Neufeld and Goodwin on the Lottery Paradox

Eric Neufeld and Scott Goodwin’s article on the Lottery Paradox and the Paradox of the Preface appearing in Computational Intelligence 14(3), 1998, is an overlooked gem. The paper offers a rebuttal to Pollock’s distinction between the lottery from the preface by citing lotteries, such as the Canadian 6-49, whose structure is similar to the preface. Neufeld and Goodwin’s discussion is an important contribution to the body of commentary that is critical of tailor-made solutions designed to fit the particulars of each paradox.


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Neufeld and Goodwin on the Lottery Paradox — 1 Comment

  1. There must be some interesting reason why the Lottery does not have a consistent representation in 1st-order quantificational (with belief). Maybe the logics of belief in general preclude it, but these seem perfectly consistent.

    (1) I believe every ticket will not win
    (Vx) I believe x does not win
    (2) I believe some ticket (or other) will win
    I believe (Ex) x will win.

    It is similar to representing the belief about each particular person that he is not the shortest person in the room and believing that someone or other is the shortest person in the room.

    (1′) (Vx) I believe x is not such that no one is shorter.

    Certainly, having met everyone in the room, there might be for each person I met another person that appeared to me shorter. Still I realize that someone or other is shortest.

    (2′) I believe (Ex) x is such that no one is shorter.

    Maybe there is some reason why the beliefs in (1) and (1′) should entail respectively (1a) and (1a’).

    (1a) I believe (Vx) x does not win.
    (1a’) I believe (Vx) x is not such that no one is shorter.

    These beliefs would cause a problem. But I can’t think of any reason why anyone in the Lottery would have the belief in (1a) (or, in the other case, (1a’)).

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