Convergence to the Truth Without Countable Additivity

Must probabilities be countably additive? On the one hand, arguably, requiring countable additivity is too restrictive. As de Finetti pointed out, there are situations in which it is reasonable to use merely finitely additive probabilities. On the other hand, countable additivity is fruitful. It can be used to prove deep mathematical theorems that do not follow from finite additivity alone. One of the most philosophically important examples of such a result is the Bayesian convergence to the truth theorem, which says that conditional probabilities converge to 1 for true hypotheses and to 0 for false hypotheses. In view of the long-standing debate about countable additivity, it is natural to ask in what circumstances finitely additive theories deliver the same results as the countably additive theory. This paper addresses that question and initiates a systematic study of convergence to the truth in a finitely additive setting. There is also some discussion of how the formal results can be applied to ongoing debates in epistemology and the philosophy of science.

     

Finite additivity,another lottery paradox and conditionalisation

In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no paradox, and that what it shows is that conditionalisation, often claimed to be integral to the Bayesian canon, has to be rejected as a general rule in a finitely additive environment.     

Has Industrialization Benefited No One? Climate Change and the Non-Identity Problem

Within the climate justice debate, the ‘beneficiary pays’ principle holds that those who benefit from greenhouse emissions associated with industrialization ought to pay for the costs of mitigating and adapting to their adverse effects. This principle constitutes a claim of inter-generational justice, and it is widely believed that the non-identity problem raises serious difficulties for any such claim. After briefly sketching the rationale behind ‘beneficiary pays,’ this paper offers a new way of understanding the claim that persons in developed societies have benefited from industrialization. It argues that when we think of the claim in this new way, it evades the non-identity problem entirely. Some objections to this approach are then considered and rebutted. The paper concludes by comparing the present, relatively modest solution to the nonidentity problem with a much more ambitious attempt from the recent literature.     

Ross on sleeping beauty

In two excellent recent papers, Jacob Ross has argued that the standard arguments for the ‘thirder’ answer to the Sleeping Beauty puzzle lead to violations of countable additivity. The problem is that most arguments for that answer generalise in awkward ways when he looks at the whole class of what he calls Sleeping Beauty problems. In this note I develop a new argument for the thirder answer that doesn't generalise in this way.     

Possibility and probability

Conclusion De Finetti was a strong proponent of allowing 0 credal probabilities to be assigned to serious possibilities. I have sought to show that (pace Shimony) strict coherence can be obeyed provided that its scope of applicability is restricted to partitions into states generated by finitely many ultimate payoffs. When countable additivity is obeyed, a restricted version of ISC can be applied to partitions generated by countably many ultimate payoffs. Once this is appreciated, perhaps the compelling character of the Shimony argument will be less overwhelming and the attractiveness of de Finetti's more permissive attitude will become more apparent.I want to push the permissive tendency in de Finetti still further. It seems doubtful that RUIWC should be required as de Finetti apparently suggested. It is also excessively dogmatic and restrictive to require that the credal states of ideally situated rational agents be numerically definite (Levi 1974, 1980). And de Finetti's rejection of objectivism in statistics overreached itself when he dismissed objective probabilities as meaningless metaphysical artefacts (Levi 1986). In this respect, the philosophically most important lessons de Finetti has to teach us are to be found not in his celebrated representation theorem but in his discussions of the relations between 0-probability and possibility, conditional probability and countable additivity. Perhaps, the technical issues involved are remote and pedantic. But the attitude de Finetti sought to inculcate is of profound importance.Thanks are due to Teddy Seidenfeld whose comments have improved this paper substantially. He is not to blame for its lingering defects.     

The Possibility of a Fair Play Account of Legitimacy

The philosophical literature on state legitimacy has recently seen a significant conceptual revision. Several philosophers have argued that the state's right to rule is better characterized not as a claim right to obedience, but as a power right. There have been few attempts to show that traditional justifications for the claim right might also be used to justify a power right, and there have been no such attempts involving the principle of fair play, which is widely regarded as the most promising basis for a claim right to obedience. William Edmundson argues that the principle of fair play cannot generate power rights, and so any attempt at a fair play account of legitimacy must fail. I explain how fair play could generate a power right, owing to its stipulation that the rules of a cooperative scheme specify the form of participants' repayment. 1     

Open-Mindedness as a Critical Virtue

This paper proposes to examine Daniel Cohen’s recent attempt to apply virtues to argumentation theory, with special attention given to his explication of how open-mindedness can be regarded as an argumentational or critical virtue. It is argued that his analysis involves a contentious claim about open-mindedness as an epistemic virtue, which generates a tension for agents who are simultaneously both an arguer and a knower (or who strive to be both). I contend that this tension can be eased or resolved by clarifying the nature of open-mindedness and by construing open-mindedness in terms of its function. Specifically, a willingness to take a novel viewpoint seriously is sufficient for making open-mindedness both an epistemic and a critical virtue.     

Legislation and Non-neutral Principles: A Lockean Approach

When citizens and legislators attempt to justify coercive acts, such as fines or imprisonment, they often do so on the basis of controversial justificatory principles. There are at least two ways a principle can be controversial: one may claim that the principle in question is false; or one may claim that the principle, correctly applied, does not actually justify the specific act in question. Thus, suppose the state invokes the principle 'false beliefs should be censored' to justify silencing a dissident. The dissident might disagree because she thinks the state should not be in the business of censoring false beliefs, or she might agree with the principle but object to the action because she is quite convinced that her beliefs are not false.     

Chinese Religiosity and Chinese Science of Nature

Fung Yu-lan has suggested that Chinese philosophers have been unreceptive to modern science. This suggestion, however, has not been substantiated. This essay is an attempt to provide a justification of Fung＇s assertion through an existential analysis of the Chinese concepts of nature. The essay will examine Chinese existential concerns prevailing in Daoism and Confucianism, and these systems＇ distaste for the type of scientific study which has become prevalent in the modern world. I also intend to defend the claim that the ultimate concern of the Zhuangzi and the Zhongyong is completely contrary to the one that sustains modern science. A brief comparative discussion between Xu Guangqi and Galileo Galilei will be used to support this claim. My discussion will raise the contention that, to have a better understanding of the development of modern science in China, we have to understand the attitude toward religion that has underpinned modern science.     

Judging as a non-voluntary action

Many philosophers categorise judgment as a type of action. On the face of it, this claim is at odds with the seeming fact that judging a certain proposition is not something you can do voluntarily. I argue that we can resolve this tension by recognising a category of non-voluntary action. An action can be non-voluntary without being involuntary. The notion of non-voluntary action is developed by appeal to the claim that judging has truth as a constitutive goal. This claim, when combined with a conception of judging as a way of settling a question, explains both why judging is genuinely agential, and why it is nevertheless non-voluntary.     

SINGER, SOCIOBIOLOGY, AND VALUES: PURE REASON VERSUS EMPIRICAL REASON

Abstract. E. O. Wilson argues that we must use scientifically based reason to solve the values dilemma created by the loss of a transcendent foundation for values. Peter Singer allows that sociobiology can help us understand the evolutionary origin of ethics, but denies the claim that sociobiology or any science can furnish us with ultimate ethical principles. We argue that Singer's critique of Wilson's attempt to bridge the gap between fact and value using empirical reason is unconvincing and that Singer's own ethical principle of disinterestedness requires major support from empirical reason and is not sustainable by pure reason alone.     

Constraints on computational models of basic processes in reading

There are numerous reports in the visual word recognition literature that the joint effects of various factors are additive on reaction time. A central claim by D. C. Plaut and J. R. Booth (2000, 2006) is that their parallel distributed processing model simulates additive effects of stimulus quality and word frequency in the context of lexical decision. If correct, this success would have important implications for computational accounts of reading processes. However, the results of further simulations with this model undermine this claim given that the joint effects of stimulus quality and word frequency yield a nonmonotonic function (underadditivity, additivity, and overadditivity) depending on the size of the stimulus quality effect, whereas skilled readers yield additivity more broadly. The implications of these results both locally and more globally are discussed, and a number of other issues are noted. Additivity of factor effects constitutes a benchmark that computational accounts should strive to meet.     

On Aesthetic Judgement and our Relation to Nature: Kant's Concept of Purposiveness

I offer a critical reconstruction of Kant's thesis that aesthetic judgement is founded on the principle of the purposiveness of nature. This has been taken as equivalent to the claim that aesthetics is directly linked to the systematicity of nature in its empirical laws. I take issue both with Henry Allison, who seeks to marginalize this claim, and with Avner Baz, who highlights it in order to argue that Kant's aesthetics are merely instrumental for his epistemology. My solution is that aesthetic judgement operates as an exemplary presentation of our general ability to schematise an intuition with a concept at the empirical level. I suggest that this counts as an empirical schematism. Although aesthetic judgement is not based on empirical systematicity, it can nevertheless offer indirect support for the latter in so far as it is a particular revelation of purposiveness in general.     

Dead People and the All-Affected Principle

Discussions of the all-affected principle as a solution to the boundary problem – how do we specify the group making democratic decisions? – have focused extensively on future people. We have yet to focus on dead people, however. This article tries to bridge this gap by arguing that the all-affected principle – i.e. the all actually affected interests principle – entails inclusion of dead people. This is true because dead people can be harmed or legally affected, and this is sufficient for having a claim to democratic inclusion. The last part of the article discusses where this leaves the all-affected principle in the quest for the proper boundary principle, including a discussion of possible institutional solutions to the enfranchisement of dead people.     

Contractualism,Person-Affecting Wrongness and the Non-identity Problem

A number of theorists have argued that Scanlon's contractualist theory both "gets around" and "solves" the non-identity problem. They argue that it gets around the problem because hypothetical deliberation on general moral principles excludes the considerations that lead to the problem. They argue that it solves the problem because violating a contractualist moral principle in one's treatment of another wrongs that particular other, grounding a person-affecting moral claim. In this paper, I agree with the first claim but note that all it shows is that the act is impersonally wrong. I then dispute the second claim. On Scanlon's contractualist view, one wrongs a particular other if one treats the other in a way that is unjustifiable to that other on reasons she could not reasonably reject. We should think of person-affecting wronging in terms of the reasons had by the actual agent and the actual person affected by the agent's action. In non-identity cases, interpersonal justifiability is therefore shaped both by the reason to reject the treatment provided by the bad suffered and the reason to affirm the treatment provided by the goods had as a result of existing. I argue it would be reasonable for the actual person to find the treatment justifiable, and so I conclude that Scanlon's contractualist metaethics does not provide a narrow person-affecting solution to the non-identity problem on its own terms. I conclude that the two claims represent a tension within Scanlon's contractualist theory itself.     

Slow magic: psychoanalysis and "the disenchantment of the world"

Freud's work can be situated in terms of the debate between Enlightenment and anti-Enlightenment thought. The attempts of both sides to claim Freud for their position have merit, but they miss the crucial point: namely, that the tension between its Enlightenment and anti-Enlightenment tendencies is what gives Freud's thinking much of its vitality and depth. The task that faces the interpreter is therefore to elucidate that tension and assess the alignment of forces between the two strands in his thought. An examination of the concept of magic in Freud's theory provides an opportunity to pursue this interpretive task. Although the Enlightenment position he often seems to embrace advocates the complete elimination of magic, many "magical" elements remain in his theory and clinical practice. Nor should this situation be deplored, for the ambition to completely exorcise "enchantment" from human experience is one of the misguided excesses of the Enlightenment. The question of an appropriate fate for magic in psychoanalysis is discussed in relation to the vicissitudes of the transference. Finally, the science versus hermenueutics debate is examined in the light of these considerations in an attempt to specify the unique nature of the psychoanalytic experience.     

Common-Sense Virtue Ethics and Moral Luck

Moral luck poses a problem for out conception of responsibility because it highlights a tension between morality and lack of control. Michael Slote’s common-sense virtue ethics claims to avoid this problem. However there are a number of objections to this claim. Firstly, it is not clear that Slote fully appreciates the problem posed by moral luck. Secondly, Slote’s move from the moral to the ethical is problematic. Thirdly it is not clear why we should want to abandon judgements of moral blame in favour of judgements of ethical deplorability. Finally this paper defends an alternative solution to the problem of moral luck, which focuses on judgements of probability, but which has been rejected by Slote.     

The Special Science Dilemma and How Culture Solves It

I argue that there is a tension between the claim that at least some kinds in the special sciences are multiply realized and the claim that the reason why kinds are prized by science is that they enter into a variety of different empirical generalizations. Nevertheless, I show that this tension ceases in the case of ‘cultural homologues’—such as specific ideologies, religions, and folk wisdom. I argue that the instances of such special science kinds do have several projectable properties in common due to their shared history of reproduction, and that the social learning involved means that we should also expect these kinds to be multiply realized.