>PRESENTATION:
Giovanni Valente is a PhD student in the Committee for Philosophy and
the Sciences at University of Maryland, where he works on foundations
of Quantum Mechanics under Jeff Bub. He received his degree in philosophy
at University of Padua in 2003 with a thesis on the Bayesian interpretation
of quantum probability. He also spent periods of study at the Subfaculty
of Philosophy in Oxford (Spring 2003) and at the Eotvos Lorand University
in Budapest (Spring 2004). He mainly deals with philosophy of quantum
mechanics, algebraic approach to physical theories, quantum information
and philosophy of probability. 


In this talk I shall start by reviewing a noncommutative
conditionalization rule which generalizes the classical Bayes rule in
algebraic terms. Accordingly, the existence of a wellbehaving conditional
expectation proves a necessary condition for a Bayesian interpretation
of probabilities in Quantum Mechanics. In particular, one needs to account
for the case in which the agentobserver allegedly revises her degrees
of belief, namely the quantum states, in light of knowing that a quantum
measurement has been performed. A stability condition formulated by the
philosopher Miklos Redei gives rise to a rationality constraint on conditional
probabilities which characterises Bayesianism. That places a strong requirement
on the conditional expectation map, which fails to hold in Quantum Mechanics,
thus challenging the tenability of a Bayesian interpretation of quantum
probabilities. I shall raise and critically survey three possible solutions
to Redei's argument; by doing this, I shall introduce additional rationality
constraints, further showing what it takes for quantum states to be degrees
of belief of a rational agent.
