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This book collects research papers on the philosophical foundations
of probability, causality, spacetime and quantum theory. The papers
are related to talks presented in six subsequent workshops
organized by The Budapest-Krakow Research Group on Probability,
Causality and Determinism. Coverage consists of three parts. Part I
focuses on the notion of probability from a general philosophical
and formal epistemological perspective. Part II applies
probabilistic considerations to address causal questions in the
foundations of quantum mechanics. Part III investigates the
question of indeterminism in spacetime theories. It also explores
some related questions, such as decidability and observation. The
contributing authors are all philosophers of science with a strong
background in mathematics or physics. They believe that paying
attention to the finer formal details often helps avoiding pitfalls
that exacerbate the philosophical problems that are in the center
of focus of contemporary research. The papers presented here help
make explicit the mathematical-structural assumptions that underlie
key philosophical argumentations. This formally rigorous and
conceptually precise approach will appeal to researchers and
philosophers as well as mathematicians and statisticians.
This book collects research papers on the philosophical foundations
of probability, causality, spacetime and quantum theory. The papers
are related to talks presented in six subsequent workshops
organized by The Budapest-Krakow Research Group on Probability,
Causality and Determinism. Coverage consists of three parts. Part I
focuses on the notion of probability from a general philosophical
and formal epistemological perspective. Part II applies
probabilistic considerations to address causal questions in the
foundations of quantum mechanics. Part III investigates the
question of indeterminism in spacetime theories. It also explores
some related questions, such as decidability and observation. The
contributing authors are all philosophers of science with a strong
background in mathematics or physics. They believe that paying
attention to the finer formal details often helps avoiding pitfalls
that exacerbate the philosophical problems that are in the center
of focus of contemporary research. The papers presented here help
make explicit the mathematical-structural assumptions that underlie
key philosophical argumentations. This formally rigorous and
conceptually precise approach will appeal to researchers and
philosophers as well as mathematicians and statisticians.
The main topic of the book is how to argue for formal epistemic
norms of credence. The author advocates formal justificational
pluralism, suggesting that it is reasonable to use various formal
tools, e.g. different "scoring rules," in arguments for synchronic
and diachronic norms. Leszek Wronski first examines various
occasions on which modern formal epistemology fails to live up to
its "formal" label. Among the topics considered next are: the Dutch
Book Theorem and Arguments (which fails according to the author), a
novel version of the Principal Principle, and a constructive
approach to higher order probabilities. The author argues then that
the best method for dealing with various belief update problems is
that of minimizing inverse relative entropy, and defends the claim
that for evaluating an agent's credal state at a single moment the
Brier Score seems to be the way to go.
Since its introduction by Hans Reichenbach, many philosophers have
claimed to refute the idea - known as the common cause principle -
that any surprising correlation between any two factors that do not
directly influence one another is due to some common cause. For
example, falsity of the principle is frequently inferred from
falsifiability of Bell's inequalities. The author demonstrates,
however, that the situation is not so straightforward. There is
more than one version of the principle formulated with the use of
different variants of Reichenbach-inspired notions; their falsity
still remains an open question. The book traces different
formulations of the principle and provides proofs of a few
pertinent theorems, settling the relevant questions in various
probability spaces. In exploring mathematical and philosophical
issues surrounding the principle, the book offers both
philosophical insight and mathematical rigor.
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