Cut-off points for the rational believer

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox

Nuclear astrophysical plasmas: ion distribution functions and fusion rates

This article illustrates how very small deviations from the Maxwellian exponential tail, while leaving unchanged bulk quantities, can yield dramatic effects on fusion reaction rates and discuss several mechanisms that can cause such deviations.Comment: 9 ReVTex pages including 2 color figure

News and expectations in Thermostatistics

Editorial of the International Conference (NEXT 2003): News and expectations in Thermostatistics, Sardinia 21-28 Sept. 200

Search for non-Poissonian behavior in nuclear beta-decay

We performed two independent counting experiments on a beta-emitting source of Sm151 by measuring the gamma-photon emitted in a fraction of the decays. For counting times ranging from 10**-3 to 5.12*10**4 seconds, our measurements show no evidence of deviations from Poissonian behavior and, in particular, no sign of 1/f noise. These measurements put strong limits on non-Poissonian components of the fluctuations for the subset of decays accompanied by gamma, and corresponding limits for the total number of beta-decays. In particular, the magnitude of a hypothetical flicker floor is strongly bounded also for the beta-decay. This result further constrains theories predicting anomalous fluctuations in nuclear decays.Comment: 10 pages, LaTeX, plus 2 figures added as separate uuencoded compressed postscript files. To appear in Phys. Rev. E 55 (1997

From McGee's puzzle to the Lottery Paradox

Vann McGee has presented a putative counterexample to modus ponens. I show that (a slightly modified version of) McGee’s election scenario has the same structure as a famous lottery scenario by Kyburg. More specifically, McGee’s election story can be taken to show that, if the Lockean Thesis holds, rational belief is not closed under classical logic, including classical-logic modus ponens. This conclusion defies the existing accounts of McGee’s puzzle