We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.

From his earliest student days through the writing of his last book, Charles Darwin drew diagrams. In developing his evolutionary ideas, his preferred form of diagram was the tree. An examination of several of Darwin’s trees—from sketches in a private notebook from the late 1830s through the diagram published in the Origin—opens a window onto the role of diagramming in Darwin’s scientific practice. In his diagrams, Darwin simultaneously represented both observable patterns in nature and conjectural narratives of (...) evolutionary history. He then brought these natural patterns and narratives into dialogue, allowing him to explore whether the narratives could explain the patterns. But Darwin’s diagrams did not reveal their meaning directly to passive readers; they required readers to engage dynamically with them in order to understand the connections they disclosed between patterns and narratives. Moreover, the narratives Darwin depicted in his diagrams did not represent past sequences of events that he claimed had actually occurred; the narratives were conjectural, schematic, and probabilistic. Instead of depicting actual histories in all their particularity, Darwin depicted narratives in his diagrams in order to make general claims about how nature works. The conjunction of these features of Darwin’s diagrams is central to how they do their epistemic work. (shrink)

Brackets and tables, circles and maps, 1554-1872 -- Early botanical networks and trees, 1766-1815 -- The first evolutionary tree, 1786-1820 -- Diverse and unusual trees of the early nineteenth century, 1817-1834 -- The rule of five, 1819-1854 -- Pre-Darwinian branching diagrams, 1828-1858 -- Evolution and the trees of Charles Darwin, 1837-1868 -- The trees of Ernst Haeckel, 1866-1905 -- Post-Darwinian nonconformists, 1868-1896 -- More late-nineteenth-century trees, 1874-1897 -- Trees of the early twentieth century, 1901-1930 -- The trees of (...) Alfred Sherwood Romer, 1933-1966 -- Additional trees of the mid-twentieth century, 1931-1943 -- The trees of William King Gregory, 1938-1951 -- Hints of new approaches, 1954-1969 -- Phenograms and cladograms, 1958-1966 -- Early molecular trees, 1962-1987 -- Notable trees of the past four decades, 1970-2010 -- Primeval branches and universal trees of life, 1997-2010. (shrink)

Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the game tree representation and (...) solution technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks. (shrink)

The sole diagram in On the Origin of Species is generally considered to be merely an illustration of Darwin’s ideas, but such an interpretation ignores the fact that Darwin himself expressly stated that the diagram helped him to discover and express his ideas. This article demonstrates that developing the so-called “tree diagram” substantially aided Darwin’s heuristics. This demonstration is based on an interpretation of the diagram and of 17 sketches found in Darwin’s scientific papers. The key to this interpretation (...) is the meaning that Darwin assigned to the graphic elements he used to construct the preliminary sketches and the diagram. I argue that each of the sketches contributed to the shaping of Darwin’s ideas and that, in their succession, each added new elements that ultimately resulted in the fully developed published diagram. (shrink)

This paper presents an analysis of Seneca's 58th letter to Lucilius and Porphyry's Isagoge, which were the origin of the tree diagrams that became popular in philosophy and logic from the early Middle Ages onwards. These diagrams visualise the extent to which a concept can be understood as a category, genus, species or individual and what the method of dihairesis (division) means. The paper explores the dissimilarities between Seneca's and Porphyry's tree structures, scrutinising them through the (...) perspective of modern graph theory. Although traditional trees can be interpreted in a modern way, their terms and definitions defy modern standardisation. These distinctions are not only useful for differentiating between Seneca's and Porphyry's trees, but also for comprehending the evolution of this philosophical tradition. Thus the paper highlights the continued significance of these tree diagrams in analysing concepts and categories in philosophy and structuring objects and information in modern fields such as artificial intelligence, computer science, bioinformatics, graph theory, and many more. (shrink)

"The Natural System" is the name given to the underlying arrangement present in the diversity of life. Unlike a classification, which is made up of classes and members, a system or arrangement is an integrated whole made up of connected parts. In the pre-evolutionary period a variety of forms were proposed for the Natural System, including maps, circles, stars, and abstract multidimensional objects. The trees sketched by Darwin in the 1830s should probably be considered the first genuine evolutionary diagrams (...) of the Natural System—the first genuine evolutionary trees. Darwin refined his image of the Natural System in the well-known evolutionary tree published in the Origin of Species, where he also carefully distinguished between arrangements and classifications. Following the publication of the Origin, there was a great burst of evolutionary tree building, but interest in trees declined substantially after 1900, only to be revived in recent years with the development of cladistic analysis. ¶ While evolutionary trees are modern diagrams of the Natural System, they are at the same time instances of another broad class of diagrams that may be called "trees of history": branching diagrams of genealogical descent and change. During the same years that Darwin was sketching his first evolutionary trees, the earliest examples of two other trees of history also appeared: the first trees of language evolution and of manuscript genealogy. Though these were apparently independent of evolutionary trees in their origin, the similarities among all these trees of history, and among the historical processes that underlie them, were soon recognized. Darwin compared biological evolution and language evolution several times in the Origin of Species, and both Ernst Haeckel and the linguist August Schleicher made similar comparisons. Both linguists and stemmaticists (students of manuscript descent) understood the principle of apomorphy—the principle that only shared innovations provide evidence of common ancestry—more clearly than did systematists, and if there had been more cross-fertilization among these fields the cladistic revolution in systematics might well have taken place in the nineteenth century. ¶ Although historical linguists and stemmaticists have in some respects had sounder theory than have systematists, at least until recently, they have also had the practical problem of very large amounts of data, a problem not often faced by systematists until the advent of molecular sequencing. The opportunity now exists for systematists to contribute to the theory and practice of linguistics and stemmatics, their sister disciplines in historical reconstruction, through application of our commonly used computer programs for tree estimation. Preliminary results from the application of numerical cladistic analysis to a large stemmatic data set have been very encouraging, and have already generated much discussion in the stemmatics community. (shrink)

Stem cells did not become a proper research object until the 1960 s. Yet the term and the basic mind-set—namely the conception of single undifferentiated cells, be they embryonic or adult, as the basic units responsible for a directed process of development, differentiation and increasing specialisation—were already in place at the end of the nineteenth century and then transmitted on a non-linear path in the form of tropes and diagrams. Ernst Haeckel and August Weismann played a special role in (...) this story. The first coined the term Stammzelle (stem cell), the second was the author of the first cellular stem-tree diagram. Even today, I shall argue, the understanding of stem cells, especially the popular perception, is to a large extent a Haeckelian–Weismannian one. After having demonstrated this, by analysing the terminology, in this essay I will focus on the use of cytogenetic tree diagrams between 1892 and 1925 and on the tacit understanding of stem cells that they transmit. (shrink)

From the 1960s, mathematical and computational tools have been developed to arrive at human population trees from various kinds of serological and molecular data. Focusing on the work of the Italian-born population geneticist Luigi Luca Cavalli-Sforza, I follow the practices of tree-building and mapping from the early blood-group studies to the current genetic admixture research. I argue that the visual language of the tree is paralleled in the narrative of the human diasporas, and I show how the (...) class='Hi'>tree was actually mapped onto the surface of the earth. This visual and textual structure is mirrored in the liberal discourse of unity in diversity that has been criticized as running counter to the socio-political effects of human population genetics. From this perspective, one may ask how far the phylogenetic diagram in its various forms is a manifestation of the physics of power that according to Michel Foucault consists in mechanisms that analyse distributions, movements, series, combinations, and that uses instruments to render visible, to register, to differentiate and to compare. It is one among other disciplinary technologies that ensure the ordering of human diversity. In the case of intra-human phylogenetic trees, population samples and labels are one issue. Another is that the separated branches seem to show groups of people, who have in reality been interacting and converging, as isolated. Often based on so-called isolated peoples, molecular tree diagrams freeze a hierarchical kinship system that is meant to represent a state before the great historical population movements. (shrink)

In this paper we analyse some questions concerning trees on κ, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in [6, Question 5.2] about the diagram for regularity properties.

The "tree of life" iconography, representing the history of life, dates from at least the latter half of the 18th century, but evolution as the mechanism providing this bifurcating history of life did not appear until the early 19th century. There was also a shift from the straight line, scala naturae view of change in nature to a more bifurcating or tree-like view. Throughout the 19th century authors presented tree-like diagrams, some regarding the Deity as the (...) mechanism of change while others argued for evolution. Straight-line or anagenetic evolution and bifurcating or cladogenetic evolution are known in biology today, but are often misrepresented in popular culture, especially with anagenesis being confounded with scala naturae. Although well known in the mid 19th century, the geologist Edward Hitchcock has been forgotten as an early, if not the first author to publish a paleontologically based "tree of life" beginning in 1840 in the first edition of his popular general geology text Elementary Geology. At least 31 editions were published and those between 1840 and 1859 had this "paleontological chart" showing two trees, one for fossil and living plants and another for animals set within a context of geological time. Although the chart did not vary in later editions, the text explaining the chart did change to reflect newer ideas in paleontology and geology. Whereas Lamarck, Chambers, Bronn, Darwin, and Haeckel saw some form of transmutation as the mechanism that created their "trees of life," Hitchcock, like his contemporaries Agassiz and Miller, who also produced "trees of life," saw a deity as the agent of change. Through each edition of his book Hitchcock denounced the newer transmutationist hypotheses of Lamarck, then Chambers, and finally Darwin in an 1860 edition that no longer presented his tree-like "paleontological chart.". (shrink)

Twenty-two years after Charles Darwin began to think of character divergence from a common ancestor in his Notebook B, the now famous and iconic branching diagram appeared in the fourth chapter of On the Origin of Species.

This article reports the results of an experiment involving 108 college students with varying backgrounds in biology. Subjects answered questions about the evolutionary history of sets of hominid and equine taxa. Each set of taxa was presented in one of three diagrammatic formats: a noncladogenic diagram found in a contemporary biology textbook or a cladogram in either the ladder or tree format. As predicted, the textbook diagrams, which contained linear components, were more likely than the cladogram formats to (...) yield explanations of speciation as an anagenic process, a common misconception among students. In contrast, the branching cladogram formats yielded more appropriate explanations concerning levels of ancestry than did the textbook diagrams. Although students with stronger backgrounds in biology did better than those with weaker biology backgrounds, they generally showed the same effects of diagrammatic format. Implications of these results for evolution education and for diagram design more generally are discussed. (shrink)

The "tree of life" iconography, representing the history of life, dates from at least the latter half of the 18th century, but evolution as the mechanism providing this bifurcating history of life did not appear until the early 19th century. There was also a shift from the straight line, scala naturae view of change in nature to a more bifurcating or tree-like view. Throughout the 19th century authors presented tree-like diagrams, some regarding the Deity as the (...) mechanism of change while others argued for evolution. Straight-line or anagenetic evolution and bifurcating or cladogenetic evolution are known in biology today, but are often misrepresented in popular culture, especially with anagenesis being confounded with scala naturae. Although well known in the mid 19th century, the geologist Edward Hitchcock has been forgotten as an early, if not the first author to publish a paleontologically based "tree of life" beginning in 1840 in the first edition of his popular general geology text Elementary Geology. At least 31 editions were published and those between 1840 and 1859 had this "paleontological chart" showing two trees, one for fossil and living plants and another for animals set within a context of geological time. Although the chart did not vary in later editions, the text explaining the chart did change to reflect newer ideas in paleontology and geology. Whereas Lamarck, Chambers, Bronn, Darwin, and Haeckel saw some form of transmutation as the mechanism that created their "trees of life," Hitchcock, like his contemporaries Agassiz and Miller, who also produced "trees of life," saw a deity as the agent of change. Through each edition of his book Hitchcock denounced the newer transmutationist hypotheses of Lamarck, then Chambers, and finally Darwin in an 1860 edition that no longer presented his tree-like "paleontological chart.". (shrink)

The history of biological systematics documents a continuing tension between classifications in terms of nested hierarchies congruent with branching diagrams (the ‘Tree of Life’) versus reticulated relations. The recognition of conflicting character distribution led to the dissolution of the scala naturae into reticulated systems, which were then transformed into phylogenetic trees by the addition of a vertical axis. The cladistic revolution in systematics resulted in a representation of phylogeny as a strictly bifurcating pattern (cladogram). Due to the ubiquity (...) of character conflict—at the genetic or morphological level, or at any level in between—some characters will necessarily have to be discarded ( qua noise) in favor of others in support of a strictly bifurcating phylogenetic tree. Pattern analysts will seek maximal congruence in the distribution of characters (ultimately of any kind) relative to a branching tree-topology; process explainers will call such tree-topologies into question by reference to incompatible evolutionary processes. Pattern analysts will argue that process explanations must not be brought to bear on pattern reconstruction; process explainers will insist that the reconstructed pattern requires a process explanation to become scientifically relevant, i.e., relevant to evolutionary theory. The core question driving the current debate about the adequacy of the ‘Tree of Life’ metaphor seems to be whether the systematic dichotomization of the living world is an adequate representation of the complex evolutionary history of global biodiversity. In ‘Questioning the Tree of Life’, it seems beneficial to draw at least four conceptual distinctions: pattern reconstruction versus process explanation as different epistemological approaches to the study of phylogeny; open versus closed systems as expressions of different kinds of population (species) structures; phylogenetic trees versus cladograms as representations of evolutionary processes versus patterns of relationships; and genes versus species as expressions of different levels of causal integration and evolutionary transformation. (shrink)

The Distributional Compositional Categorical model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that (...) could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, something which the other methods lack, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The type-logic used in the DisCoCat model is Lambekʼs pregroup grammar. Pregroup types form a posetal compact closed category, which can be passed, in a functorial manner, on to the compact closed structure of vector spaces, linear maps and tensor product. The diagrammatic versions of the equational reasoning in compact closed categories can be interpreted as the flow of word meanings within sentences. Pregroups simplify Lambekʼs previous type-logic, the Lambek calculus. The latter and its extensions have been extensively used to formalise and reason about various linguistic phenomena. Hence, the apparent reliance of the DisCoCat on pregroups has been seen as a shortcoming. This paper addresses this concern, by pointing out that one may as well realise a functorial passage from the original type-logic of Lambek, a monoidal bi-closed category, to vector spaces, or to any other model of meaning organised within a monoidal bi-closed category. The corresponding string diagram calculus, due to Baez and Stay, now depicts the flow of word meanings, and also reflects the structure of the parse trees of the Lambek calculus. (shrink)

A new construction of a certain conceptual space is presented. Elements of this conceptual space correspond to concept elements of reality, which potentially comprise an infinite number of qualities. This construction of a conceptual space solves a problem stated by Dietz and his co-authors in 2013 in the context of Voronoi diagrams. The fractal construction of the conceptual space is that this problem simply does not pose itself. The concept of convexity is discussed in this new conceptual space. Moreover, (...) the meaning of convexity is discussed in full generality, for example when space is deprived of it, its substitutes for concept domains are considered. (shrink)

The discourse marker use of the word like is considered by many to be superfluously sprinkled into talk, a bad habit best avoided. But a comparison of the use of like in successive tellings of stories demonstrates that like can be anticipated in advance and planned into stories. In this way, like is similar to other words and phrases tellers recycle during story telling. The anticipation of like contrasted with the uses of other discourse markers such as oh, you know, (...) and well, which almost never re-occurred in similar locations across tellings. Um and uh did sometimes re-occur; these uses are contrasted with like. Although discourse markers are generally used on the fly to handle various issues that come up in coordinating talk as it unfolds, like can be used as an integral part of the story -a marked contrast to the prevalent idea that likes are speech tics. (shrink)

Words like well, oh, and you know have long been observed and studied in spontaneous speech. With the proliferation of on-line dialogues, such as instant messaging between friends or back-and-forth postings at websites, there are increasing opportunities to observe them in spontaneous writing. In Experiment 1, the interpretation of discourse markers in on-line debates was compared to proposed functions of those markers identified in other settings. In Experiment 2, the use of discourse markers in spontaneous speech was compared to their (...) uses in spontaneous writing. Results support the conclusion that although they vary in frequency in spoken versus written domains, discourse markers are used similarly across domains, but with particular communicative functions that make them non-interchangeable. (shrink)

To generate empathy in the care of vulnerable older persons requires care providers to reflect critically on their care practices. Ethics education and training must provide them with tools to accomplish such critical reflection. It must also create a pedagogical context in which good care can be taught and cultivated. The care-ethics lab ‘sTimul’ originated in 2008 in Flanders with the stimulation of ethical reflection in care providers and care providers in training as its main goal. Also in 2008, sTimul (...) commenced the organization of empathy sessions as an attempt to achieve this goal by simulation. The empathy session is a practical and fairly straightforward way of working to provoke care providers and care providers in training to engage in ethical reflection. Characteristic of the empathy session in the care-ethics lab is the emphasis on experience as a basis for ethical reflection. (shrink)

Observing others in conversation is a common format for comprehending language, yet little work has been done to understand dialog comprehension. We tested whether overhearers use addressee backchannels as predictive cues for how to integrate information across speaker turns during comprehension of spontaneously produced collaborative narration. In Experiment 1, words that followed specific backchannels were recognized more slowly than words that followed either generic backchannels or pauses. In Experiment 2, we found that when the turn after the backchannel was a (...) continuation of the narrative, specific backchannels prompted the fastest verification of prior information. When the turn after was an elaboration, they prompted the slowest, indicating that overhearers took specific backchannels as cues to integrate preceding talk with subsequent talk. These findings demonstrate that overhearers capitalize on the predictive relationship between backchannels and the development of speakers’ talk, coordinating information across conversational roles. (shrink)

We explored the differential impact of auditory information and written contextual information on the recognition of verbal irony in spontaneous speech. Based on relevance theory, we predicted that speakers would provide acoustic disambiguation cues when speaking in situations that lack other sources of information, such as a visual channel. We further predicted that listeners would use this information, in addition to context, when interpreting the utterances. People were presented with spontaneously produced ironic and nonironic utterances from radio talk shows in (...) written or auditory form, with or without written contextual information. When the utterances were read without written contextual information, all utterances were rated as equally ironic. But when they were heard as opposed to read, or when they were presented in irony-biasing contexts, originally ironic utterances were rated as more sarcastic than originally nonironic utterances. This evidence suggests both acoustic and contextual information are used when inferring ironic intent in spontaneous speech, and validates previous manipulations of intonation in studies of irony understanding. (shrink)

A generation before Beardsley, legal scholar John Henry Wigmore invented a scheme for representing arguments in a tree diagram, aimed to help advocates analyze the proof of facts at trial. In this essay, I describe Wigmore's "Chart Method" and trace its origin and influence. Wigmore, I argue, contributes to contemporary theory in two ways. His rhetorical approach to diagramming provides a novel perspective on problems about the theory of reasoning, premise adequacy, and dialectical obligations. Further, he advances a novel (...) solution to the problem of assessing argument quality by representing the strength of argument in meeting objections. (shrink)

The COVID-19 pandemic has presented a global threat to physical and mental health worldwide. Research has highlighted adverse impacts of COVID-19 on wellbeing but has yet to offer insights as to how wellbeing may be protected. Inspired by developments in wellbeing science and guided by our own theoretical framework, we examined the role of various potentially protective factors in a sample of 138 participants from the United Kingdom. Protective factors included physical activity, tragic optimism, gratitude, social support, and nature connectedness. (...) Initial analysis involved the application of one-sample t-tests, which confirmed that wellbeing in the current sample was significantly lower compared to previous samples. Protective factors were observed to account for up to 50% of variance in wellbeing in a hierarchical linear regression that controlled for a range of sociostructural factors including age, gender, and subjective social status, which impact on wellbeing but lie beyond individual control. Gratitude and tragic optimism emerged as significant contributors to the model. Our results identify key psychological attributes that may be harnessed through various positive psychology strategies to mitigate the adverse impacts of hardship and suffering, consistent with an existential positive psychology of suffering. (shrink)

This article discusses ways to operationalise the concept of culturally appropriate computer-mediated communication, utilising information systems (IS) development methodologies and adopting a postmodern and postcolonial perspective. By way of illustration, it describes progress on the participative development of the Ieramugadu Cultural Information System. This project is designed to develop and evaluate innovative procedures for elicitation, analysis, storage and communication of indigenous cultural heritage information. It is investigating culturally appropriate IS design techniques, multimedia approaches and ways to ensure protection of secret/sacred (...) information. Ethical issues are foregrounded. (shrink)

Peerages and baronetages were successful commercial directories sold by a number of prominent London booksellers from the beginning of the 18th century. They provided an account of most titled families (peers as well as baronets). As serial publications, they were intended for a larger public in need of identification tools in a context of expanding urban sociability and of major recomposition within the elites. In these pocket books, there were no longer the elaborate tree diagrams that had ornamented (...) most of the visitation books of the College of Arms, and which still could be found among ancient family papers. This transition was required for technical, commercial, and also ideological reasons. The selling point for publishers was to provide an up-to-date account of the ‘modern’ families, which could be better achieved through alphabetical listings, biographical discourses, or tabular charts. However, this formal reconfiguration led to many criticisms. These family directories were accused of compromising the dignity of titled families. The idea of a lost Golden Age when ancient lineages had been exhibited on stone, wooden panels, or vellum regained some appeal among social commentators. After 1760, with the renewal of radicalism and the onset of the age of revolutions, tree thinking came to be rehabilitated, but was also reinvented to better defend and naturalise social hierarchies. In this context, trees were increasingly used as powerful national emblems and less as dynastic emblems. The changing fortunes of family trees in 18th-century British prints enable us to reflect on the ideological aspects of the visualisation of kinship. (shrink)

There has been little previous scholarship regarding the aims, options and impact of ethics education on residential care‐givers. This manuscript details findings from a pragmatic cluster trial evaluating the impact of three different approaches to ethics education. The focus of the article is on one of the interventions, an immersive simulation experience. The simulation experience required residential care‐givers to assume the profile of elderly care‐recipients for a 24‐hr period. The care‐givers were student nurses. The project was reviewed favourably by a (...) university ethics committee, and participants provided informed consent. Data from six postsimulation experience focus groups were analysed thematically and three themes were identified: the experience of vulnerability, dignity in care and the organisation of care. Findings suggest that the immersive simulation experience had a powerful immediate impact as participants described epiphanous insights relating to their care experiences. It is suggested that reflecting on and recording epiphanous events has the potential to sustain ethical care practices. Further research is required to evaluate the impact of different ethics education interventions in different cultural contexts. Exploration is also required regarding the meaning and significance of care epiphanies, those “most delicate and evanescent of moments,” for the sustainability of ethical care. (shrink)

Bilingualism has been identified as a potential cognitive factor linked to delayed onset of dementia as well as boosting executive functions in healthy individuals. However, more recently, this claim has been called into question following several failed replications. It remains unclear whether these contradictory findings reflect how bilingualism is defined between studies, or methodological limitations when measuring the bilingual effect. One key issue is that despite the claims that bilingualism yields general protection to cognitive processes, studies reporting putative bilingual differences (...) are often focused on domain specific experimental paradigms. This study chose a broader approach, by considering the consequences of bilingualism on a wide range of cognitive functions within individuals. We utilised 19 measures of different cognitive functions commonly associated with bilingual effects, to form a “cognitive profile” for 215 non-clinical participants. We recruited Welsh speakers, who as a group of bilinguals were highly homogeneous, as means of isolating the bilingualism criterion. We sought to determine if such analyses would independently classify bilingual/monolingual participant groups based on emergent patterns driven by collected cognitive profiles, such that population differences would emerge. Multiple predictive models were trained to independently recognise the cognitive profiles of bilinguals, older adults and higher education attainment. Despite managing to successfully classify cognitive profiles based on age and education, the model failed to differentiate between bilingual and monolingual cognitive ability at a rate greater than that of chance. Repeated modelling using alternative definitions of bilingualism, and just the older adults, yielded similar results. In all cases then, using our “bottom–up” analytical approach, there was no evidence that bilingualism as a variable indicated differential cognitive performance – as a consequence, we conclude that bilinguals are not cognitively different from their monolingual counterparts, even in older demographics. We suggest that studies that have reported a bilingual advantage could well have confounded other key variables that may be driving reported advantages. We recommend that future research refine the machine learning methods used in this study to further investigate the complex relationship between bilingualism and cognition. (shrink)

The aim of this chapter is to develop a semantics for Calculus CL. CL is a diagrammatic calculus based on a logic machine presented by Johann Christian Lange in 1714, which combines features of Euler-, Venn-type, tree diagrams, squares of oppositions etc. In this chapter, it is argued that a Boolean account of formal ontology in CL helps to deal with logical oppositions and inferences of extended syllogistics. The result is a combination of Lange’s diagrams with an (...) algebraic semantics of terms: Bit-CL, in which any ordered objects are identified by characteristic bitstrings. Then, a number of objections to Bit-CL are answered to, and the process of inference is explained in this new logical framework. (shrink)

For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer & Hoffrage, 1995). In a recent meta-analysis, McDowell & Jacobs (2017) showed that presenting a task in natural frequency format increases performance rates to 24% compared to only 4% when the same task is presented in probability format. Nevertheless, on average three quarters of participants in their meta-analysis failed to obtain the correct solution for such a task (...) in frequency format. In this paper, we present an empirical study on what participants typically do wrong when confronted with natural frequencies. We found that many of them did not actually use natural frequencies for their calculations, but translated them back into complicated probabilities instead. This switch from the intuitive presentation format to a less intuitive calculation format will be discussed within the framework of psychological theories (e.g., the Einstellung effect). (shrink)

People often struggle with Bayesian reasoning. However, research showed that people’s performance (and rationality) can be supported by the way of representing the statistical information. First, research showed that using natural frequencies instead of probabilities as format of statistical information increases people’s performance in Bayesian situations thoroughly. Second, research also yielded that people’s performance increases through using visualization. We build our paper on existing research in this field. The main aim is to analyse people’s strategies in Bayesian situations that are (...) still erroneous although statistical information is represented by natural frequencies and visualizations. In particular, we compare two pairs of visualization with similar numerical information (tree diagram vs. unit square and double-tree diagram vs. 2x2-table) concerning their impact on people’s erroneous strategies in Bayesian situations. For this aim, we conducted an experiment with 540 university students. The students were randomly assigned to four conditions that are defined by the four different visualizations of statistical information. The students were asked to indicate a fraction as response in four Bayesian situations. We documented the numerator and the denominator of the students’ responses representing a basic set and a subset in a Bayesian situation. Our results show that people’s erroneous strategies are highly dependent on the visualization. A central finding is that the visualization’s characteristic of making the nested-sets structure of a Bayesian situation transparent has a facilitating effect on people’s Bayesian reasoning. For example, compared to the unit square, a tree diagram does not explicitly visualize the set-subset relations that are relevant in a Bayesian situation. Accordingly, compared to a unit square, a tree diagram partly hinders people to find the correct denominator in a Bayesian situation, and, in particular, triggers to select a wrong numerator. By analyzing people’s erroneous strategies in Bayesian situations, we contribute to investigating approaches to facilitate Bayesian reasoning and to further develop the teaching of Bayesian reasoning. (shrink)

Bayes’ formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes’ formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies. In addition to this numerical format, we used five visualizations: a 2×2-table, a unit (...) square, an icon array, a tree diagram, and a double-tree diagram. In an experiment with 688 undergraduate students, we empirically investigated the effectiveness of three graphical properties of visualizations: area-proportionality, use of discrete and countable statistical entities, and graphical transparency of the nested-sets structure. We found no additional beneficial effect of area-proportionality. In contrast, the representation of discrete objects seems to be beneficial. Furthermore, our results show a strong facilitating effect of making the nested-sets structure of a Bayesian situation graphically transparent. Our results contribute to answering the questions of how and why a visualization could facilitate judgment and decision making in situations of uncertainty. (shrink)

In teaching statistics in secondary schools and at university, two visualizations are primarily used when situations with two dichotomous characteristics are represented: 2×2 tables and tree diagrams. Both visualizations can be depicted either with probabilities or with frequencies. Visualizations with frequencies have been shown to help students significantly more in Bayesian reasoning problems than probability visualizations do. Because tree diagrams or double-trees (which are largely unknown in school) are node-branch-structures, these two visualizations (compared to the 2×2 (...) table) can even simultaneously display probabilities on branches and frequencies inside the nodes. This is a teaching advantage as it allows the frequency concept to be used to better understand probabilities. However, 2×2 tables and (double-) trees have a decisive disadvantage: While joint probabilities (e.g., P(AB)) are represented in 2×2 tables but no conditional probabilities (e.g., P(A|B)), it is exactly the other way around with (double-) trees. Therefore, a visualization that is equally suitable for the representation of joint probabilities and conditional probabilities is desirable. In this article, we present a new visualization—the frequency net—in which all absolute frequencies and all types of probabilities can be depicted. In addition to a detailed theoretical analysis of the frequency net, we report the results of a study with 249 university students that shows that “net diagrams” can improve reasoning without previous instruction to a similar extent as 2×2 tables and double-trees. Regarding questions about conditional probabilities, frequency visualizations (2×2 table, double-tree, or net diagram with natural frequencies) are consistently superior to probability visualizations. The frequency net performs as well as the frequency double-tree. Only the 2×2 table with frequencies—the only visualization that participants were already familiar with —led to higher performance rates. If, on the other hand, a question about a joint probability had to be answered, all implemented visualizations clearly supported participants’ performance, and no uniform format effect becomes visible. Participants reached the highest performance in the versions with probability 2×2 tables and probability net diagrams. Furthermore, after conducting a detailed error analysis, we report interesting error shifts between the two information formats and the different visualizations and give recommendations for teaching probability. (shrink)

Philology, as Stephen Nichols suggests in his introductory remarks, has come to be equated in the minds of many with a dessicated and dogmatic textual praxis which, through the minutious methodologies of paleography, historical grammar, and the textual criticism of “Monsieur Procuste, Philologue,” has reduced medieval literary “monuments” to the status of “documents.” The Oxford Roland, in my initial philological encounter with it, was alternately a subtext for deciphering sound laws or a node in a tree diagram mapping the (...) scriptural genesis of a legend. And there it ended. (shrink)

How does one understand a sentence, in particular its syntactic structure? We have reason to think that the competence, in particular the parser in the competence analyses the sentence, and ends up with some mental equivalent of the tree diagram. And this is the main job to be done. If competence is doing this, then it plays the main role. If Dunja admits this, how can she be an ordinarist, rather that a competentialist? If Devitt agrees with her, how (...) can he be an ordinarist? Alternatively, further research might show that competence does also issue a verdict, and I hope this is what will happen. My reason for thinking it is that I think competence participates in other linguistic tasks, in particular in immediate linguistic understanding. The ordinarists about linguistic intuitions suggest that „given what else we know about the mind“ we should believe that ordinary human central processor can read SDs of complicated sentences with more than one embedding, and that it is just our general intelligence that deciphers them. It is argued that this proposal is quite unconvincing. (shrink)

Various theories of moral cognition posit that moral intuitions can be understood as the output of a computational process performed over structured mental representations of human action. We propose that action plan diagrams—“act trees”—can be a useful tool for theorists to succinctly and clearly present their hypotheses about the information contained in these representations. We then develop a methodology for using a series of linguistic probes to test the theories embodied in the act trees. In Study 1, we validate (...) the method by testing a specific hypothesis (diagrammed by act trees) about how subjects are representing two classic moral dilemmas and finding that the data support the hypothesis. In Studies 2–4, we explore possible explanations for discrete and surprising findings that our hypothesis did not predict. In Study 5, we apply the method to a less well‐studied case and show how new experiments generated by our method can be used to settle debates about how actions are mentally represented. In Study 6, we argue that our method captures the mental representation of human action better than an alternative approach. A brief conclusion suggests that act trees can be profitably used in various fields interested in complex representations of human action, including law, philosophy, psychology, linguistics, neuroscience, computer science, robotics, and artificial intelligence. (shrink)