Online research in philosophy

A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common‐cause and it is shown that there exists pairs of correlated events, probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common‐cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition of common‐cause. The significance of the difference between common‐causes and common common‐causes is emphasized from the perspective of Reichenbach's Common Cause Principle.

Russell (1948), Reichenbach (1956), and Salmon (1975, 1979) have argued that a fundamental principle of science and common sense is that "matching" events should not be chalked up to coincidence, but should be explained by postulating a common cause. Reichenbach and Salmon provided this intuitive idea with a probabilistic formulation, which Salmon used to argue for a version of scientific realism. Van Fraassen (1980, 1982) showed that the principle, so construed, runs afoul of certain results in quantum mechanics. In this paper a new formulation of the principle is offered that emerges from its use in evolutionary theory. This characterization identifies fairly general conditions in which postulating common causes will be more explanatory than postulating separate causes.

I consider the problem of extending Reichenbach's principle of the common cause to more than two events, vis-a-vis an example posed by Bernstein. It is argued that the only reasonable extension of Reichenbach's principle stands in conflict with a recent proposal due to Horwich. I also discuss prospects of the principle of the common cause in the light of these and other difficulties known in the literature and argue that a more viable version of the principle is the one provided by Penrose and Percival (1962).

The common cause principle states that correlations have prior common causes which screen off those correlations. I argue that the common cause principle is false in many circumstances, some of which are very general. I then suggest that more restricted versions of the common cause principle might hold, and I prove such a restricted version.

We propose an empirical mode decomposition (EMD-) based method to extract features from the multichannel recordings of local field potential (LFP), collected from the middle temporal (MT) visual cortex in a macaque monkey, for decoding its bistable structure-from-motion (SFM) perception. The feature extraction approach consists of three stages. First, we employ EMD to decompose nonstationary single-trial time series into narrowband components called intrinsic mode functions (IMFs) with time scales dependent on the data. Second, we adopt unsupervised K-means clustering to group the IMFs and residues into several clusters across all trials and channels. Third, we use the supervised common spatial patterns (CSP) approach to design spatial filters for the clustered spatiotemporal signals. We exploit the support vector machine (SVM) classifier on the extracted features to decode the reported perception on a single-trial basis. We demonstrate that the CSP feature of the cluster in the gamma frequency band outperforms the features in other frequency bands and leads to the best decoding performance. We also show that the EMD-based feature extraction can be useful for evoked potential estimation. Our proposed feature extraction approach may have potential for many applications involving nonstationary multivariable time series such as brain-computer interfaces (BCI).

In a recent article, Elliot Sober responds to challenges to a counter-example that he posed some years earlier to the Principle of the Common Cause (PCC). I agree that Sober has indeed produced a genuine counter-example to the PCC, but argue against the methodological moral that Sober wishes to draw from it. Contrary to Sober, I argue that the possibility of exceptions to the PCC does not undermine its status as a central assumption for methods that endeavor to draw causal conclusions from statistical data. 1 The PCC and the counter-example 2 Making non-stationary time series stand still 3 Sober's alternative.

Is the common cause principle merely one of a set of useful heuristics for discovering causal relations, or is it rather a piece of heavy duty metaphysics, capable of grounding the direction of causation itself? Since the principle was introduced in Reichenbach’s groundbreaking work The Direction of Time (1956), there have been a series of attempts to pursue the latter program—to take the probabilistic relationships constitutive of the principle of the common cause and use them to ground the direction of causation. These attempts have not all explicitly appealed to the principle as originally formulated; it has also appeared in the guise of independence conditions, counterfactual overdetermination, and, in the causal modelling literature, as the causal markov condition. In this paper, I identify a set of difficulties for grounding the asymmetry of causation on the principle and its descendents. The first difficulty, concerning what I call the vertical placement of causation, consists of a tension between considerations that drive towards the macroscopic scale, and considerations that drive towards the microscopic scale—the worry is that these considerations cannot both be comfortably accommodated. The second difficulty consists of a novel potential counterexample to the principle based on the familiar Einstein Podolsky Rosen (EPR) correlations in quantum mechanics.

The common cause principle states that common causes produce correlations amongst their effects, but that common effects do not produce correlations amongst their causes. I claim that this principle, as explicated in terms of probabilistic relations, is false in classical statistical mechanics. Indeterminism in the form of stationary Markov processes rather than quantum mechanics is found to be a possible saviour of the principle. In addition I argue that if causation is to be explicated in terms of probabilities, then it should be done in terms of probabilistic relations which are invariant under changes of initial distributions. Such relations can also give rise to an asymmetric cause-effect relationship which always runs forwards in time.

It is still a controversial issue whether Reichenbach’s Principle of the Common Cause (RPCC) is a sound method for causal inference. In fact, the status of the principle has been a subject of intense philosophical debate. An extensive literature has been thus generated both with arguments in favor and against the adequacy of the principle. A remarkable argument against the principle, first proposed by Elliott Sober (Sober, 1987, 2001), consists on a counterexample which involves corelations between bread prices in Britain and sea levels in Venice. The aim of this paper is to put into perspective criticisms to RPCC of the kind of Sober’s in the light of recent formal results regarding the so-called extendability and common cause completability.

When two causally independent processes each have a quantity that increases monotonically (either deterministically or in probabilistic expectation), the two quantities will be correlated, thus providing a counterexample to Reichenbach's principle of the common cause. Several philosophers have denied this, but I argue that their efforts to save the principle are unsuccessful. Still, one salvage attempt does suggest a weaker principle that avoids the initial counterexample. However, even this weakened principle is mistaken, as can be seen by exploring the concepts of homology and homoplasy used in evolutionary biology. I argue that the kernel of truth in the principle of the common cause is to be found by separating metaphysical and epistemological issues; as far as the epistemology is concerned, the Likelihood Principle is central.