A Model of Tolerance

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non-existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity of the consequence relation. A lattice-theoretical framework for a whole family of (zeroth-order) “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic.     

Bayes factors: Prior sensitivity and model generalizability

Model selection is a central issue in mathematical psychology. One useful criterion for model selection is generalizability; that is, the chosen model should yield the best predictions for future data. Some researchers in psychology have proposed that the Bayes factor can be used for assessing model generalizability. An alternative method, known as the generalization criterion, has also been proposed for the same purpose. We argue that these two methods address different levels of model generalizability (local and global), and will often produce divergent conclusions. We illustrate this divergence by applying the Bayes factor and the generalization criterion to a comparison of retention functions. The application of alternative model selection criteria will also be demonstrated within the framework of model generalizability.     

A Process Interpretation of Daoist Thought

Despite the fact that the Dao De Jing道德經 is one of the mos frequently translated texts in history,most of these translations share certain unexamined and problematic assumptions which often make it seem as though the text is irrational,incoherent,and full of non sequiturs.Frequently,these assumptions involve the imposition of historically anachronous,linguistically unsound,and philosophically problematic categories and attitudes onto the text.One of the main causes of the problem is the persistent tendency on the part of most translators to read the first line of the text as referring to or implying the existence of some kind of "eternal Dao." These are what I term "ontological "readings,as opposed to the "process" reading I will be articulating here.     

Sub-Optimal Choice by Pigeons: Failure to Support The Allais Paradox

Pigeons show a preference for an alternative that provides them with discriminative stimuli (sometimes a stimulus that predicts reinforcement and at other times a stimulus that predicts the absence of reinforcement) over an alternative that provides them with nondiscriminative stimuli, even if the nondiscriminative stimulus alternative is associated with 2.5 times as much reinforcement (Stagner & Zentall, 2010). In Experiment 1 we found that the delay to reinforcement associated with the nondiscriminative stimuli could be reduced by almost one half before the pigeons were indifferent between the two alternatives. In Experiment 2 we tested the hypothesis that the preference for the discriminative stimulus alternative resulted from the fact that, like humans, the pigeons were attracted by the stimulus that consistently predicted reinforcement (the Allais paradox). When the probability of reinforcement associated with the discriminative stimulus that predicted reinforcement was reduced from 100% to 80% the pigeons still showed a strong preference for the discriminative stimulus alternative. Thus, under these conditions, the Allais paradox cannot account for the sub-optimal choice behavior shown by pigeons. Instead we propose that sub-optimal choice results from positive contrast between the low expectation of reinforcement associated with the discriminative stimulus alternative and the much higher obtained reinforcement when the stimulus associated with reinforcement appears. We propose that similar processes can account for sub-optimal gambling behavior by humans.     

Philosophy for Computers: Some Explorations in Philosophical Modeling

Philosophical modeling has a long and distinguished history, but the computer offers new and powerful prospects for the creation and manipulation of models. It seems inevitable that the computer will become a major tool in future philosophical research. Here I offer an overview of explorations in philosophical computer modeling that we in the Group for Logic and Formal Semantics at SUNY Stony Brook have undertaken: explorations regarding (1) the potential emergence of cooperation in a society of egoists, (2) self-reference and paradox in fuzzy logic, (3) a fractal approach to formal systems, and (4) on-going explorations with models for the emergence of communication. The attempt is not to give a detailed report on any of these but to give a bird s-eye view of them all, emphasizing the general form that the models take, the philosophical motivations behind them, and the kinds of philosophical results that they may have to offer.     

Probabilistic Cause and the Thirsty Traveler

In this paper I start by briefly presenting an analysis of token cause and of token causal relevance that I developed elsewhere, and then apply it to the famous thirsty traveler riddle. One general outcome of the analysis of causal relevance employed here is that in preemption cases (early or late) the preempted cause is not a cause since it is causally irrelevant to the effect. I consider several variations of the thirsty traveler riddle. In the first variation the first enemy emptied the canteen and the second enemy threw it away. On this variation, the act of neither enemy comes out, on the analysis employed here, as causally relevant to, and thus not as a cause of, the fact that the traveler died, but the conjunction of the two acts is a cause of it. This version is a case of mutual preemption. I argue that it has the same structure as the voting paradox, which thus has an analogous solution. In the standard version, in which the first enemy added poison to the water in the traveler's canteen, the act of the second enemy (who threw the canteen away) comes out, on the analysis used here, as causally relevant to and as a cause of the fact that the traveler died, but the act of the first enemy comes out as neither. I also make a comparison with Lewis' accounts, and discuss alternative treatments of the puzzle such as those of Hart and Honore and of Gavison, Margalit, and Ullmann-Margalit.     

The Train Paradox

When two omnipotent beings are randomly and sequentially selecting positive integers, the being who selects second is almost certain to select a larger number. I then use the relativity of simultaneity to create a paradox by having omnipotent beings select positive integers in different orders for different observers.

归纳接受与知识

归纳推理的结论进入知识集合的时候有一个“跳跃”的过程。根据什么规则接受归纳结论是归纳逻辑研究中的一个重要问题。概率接受规则与知识集合应当满足的一致性条件和演绎封闭条件之间存在着不协调,这种不协调性导致了抽彩悖论。该文介绍有代表性的归纳接受理论,指出归纳接受问题对归纳逻辑发展的影响。     

Logical, Semantic and Cultural Paradoxes

The property common to three kinds of paradoxes (logical, semantic, and cultural) is the underlying presence of an exclusive disjunction: even when it is put to a check by the paradox, it is still invoked at the level of implicit discourse. Hence the argumentative strength of paradoxical propositions is derived. Logical paradoxes (insolubilia) always involve two contradictory, mutually exclusive, truths. One truth is always perceived to the detriment of the other, in accordance with a succession which is endlessly repetitive. A check is put on the principle of the excluded middle by the logical paradoxes, because self-reference leads to an endlessly repeating circle, out of which no resolution is conceivable. Logical paradoxes are to be compared with the `objective ambiguity' prevalent in oracles (Gallet, 1990). Semantic paradoxes are contextually-determined occurrences, whose resolution at the metalinguistic level is made possible by the discovery of a middle term. They express a wilful ambiguity, in which the interlocutor is invited to take an active part in the construction of sense, since what must be found is the unexpected sense thanks to which A and not-A can be asserted simultaneously. Cultural paradoxes play about doxa (`common sense') and openly challenge common opinion because of their character as inopinata (`unexpected'). My aim is to show that even cultural paradoxes hide sometimes a flaw of argumentation similar to logical or semantic paradox; they too imply an exclusive disjunction leading to the disappearance of the middle terms. Finally, basing myself on the theory of topoi (Anscombre and Ducrot, 1983), a tentative resolution of the cultural paradoxes will be suggested.     

Belief,Credence, and the Preface Paradox

Many discussions of the ‘preface paradox’ assume that it is more troubling for deductive closure constraints on rational belief if outright belief is reducible to credence. I show that this is an error: we can generate the problem without assuming such reducibility. All that we need are some very weak normative assumptions about rational relationships between belief and credence. The only view that escapes my way of formulating the problem for the deductive closure constraint is in fact itself a reductive view: namely, the view that outright belief is credence 1. However, I argue that this view is unsustainable. Moreover, my version of the problem turns on no particular theory of evidence or evidential probability, and so cannot be avoided by adopting some revisionary such theory. In sum, deductive closure is in more serious, and more general, trouble than some have thought.