When can statistical theories be causally closed?

The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbach's Common Cause Principle (RCCP)

Maxwell and the normal distribution: A colored story of probability, independence, and tendency toward equilibrium

In the first part of the paper we investigate Maxwell’s attempt to justify the mathematical assumptions behind his 1860 Proposition IV according to which the velocity components of colliding particles follow the normal distribution. Contrary to the com- monly held view we find that his molecular collision model plays a crucial role in reaching this conclusion, and that his model assumptions also permit inference to a non-reversible equalization of mean kinetic energies, which is what he intended to prove in his widely discredited Proposition VI. If we take a charitable reading of his own proof or Proposition VI then it was Maxwell, and not Boltzmann, who gave the first proof of a tendency towards equilibrium. In the second half of the paper we add a further, not yet investigated, piece to the historical and intellectual puzzle surrounding his derivation. We argue that Maxwell’s prior and contemporaneous work on color vision provided him familiarity with and sensitivity to application of statistical reasoning in physics. This includes an encounter with distributions outside the context of error theory. We also call attention to a notion of independence of variables employed in his works on color vision that might have impacted the mistake he made in his proof of Proposition IV

Determinizmus és interpretáció

We argue that the truth of determinism is not an interpretation-free fact and we systematically overview relevant interpretational choices that are less known in the philosophical literature. After bypassing the well known interpretational problem that arises in quantum mechanics we identify three further questions about the representational role of the mathematical structures employed by physical theories. Finally we point out that even if we settle all representational issues the received view of physical possibility may also allow the truth of determinism to depend on prior philosophical convictions, notably on one's philosophical account of the nature of laws

Determinism, Physical Possibility, and Laws of Nature

We call attention to different formulations of how physical laws relate to what is physically possible in the philosophical literature, and argue that it may be the case that determinism fails under one formulation but reigns under the other. Whether this is so depends on our view on the nature of laws, and may also depend on the inter-theoretical relationships among our best physical theories, or so shall we argue

Reichenbachi közös-ok zárt rendszerek

Az ok, okozat, okság háromság mindig is sokat foglalkoztatta a filozófiát; amilyen nagy tisztelettel magasztalták egyesek, olyan mély lenézéssel illették mások. A küzdelem nem csak a "véget nem érő viták harcterén", hanem a tudományok porondján is zajlott, s a felmerülő kérdések megoldatlansága miatt a porfelhők még ma sem ültek el. Hova soroljuk az okozatiság fogalmát? Episztemológiai, netán ontológiai kategória? Milyen kapcsolatban áll a szükségszerűség, determináció, törvényszerűség, elv, stb. terminusokkal? Milyen szerepet játszik az okság elve a tudományban

Maxwell and the normal distribution : A colored story of probability, independence, and tendency toward equilibrium

We investigate Maxwell's attempt to justify the mathematical assumptions behind his 1860 Proposition IV according to which the velocity components of colliding particles follow the normal distribution. Contrary to the commonly held view we find that his molecular collision model plays a crucial role in reaching this conclusion, and that his model assumptions also permit inference to equalization of mean kinetic energies (temperatures), which is what he intended to prove in his discredited and widely ignored Proposition VI. If we take a charitable reading of his own proof of Proposition VI then it was Maxwell, and not Boltzmann, who gave the first proof of a tendency towards equilibrium, a sort of H-theorem. We also call attention to a potential conflation of notions of probabilistic and value independence in relevant prior works of his contemporaries and of his own, and argue that this conflation might have impacted his adoption of the suspect independence assumption of Proposition IV

Korrelációk kauzális magyarázata

Nincs korreláció kauzalitás nélkül – így hangzik tömören az a metafizikai elv, amelyre a tudományfilozófiában Reichenbach közös ok elve ként szokás hivatkozni. Kevésbé tömören fogalmazva a közös ok elve azt állítja, hogy a világban fel- mutatható bármely korreláció vagy a korreláló események közötti közvetlen kauzális kapcsolatból eredeztethető, vagy egy harmadik eseményre, a korrelá- ló események úgynevezett közös okára vezethető vissza. Az alábbiakban arról a mintegy tizenöt évet átfogó munkáról szeretnénk rövid áttekintést nyújtani, amelyet e tanulmány szerzői a reichenbachi közös ok elv, vagyis a korrelációk kauzális magyarázatának tanulmányozása terén folytattak