511 research outputs found
On a Straw Man in the Philosophy of Science - A Defense of the Received View
I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to make the concept of a theory more precise. Rather, it is meant as a generalizable framework for explicating specific theories
Quantum information as a non-Kolmogorovian generalization of Shannon's theory
In this article we discuss the formal structure of a generalized information
theory based on the extension of the probability calculus of Kolmogorov to a
(possibly) non-commutative setting. By studying this framework, we argue that
quantum information can be considered as a particular case of a huge family of
non-commutative extensions of its classical counterpart. In any conceivable
information theory, the possibility of dealing with different kinds of
information measures plays a key role. Here, we generalize a notion of state
spectrum, allowing us to introduce a majorization relation and a new family of
generalized entropic measures
The solution of the Sixth Hilbert Problem: the Ultimate Galilean Revolution
I argue for a full mathematisation of the physical theory, including its
axioms, which must contain no physical primitives. In provocative words:
"physics from no physics". Although this may seem an oxymoron, it is the royal
road to keep complete logical coherence, hence falsifiability of the theory.
For such a purely mathematical theory the physical connotation must pertain
only the interpretation of the mathematics, ranging from the axioms to the
final theorems. On the contrary, the postulates of the two current major
physical theories either don't have physical interpretation (as for von
Neumann's axioms for quantum theory), or contain physical primitives as
"clock", "rigid rod ", "force", "inertial mass" (as for special relativity and
mechanics). A purely mathematical theory as proposed here, though with limited
(but relentlessly growing) domain of applicability, will have the eternal
validity of mathematical truth. It will be a theory on which natural sciences
can firmly rely. Such kind of theory is what I consider to be the solution of
the Sixth Hilbert's Problem. I argue that a prototype example of such a
mathematical theory is provided by the novel algorithmic paradigm for physics,
as in the recent information-theoretical derivation of quantum theory and free
quantum field theory.Comment: Opinion paper. Special issue of Philosophical Transaction A, devoted
to the VI Hilbert problem, after the Workshop "Hilbert's Sixth Problem",
University of Leicester, May 02-04 201
On the Intuition of Rank-Dependent Utility
Among the most popular models for decision under risk and uncertainty are the rank-dependent models, introduced by Quiggin and Schmeidler.Central concepts in these models are rank-dependence and comonotonicity.It has been suggested in the literature that these concepts are technical tools that have no intuitive or empirical content.This paper describes such contents.As a result, rank-dependence and comonotonicity become natural concepts upon which preference conditions, empirical tests, and improvements for utility measurement can be based.Further, a new derivation of the rank-dependent models is obtained.It is not based on observable preference axioms or on empirical data, but naturally follows from the intuitive perspective assumed.We think that the popularity of the rank-dependent theories is mainly due to the natural concepts adopted in these theories.rank-dependence;comonotonicity;Choquet integral;pessimism;uncertainty aversion;prospect theory
Bayesian Decision Theory and Stochastic Independence
As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework
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