Backwards Causation
(Apropos the post over at Fake Barn Country).
The most popular way to attempt to analyse the asymmetry of causation without stipulating that it goes with the direction of time is by using the principle of the common cause, a probabilistic relation the formulation of which is due to Hans Reichenbach in his The Direction of Time. Regularity theories, law-based theories (which really should be grouped with the former, since they were mainly a development of Humean ideas), and most obviously probabilistic theories (which you left of your list) have all attempted to use this to contingently ground the direction of causation. The other popular recent approach is to appeal to the second law of thermodynamics in one way or another, since this is the only time-symmetric law that looks even remotely plausible as a candidate (this is what Doug K would have talked about, I assume; Reichenbach thought the second law of thermodynamics explained the common cause principle, incidentally). Lewis of course thought that an asymmetry of counterfactual overdetermination could ground the direction of causation, but his account doesn’t work (see Pruss, 2003). I happen to think the common cause principle can’t be made to work either, reasons for which will with luck appear in a paper of mine possibly forthcoming in Minds and Machines. I also think that backwards causation models of quantum mechanics can’t be made to work, since all of the versions I know of either do not avoid the bilking argument (Black, 1956; classic treatment by Dummett, 1964; cf. 2003, p. 49), or do not furnish a relationship amenable in principle for the purposes of manipulation (what I take to be the litmus test for a causal relationship; see Woodward, 2003). I have a paper arguing this I can send to anyone interested; a reasonably loose survey of this whole industry is in my “Explaining Causal Asymmetry” available from here. Anyone interested in backwards causation models of quantum mechanics should keep an eye on the Centre for Time webpage, where I’ll be constructing a comprehensive annotate-able bibliography of materials relating to that topic later this year.
References
Black, Max. 1956. “Why Cannot an Effect Precede its Cause”, in Analysis, Vol. 16, January 1956, pp. 49-58.
Dummett, Michael. 1964. “Bringing About The Past”, in Philosophical Review, Vol. 73, No. 3, July 1964, pp. 338-359.
Dummett, Michael. 2003. “Truth and the Past, The Dewey Lectures 2002, Lecture III: The Metaphysics of Time”, in The Journal of Philosophy, Vol. 100, No 1, January 2003, pp. 38-53.
Pruss, Alexander R. 2003. “David Lewis’s Counterfactual Arrow of Time”, in Nous, Vol. 37, Iss. 4, December 2003, pp. 606-637.
Woodward, James. 2003. Making Things Happen: A Theory of Causal Explanation, Oxford University Press, New York, 2003.