Something amazing about the Peripatetic of Pallet: Abaelard's development of Boethius' account of conditional propositions

Mediaeval logicians inherited from Boethius an account of conditional propositions and the syllogisms which may be constructed using them. In the following paper it is shown that there are considerable difficulties with Boethius' account which arise from his failure to understand the nature of compound propositions and in particular to provide for their negation. Boethius suggests that there are two different conditions which may be imposed for the truth of a conditional proposition but he really gives no adequate account of how such propositions may be obtained. The true greatness of Peter Abaelard as a philosophical logician is revealed in what he is able to do with the material which he found in Boethius. It is shown that he developed a precise theory of conditionals giving an account of how true conditionals may be obtained and principles which may be used to reject others as false. Unlike Boethius Abaelard properly appreciates that conjunctions must be treated as logical units. Even he, however, falls victim to difficulties which arise when this connective is brought into contact with negation and the conditions which he lays down for the truth of a conditional.     

Contrary-to-duty obligations

We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or pre-supposes, a certain context in which a primary obligation is already violated. This framework is presented initially as an extension of Standard Deontic Logic (SDL), a normal modal logic of type KD, and is illustrated by application to a series of examples. The concluding section is concerned with some resemblances between CTD and defeasible reasoning. We show first that the SDL-based framework contains a flaw and must be adjusted. A discussion of possible adjustments, including an alternative treatment in terms of a preference-based semantics, reveals difficulties that are reminiscent of problems in defeasible reasoning and intensional accounts of defeasible conditionals.     

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.     

A Revenge-Immune Solution to the Semantic Paradoxes

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.     

Eye movements reveal rapid concurrent access to factual and counterfactual interpretations of the world

Imagining a counterfactual world using conditionals (e.g., If Joanne had remembered her umbrella . . .) is common in everyday language. However, such utterances are likely to involve fairly complex reasoning processes to represent both the explicit hypothetical conjecture and its implied factual meaning. Online research into these mechanisms has so far been limited. The present paper describes two eye movement studies that investigated the time-course with which comprehenders can set up and access factual inferences based on a realistic counterfactual context. Adult participants were eye-tracked while they read short narratives, in which a context sentence set up a counterfactual world (If . . . then . . .), and a subsequent critical sentence described an event that was either consistent or inconsistent with the implied factual world. A factual consistent condition (Because . . . then . . .) was included as a baseline of normal contextual integration. Results showed that within a counterfactual scenario, readers quickly inferred the implied factual meaning of the discourse. However, initial processing of the critical word led to clear, but distinct, anomaly detection responses for both contextually inconsistent and consistent conditions. These results provide evidence that readers can rapidly make a factual inference from a preceding counterfactual context, despite maintaining access to both counterfactual and factual interpretations of events.     

Ranking Theory and Conditional Reasoning

Ranking theory is a formal epistemology that has been developed in over 600 pages in Spohn's recent book The Laws of Belief, which aims to provide a normative account of the dynamics of beliefs that presents an alternative to current probabilistic approaches. It has long been received in the AI community, but it has not yet found application in experimental psychology. The purpose of this paper is to derive clear, quantitative predictions by exploiting a parallel between ranking theory and a statistical model called logistic regression. This approach is illustrated by the development of a model for the conditional inference task using Spohn's (2013) ranking theoretic approach to conditionals.     

Conditioning against the Grain

This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between causal and purely stochastic dependence between variables.     

关于实验心理学中推理的现代心理测量方法(英文)

推理测验与推理实验不同。推理测验用来衡量智商;而推理实验则用来研究推理的心理过程。测验旨在找出能力的个体差异;而实验则意在突出所有个体的一般性心理过程。近年来,心理学中的推理已经发生了变化,我们在理论进化方面简要地总结了如下这些变化:关注点从推理任务中的反应过程变为个体对不同任务做反应时的差异和其中稳定的反应模式,开始考虑不同推理者的组织差异和数量差异(犹如不同游泳运动员的游泳动作和肌肉数量)。然而,这些理论创新必须有精确的建模技术的支持。我们将以条件推理材料为例,展示了现代心理测量方法可以帮我们解决理论创新中产生的三类主要的研究问题。     

Can’t We All Just be Compatibilists?: A Critical Study of John Martin Fischer’s <Emphasis Type="Italic">My Way</Emphasis>

My aim in this study is not to praise Fischer's fine theory of moral responsibility, but to (try to) bury the “semi” in “semicompatibilism”. I think Fischer gives the Consequence Argument (CA) too much credit, and gives himself too little credit. In his book, The Metaphysics of Free Will, Fischer gave the CA as good a statement as it will ever get, and put his finger on what is wrong with it. Then he declared stalemate rather than victory. In my view, Fischer’s view amounts to sophisticated compatibilism. It would be nice to be able to call it by its right name. In The Metaphysics of Free Will, Fischer develops his own version of Consequence Argument, which turns on two principles, one of which is the fixity of the past. FP: For any action Y, agent S and time t, if it is true that is S were to do Y at t, some fact about that past relative to t would not have been a fact, then S cannot at t do Y at t. I argue that the equipment needed to reject FP (and thereby defend the most plausible version of compatibilism) is needed to deal with the problem of fatalism. In addition, I argue that the rejection of FP is compatible with Fischer’s approach to Frankfurt cases and with his account of transfer principles.     

The probability of causal conditionals

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.