Ormerod and Chronicle reported that optimal solutions to traveling salesperson problems were judged to be aesthetically more pleasing than poorer solutions and that solutions with more convex hull nodes were rated as better figures. To test these conclusions, solution regularity and the number of potential intersections were held constant, whereas solution optimality, the number of internal nodes, and the number of nearest neighbors in each solution were varied factorially. The results did not support the view that the convex hull is (...) an important determinant of figural attractiveness. Also, in contrast to the findings of Ormerod and Chronicle, there were consistent individual differences. Participants appeared to be divided as to whether the most attractive figure enclosed a given area within a perimeter of minimum or maximum length. It is concluded that future research in this area cannot afford to focus exclusively on group performance measures. (shrink)

Discussing the relations between logic and probability, this book compares classical 17th- and 18th-century theories of probability with contemporary theories, explores recent logical theories of probability, and offers a new account of probability as a part of logic.

The main sources here are Hume, Husserl, and De Finetti. The problem is how phenomenological investigation has to do with partial or probabilistic judgment. Behavioristic, frequentist and subjectivistic views are briefly surveyed. A variant of Hume's account of the probability of chances is developed with the help of De Finetti's concept of exchangeability. The question of transcendental elements in or behind partial judgment is considered in the light of understanding disagreement and error in partial judgment.

In this paper I consider the question of the reality of chance. This is not what divides contemporary probabilists into the objective and subjective schools. That division is accomplished by the question whether there are objective grounds for the correctness of probability judgments. The subjectivists say that there need not be such grounds, and that probability judgments thus need not be empirically meaningful in the verificationist sense, or perhaps that they are not judgments at all, but rather expressions of attitude. (...) (See [11], pp. 156-198). The objectivists say that the truth conditions for probability judgments are such as the frequencies of traits in populations or the existence of propensities. Objectivists and subjectivists are, however, agreed that there are no objective chances. (See [2], pp. 141, 142; and [12], §16).There is a Humean argument against the reality of chance which depends mainly upon the premise that we have no experience of it. (shrink)

The interpretation of the calculus of probability as a logic of partial belief has at least two advantages: it makes the assignment of probabilities plausible in cases where classical frequentist interpretations must find such assignments meaningless, and it gives a clear meaning to partial belief and to consistency of partial belief.

How does deductive logic constrain probability? This question is difficult for subjectivistic approaches, according to which probability is just strength of (prudent) partial belief, for this presumes logical omniscience. This paper proposes that the way in which probability lies always between possibility and necessity can be made precise by exploiting a minor theorem of de Finetti: In any finite set of propositions the expected number of truths is the sum of the probabilities over the set. This is generalized to apply (...) to denumerable languages. It entails that the sum of probabilities can neither exceed nor be exceeded by the cardinalities of all consistent and closed (within the set) subsets. In general any numerical function on sentences is said to be logically coherent if it satisfies this condition. Logical coherence allows the relativization of necessity: A function p on a language is coherent with respect to the concept T of necessity iff there is no set of sentences on which the sum of p exceeds or is exceeded by the cardinality of every T-consistent and T-closed (within the set) subset of the set. Coherence is easily applied as well to sets on which the sum of p does not converge. Probability should also be relativized by necessity: A T-probability assigns one to every T-necessary sentence and is additive over disjunctions of pairwise T-incompatible sentences. Logical T-coherence is then equivalent to T-probability: All and only T-coherent functions are T-probabilities. (shrink)

We provide an overview of a transdisciplinary project about sustainable forest management under climate change. Our project is a partnership with members of the Menominee Nation, a Tribal Nation located in northern Wisconsin, United States. We use immersive virtual experiences, translated from ecosystem model outcomes, to elicit human values about future forest conditions under alternative scenarios. Our project combines expertise across the sciences and humanities as well as across cultures and knowledge systems. Our management structure, governance, and leadership behaviors have (...) both fostered and constrained our work and must be continuously responsive to changing group dynamics. Our project presents opportunities for substantial contributions to society, including insights and knowledge about complementary ways of knowing, skills training, and professional development, and opportunities for reflexive learning about effective transdisciplinary, translational, and transformative scientific processes. (shrink)

We consider the following question of Kunen: Does Con imply Con? We use core model theory to investigate consequences of the existence of such a j : M $\rightarrow$ V. We prove, amongst other things, the existence of such an embedding implies that the core model K is a model of "there exists a proper class of almost Ramsey cardinals". Conversely, if On is Ramsey, then such a j, M are definable. We construe this as a negative answer to the (...) question above. We consider further the consequences of strengthening the closure assumption on j to having various classes of fixed points. (shrink)

We consider the following question of Kunen: Does Con(ZFC + ∃M a transitive inner model and a non-trivial elementary embedding j: M $\longrightarrow$ V) imply Con (ZFC + ∃ a measurable cardinal)? We use core model theory to investigate consequences of the existence of such a j: M → V. We prove, amongst other things, the existence of such an embedding implies that the core model K is a model of "there exists a proper class of almost Ramsey cardinals". Conversely, (...) if On is Ramsey, then such a j, M are definable. We construe this as a negative answer to the question above. We consider further the consequences of strengthening the closure assumption on j to having various classes of fixed points. (shrink)

This paper challenges the traditional assumption that descriptive and prescriptive sciences are essentially distinct by presenting a study on the implicit normativity of the production and presentation of biomedical scientific facts within evidence-based medicine. This interdisciplinary study serves as an illustration of the potential worth of the concept of implicit normativity for bioethics in general and for integrated empirical ethics research in particular. It demonstrates how both the production and presentation of scientific information in an evidence-based decision-support contain implicit presuppositions (...) and values, which pre-structure the moral environment of the clinical process of decision-making. As a consequence, the evidence-based decision support did not only support the clinical decision-making process; it also transformed it in a morally significant way. This phenomenon undermines the assumption within much of the literature on patient autonomy that information disclosure is a conditional requirement before patient autonomy even starts; patient autonomy is already influenced during the production and presentation of information. These results imply an increased responsibility of those who produce and present evidence-based facts(i.e. scientists in general and physicians in particular). The insights of this study not only involve a different focus on both theory and practice of patient autonomy and informed consent, but they also call for a broader scope of morality than does traditional empirical research in bioethics. The concept of implicit normativity within integrated empirical ethics research calls for a strong cooperation between bioethicists and descriptive scientists, i.e., a cooperation that goes beyond the discipline-specific epistemic values and that takes place during all phases of the research process. (shrink)

In his thesis 'Para uma Teoria Geral dos Homomorfismos' (1944) the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we (...) tried to keep in mind, so much as possible, the gist of his standpoint. (shrink)

In this chapter we reflect on the relevance of peer review for assessing the quality of clinical ethics consultation. We contend that peer review in the narrative form as presented in this book provides an alternative to the formal clinical ethics consultation review procedures typically found in the clinical ethics literature. We elaborate on peer review as a reflection on clinical ethics consultation practice, the elements which a story should contain in order to provide a basis for peer review, and (...) the differences between the assessments of the peer reviewers. We argue that a narrative approach to assessing the quality of ethics consultation can be further developed by allowing all stakeholders who are involved in the clinical ethics practice to actively take part in the evaluation process, following a “responsive evaluation” approach. An example of this is creating a Community of Practice, the aim of which is to foster a joint learning process of all parties involved. At the end of this chapter, we draw conclusions on peer review as a dialogical tool for evaluating quality of clinical ethics consultation. (shrink)

If action theory is to be relevant for the study of social phenomena, its scope has to be enlarged so as to include social structures. A hermeneutic theory of action, which draws on the thoughts of Gadamer, Merleau-Ponty, Ricoeur and Giddens, can meet this requirement. The hermeneutic concept of action, which emphasises the importance of tradition, style and rituals, demonstrates that action and structure presuppose and explain each other. The mutual relationship between action and structure is particularly clear in theories (...) of human development in the domain of psychology, psychotherapy and education. These theories can be used to construct a theory of social evolution, as has been developed by Habermas. By integrating structural, theoretical and critical points of view, a hermeneutic theory of action opens a perspective in which action theory and social theory might be successfully combined. (shrink)

The inverse of the distance between two structures $\mathscr{A} \not\equiv \mathscr{B}$ of finite type τ is naturally measured by the smallest integer q such that a sentence of quantifier rank q - 1 is satisfied by A but not by B. In this way the space $\operatorname{Str}^\tau$ of structures of type τ is equipped with a pseudometric. The induced topology coincides with the elementary topology of $\operatorname{Str}^\tau$ . Using the rudiments of the theory of uniform spaces, in this elementary note (...) we prove the convergence of every Cauchy net of structures, for any type τ. (shrink)

The inverse of the distance between two structures $\mathscr{A} \not\equiv \mathscr{B}$ of finite type $\tau$ is naturally measured by the smallest integer $q$ such that a sentence of quantifier rank $q - 1$ is satisfied by $\mathscr{A}$ but not by $\mathscr{B}$. In this way the space $\operatorname{Str}^\tau$ of structures of type $\tau$ is equipped with a pseudometric. The induced topology coincides with the elementary topology of $\operatorname{Str}^\tau$. Using the rudiments of the theory of uniform spaces, in this elementary note we (...) prove the convergence of every Cauchy net of structures, for any type $\tau$. (shrink)

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in this paper (...) have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims atproviding an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic hasfewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations. It introduces the notion of -space for a sentence A as the basis of logical model theory, and the notion of P A /, functioning as a `private' subuniverse for A/A. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. PPC3 and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of PPC3 as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: 1a for the conjoined presuppositions of a, ã for the complement of a within 1a, and â for the complement of 1a within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical (Boolean) foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in this (...) paper have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims at providing an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic has fewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic ${\rm PPC}_{3}$ , with two kinds of falsity and two negations. It introduces the notion of Σ-space for a sentence A (or / A /, the set of situations in which A is true) as the basis of logical model theory, and the notion of / ${\bf P}^{A}$ / (the Σ-space of the presuppositions of A), functioning as a 'private' subuniverse for / A /. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. ${\rm PPC}_{3}$ and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of ${\rm PPC}_{3}$ as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: $1_{a}$ for the conjoined presuppositions of a, ã for the complement of a within $1_{a}$ , and â for the complement of $1_{a}$ within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned. (shrink)

Summary If action theory is to be relevant for the study of social phenomena, its scope has to be enlarged so as to include social structures. A hermeneutic theory of action, which draws on the thoughts of Gadamer, Merleau-Ponty, Ricoeur and Giddens, can meet this requirement. The hermeneutic concept of action, which emphasises the importance of tradition, style and rituals, demonstrates that action and structure presuppose and explain each other. The mutual relationship between action and structure is particularly clear in (...) theories of human development in the domain of psychology, psychotherapy and education. These theories can be used to construct a theory of social evolution, as has been developed by Habermas. By integrating structural, theoretical and critical points of view, a hermeneutic theory of action opens a perspective in which action theory and social theory might be successfully combined. (shrink)

Being attentive to the needs of others, feeling responsible for each other, and taking care are necessary elements for the good life. Care, however, is a fragile activity: it is hard to predict its results. In this article, Homer's story of the Phaeacians bringing Odysseus back to Ithaca is interpreted to investigate what care could be when we admit the fragility of care. We consider two theoretical perspectives on care to interpret the story, namely Martha Nussbaum’s Aristotelian ethics, and the (...) Ethics of Care approach of authors like Ruddick, Sevenhuijsen, Tronto, Verkerk and others. In the first approach, the emphasis is on the attitude of care; in the second, on care as a social practice. Following Nussbaum, the caring response of the Phaeacians can be understood as an example of what Aristotle called ‘practical rationality’. The unexpected result of their care – they come into conflict with Poseidon – shows the fragility of human life and the tragic condition of humanity. According to Nussbaum, one should take responsibility for the fact that choosing for the one implies neglecting the other . From the perspective of Ethics of Care, the caring response is not so much the result of individual virtues; it is rather an element of a care practice that motivates people to act in conformity with basic values like solidarity and responsibility. The fragility of care is regarded as an ordinary quality of praxis and humanity rather than something essentially tragic. In the process of caring, misfortunes can never be totally prevented. Whenever they happen, they should be used as a way to learn and develop more adequate ways of handling the situation. The comparison of the two perspectives, both inspired by Aristotle's philosophy, gives rise to a richer view of the fragility of care. (shrink)

The complex hexaploid wheat genome offers many challenges for genomics research. Expressed sequence tags facilitate the analysis of gene-coding regions and provide a rich source of molecular markers for mapping and comparison with model organisms. The objectives of this study were to construct a high-density EST chromosome bin map of wheat homoeologous group 2 chromosomes to determine the distribution of ESTs, construct a consensus map of group 2 ESTs, investigate synteny, examine patterns of duplication, and assess the colinearity with rice (...) of ESTs assigned to the group 2 consensus bin map. A total of 2600 loci generated from 1110 ESTs were mapped to group 2 chromosomes by Southern hybridization onto wheat aneuploid chromosome and deletion stocks. A consensus map was constructed of 552 ESTs mapping to more than one group 2 chromosome. Regions of high gene density in distal bins and low gene density in proximal bins were found. Two interstitial gene-rich islands flanked by relatively gene-poor regions on both the short and long arms and having good synteny with rice were discovered. The map locations of two ESTs indicated the possible presence of a small pericentric inversion on chromosome 2B. Wheat chromosome group 2 was shown to share syntenous blocks with rice chromosomes 4 and 7. (shrink)