Online research in philosophy

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant to that hypothesis. However, that result depends on a very strong equal relevance condition on individual pieces of evidence. In this essay, we prove tracking results for focused correlation analogous to Wheeler and Scheines’s results but for cases involving unequal relevance. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation.

We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles' angular momenta along axes with different orientations. It is shown that for certain observables, the correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the counterfactual event that plays a prominent role in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.

A philosophical interpretation of quantum mechanics presupposes a clear understanding of what is asserted by this theory. The aim of this paper is to help clarify one specific theorem of quantum mechanics, namely the so-called uncertainty relations. The surprisingly wide spread belief that these relations generally imply a reciprocal or inversely proportional relationship between the respective uncertainties is shown to be mistaken. Several reasons why this mistaken belief has been embraced are suggested. The conditions under which one could say that the uncertainty relations imply an inversely proportional relationship between uncertainties are specified.

We present a rigorous way to evaluate the visual perception of correlation in scatterplots, based on classical psychophysical methods originally developed for simple properties such as brightness. Although scatterplots are graphically complex, the quantity they convey is relatively simple. As such, it may be possible to assess the perception of correlation in a similar way.

Philosophers and scientists have maintained that causation, correlation, and "partial correlation" are essentially related. These views give rise to various rules of causal inference. This essay considers the "claims of several philosophers and social scientists for causal systems with dichotomous variables. In section 2 important commonalities and differences are explicated among four major conceptions of correlation. In section 3 it is argued that whether correlation can serve as a measure of A's causal influence on B depends upon the conception of causation being used and upon certain background assumptions. In section 4 five major kinds of "partial correlation" are explicated, and some of the important relations are established among two conceptions of "partial correlation", the conception of "screening off", the conception of "partitioning", and the measures of causal influence which have been suggested by advocates of path analysis or structural equation methods. In section 5 it is argued that whether any of these five conceptions of "partial correlation" can serve as a measure of causal influence depends upon the conception of causation being used and upon certain background assumptions. The important conclusion is that each of the approaches (considered here) to causal inference for causal systems with dichotomous variables stands in need of important qualifications and revisions if they are to be justified.

Philosophers and scientists have maintained that causation, correlation, and partial correlation are essentially related. These views give rise to various rules of causal inference. This essay considers the claims of several philosophers and social scientists for causal systems with dichotomous variables. In section 2 important commonalities and differences are explicated among four major conceptions of correlation. In section 3 it is argued that whether correlation can serve as a measure of A's causal influence on B depends upon the conception of causation being used and upon certain background assumptions. In section 4 five major kinds of partial correlation are explicated, and some of the important relations are established among two conceptions of partial correlation, the conception of screening off, the conception of partitioning, and the measures of causal influence which have been suggested by advocates of path analysis or structural equation methods. In section 5 it is argued that whether any of these five conceptions of partial correlation can serve as a measure of causal influence depends upon the conception of causation being used and upon certain background assumptions.The important conclusion is that each of the approaches (considered here) to causal inference for causal systems with dichotomous variables stands in need of important qualifications and revisions if they are to be justified.

Uncertainty relations and complementarity of canonically conjugate position and momentum observables in quantum theory are discussed with respect to some general coupling properties of a function and its Fourier transform. The question of joint localization of a particle on bounded position and momentum value sets and the relevance of this question to the interpretation of position-momentum uncertainty relations is surveyed. In particular, it is argued that the Heisenberg interpretation of the uncertainty relations can consistently be carried through in a natural extension of the usual Hilbert space frame of the quantum theory.

A coherent account of the connections and contrasts between the principles of complementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on Mach-Zehnder interferometry. In particular, path detection via entanglement with a probe system and (quantitative) quantum erasure are exhibited to constitute instances of joint unsharp measurements of complementary pairs of physical quantities, path and interference observables. The analysis uses the representation of observables as positive-operator-valued measures (POVMs). The reconciliation of complementary experimental options in the sense of simultaneous unsharp preparations and measurements is expressed in terms of uncertainty relations of different kinds. The feature of complementarity, manifest in the present examples in the mutual exclusivity of path detection and interference observation, is recovered as a limit case from the appropriate uncertainty relation. It is noted that the complementarity and uncertainty principles are neither completely logically independent nor logical consequences of one another. Since entanglement is an instance of the uncertainty of quantum properties (of compound systems), it is moot to play out uncertainty and entanglement against each other as possible mechanisms enforcing complementarity.

This essay presents results about a deviation from independence measure called focused correlation . This measure explicates the formal relationship between probabilistic dependence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield's ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson's claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted. Introduction Correlation Measures 2.1 Standard covariance and correlation measures 2.2 The Wayne–Shogenji measure 2.3 Interpreting correlation measures 2.4 Correlation and evidential independence Focused Correlation Conclusion Appendix CiteULike Connotea Del.icio.us What's this?

Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.