We consider an oscillator subjected to a sudden change in equilibrium position or in effective spring constant, or both—to a “squeeze” in the language of quantum optics. We analyze the probability of transition from a given initial state to a final state, in its dependence on final-state quantum number. We make use of five sources of insight: Bohr-Sommerfeld quantization via bands in phase space, area of overlap between before-squeeze band and after-squeeze band, interference in phase space, Wigner function (...) as quantum update of B-S band and near-zone Fresnel diffraction as mockup Wigner function. (shrink)

For many among the scientifically informed public, and even among physicists, Heisenberg's uncertainty principle epitomizes quantum mechanics. Nevertheless, more than 86 years after its inception, there is no consensus over the interpretation, scope, and validity of this principle. The aim of this chapter is to offer one such interpretation, the traces of which may be found already in Heisenberg's letters to Pauli from 1926, and in Dirac's anticipation of Heisenberg's uncertainty relations from 1927, that stems form the hypothesis of finite (...) nature. Instead of a mere mathematical theorem of quantum theory, or a manifestation of "wave-particle duality", the uncertainty relations turn out to be a result of a more fundamental premise, namely, the inherent limitation on spatial resolution that follows from the bound on physical resources. The implication of this view are far reaching: it depicts the Hilbert space formalism as a phenomenological, "effective", formalism that approximates an underlying discrete structure; it supports a novel interpretation of probability in statistical physics that sees probabilities as deterministic, dynamical transition probabilities which arise from objective and inherent measurement errors; and it helps to clarify several puzzles in the foundations of statistical physics, such as the status of the "disturbance" view of measurement in quantum theory, or the tension between ontology and epistemology in the attempts to describe nature with physical theories whose formalisms include subjective probabilities. Finally, this view also renders obsolete the entire class of interpretations of quantum theory that adhere to "the reality of the wave function". (shrink)

The question of when and how bottom‐up input is integrated with top‐down knowledge has been debated extensively within cognition and perception, and particularly within language processing. A long running debate about the architecture of the spoken‐word recognition system has centered on the locus of lexical effects on phonemic processing: does lexical knowledge influence phoneme perception through feedback, or post‐perceptually in a purely feedforward system? Elman and McClelland (1988) reported that lexically restored ambiguous phonemes influenced the perception of the following (...) phoneme, supporting models with feedback from lexical to phonemic representations. Subsequently, several authors have argued that these results can be fully accounted for by diphone transitional probabilities in a feedforward system (Cairns et al., 1995; Pitt & McQueen, 1998). We report results strongly favoring the original lexical feedback explanation: lexical effects were present even when transitional probability biases were opposite to those of lexical biases. (shrink)

This article reflects on the contribution that stakeholder involvement could give to circular bioeconomy transformation (CBE). By comparing argument for stakeholder involvement in literature as well as on our own experiences in six stakeholder involvement workshops, we argue that it is probably unrealistic to fully achieve both normative and co-design goals in a single workshop. Furthermore, stakeholder involvement can help to acquire insight into dependencies in the market and offer an opportunity to connect people to deal with them. Therefore we (...) propose for future stakeholder involvement initiatives for CBE to focus on (1) identify relationships of dependency which make it hard for players in the market to change, (2) develop strategies to change while mitigating the detrimental effects on already existing relationships and (3) gradually breaking down relationships and building new ones that support CBE. (shrink)

The study of culture and cultural selection from a biological perspective has been hampered by the lack of any firm theoretical basis for how the information for cultural traits is stored and transmitted. In addition, the study of any living system with a decentralized or multi-level information structure has been somewhat restricted due to the focus in genetics on the gene and the particular hereditary structure of multicellular organisms. Here a different perspective is used, one which regards living systems as (...) self-constructing energy users that utilize their genome as a library of information, making the genetic system just another component that adds fitness to the overall integrated unit. In this framework, basic fitness is measured as the ability to gather energy for growth and reproduction, and the fitness of the genetic system is broken down into two aspects: first, the effectiveness in searching for new somatic functional information, and second, the effectiveness in searching for better structures to store and process information. With this more generalized perspective, major evolutionary transitions to higher levels of organization become competitions between different information structures; furthermore the functioning and fitness of cultural systems can be more easily described and compared with other modes of information storage within biological systems. Modern technological societies are self-constructing systems that rely on written (symbolic) information storage and very complex algorithms that effectively search for variation with a high probability of successful selection. These systems are currently competing with traditional organic systems, and this competition constitutes the latest major evolutionary transition. Upon comparison of the energy-gathering potential of symbolic-based systems with DNA-based life, it appears that symbolic systems have a tremendous fitness potential and the current shift to a higher level of selection may be as significant and far-reaching as any of the previous major evolutionary transitions. (shrink)

It has been well documented how language‐specific cues may be used for word segmentation. Here, we investigate what role a language‐independent phonological universal, the sonority sequencing principle (SSP), may also play. Participants were presented with an unsegmented speech stream with non‐English word onsets that juxtaposed adherence to the SSP with transitional probabilities. Participants favored using the SSP in assessing word‐hood, suggesting that the SSP represents a potentially powerful cue for word segmentation. To ensure the SSP influenced the segmentation process (i.e., (...) during learning), we presented two additional groups of participants with either (a) no exposure to the stimuli prior to testing or (b) the same stimuli with pauses marking word breaks. The SSP did not influence test performance in either case, suggesting that the SSP is important for word segmentation during the learning process itself. Moreover, the fact that SSP‐independent segmentation of the stimulus occurred (in the latter control condition) suggests that universals are best understood as biases rather than immutable constraints on learning. (shrink)

It has been well documented how language-specific cues may be used for word segmentation. Here, we investigate what role a language-independent phonological universal, the sonority sequencing principle (SSP), may also play. Participants were presented with an unsegmented speech stream with non-English word onsets that juxtaposed adherence to the SSP with transitional probabilities. Participants favored using the SSP in assessing word-hood, suggesting that the SSP represents a potentially powerful cue for word segmentation. To ensure the SSP influenced the segmentation process (i.e., (...) during learning), we presented two additional groups of participants with either (a) no exposure to the stimuli prior to testing or (b) the same stimuli with pauses marking word breaks. The SSP did not influence test performance in either case, suggesting that the SSP is important for word segmentation during the learning process itself. Moreover, the fact that SSP-independent segmentation of the stimulus occurred (in the latter control condition) suggests that universals are best understood as biases rather than immutable constraints on learning. (shrink)

While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, (...) if and only if the subject’s comparative judgments preclude representation by a standard probability measure. (shrink)

Sen’s Liberal paradox describes a conflict between weak Pareto, minimal liberalism, and either transitivity or a best element over a domain of individual preferences. This paper examines variants of that paradox with varying amounts of unconditional preferences. We define a notion of unconditional preferences under which, in the absence of Pareto, there can be no cycles. We then define a stronger condition, that makes an individual’s preferences for her own private attributes independent of all other attributes. Under this assumption, there (...) can be no cycles with or without Pareto. We also show there exists a social decision function satisfying those conditions. We then determine the probability of a cycle assuming a much weaker independence condition that does not restrict the domain. This probability converges to one as the number of non-private attributes within the social states increases. Finally, we use simulations to determine the probability that liberalism and Pareto conflict with best elements, maximal elements, and transitivity separately. (shrink)

Grandparental presence is known to correlate with the number of grandchildren born, and this effect may vary according to grandparental sex and lineage. However, existing studies of grandparental effects on fertility mostly concern traditional subsistence societies, while evidence from contemporary developed societies is both scarce and mixed. Here, we explore how grandparents affect the transition to second and subsequent children in the contemporary United Kingdom. The longitudinal Millennium Cohort Study (n = 10,295 families) was used to study the (...) association between grandparental investment and parents’ probability of having a new child within 4.5 years. Results show that contact with paternal grandparents is associated with higher probability of parents having a second child. In contrast, contact with maternal grandparents is associated with lower probability of having a third or subsequent child. Kin may have opposite effects on fertility even in contemporary societies, which may explain the lack of consistent effects of grandparental investment on fertility in previous studies. (shrink)

The main objective of Zika transmission studies is to work out the simplest approach to scale back human mortality and morbidity caused by the disease. Therefore, it is essential to spot the relative importance of the various factors contributing to the transmission and prevalence of the disease. Many mathematical models have been formulated incorporating vector-to-human transmission or human-to-human transmission. However, they do not take into consideration the mixture of both sorts of transmission. It raises the question of the impact of (...) both sorts of transmission on the disease dynamics. We develop a mathematical model of Zika with the vertical transmission in the vector population and human-to-human transmission to answer this question. It includes the immature phase of mosquitoes, adult mosquitoes, and human hosts. Results show that neglecting sexual transmission results in an understatement of the proportion of the infected population. Furthermore, it reduces the speed of disease spreading. On the other hand, vertical transmission in mosquitoes has a negligible effect on the dynamics of disease spread. We perform a sensitivity analysis of the reproductive number R 0 to raise to understand the parameters driving the dynamics of the disease. It appears that the most sensitive parameters in decreasing order are as follows: the adult mosquito death rate, the sting rate, the transmission probability of mosquito to human, and, therefore, the transmission probability of human to mosquito. Furthermore, the proportion at the equilibrium of infected humans is extremely sensitive to the transition rate from the immature vector stage to the adult stage, the human-to-human transmission rate, and, therefore, the human recovery rate. These results confirm that control policies targeting the vector population and, therefore, the recovery rate of people are pretty effective solutions. To validate the model and estimate the important parameters of the model and the prediction of the disease, we consider the real cases in Colombia from 2016. In a series of graphic maps, we presented the comparative study to estimate the disease scenarios and to predict the time limit of the epidemic control measure. (shrink)

Salutary reading for all philosophers, and not only for inductive logicians, philosophers of science and law, this important book presents an elaborate theory of inductive reasoning whose substantive features are as strikingly original as the approach is rare. First, the theory is based on concrete, real, actual, and significant instances of inductive reasoning, e.g., Karl von Frisch’s work on bees; that is, though its aim is genuinely theoretical in the sense that it engages in the proper amounts of idealization, abstraction, (...) systematization, precision, and rigor, it never loses sight of the fact that "theories in the philosophy of science, like theories in science itself, have to face up to the challenge of appropriately accredited experience within their appointed domains". Second, a central subject matter being analyzed is legal reasoning, that is, the types of proofs and arguments used by juries, judges, and lawyers in the Anglo-American system of jurisprudence, where criminal charges have to be proved beyond reasonable doubt and civil cases have to be argued on the balance of probability. Thus, in effect, Cohen’s synthesis of juridical and of scientific reasoning is an admirable example of the bridging of two "cultures." Third, and most importantly, the concept of "inductive probability," in terms of which Cohen makes sense out of his subject matter, is incommensurable with that of "mathematical probability," namely the classical calculus of chance according to which probability is measurable, additive, transitive, and obeys a multiplicational principle for conjunction and a complementational one for negation. This is not to say that "inductive probability" is a hazy, mysterious, or unstructured concept, and Cohen goes to great lengths to show that it is ordinal, modal, and formally analyzable; what it does mean is that essential types of reasoning in science and in law involve probable inferences whose probabilities are nonquantitative. Hence, though Cohen does not stress the qualitative nature of inductive probability, his book will be welcome by those who conceive of philosophy as scientia qualitatum. Specific conclusions reached by Cohen are that, in general, probability may be conceived as degree of provability, that differences in proof-rules generate different special cases of probability, that inductive probability may be viewed as the special case where the proof-rules are incomplete, that inductive probability is to inductive support as deducibility is to logical truth, and that some recent epistemological scepticism may be refuted by Cohen’s inductive logic. Finally, he sees himself in the British inductivist tradition, interpreting his predecessors as groping toward a logic of inductive support and probability rather than a methodology of discovery: from Bacon he develops the notion of eliminative induction but rejects that of induction by enumeration; Mill’s canons are analyzed as special cases of Cohen’s own "method of relevant variables," except for the method of residues, which is rejected as invalid ; he takes his critique of mathematical probability as a vindication of Hume’s thesis that "probability or reasoning from conjecture may be divided into two kinds, viz., that which is founded on chance and that which arises from causes" ; Whewell’s consilience of induction is justified ; and from Keynes, he develops the notion of the "weight" of evidence but rejects his mathematicist approach.—M. A. F. (shrink)

In social networks, individual heterogeneity is widely existed, and an individual often tends to contact more frequently with friends of similar status or opinion. It is worth noting that the contact preference characteristic among heterogeneous individuals will have a significant effect on social contagions. Thus, we propose a social contagion model which takes the heterogeneity of individual influence and contact preference into account, and make a theoretical analysis of the social spreading process by developing an edge-based compartmental theory. We find (...) that the competition between simple contagion and complex contagion leads to the emergence of crossover phase transition phenomena when the influence of ordinary individuals is low: it changes from being hybrid to continuous, then to hybrid, and eventually to continuous phase transition with the increase of the contact probability of homogeneous individuals. However, it changes from being first-order to continuous phase transition when the influence strength of ordinary individuals is relatively high. In addition, there is an optimal value or range of contact probability of homogeneous individuals which maximizes the spreading size, and the optimal value or lower bound of the optimal range decreases with the increase of transmission probability. Our theoretical prediction results are in good agreement with the simulation results. (shrink)

Transition Probability (fidelity) for pairs of density operators can be defined as a “functor” in the hierarchy of “all” quantum systems and also within any quantum system. The Introduction of “amplitudes” for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong relations to the Riemann-Bures metric.

This study, based on the self-determination theory, investigates the link between university students' social peer and teacher integration and intrinsic motivation development. Both integration contexts are expected to contribute to the student's development, either additive or compensatory. The analyses rely on a nationally representative sample of 7,619 German university students and cover the time between the 3rd and 5th semesters in a longitudinal design. Person-centered analytical tools were applied to tap interindividual differences in the motivational trajectories as well as in (...) integration profiles. Latent transition analyses revealed distinct links between the motivational trajectories and the integration profiles, pointing to additive effects of teacher and peer integration. Positive trajectories were more likely in the Highly than in Moderately Integrated profiles. The two profiles pointing to below-average integration levels showed the same probabilities for rather negative trajectories. The results are discussed against the backdrop of self-determination theory and additive vs. compensatory effects of teacher and peer integration, proposing a threshold model. (shrink)

The modal interpretation of quantum theory ascribes at each instant physical magnitudes with definite values to quantum systems. Starting from certain natural requirements, I determine unique solutions for the evolution of these possessed magnitudes in free systems and in special cases of interacting systems. The evolution is given in terms of transition probabilities that relate the values of the possessed magnitudes at one instant to the values at a second instant. I also determine a joint property ascription to a (...) composite system and its separate subsystems. Finally, I give a proof that the predictions of the modal interpretation with respect to measurement outcomes agree with the predictions of the standard interpretation. (shrink)

SummaryFrom 1996 to 2006, Nepal experienced a substantial fertility decline, with the total fertility rate dropping from 4.6 to 3.1 births per woman. This study examines the associations between progress towards universal primary and secondary schooling and fertility decline in rural Nepal. Several hypotheses regarding mechanisms through which education affects current fertility behaviour are tested, including: the school environment during women's childhood; current availability of schools; knowledge of educational costs; and women's own educational attainment. Data for the analysis come from (...) the 2003–04 Nepal Living Standards Survey, a nationally representative random sample of households, which includes detailed data on fertility, household expenditure, educational attainment, demographic characteristics and the use of social services. Census and administrative data are also used to construct district-level gross enrolment ratios for primary and secondary schools during the women's childhood. Discrete dependent variable modelling techniques are used to estimate the effects of the following variables on the probability of women giving birth in a given year: district-level gross enrolment ratios for primary and secondary schools during women's childhood; having had a child previously in school; women's own educational level; current school availability; and other covariates. Separate models are estimated for the overall sample of rural women of reproductive age, and for parity-specific sub-samples. The results suggest that district-level gross enrolment ratios for secondary schools and, in some instances, having had a previous child enrolled in school are significant determinants of fertility in rural areas. These results are highly independent of women's own educational levels. Overall, the results suggest that, in the rural Nepal context, mass schooling influences the fertility transition through both community- and household-level pathways. (shrink)

Although social anthropologists have mostly abandoned the essentialist view of?culture? and?tradition?, these static notions are still frequently used in Serbian public discourse regarding women?s rights. I believe that analysing the production of cultural meaning and knowledge among different social actors and the state is important when exploring the implementation, transformation and protection of women?s rights at a local level. In this article, I shall investigate how?culture? and?tradition? are being constructed and used by certain right wing groups, political leaders, intellectuals and (...) by the Serbian Orthodox Church. On one side, arguments of?culture? and?tradition? are used in order to?preserve the national identity? and save it from?imposed Western norms? and?Western imperialism?, while on the other, they are used to explain the cultural obstacles regarding the effective protection of women?s rights.?Tradition?, often constructed as a linear project of inherited?cultural? and?moral? values and practices, stands in opposition to the EU; therefore, it calls to be nurtured and protected or changed and abandoned. Consequently, I see women rights issues trapped into a pro-EU or against EU, pro-traditional values or pro-liberal values discourse. I conclude that women rights in Serbia are and probably will be affected more by the use and abuse of different concepts of?culture? and?tradition?. nema. (shrink)

Window opening behavior in residential buildings has important theoretical significance and practical value for improving energy conservation, indoor thermal comfort, and indoor air quality. Climate and cultural differences may lead to different window opening behavior by residents. Currently, research on residential window opening behavior in northwest China has focused on indoor air quality, and few probabilistic models of residential window behaviors have been established. Therefore, in this study, we focused on an analysis of factors influencing window opening behavior and the (...) establishment of a predictive model for window opening behavior. Four typical residential buildings in different locations and building types in Xi’an were selected. The indoor and outdoor environments and window opening states were measured. Subsequently, a multivariate analysis of variance was used to determine the factors that had a significant effect on window opening behavior. Single- and multiparameter logistic regression models for window opening behavior were established. Of all the measured factors, we found that indoor temperature and CO2 concentration, outdoor temperature, and relative humidity had significant effects on window opening behavior, and indoor relative humidity and noise did not. Meanwhile, the temperature was positively correlated with the window opening probability, whereas indoor CO2 concentration and outdoor relative humidity were negatively correlated. The prediction accuracy of the multiparameter model was promising, at almost 75%, and the model can provide theoretical support for modelling residential buildings in Xi’an. (shrink)

The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but in all the examples considered there it remains symmetric. Here we present a class of binary models where the transition probability is not symmetric, using the extreme points of the unit interval in an order unit space as quantum logic. We show that their (...) state spaces are strictly convex smooth compact convex sets and that each such set _K_ gives rise to a quantum logic of this class with the state space _K_. The transition probabilities are symmetric iff _K_ is the unit ball in a Hilbert space. In this case, the quantum logic becomes identical with the projection lattice in a spin factor which is a special type of formally real Jordan algebra. (shrink)

Cognitive Science, Volume 46, Issue 4, April 2022.

There are two main approaches to how statistical patterns are extracted from sequences: The transitional probability approach proposes that statistical learning occurs through the computation of probabilities between items in a sequence. The chunking approach, including models such as PARSER and TRACX, proposes that units are extracted as chunks. Importantly, the chunking approach suggests that the extraction of full units weakens the processing of subunits while the transitional probability approach suggests that both units and subunits should strengthen. Previous (...) findings using sequentially organized, auditory stimuli or spatially organized, visual stimuli support the chunking approach. However, one limitation of prior studies is that most assessed learning with the two-alternative forced-choice task. In contrast, this pre-registered experiment examined the two theoretical approaches in sequentially organized, visual stimuli using an online self-paced task—arguably providing a more sensitive index of learning as it occurs—and a secondary offline familiarity judgment task. During the self-paced task, abstract shapes were covertly organized into eight triplets (ABC) where one in every eight was altered (BCA) from the canonical structure in a way that disrupted the full unit while preserving a subunit (BC). Results from the offline familiarity judgment task revealed that the altered triplets were perceived as highly familiar, suggesting the learned representations were relatively flexible. More importantly, results from the online self-paced task demonstrated that processing for subunits, but not unit-initial stimuli, was impeded in the altered triplet. The pattern of results is in line with the chunking approach to statistical learning and, more specifically, the TRACX model. (shrink)

Statistical properties in the visual environment can be used to improve performance on visual working memory tasks. The current study examined the ability to incidentally learn that a change is more likely to occur to a particular feature dimension and use this information to improve change detection performance for that dimension . Participants completed a change detection task in which one change type was more probable than others. Change probability effects were found for color and shape changes, but (...) not location changes, and intentional strategies did not improve the effect. Furthermore, the change probability effect developed and adapted to new probability information quickly. Finally, in some conditions, an improvement in change detection performance for a probable change led to an impairment in change detection for improbable changes. (shrink)

In 2006, Perruchet and Pacton (2006) asked whether implicit learning and statistical learning represent two approaches to the same phenomenon. This article represents an important follow‐up to their seminal review article. As in the previous paper, the focus is on the formation of elementary cognitive units. Both approaches favor different explanations on what these units consist of and how they are formed. Perruchet weighs up the evidence for different explanations and concludes with a helpful agenda for future research.

We construct, for any finite dimension n, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For n=2 our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions n .≥ 3 We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and (...) their relationship with the results of Fine [J. Math. Phys. 23 1306 (1982)]. (shrink)

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study (...) selected probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults. (shrink)

Identifying wordlike units in language is typically done by applying a battery of criteria, though how to weight these criteria with respect to one another is currently unknown. We address this question by investigating whether certain criteria are also used as cues for learning an artificial language—if they are, then perhaps they can be relied on more as trustworthy top‐down diagnostics. The two criteria for grammatical wordhood that we consider are a unit's free mobility and its internal immutability. These criteria (...) also map to two cognitive mechanisms that could underlie successful statistical learning: learners might orient themselves around the low transitional probabilities at unit boundaries, or they might seek chunks with high internal transitional probabilities. We find that each criterion has its own facilitatory effect, and learning is best where they both align. This supports the battery‐of‐criteria approach to diagnosing wordhood, and also suggests that the mechanism behind statistical learning may not be a question of either/or; perhaps the two mechanisms do not compete, but mutually reinforce one another. (shrink)

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.

We obtained an exact solution for a uniformly accelerated Unruh–DeWitt detector interacting with a massless scalar field in (3 + 1) dimensions which enables us to study the entire evolution of the total system, from the initial transient to late-time steady state. We find that the conventional transition probability of the detector from its initial ground state to excited states, as derived from time-dependent perturbation theory over an infinitely long duration of interaction, is valid only in the transient (...) stage and is invalid for cases with proper acceleration smaller than the damping constant. We also found that, unlike in (1 + 1)D results, the (3 + 1)D uniformly accelerated Unruh– DeWitt detector in a steady state does emit a positive radiated power of quantum nature at late-times, but it is not connected to the thermal radiance experienced by the detector in the Unruh effect proper. (shrink)

Despite recent efforts to improve on counterfactual theories of causation, failures to explain how effects depend on their causes are still manifest in a variety of cases. In particular, theories that do a decent job explaining cases of causal preemption have problems accounting for cases of causal intransitivity. Moreover, the increasing complexity of the counterfactual accounts makes it difficult to see why the concept of causation would be such a central part of our cognition. In this paper, I propose (...) an account of our causal thinking that not only explains the hitherto puzzling variety of causal judgments, but also makes it intelligible why we would employ such an elusive concept. (shrink)