The article describes a capstone engineering course for preservice and inservice secondary science and mathematics teachers and shows teacher attitudes toward engineering before and after the course and results of a comparison with a convenience sample. It also gives the results of the attitudes of high school student experimental and control groups toward engineering in a pretest-posttest design. Four findings were made: (a) The science and mathematics preservice and inservice teacher attitudes toward engineering became more favorable after the capstone course; (...) (b) the attitudes of the convenience sample of secondary graduate students were less favorable toward engineering than they were among the treatment group in the capstone course; (c) the attitudes of the experimental group of high school students became significantly more favorable toward engineering after a 3-week unit on engineering; and (d) the attitudes of the experimental group became significantly more favorable toward engineering than did those of the control group after the 3-week unit. (shrink)

The calculus of relations was created and developed in the second half of the nineteenth century by Augustus De Morgan, Charles Sanders Peirce, and Ernst Schröder. In 1940 Alfred Tarski proposed an axiomatization for a large part of the calculus of relations. In the next decade Tarski's axiomatization led to the creation of the theory of relation algebras, and was shown to be incomplete by Roger Lyndon's discovery of nonrepresentable relation algebras. This paper introduces the calculus of relations and the (...) theory of relation algebras through a review of these historical developments. (shrink)

The set of equations which use only one variable and hold in all representable relation algebras cannot be derived from any finite set of equations true in all representable relation algebras. Similar results hold for cylindric algebras and for logic with finitely many variables. The main tools are a construction of nonrepresentable one-generated relation algebras, a method for obtaining cylindric algebras from relation algebras, and the use of relation algebras in defining algebraic semantics for first-order logic.

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.

Conjecture (1) of [Ma83] is confirmed here by the following result: if $3 \leq \alpha < \omega$, then there is a finite relation algebra of dimension α, which is not a relation algebra of dimension α + 1. A logical consequence of this theorem is that for every finite α ≥ 3 there is a formula of the form $S \subseteq T$ (asserting that one binary relation is included in another), which is provable with α + 1 variables, but not (...) provable with only α variables (using a special sequent calculus designed for deducing properties of binary relations). (shrink)

We confirm a conjecture, about neat embeddings of cylindric algebras, made in 1969 by J. D. Monk, and a later conjecture by Maddux about relation algebras obtained from cylindric algebras. These results in algebraic logic have the following consequence for predicate logic: for every finite cardinal α ≥ 3 there is a logically valid sentence X, in a first-order language L with equality and exactly one nonlogical binary relation symbol E, such that X contains only 3 variables (each of (...) which may occur arbitrarily many times), X has a proof containing exactly α + 1 variables, but X has no proof containing only α variables. This solves a problem posed by Tarski and Givant in 1987. (shrink)

This is a supplement to the paper “Finitary Algebraic Logic” [1]. It includes corrections for several errors and some additional results. MSC: 03G15, 03G25.

If K is a class of semiassociative relation algebras and K contains the relation algebra of all binary relations on a denumerable set, then the word problem for the free algebra over K on one generator is unsolvable. This result implies that the set of sentences which are provable in the formalism Lwx is an undecidable theory. A stronger algebraic result shows that the set of logically valid sentences in Lwx forms a hereditarily undecidable theory in Lwx. These results generalize (...) similar theorems, due to Tarski, concerning relation algebras and the formalism Lx. (shrink)

Relation algebras were invented by Tarski and his collaborators in the middle of the 20th century. The concept of integrality arose naturally early in the history of the subject, as did various constructions of finite integral relation algebras. Later the concept of finite-dimensionality was introduced for classifying nonrepresentable relation algebras. This concept is closely connected to the number of variables used in proofs in first-order logic. Some results on these topics are presented in chronological order.

There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations.

For every finite n ≥ 4 there is a logically valid sentence φ n with the following properties: φ n contains only 3 variables (each of which occurs many times); φ n contains exactly one nonlogical binary relation symbol (no function symbols, no constants, and no equality symbol): φ n has a proof in first-order logic with equality that contains exactly n variables, but no proof containing only n - 1 variables. This result was first proved using the machinery of (...) algebraic logic developed in several research monographs and papers. Here we replicate the result and its proof entirely within the realm of (elementary) first-order binary predicate logic with equality. We need the usual syntax, axioms, and rules of inference to show that φ n has a proof with only n variables. To show that φ n has no proof with only n - 1 variables we use alternative semantics in place of the usual, standard, set-theoretical semantics of first-order logic. (shrink)

It is known that for all finite n ≥ 5, there are relation algebras with n-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no n-dimensional relational bases. In symbols: neither of the classes RA n and wRRA contains the other.

Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared between relevance logics (...) and relation algebras. Some details of certain incompleteness results, however, pinpoint where relevance logics and relation algebras diverge. To carry out these semantic investigations, we define a new tableaux formalization and new sequent calculi (with the single cut rule admissible) for various relevance logics. (shrink)

This volume is not restricted to papers presented at the 1988 Colloquium, but instead aims to provide the reader with a (relatively) coherent reading on Algebraic Logic, with an emphasis on current research. To help the non-specialist reader, the book contains an introduction to cylindric and relation algebras by Roger D. Maddux and an introduction to Boolean Algebras by Bjarni Joacute;nsson.

Built on the foundations laid by Peirce, Schröder, and others in the 19th century, the modern development of relation algebras started with the work of Tarski and his colleagues [21, 22]. They showed that relation algebras can capture strong first‐order theories like ZFC, and so their equational theory is undecidable. The less expressive class WA of weakly associative relation algebras was introduced by Maddux [7]. Németi [16] showed that WA's have a decidable universal theory. There has been extensive research (...) on increasing the expressive power of WA by adding new operations [1, 4, 11, 13, 20]. Extensions of this kind usually also have decidable universal theories. Here we give an example – extending WA's with set‐theoretic projection elements – where this is not the case. These “logical” connectives are set‐theoretic counterparts of the axiomatic quasi‐projections that have been investigated in the representation theory of relation algebras [22, 6, 19]. We prove that the quasi‐equational theory of the extended class PWA is not recursively enumerable. By adding the difference operator D one can turn WA and PWA to discriminator classes where each universal formula is equivalent to some equation. Hence our result implies that the projections turn the decidable equational theory of “WA + D ” to non‐recursively enumerable (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

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

Engaging Polanyi’s embeddedness–disembeddedness framework, this study explored the work experiences of Bhil children employed in Indian Bt cottonseed GPNs. The innovative visual technique of drawings followed by interviews was used. Migrant children, working under debt bondage, underwent greater exploitation and perennial and severe depersonalized bullying, indicative of commodification of labour and disembeddedness. In contrast, children working in their home villages were not under debt bondage and underwent less exploitation and occasional and mild depersonalized bullying, indicative of how civil society organizations, (...) along with the state, attempt to re-embed economic activities in the social context. Polanyi’s double movement was evident. ‘Place’ emerged as the pivotal factor determining children’s experiences. A ‘protective alliance’ of community controls and social power, associated with in-group affiliations and cohesive ties, stemming from a common village and tribal identity, aided children working at home for Bhil farmers. ‘Asymmetric intergroup inequality’ due to pronounced social identity and class differences, coupled with locational constraints and developmental disadvantage, made migrant children vulnerable targets. Social embeddedness influences how child workers are treated because it forces employers to be ethical and not engage in bullying. However, by shifting production to children’s home villages, there is an attempt to obscure the difference between child labour and child work. Thus, the seeds of disembeddedness are sown through the very act of re-embeddeding, potentially hampering future interventions. (shrink)

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical (...) theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the “projection postulate.” But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory. (shrink)

Inappropriate authorship is a common problem in biomedical research and may be becoming one in bioethics, due to the increase in multiple authorship. This paper investigates the authorship policies of bioethics journals to determine whether they provide adequate guidance for researchers who submit articles for publication, which can help deter inappropriate authorship. It was found that 63.3% of bioethics journals provide no guidance on authorship; 36.7% provide guidance on which contributions merit authorship, 23.3% provide guidance on which contributions do not (...) merit authorship, 23.3% require authors to take responsibility for their contributions or for the article as a whole, 20% provide guidance on which contributions merit an acknowledgement but not authorship, 6.7% require authors to describe their contributions, and only 3.3% distinguish between authorship in empirical and conceptual research. To provide authors with effective guidance and promote integrity in bioethics research, bioethics journals should adopt authorship policies that address several important topics, such as the qualifications for authorship, describing authorship contributions, taking responsibility for the research and the difference between authorship in empirical and conceptual research. (shrink)

From the first months of life, human infants produce “protophones,” speech-like, non-cry sounds, presumed absent, or only minimally present in other apes. But there have been no direct quantitative comparisons to support this presumption. In addition, by 2 months, human infants show sustained face-to-face interaction using protophones, a pattern thought also absent or very limited in other apes, but again, without quantitative comparison. Such comparison should provide evidence relevant to determining foundations of language, since substantially flexible vocalization, the inclination to (...) explore vocalization, and the ability to interact socially by means of vocalization are foundations for language. Here we quantitatively compare data on vocalization rates in three captive bonobo (Pan paniscus) mother–infant pairs with various sources of data from our laboratories on human infant vocalization. Both humans and bonobos produced distress sounds (cries/screams) and laughter. The bonobo infants also produced sounds that were neither screams nor laughs and that showed acoustic similarities to the human protophones. These protophone-like sounds confirm that bonobo infants share with humans the capacity to produce vocalizations that appear foundational for language. Still, there were dramatic differences between the species in both quantity and function of the protophone and protophone-like sounds. The bonobo protophone-like sounds were far less frequent than the human protophones, and the human protophones were far less likely to be interpreted as complaints and more likely as vocal play. Moreover, we found extensive vocal interaction between human infants and mothers, but no vocal interaction in the bonobo mother–infant pairs—while bonobo mothers were physically responsive to their infants, we observed no case of a bonobo mother vocalization directed to her infant. Our cross-species comparison focuses on low- and moderate-arousal circumstances because we reason the roots of language entail vocalization not triggered by excitement, for example, during fighting or intense play. Language appears to be founded in flexible vocalization, used to regulate comfortable social interaction, to share variable affective states at various levels of arousal, and to explore vocalization itself. (shrink)

Chronic pain patients often miss receiving acknowledgement for the multidimensional struggles they face with their specific conditions. People suffering from chronic pain experience a type ofinvisibilitythat is also borne by other chronically ill people and their respective medical conditions. However, chronic pain patients face both passive and active exclusion from social participation in activities like family interactions or workplace inclusion. Although such aspects are discussed in the debates lead by the bio-psycho-social model of pain, there seems to be a lack (...) of a distinct interest in assessing more specifically the social aspects regarding chronic pain. As a result, the social aspects have yet to be taken into a more thorough theoretical consideration of chronic pain and to be practically implemented to help affected patients. By addressing chronic pain patients’ struggle for recognition, this paper attempts to shed light on some of these social aspects. We base this attempt on a theoretical framework that combines patients’ statements with an adaptation of Axel Honneth’s social-philosophical work onrecognition. Thus, this paper tries to make a suggestion on how the bio-psycho-social model of pain can live up to its name by helping to address more adequately some of the more neglected aspects in chronic pain patients’ suffering than has been possible to date. (shrink)

This is part of a three-volume collection of most of David Lewis' papers in philosophy, except for those that previously appeared in his Philosophical Papers (Oxford University Press, 1983 and 1986). They are now offered in a readily accessible form. This second volume is devoted to Lewis' work in metaphysics and epistemology. The purpose of this collection, and the volumes that precede and follow it, is to disseminate more widely the work of an eminent and influential contemporary philosopher. The volume (...) will serve as a useful work of reference for teachers and students of philosophy. (shrink)

In philosophical interpretations of the Laozi the function of the ‘sage’ is a relatively under concentrated on topic. Although nearly every scholar does have something to say about the sage, comments are usually brief and often revolve around the sage as some particular character-type; for example highlighting the sage as a ‘sage-ruler’. In this article we will argue that the sage serves as a tool for understanding the major concepts, thinking, and logic of the Laozi. While the sage does often (...) refer to the sage-ruler this does not mean all references are politically orientated, and even those that are can easily be applied to a host of social situations. This paper thus seeks to appreciate the context for what the Laozi says by looking at how the text itself envisions the embodiment of its ideas through reference to the sage. (shrink)

Perforation or gap formation in a vegetation is a major process in landscape transformation. The occurrence of gaps profoundly alters the microclimatical conditions in a vegetation. A method is proposed to quantify perforation by using the three main 2-D characteristics of the gaps: area, number and boundary length. New measures are developed by normalizing the observed values to the reference status of minimum and maximum perforation. As minimum perforation status, the presence of one single gap with area equal to the (...) map resolution is assumed. The new measures are combined using a 3-D Euclidean distance to visualize the process and to detect changes. The method is exemplified using a field case of gaps in a tropical terra firme rainforest at Tiputini, Ecuador. (shrink)

Chez les commentateurs platoniciens de l’époque impériale, l’un des problèmes majeurs liés à la théorie des Idées concernait le domaine d’application de cette doctrine. L’exégèse de la première partie du Parménide de Platon donnait occasion à diverses discussions sur ce sujet. Le Commentaire de Proclus sur le Parménide est sans doute la plus précieuse source qui soit parvenue de l’Antiquité jusqu’à nous pour la reconstitution de ces débats. Alors que la grande majorité des commentateurs anciens étaient convaincus que les Idées (...) ont un domaine assez restreint, le Commentaire de Proclus nous révèle l’existence d’une lecture alternative, selon laquelle il y a des Idées de « toutes choses ». Proclus relie cette interprétation alternative en particulier à l’existence des Idées de choses mauvaises et d’individus, probablement parce que ces deux classes d’objets étaient vraiment les dernières choses dont un platonicien orthodoxe voudrait admettre des Idées. Amélius est le seul néoplatonicien connu pour avoir soutenu l’existence des Idées de choses mauvaises. Dans cet article j’essaie de montrer que, selon toute vraisemblance, Amélius est également la cible de la réfutation des Idées d’individus par Proclus dans son Commentaire. La conclusion qui s’ensuit naturellement est qu’Amélius était très probablement l’un de ces philosophes qui, d’après Proclus, admettaient des Idées « de toutes choses ». (shrink)

D. H. Mellor; VI*—I and Now, Proceedings of the Aristotelian Society, Volume 89, Issue 1, 1 June 1989, Pages 79–94, https://doi.org/10.1093/aristotelian/89.1.79.

There is a common view in medical ethics that the patient's right to be informed entails, as well, a correlative right not to be informed, i.e., to waive one's right to information. This paper argues, from a consideration of the concept of autonomy as the foundation for rights, that there can be no such ‘right’ to refuse relevant information, and that the claims for such a right are inconsistent with both deontological and utilitarian ethics. Further, the right to be informed (...) is shown to be a mandatory right (though not a welfare right); persons are thus seen to have both a right and a duty to be informed. Finally, the consequences of this view are addressed: since the way in which we conceptualize our problems tends to determine the actions we take to resolve them, it is important properly to conceptualize patients' requests not to be informed. There may be many reasons for acting in accord with such a request, but it is a mistake to conceptualize one's act as ‘respecting a right possessed by persons’. Keywords: medical ethics, informed consent, autonomy, information-waivers, rights, obligations CiteULike Connotea Del.icio.us What's this? (shrink)