While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti's central argument against countable additivity and provide a new Dutch book proof of the principle, To argue that if we accept the Dutch book foundations of subjective probability, countable additivity is an unavoidable constraint.

Many philosophers hold that whether an act is overall morally obligatory is an ‘objective’ matter, many that it is a ‘subjective’ matter, and some that it is both. The idea that it is or can be both may seem to promise a helpful answer to the question ‘What ought I to do when I do not know what I ought to do?’ In this article, three broad views are distinguished regarding what it is that obligation essentially concerns: the maximization of (...) actual value, the maximization of expected value, and the perceived maximization of actual value. The first and third views are rejected; the second view is then refined and defended. The unfortunate upshot is that there may be no very helpful answer to the question just mentioned. As to the question posed in the title of the article, the answer unsurprisingly depends on what ‘objective’ and ‘subjective’ are taken to mean. (Published Online November 24 2006). (shrink)

One resolution of the St. Petersburg paradox recognizes that a gamble carries a risk sensitive to the gamble's stakes. If aversion to risk increases sufficiently fast as stakes go up, the St. Petersburg gamble has a finite utility.

In Pascal's Wager: A Study Of Practical Reasoning In Philosophical Theology ,[1] Nicholas Rescher aims to show that, contrary to received philosophical opinion, Pascal's Wager argument is "the vehicle of a fruitful and valuable insight--one which not only represents a milestone in the development of an historically important tradition of thought but can still be seen as making an instructive contribution to philosophical theology".[2] In particular, Rescher argues that one only needs to adopt a correct perspective in order to see (...) that Pascal's Wager argument is a good argument. Moreover, there seems to be a certain amount of contemporary support for Rescher's claim that Pascal's Wager argument can be seen to be a good argument when properly construed .[3] However, despite this recent trend to adopt a more sympathetic stance towards Pascal's Wager argument, I propose to defend the traditional view that Pascal's Wager argument is almost entirely worthless--at least from the theological standpoint. (No doubt, it has historical significance from the standpoint of decision theory; but that's a separate matter.). (shrink)

Can Pascal's wager for the existence of God be turned against the religious believer and used as an argument for not believing in God? Although such an argument has been very briefly sketched by others its details have remained undeveloped. In this paper this argument is worked out in detail in the context of decision theory and is defended against objections. The result is a plausible argument for atheism.

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

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The central thesis of Spinoza’s Theological-Political Treatise is that the state not only can permit freedom of philosophizing without endangering piety or the public peace, but that it must do so if it is not to destroy piety and the public peace. Spinoza’s argument is not limited to religious toleration, but is an argument for freedom of philosophizing generally. Nevertheless, freedom of philosophizing in religion is the central case. In making such an argument, he contributed greatly toward the transformation of (...) Western culture with respect to toleration and religious liberty. As an historian, I want to understand how this transformation came about and what role Spinoza played in it. As a philosopher, I also want to know whether any of the arguments philosophers made in favor of religious toleration deserved to be effective in bringing about this transformation. (shrink)

000000001. Introduction Call a theory of the good—be it moral or prudential—aggregative just in case (1) it recognizes local (or location-relative) goodness, and (2) the goodness of states of affairs is based on some aggregation of local goodness. The locations for local goodness might be points or regions in time, space, or space-time; or they might be people, or states of nature.1 Any method of aggregation is allowed: totaling, averaging, measuring the equality of the distribution, measuring the minimum, etc.. Call (...) a theory of the good finitely additive just in case it is aggregative, and for any finite set of locations it aggregates by adding together the goodness at those locations. Standard versions of total utilitarianism typically invoke finitely additive value theories (with people as locations). A puzzle can arise when finitely additive value theories are applied to cases involving an infinite number of locations (people, times, etc.). Suppose, for example, that temporal locations are the locus of value, and that time is discrete, and has no beginning or end.2 How would a finitely additive theory (e.g., a temporal version of total utilitarianism) judge the following two worlds? Goodness at Locations (e.g. times) w1:..., 2, 2, 2, 2, 2, 2, 2, 2, 2, ..... w2:..., 1, 1, 1, 1, 1, 1, 1, 1, 1, ..... Example 1 At each time w1 contains 2 units of goodness and w2 contains only 1. Intuitively, we claim, if the locations are the same in each world, finitely additive theorists will want to claim that w1 is better than w2. But it's not clear how they could coherently hold this view. For using standard mathematics the sum of each is the same infinity, and so there seems to be no basis for claiming that one is better than the other.3 (Appealing to Cantorian infinities is of no help here, since for any Cantorian infinite N, 2xN=1xN.). (shrink)

Traditional utilitarianism, when applied, implies a surprising prediction about the future, viz., that all experience of pleasure and pain must end once and for all, or infinitely dwindle. Not only is this implication surprising, it should render utilitarianism unacceptable to persons who hold any of the following theses: that evaluative propositions may not imply descriptive, factual propositions; that evaluative propositions may not imply contingent factual propositions about the future; that there will always exist beings who experience pleasure or pain.