ways of defining surprise,
which is both intuitive and in line with a recent,
empirically-informed, logic of surprise developed in Lorini and
Castelfranchi (2007), allows us to model the scenario of the surprise
examination paradox in such a way that all the conditions of Wright
and Sudbury are respected and the students end up as being surprised
even after the teacher’s announcement.