Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

Monotonicity in Practical Reasoning

Classic deductive logic entails that once a conclusion is sustained by a valid argument, the argument can never be invalidated, no matter how many new premises are added. This derived property of deductive reasoning is known as monotonicity. Monotonicity is thought to conflict with the defeasibility of reasoning in natural language, where the discovery of new information often leads us to reject conclusions that we once accepted. This perceived failure of monotonic reasoning to observe the defeasibility of natural-language arguments has led some philosophers to abandon deduction itself (!), often in favor of new, non-monotonic systems of inference known as `default logics'. But these radical logics (e.g., Ray Reiter's default logic) introduce their desired defeasibility at the expense of other, equally important intuitions about natural-language reasoning. And, as a matter of fact, if we recognize that monotonicity is a property of the form of a deductive argument and not its content (i.e., the claims in the premise(s) and conclusion), we can see how the common-sense notion of defeasibility can actually be captured by a purely deductive system.     

Monotonicity and Reasoning with Exceptions

A proposal by Ferguson [2003, Argumentation 17, 335–346] for a fully monotonic argument form allowing for the expression of defeasible generalizations is critically examined and rejected as a general solution. It is argued that (i) his proposal reaches less than the default-logician’s solution allows, e.g., the monotonously derived conclusion is one-sided and itself not defeasible. (ii) when applied to a suitable example, his proposal derives the wrong conclusion. Unsuccessful remedies are discussed.     

Defending Particularism

In this brief response I argue that Sinnott-Armstrong has underestimated the complexities that moral principles will have to circumvent if they are to survive particularist criticism. I also argue that we cannot yet accept Gert's accounts of moral relevance and of how a sound moral rule can survive exceptions.     

Kant's arguments in support of the maxim “Do what is right though the world should perish”

This article takes up the challenge that the motto Do What is Right Though the World Should Perish invites for an answer to Kant's arguments in defense of the motto. His argumentation is discussed, as well as the underlying assumptions concerning the role of Providence, the rejection of moral conflict, and the prudential risks associated with abandoning moral absolutism. The first two are rejected, the third seen as only partially tenable. Finally, the question is taken up what to do about moral prohibitions in a world in which they can quite literally prevent or bring about universal perishing.     

A fallacious argument against moral absolutes

The denial of moral absolutes rests, I think, on a seductive but fallacious argument, which I shall attempt both to expound and to refute here. Human beings are highly complex creatures living in a highly complex world. Every human being is different from every other, every interaction or relationship between or among human beings is unique. Hence also every occasion for moral choice is also unique, and all those action kinds - be theyadultery, murder, rape, theft, ortorture on which moralists are accustomed to pass judgment include an enormous variety of differing transactions, which ideally ought to be evaluated one by one. Moreover, each proposed action has a variety of different aspects: intention, foreseen consequence, conventional meaning, and symbolic significance for example, which bear on moral choice in a wide variety of ways. Moral rules are therefore rules of thumb, open to exceptions whenever persuasive arguments for making them are provided.     

急诊医疗中的知情同意问题

急诊医疗中的知情同意似乎与通常的临床情形不同,它不需要完全的知情同意,甚至可以被免除。这一特点可能给人以一种印象,即在急诊情况下对知情同意的考量,或可与其他情形有所不同。其实急诊情形下之所以出现知情同意的例外或免除,并非知情同意原则在急诊情况下不适用,或者是知情同意原则做出了让步。真正的原因是,知情同意在急诊治疗中往往以特殊或不同的形式表现出来。     

Protecting Privacy and Confidentiality

Summary

This article discusses the confidentiality of communications between therapist and patient and the scope of, and exceptions to, the privilege preventing such communications from being disclosed. Ethical principles, statutes, and case law will be explored.