We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near perfect (...) predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

A recent argument by Hawthorne and Lasonen-Aarnio purports to show that we can uphold the principle that competently forming conjunctions is a knowledge-preserving operation only at the cost of a rampant skepticism about the future. A key premise of their argument is that, in light of quantum-mechanical considerations, future contingents never quite have chance 1 of being true. We argue, by drawing attention to the order of magnitude of the relevant quantum probabilities, that the skeptical threat of Hawthorne and Lasonen-Aarnio’s (...) argument is illusory. (shrink)

Purely parallel neural networks can model object recognition in brief displays – the same conditions under which illusory conjunctions have been demonstrated empirically. Correcting errors of illusory conjunction is the “tag-assignment” problem for a purely parallel processor: the problem of assigning a spatial tag to nonspatial features, feature combinations, and objects. This problem must be solved to model human object recognition over a longer time scale. Our model simulates both the parallel processes that may underlie illusory (...) conjunctions and the serial processes that may solve the tag-assignment problem in normal perception. One component of the model extracts pooled features and another provides attentional tags that correct illusory conjunctions. Our approach addresses two questions: How can objects be identified from simultaneously attended features in a parallel, distributed representation? How can the spatial selectional requirements of such an attentional process be met by a separation of pathways for spatial and nonspatial processing? Our analysis of these questions yields a neurally plausible simulation of tag assignment based on synchronizing feature processing activity in a spatial focus of attention. (shrink)

Many studies focused on the letter and sound co-occurrences to account for the well-documented syllable-based effects in French in visual (pseudo)word processing. Although these language-specific statistical properties are crucial, recent data suggest that studies which go all-in on phonological and orthographic regularities may be misguided in interpreting how – and why – readers locate syllable boundaries and segment clusters. Indeed, syllable-based effects could depend on more abstract, universal phonological constraints that rule and govern how letter and sound occur and co-occur, (...) and readers could be sensitive to sonority – a universal phonological element – for processing (pseudo)words. Here, we investigate whether French adult skilled readers rely on universal phonological sonority-related markedness continuum across the syllable boundaries for segmentation (e.g., from marked, illegal intervocalic clusters /zl/ to unmarked, legal intervocalic clusters /lz/). To address this question, we ran two tasks with 128 French adult skilled readers using two versions of the illusory conjunction paradigm (Task 1 without white noise; Task 2 with white noise). Our results show that syllable location and segmentation in reading is early and automatically modulated by phonological sonority-related markedness in the absence or quasi-absence of statistical information, and does not require acoustic-phonetic information. We discuss our results towards the overlooked role of phonological universals and the over-trusted role of statistical information during reading processes. (shrink)

Naïve realism is the view that veridical experiences are fundamentally relations of acquaintance to external objects and their features, and multidisjunctivism is the conjunction of naïve realism and the view that hallucinatory experiences don’t share a common fundamental kind. Multidisjunctivism allegedly removes the screening-off worry over naïve realism, and the relevant literature suggests that multidisjunctivism is one of the naïve realist responses to the worry. The present paper argues that the multidisjunctive solution is implicitly changing the subject, so the (...) impression that the multidisjunctivist is addressing the screening-off problem is illusory. (shrink)

Many philosophers believe that true belief is of epistemic value, but that knowledge is of even more epistemic value. Some claim that this surplus value is instrumentally valuable to the value of true belief. I call the conjunction of these claims the Instrumentalist’s Conjunction. The so-called “Swamping Problem” is meant to show that Instrumentalist’s Conjunction is inconsistent. Crudely put, the problem is that if knowledge only has surplus value to the value of true belief, and a belief (...) is true because known, then knowledge cannot be of any more value than true belief. Given the inconsistency, most philosopher reject the claim the surplus value of knowledge is instrumental to the value of true belief. This paper argues that the Swamping Problem is illusory. Once we clean up the problem and pay attention to the distinction between token/type properties, we can see that Instrumentalist’s Conjunction is perfectly coherent. (shrink)

Abstract Sankara's philosophy fails definitively at the point where he leaves the human experience??sinning and suffering??unaccounted for. What in each of us, he asks, sins and suffers? Is it the antahkarana, the ?mental organ? giving rise to the series of mental states (buddins) that file by illumined by the atman? Impossible, he says, for the antahkarana by itself is material (jada,) and therefore unconscious (acit). Then is it the ?tman, upon which the antahkarana is superimposed? Inconceivable, he says, for the (...) atman is identical with Brahman, and Brahman is by definition pure bliss?consciousness, as far removed from sin and suffering as can be imagined. Then is the atman in conjunction with the antahkarana?a partnership that Sankara calls the jiva (or soul)?the sinner and sufferer? Yes, he says, as long as you remember that the sin and suffering are ultimately illusory, as illusory as the antahkarana itself. I show why Sankara's answer fails and what the failure implies, then suggest a fruitful way to approach Sankara and teach his philsophy to our students. (shrink)

The problem of evil is an intellectual challenge for philosophers and theologians and an existential threat to many religious believers. It is sustained by the commitments of what is now called perfect being theology, which is above all a philosophical theology centered on the conception of God as creator of the cosmos and as omniscient, omnipotent, and perfectly good. With Kontny and Müller-Salo, I do not try to evade the problem by treating evil as illusory or subjective. I agree (...) that there are genuine evils of horrendous proportions. The question why there is evil at all is urgent enough in a world under an omnicompetent God—‘omnicompetence’ being shorthand for the conjunction of omniscience, omnipotence, and perfect goodness. But the question why there is so much and such excruciating evil seems on the face of it unanswerable. Kontny and Müller-Salo have contributed much to our understanding of the problem, and here, rather than elaborate on all of their points, I shall simply reply to those that indicate a need to reinforce or extend major theses I have defended. (shrink)

A conjunction of two hypotheses may provide a better explanation than either one of them individually, even if each already provides a good explanation on its own. An appropriate measure of explanatory power should reflect this, but none of the measures discussed in the literature do so because they only consider how much an explanatory hypothesis reduces our surprise at the evidence – which is problematic. This chapter introduces and defends a class of coherentist measures of explanatory power, and (...) shows that one particular such measure that combines different intuitions underlying the epistemological notion of coherence overcomes the aforementioned problems of surprise reduction measures. (shrink)

Descartes held that it is impossible to make true statements about what we perceive, but I go over alleged cases of illusory experience to show why such a skeptical conclusion (and recourse to God) is overblown. The overreaction, I contend, stems from an insufficient awareness of the habitual expectations brought to any given experience. These expectations manifest themselves in motor terms, as perception constantly prompts and updates an embodied posture of readiness for what might come next. Such habitual anticipations (...) work best when they efface themselves, so it is easy to blame perception when our expectations get frustrated. I illustrate this misdirected blame with the example of a stick partially in water: it is only because we expect the stick to be straight that its appearance as bent is deemed problematic. I thus conclude that, if we factor in the habitual interpretations operative in perception and switch to a processual view that allows practical engagement, we can deflate the worries that led Descartes to rule out perceptual truths. Distancing myself from the naïve “sign” of folk semiotics, my critique draws inspiration from the triadic semiotic model developed in some late medieval schools of Portugal. (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. (...) While non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

This article discusses the reasons why illusory contours are likely to result from adaptive perceptual mechanisms that have evolved across species to promote behavioral success.

Inference to the Best Explanation (IBE) advises reasoners to infer exactly one explanation. This uniqueness claim apparently binds us when it comes to “conjunctive explanations,” distinct explanations that are nonetheless explanatorily better together than apart. To confront this worry, explanationists qualify their statement of IBE, stipulating that this inference form only adjudicates between competing hypotheses. However, a closer look into the nature of competition reveals problems for this qualified account. Given the most common explication of competition, this qualification artificially and (...) radically constrains IBE’s domain of applicability. Using a more subtle, recent explication of competition, this qualification no longer provides a compelling treatment of conjunctive explanations. In light of these results, I suggest a different strategy for accommodating conjunctive explanations. Instead of modifying the form of IBE, I suggest a new way of thinking about the structure of IBE’s lot of considered hypotheses. (shrink)

In a recent article, Kim Sterelny and Philip Kitcher5 defend a version of genic selectionism and attempt to refute the criticisms I made of that doctrine. Their defense has two components. First, they find fault with the account I gave of the units-of-selection controversy-an account which uses the idea of probabilistic causality as a tool of explication. Second, they provide a positive account of their own of what that controversy concerns, one which they think allows genic selectionism to emerge as (...) a successful thesis. I believe that the position they sketch is mistaken, both in its general orientation and in its details. I believe that the Sterelny/ Kitcher position misunderstands what the biological question of the units of selection is about and that their criticisms of my own proposal are mistaken as well. (shrink)

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them (...) discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. (shrink)

It has been suggested that the difference between misremembering (Orwellian) and misrepresentation (Stalinesque) models of consciousness cannot be differentiated (Dennett, 1991). According to an Orwellian account a briefly presented stimulus is seen and then forgotten; whereas, by a Stalinesque account it is never seen. At the same time, Dennett suggested a method for assessing whether an individual is conscious of something. An experiment was conducted which used the suggested method for assessing consciousness to look at Stalinesque and Orwellian distinctions. A (...) visual illusion, illusory line motion, was presented and participants were requested to make judgments that reflected what they were aware of. The participants were able to make responses indicating that they were aware of the actual stimulus in some conditions, but only of the illusion in others. This finding supports a claim that the difference between the Orwellian and Stalinesque accounts may be empirically observable, and that both types of events may occur depending on task and stimulus parameters. (shrink)

1. In both Benedetto Croce's and Hegel's own terminology, dialectics can be understood as dottrina degli opposti (the doctrine of the opposites – Lehre der Gegensätze).1 In the dialectical process,...

What we might usefully call “playing full-stop” and playing games plausibly figure in a well-lived life. Yet there are reasons to worry that the two not only do not naturally go hand in hand, but are in fact deeply opposed. In this essay I investigate the apparent tension between playing full-stop and playing competitive games. I argue that the nature of this tension is easily exaggerated. While there is a psychological tension between simultaneously engaging in earnest competitive game play and (...) playing fullstop, there is no logical contradiction between the two. Somewhat surprisingly, seeing how this tension is best understood teaches us something about the nature of willing an end and the “guise of the good.” With a resolution of the apparent tension between playing full-stop and playing competitive games, I turn to the practical worry that playing competitive games is destructive precisely for the very reasons it is opposed to playing full-stop. Here I develop a positive proposal to mitigate the tension between playing full-stop and playing competitive games. This proposal draws on the idea of “striving play” as recently developed by Thi Nguyen and some ideas from classical Stoicism. (shrink)

I argue that it is rational for a person to believe the conjunction of her beliefs. This involves responding to the Lottery and Preface Paradoxes. In addition, I suggest that in normal circumstances, what it is to believe a conjunction just is to believe its conjuncts.

Plurality, Conjunction and Events presents a novel theory of plural and conjoined phrases, in an event-based semantic framework. It begins by reviewing options for treating the alternation between `collective' and `distributive' readings of sentences containing plural or conjoined noun phrases, including analyses from both the modern and the premodern literature. It is argued that plural and conjoined noun phrases are unambiguously group-denoting, and that the collective/distributive distinction therefore must be located in the predicates with which these noun phrases combine. (...) More specifically, predicates must have a hidden argument place for events; the collective/distributive distinction may then be represented in the part/whole structure of these events. This allows a natural treatment of `collectivizing' adverbial expressions, and of `pluractional' affixes; it also allows a unified semantics for conjunction, in which conjoined sentences and predicates denote groups of events, much like conjoined noun phrases denote groups of individuals. (shrink)

Despite the fact about colour, that it is one of the most obvious and conspicuous features of the world, there is a vast number of different theories about colour, theories which seem to be proliferating rather than decreasing. How is it possible that there can be so much disagreement about what colours are? Is it possible that these different theorists are not talking about the same thing? Could it be that more than one of them is right? Indeed some theorists, (...) e.g. Leo M. Hurvich, D. L. McAdam and K. Nassau, say that the term ‘colour’ is used to identify a range of different properties, e.g. pigments, properties of light, and sensations. Such a view has its attractions, but it raises the question of what it is that unites these various concepts – what is it that would make them all concepts of colour? What is it that justifies using the same terms, ‘yellow’, ‘blue’, ‘pink’, mauve’, and so on?This paper aims to address this question, arguing that its answer supports the conclusion that the best theory of colour is a form of anti-realism: the Illusory theory of colours. There are two parts to this thesis, one negative, the other positive. The negative part is that there are no colours, as they are ordinarily conceived. The positive part is that, nevertheless, the world is such that ‘it is as if there are such colours’. Such a theory has important implications. One is that it doesn’t fall neatly into the usual taxonomy of philosophical theories. In particular, it does not deserve the label ‘eliminativist’. Another is that it allows some space for the views expressed by Hurvich, McAdam and Nassau, but not quite in the sense that they intend. (shrink)

The psychological study of reasoning with quantifiers has predominantly focused on inference patterns studied by Aristotle about two millennia ago. Modern logic has shown a wealth of inference patterns involving quantifiers that are far beyond the expressive power of Aristotelian syllogisms, and whose psychology should be explored. We bring to light a novel class of fallacious inference patterns, some of which are so attractive that they are tantamount to cognitive illusions. In tandem with recent insights from linguistics that quantifiers like (...) “some” are treated as wh-questions, these illusory inferences are predicted by the erotetic theory of reasoning, which postulates that a process akin to question asking and answering is behind human inference making. (shrink)

Despite the fact about colour, that it is one of the most obvious and conspicuous features of the world, there is a vast number of different theories about colour, theories which seem to be proliferating rather than decreasing. How is it possible that there can be so much disagreement about what colours are? Is it possible that these different theorists are not talking about the same thing? Could it be that more than one of them is right? Indeed some theorists, (...) e.g. Leo M. Hurvich, D. L. McAdam and K. Nassau, say that the term ‘colour’ is used to identify a range of different properties, e.g. pigments, properties of light, and sensations. Such a view has its attractions, but it raises the question of what it is that unites these various concepts – what is it that would make them all concepts of colour? What is it that justifies using the same terms, ‘yellow’, ‘blue’, ‘pink’, mauve’, and so on?This paper aims to address this question, arguing that its answer supports the conclusion that the best theory of colour is a form of anti‐realism: the Illusory theory of colours. There are two parts to this thesis, one negative, the other positive. The negative part is that there are no colours, as they are ordinarily conceived. The positive part is that, nevertheless, the world is such that ‘it is as if there are such colours’. Such a theory has important implications. One is that it doesn’t fall neatly into the usual taxonomy of philosophical theories. In particular, it does not deserve the label ‘eliminativist’. Another is that it allows some space for the views expressed by Hurvich, McAdam and Nassau, but not quite in the sense that they intend. (shrink)

Gonzalo Rodriguez-Pereyra (2006) argues against attempts to preserve the entailment principle (or a restriction of it) while avoiding the explosion of truthmakers for necessities and truthmaker triviality. In doing so, he both defends the disjunction thesis--if something makes true a disjunctive truth, then it makes true one of its disjuncts--, and rejects the conjunction thesis--if something makes tue a conjunctive truth, then it makes true each of its conjuncts. In my discussion, I provide plausible counterexamples to the disjunction thesis, (...) and contend that Rodriguez-Pereyra's general defence of it fails. Then I defend the conjunction thesis from Rodriguez-Pereyra's case against it. (shrink)

I put in question in this article the existence of conjunctive properties. In the second section, after having provided a characterization of conjunctive properties, I develop an argument based on the principle of ontological parsimony: if we accept that there are conjunctive properties in the universe then, ceteris paribus, our ontology turns out to be less ontologically parsimonious than if we reject them. Afterwards, in the third section, I distinguish between maximalist and non-maximalist and reductionist and non-reductionist theories of conjunctive (...) properties., as well as between reductionist and non-reductionist theories that reject conjunctive properties. Such distinctions help to clarify the options at hand when accepting or rejecting conjunctive properties. In light of these distinctions, I then tackle two objections against the argument from ontological parsimony. Finally, in the remaining sections, I deal with two arguments defended by D. M. Armstrong for the existence of conjunctive properties: the argument from infinite complexity and the argument from causal powers. I show that there are several ways to resist these arguments and their conclusion. (shrink)

The so‐called problem of irrelevant conjunction has been seen as a serious challenge for theories of confirmation. It involves the consequences of conjoining irrelevant statements to a hypothesis that is confirmed by some piece of evidence. Following Hawthorne and Fitelson, we reconstruct the problem with reference to Bayesian confirmation theory. Then we extend it to the case of conjoining irrelevant statements to a hypothesis that is dis confirmed by some piece of evidence. As a consequence, we obtain and formally (...) present a novel and more troublesome problem of irrelevant conjunction. We conclude by indicating a possible solution based on a measure‐sensitive approach and by critically discussing a major alternative way to address the problem. *Received December 2008; revised August 2009. †To contact the authors, please write to: Department of Philosophy, University of Turin, via Sant'Ottavio 20, 10124 Turin, Italy; e‐mail: [email protected] ; [email protected] or [email protected]. (shrink)

The conjunction fallacy is the well-documented empirical finding that subjects sometimes rate a conjunction A&B as more probable than one of its conjuncts, A. Most explanations appeal in some way to the fact that B has a high probability. But Tentori et al. (2013) have recently challenged such approaches, reporting experiments which find that (1) when B is confirmed by relevant evidence despite having low probability, the fallacy is common, and (2) when B has a high probability but (...) has not been confirmed by relevant evidence, the fallacy is less common. They conclude that degree of confirmation, rather than probability, is the central determinant of the conjunction fallacy. In this paper, we address a confound in these experiments: Tentori et al. (2013) failed to control for the fact that their (1)-situations make B conversationally relevant, while their (2)-situations do not. Hence their results are consistent with the hypothesis that con- versationally relevant high probability is an important driver of the conjunction fallacy. Inspired by recent theoretical work that appeals to conversational relevance to explain the conjunction fallacy, we report on two experiments that control for this issue by making B relevant without changing its degree of probability or confirmation. We find that doing so increases the rate of the fallacy in (2)-situations, and leads to comparable fallacy-rates as (1)-situations. This suggests that (non-probabilistic) conversational relevance indeed plays a role in the conjunction fallacy, and paves the way toward further work on the interplay between relevance and confirmation. (shrink)

We argue against some of Reichenbach's claims about causal forks are incorrect. We do not see why the Second Law of Thermodynamics rules out the existence of conjunctive forks open to the past. In addition, we argue that a common effect rarely forms a conjunctive fork with its joint causes, but it sometimes does. Nevertheless, we think there is something to be said for Reichenbach's idea that forks of various kinds are relevant to explaining why we know more about the (...) past than about the future. And entropy turns out to play a role in the explanation, though not the determining role that Reichenbach envisions. (shrink)

Illusory Abiding: The Cultural Construction of the Chan Monk Zhongfeng Mingben. By Natasha Heller. Harvard East Asian Monographs, vol. 368. Cambridge, Mass.: Harvard Univ. Asia Center, Harvard Univ. Press, 2014. Pp. xiv + 471. $49.95.

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we (...) give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold. (shrink)

This contribution explores the psychological basis of illusion and the feeling of what is real in relation to a process theory (microgenesis) of mind/brain states. The varieties of illusion and the alterations in the feeling of realness are illustrated in cases of clinical pathology, as well as in everyday life. The basis of illusion does not rest in a comparison of appearance to reality nor in the relation of image to object, since these are antecedent and consequent phases in the (...) same mental state. The study of pathological illusions and hallucinations shows that the feeling of realness in an object depends on its coherence within and across perceptual modalities. Illusion is shown to be not the taking of the phenomenal for the real, but the overlooking of the real in the phenomenal, since all things exist, i.e. are real, as categories of intrinsic relations in the unique mode of their conception. Finally, the implications of the account are discussed in relation to moral conduct, self-realization, acceptance, and the will to enjoy a world of 'brain-born' mental phenomena. (shrink)

Leibniz has often been described as holding to a kind of phenomenalism. Yet Leibniz did not have a single account of perception, or of the embodied mind, or of the monad, but a set of conflicting and mutually inconsistent accounts that preclude the possibility that there is any such thing as “Leibniz's System.” This difficulty raises problems of interpretation, since it is sometimes maintained that the principle of charity precludes the assignment of frankly inconsistent views to a philosopher. The essay (...) argues that we should not be misled by the intentionalist fallacy into looking for order within a text as opposed to order commentators can impose by making a philosopher's inconsistencies intelligible. (shrink)

Neurological disorders of body representation have for a long time suggested the importance of multisensory processing of bodily signals for self-consciousness. One such group of disorders – illusory own body perceptions affecting the entire body – has been proposed to be especially relevant in this respect, based on neurological data as well as philosophical considerations. This has recently been tested experimentally in healthy subjects showing that integration of multisensory bodily signals from the entire body with respect to the three (...) aspects: self-location, first-person perspective, and self-location, is crucial for bodily self-consciousness. Here we present clinical and neuroanatomical data of two neurological patients with paroxysmal disorders of full body representation in whom only one of these aspects, self-identification, was abnormal. We distinguish such disorders of global body representation from related but distinct disorders and discuss their relevance for the neurobiology of bodily self-consciousness. (shrink)

We show that the elimination rule for the multiplicative conjunction $\wedge$ is admissible in many important multiplicative substructural logics. These include LL$_m$ and RMI$_m$ An exception is R$_m$. Let SLL$_m$ and SR$_m$ be, respectively, the systems which are obtained from LL$_m$ and R$_m$ by adding this rule as a new rule of inference. The set of theorems of SR$_m$ is a proper extension of that of R$_m$, but a proper subset of the set of theorems of RMI$_m$. Hence it (...) still has the variable-sharing property. SR$_m$ has also the interesting property that classical logic has a strong translation into it. We next introduce general algebraic structures, called strong multiplicative structures, and prove strong soundness and completeness of SLL$_m$ relative to them. We show that in the framework of these structures, the addition of the weakening axiom to SLL$_m$ corresponds to the condition that there will be exactly one designated element, while the addition of the contraction axiom corresponds to the condition that there will be exactly one nondesignated element. Various other systems in which multiplicative conjunction functions as a true conjunction are studied, together with their algebraic counterparts. (shrink)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners’ interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems. © 2004 Cognitive Science Society, Inc. All rights reserved.

The perception of brightness differences in Ehrenstein figures and of illusory contours in phase-shifted line gratings was investigated as a function of the contrast polarity of the inducing elements. We presented either continuous lines or line-like arrangements composed of aligned dashes or dots whose spacing was varied. A yes/no procedure was used in which naive observers had to decide whether or not they perceived a brightness difference in a given Ehrenstein figure or an illusory contour in a phase-shifted (...) line grating. The results show that brightness differences are perceived to some extent in Ehrenstein figures with inducers of opposite polarity of contrast; however, the percentage of yes response was systematically lower and response times were longer than for figures with inducers of the same polarity. Phase-shifted line gratings with lines of opposite polarity of contrast yielded stronger illusory contours and shorter response times than those with lines of the same polarity. When the sign of contrast was not the same within a given line of induction, neither differences in brightness nor illusory contours were perceived. The results suggest that the mechanisms that lead to apparent differences in brightness are more sensitive to input of the same contrast polarity, the mechanisms generating illusory contours more sensitive to input of opposite polarity. The data are discussed in the light of a multistage approach to illusory form perception and some implications for cortical models of illusory contour integration are discussed. (shrink)