The hypothesis that structural properties and not frequencies per se improve base-rate sensitivity is supported from the perspective of natural sampling. Natural sampling uses a special frequency format that makes base-rates redundant. Unfortunately, however, it does not allow us to empirically investigate human understanding of essential properties of uncertainty – most importantly, the understanding of conditional probabilities in Bayes' Theorem.

ABSTRACTTo build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: the conditional event interpretation in the coherencebased probability logic, the discourse processingtheory of Hans Kamp, and the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, (...) a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction. (shrink)

Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. We report four experiments which investigate three rules of SYSTEMP, namely the AND, the LEFT LOGICAL EQUIVALENCE, and the OR rule. The actual inferences of the subjects are compared with the coherent normative upper and lower probability bounds derived from a non-infinitesimal probability semantics of SYSTEM P. We found a relatively good agreement of human reasoning and principles of nonmonotonic (...) reasoning. Contrary to the results reported in the ‘heuristics and biases’ tradition, the subjects committed relatively few upper bound violations (conjunction fallacies). (shrink)

This commentary discusses three points: (1) The implications of the fact that it is rational to ignore base rates if probabilities are estimated by frequencies from samples without missing data (natural sampling); (2) second order probabilities distributions are a plausible way to model imprecise probabilities; and (3) Bayesian networks represent a normative reference for multi-cue models of probabilistic inference.

We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.

Probabilistic inference forms lead from point probabilities of the premises to interval probabilities of the conclusion. The probabilistic version of Modus Ponens, for example, licenses the inference from \({P(A) = \alpha}\) and \({P(B|A) = \beta}\) to \({P(B)\in [\alpha\beta, \alpha\beta + 1 - \alpha]}\) . We study generalized inference forms with three or more premises. The generalized Modus Ponens, for example, leads from \({P(A_{1}) = \alpha_{1}, \ldots, P(A_{n})= \alpha_{n}}\) and \({P(B|A_{1} \wedge \cdots \wedge A_{n}) = \beta}\) to an according interval for (...) P(B). We present the probability intervals for the conclusions of the generalized versions of Cut, Cautious Monotonicity, Modus Tollens, Bayes’ Theorem, and some SYSTEM O rules. Recently, Gilio has shown that generalized inference forms “degrade”—more premises lead to less precise conclusions, i.e., to wider probability intervals of the conclusion. We also study Adam’s probability preservation properties in generalized inference forms. Special attention is devoted to zero probabilities of the conditioning events. These zero probabilities often lead to different intervals in the coherence and the Kolmogorov approach. (shrink)

An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval (...) [0, 1]. Not all logically valid inference rules are probabilistically informative and vice versa. The relationship between logically valid and probabilistically informative inference rules is discussed and illustrated by examples such as the modus ponens or the affirming the consequent. We propose a method to evaluate the strength of CPL inference. (shrink)

Probability logic studies the properties resulting from the probabilistic interpretation of logical argument forms. Typical examples are probabilistic Modus Ponens and Modus Tollens. Argument forms with two premises usually lead from precise probabilities of the premises to imprecise or interval probabilities of the conclusion. In the contribution, we study generalized inference forms having three or more premises. Recently, Gilio has shown that these generalized forms ``degrade'' -- more premises lead to more imprecise conclusions, i. e., to wider intervals. We distinguish (...) different forms of degradation. We analyse Predictive Inference, Modus Ponens, Bayes' Theorem, and Modus Tollens. Special attention is devoted to the case where the conditioning events have zero probabilities. Finally, we discuss the relation of degradation to monotonicity. (shrink)

The paper investigates exchangeability in the context of probability logic. We study generalizations of basic inference rules and inferences involving cardinalities. We compare the results with those obtained in the case in which only identical probabilities are assumed.

A system of intermediate quantifiers (“Most S are P”, “m/n S are P”) is proposed for evaluating the rationality of human syllogistic reasoning. Some relations between intermediate quantifiers and probabilistic interpretations are discussed. The paper concludes by the generalization of the atmosphere, matching and conversion hypothesis to syllogisms with intermediate quantifiers. Since our experiments are currently still running, most of the paper is theoretical and intended to stimulate psychological studies.

Conditionals are central to inference. Before people can draw inferences about a natural language conditional, they must interpret its meaning. We investigated interpretation of uncertain conditionals using a probabilistic truth table task, focussing on (i) conditional event, (ii) material conditional, and (iii) conjunction interpretations. The order of object (shape) and feature (color) in each conditional's antecedent and consequent was varied between participants. The conditional event was the dominant interpretation, followed by conjunction, and took longer to process than conjunction (mean di (...) erence 500 ms). Material conditional responses were rare. The proportion of conditional event responses increased from around 40% at the beginning of the task to nearly 80% at the end, with 55% of participants showing a qualitative shift of interpretation. Shifts to the conditional event occurred later in the feature-object order than in the object-feature order. We discuss the results in terms of insight and suggest implications for theories of interpretation. (shrink)

We investigated how people interpret conditionals and how stable their interpretation is over a long series of trials. Participants were shown the colored patterns on each side of a six-sided die, and were asked how sure they were that a conditional holds of the side landing upwards when the die is randomly thrown. Participants were presented with 71 trials consisting of all combinations of binary dimensions of shape (e.g., circles and squares) and color (e.g., blue and red) painted onto the (...) sides of each die. In two experiments (N1 = 66, N2 = 65), the conditional event was the dominant interpretation, followed by conjunction, and material conditional responses were negligible. In both experiments, the percentage of participants giving a conditional event response increased from around 40% at the beginning of the task to nearly 80% at the end, with most participants shifting from a conjunction interpretation. The shift was moderated by the order of shape and color in each conditional’s antecedent and consequent: participants were more likely to shift if the antecedent referred to a color. In Experiment 2 we collected response times: conditional event interpretations took longer to process than conjunction interpretations (mean difference 500 ms). We discuss implications of our results for mental models theory and probabilistic theories of reasoning. (shrink)

Recently, there has been renewed interest in so-called evidence-based policy making. Enticed by the grand promises of Big Data, public officials seem increasingly inclined to experiment with more data-driven forms of governance. But while the rise of Big Data and related consequences has been a major issue of concern across different disciplines, attempts to develop a better understanding of the phenomenon's historical foundations have been rare. This short commentary addresses this gap by situating the current push for numerical evidence within (...) a broader socio-political context, demonstrating how the epistemological claims of Big Data science intersect with specific forms of trust, truth, and objectivity. We conclude by arguing that regulators' faith in numbers can be attributed to a distinct political culture, a representative democracy undermined by pervasive public distrust and uncertainty. (shrink)

The notion of trustworthy AI has been proposed in response to mounting public criticism of AI systems, in particular with regard to the proliferation of such systems into ever more sensitive areas of human life without proper checks and balances. In Europe, the High-Level Expert Group on Artificial Intelligence has recently presented its Ethics Guidelines for Trustworthy AI. To some, the guidelines are an important step for the governance of AI. To others, the guidelines distract effort from genuine AI regulation. (...) In this chapter, we engage in a critical discussion of the concept of trustworthy AI by probing the concept both on theoretical and practical grounds, assessing its substance and the feasibility of its intent. We offer a concise overview of the guidelines and their vision for trustworthy AI and examine the conceptual underpinnings of trustworthy AI by considering how notions of 'trust' and 'trustworthiness' have been discussed in the philosophical literature. We then discuss several epistemic obstacles and moral requirements when striving to achieve trustworthy AI in practice before concluding with an argument in support of the establishment of a trustworthy AI culture that respects and protects foundational values. (shrink)

The threat-advantage hypothesis that threatening or negative faces can be discriminated preattentively has often been tested in the visual search paradigm with schematic stimuli. The results have been heterogeneous, suggesting that the choice of particular stimuli have profound effects on search efficiency. Because this conclusion is hampered by differences in experimental procedure, I selected examples from past literature and presented replicas of stimulus pairs (schematic positive and negative faces) in a within-participants design. Although there was a consistent advantage for angry-face (...) targets, search efficiency varied between 8 and 35 ms/item, yielding no clear evidence for the threat-advantage hypothesis. Furthermore, search efficiency for negative- and positive-face targets was highly correlated over stimulus pairs, which implies that whatever complicates the search for the negative face of a pair also complicates the search for the positive face. This results pattern argues against the hypothesised preattentive detector. (shrink)

Cognitive and biological theories of emotion consider surprise as an emotional response to unexpected events. Four experiments examined the latency and the duration of one behavioural component of surprise: The interruption of ongoing action. Participants were presented with an unannounced visual event—the appearance of new perceptual objects—during the execution of a continuous action—a rapid alternate finger tapping—which allowed a precise measurement of the latency, and the duration of an action interruption induced by the surprising event. Of the participants, 78% interrupted (...) the tapping with a mean latency of 214 ms and a mean duration of 995 ms. Variations of the number and perceptual heterogeneity of the new objects revealed that the perceptual analysis of the surprising event contributes significantly to the interruption duration. (shrink)

The properties of the phosphate uptake system of the cyanobacterium Anacystis nidulans have been studied during the transition from a phosphate-deficient non-growing state to a non-deficient growing state. In the phosphate-deficient state the high affinity phosphate transport system in the cell membrane is extremely adaptive. As a result of these adaptive features the phosphate transport system cannot be described by determinate, fixed parameters, because the transport system is influenced by the measurement of the uptake process itself. When the growing state (...) has been initiated by a persisting phosphate pulse, the transport system rapidly loses its adaptive features and can then be characterized by determinate parameters that remain unchanged for a long period of time, even if no uptake occurs in that time. Depending on the amount of phosphate stored during a pulse the cell makes a choice between slow or fast growth. In the latter case the light harvesting and energy converting machinery is completely reorganized before growth commences. Thereby the components of this machinery conform to each other and to the stable properties of the phosphate transport system. It is suggested that the mutual adjustment of these adaptive energy converting subunits is guided by attractors that function as the final cause for the development of the whole system.An application of this model to an analysis of the selforganization of aquatic ecosystems is discussed. (shrink)

Die zentrale Rolle des Gedächtnisses in der Entwicklung von Lebewesen wurde von Biologen wie Ernst Haeckel, Ewald Hering und Jakob von Uexküll erkannt, wobei zwischen einem Artgedächtnis und einem individuellen Gedächtnis unterschieden wird. Ersteres ist für die Aufrechterhaltung und Weiterentwicklung einer artspezifischen Erscheinungsform verantwortlich, letzteres gestaltet die Erinnerung an individuelle Erfahrungen. Im vorliegenden Band werden die Vorstellungen dieser Biologen mit Ideen der Philosophen G.W.F. Hegel, Alfred N. Whitehead, John Dewey, Ernst Cassirer, Henri Bergson und Reto L. Fetz in einer kohärenten (...) Theorie der Organismen, die auch den Menschen und seine Geschichte umfasst, aufeinander abgestimmt. (shrink)

Using a generalized conception of experience, from which all features characteristic for higher animals (such as consciousness and thought) have been removed, allowed relating experience to adaptive processes in lower organisms. The temporal vector character of every current experience, containing as well memories of past experiences as intentions for future activities, can then be found in the adaptive response of cyanobacteria to alterations in phosphate supply, particularly in energetic manifestations of this phenomenon. A possible analogy between adaptive events as the (...) “atomic units” of physiological adaptation and Whitehead's actual occasion of experience is discussed. (shrink)

In an everyday private practice setting, regularly also existential topics will emerge from doctor-patient encounters. These are often questions of coping with life and lifestyle. To enable a thorough discussion of such topics, an implicit, and sometimes also explicit reference to a philosophical background is needed. Philosophical concepts to be used in this realm are discussed. An individual patient-doctor interaction is used as an example to demonstrate the doctor’s choice of hermeneutical and phenomenological philosophical concepts.

In an everyday private practice setting, regularly also existential topics will emerge from doctor-patient encounters. These are often questions of coping with life and lifestyle. To enable a thorough discussion of such topics, an implicit, and sometimes also explicit reference to a philosophical background is needed. Philosophical concepts to be used in this realm are discussed. An individual patient-doctor interaction is used as an example to demonstrate the doctor’s choice of hermeneutical and phenomenological philosophical concepts.

This essay raises a philosophical question concerning the language of Life Theory. It aims to prove the assumption that in contrast to Life Science, which today is connected to neuroscience and biotechnology, a theory that comprehends “life itself” must exceed the computerized mathematics of modern materialistic positivism. For this purpose, the conceptual possibility of such a theory is analysed from the perspective of 20th century philosophy of life. Beginning with Henri Bergson, who developed an immanent concept of life“from within itself” (...) in L’évolution créatrice, the analysis turns to Alain Badiou, whose fundamental onto-phenomenology of being is summed up in Logiques des mondes by answering the question “what is it to live”. The comparison between the two philosophies exposes the conditions of a Life Theory that encompasses, beyond the results of the digitalizable language translated from the neurons of the human brain, the uncountable and unpredictable aspects of living and being alive. These conditions are: an ethics of universality, a differential philosophy of time, and a concept of independent novelty enforced by the aesthetics of subjective creation. (shrink)