Lina Maria Lissia

McGee notably provided a putative counterexample to Modus Ponens. McGee’s puzzle is based on a scenario involving three candidates running for president in the 1980 United States elections. We will present a slightly modified version of McGee’s election scenario, in which the probability of one of the candidates (i.e., Ronald Reagan) winning is reduced to a conveniently low value. As we will see, two ways out of the puzzle, suggested by Fulda and Paoli respectively, do not survive this minor change in the scenario. In addition, we will point to the fact that our modified election scenario also gives rise to a lottery-style paradox.

This paper examines the relations between stubbornness and weakness of will, adopting Holton’s definition of weakness of will as an over-readiness to revise one’s resolutions. It posits that both stubbornness and weakness of will are responses to pessimism – the negative perception of a task or its outcome. Contrary to naive judgement, stubbornness is not merely the opposite of weakness; rather, it serves as a preventive behaviour stemming from a fear of weakness of will. Weakness of will and stubbornness can be viewed as two facets of the same phenomenon, both influenced by pessimism. The paper explores the implications of this unified account, particularly at the therapeutic level, suggesting that enhancing self and other trust could reduce both weak and stubborn behaviours.

This paper generalizes the preface paradox beyond the conjunctive aggregation of beliefs and constructs an analogous paradox for deontic reasoning. The analysis of the deontic case suggests a systematic restriction of intuitive rules for reasoning with obligations. This proposal can be transferred to the epistemic case: it avoids the preface and the lottery paradox and saves one of the two directions of the Lockean Thesis (i.e., high credence is sufficient, but not necessary for rational belief). The resulting account compares favorably to competing proposals; in particular, we can formulate the rules of correct doxastic reasoning without reference to probabilistic features of the involved propositions.

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.