Assessing the Status of the Common Cause Principle

Rédei, Miklós

doi:10.1007/978-3-319-04382-1_29

Cited by 3 publications

(3 citation statements)

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“…The difficulty in giving a definite answer to this question is that the Common Cause Principle has metaphysical character: it is a strictly universal claim containing two general existential statements. Standard arguments well known from the history of philosophy show that such general claims can be neither verified nor falsified conclusively; thus, as it was argued in [10] (Chapters 1 and 10) and [17], the only option one has when it comes to the problem of assessing the epistemic status of the principle is to have a look at the best available evidence relevant for the principle and see whether they are in harmony with the principle or not. Such evidence is provided by the empirical sciences.…”

Section: Common Cause Completability and The Common Cause Principlementioning

confidence: 99%

“…A possible (and very natural [10] (Chapters 1 and 10), [17]) line of reasoning aimed at assessing the Common Cause Principle in this spirit is the following: Suppose a theory T applies a non-classical probability theory (L, φ) to describe phenomena and predicts correlation between elements a, b in L such that, according to T , there is no (cannot be) a direct causal connection between a and b. The first question one would want to ask then: Is there a common cause c in L of the correlation between a and b?…”

Section: Common Cause Completability and The Common Cause Principlementioning

confidence: 99%

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Common cause completability of non classical probability spaces

Gyenis¹,

Rédei²

2016

Belgr Philosop Ann

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We prove that under some technical assumptions on a general, non-classical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause Principle against certain attempts of falsification. Some open problems concerning possible strengthening of the common cause completability result are formulated. Main resultIn this paper we prove a new result on the problem of common cause completability of non-classical probability spaces. A non-classical (also called: general) probability space is a pair (L, φ), where L is an orthocomplemented, orthomodular, non-distributive lattice and φ : L → [0, 1] is a countably additive probability measure. Taking L to be a distributive lattice (Boolean algebra), one recovers classical probability theory; taking L to be the projection lattice of a von Neumann algebra, one obtains quantum probability theory. A general probability space (L, φ) is called common cause completable if it can be embedded into a larger general probability space which is common cause complete (closed) in the sense of containing a common cause of every correlation in it. Our main result (Proposition 4.2.3) states that under some technical conditions on the lattice L a general probability space (L, φ) is common cause completable. This result utilizes earlier results on common cause closedness of general probability theories ( The main conceptual-philosophical significance of the common cause extendability result proved in this paper is that it allows one to deflect the arrow of falsification directed against the Common Cause Principle for a very large and abstract class of probability theories. This will be discussed in section 5 in the more general context of how one can assess the status of the Common Cause Principle, viewed as a general metaphysical claim about the causal structure of the world. Further sections of the paper are organized as follows: Section 2 fixes some notation and recalls some facts from lattice theory and general probability spaces needed to formulate the main result. Section 3

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Section: Common Cause Completability and The Common Cause Principlementioning

confidence: 99%

Section: Common Cause Completability and The Common Cause Principlementioning

confidence: 99%

Common cause completability of non classical probability spaces

Gyenis¹,

Rédei²

2016

Belgr Philosop Ann

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“…Thus, rather than trying to verify or falsify the Common Cause Principle, one should settle on a more modest goal: to look at our best, confirmed scientific theories to see whether they offer evidence in favor or against the truth of the Common Cause Principle (for a more detailed discussions of this point see [11][Chapter 10] and [22]). It is in connection with such an evaluation of the Common Cause Principle that common cause closedness becomes relevant: If a probabilistic theory is such that the probability theory it employs to describe phenomena is common cause closed then that theory is a strong candidate for being a confirming evidence in favor of the Common Cause Principle.…”

Section: Common Cause Closedness and The Common Cause Principlementioning

confidence: 99%

Characterizing common cause closedness of quantum probability theories

Kitajima

Rédei

2015

Studies in History and Philosophy of Science Part B: Studies in

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This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.Characterizing common cause closedness of quantum probability theories AbstractWe prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a non-commutative von Neumann algebra together with a countably additive probability measure on the lattice. Common cause closedness is the feature that for every correlation between a pair of commuting projections there exists in the lattice a third projection commuting with both of the correlated projections and which is a Reichenbachian common cause of the correlation. The main result we prove is that a quantum probability space is common cause closed if and only if it has at most one measure theoretic atom. This result improves earlier ones published in [1]. The result is discussed from the perspective of status of the Common Cause Principle. Open problems on common cause closedness of general probability spaces (L, ϕ) are formulated, where L is an orthomodular bounded lattice and ϕ is a probability measure on L.

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Characterizing common cause closedness of quantum probability theories

Kitajima

Rédei

2015

Preprint

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Assessing the Status of the Common Cause Principle

Cited by 3 publications

References 28 publications

Common cause completability of non classical probability spaces

Common cause completability of non classical probability spaces

Characterizing common cause closedness of quantum probability theories

Characterizing common cause closedness of quantum probability theories

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