Axiomatizing collective judgment sets in a minimal logical language

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula expresses that is collectively accepted, or that is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where holds if a majority of individuals accepts, consensus voting, where holds if all individuals accept, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures.     

A Qualitative Study of the Supports Women Find Most Beneficial When Dealing with a Spouse’s Sexually Addictive or Compulsive Behaviors: Insights for Pastoral Counselors and Clergy

There is currently a void in the literature regarding the kinds of support women find most beneficial when dealing with a spouse’s sexually addictive or compulsive behaviors. Addressing this void is particularly relevant for clergy, seeing as they are increasingly sought out as an initial and/or primary support for dealing with this marital issue. Using grounded theory methodology, 22 women from Canada and the USA were interviewed to find out what they found most helpful as they sought support to cope with a spouse’s sexually addictive and compulsive behaviors. Insights for pastoral counselors and clergy were highlighted.     

Deductivism and the Informal Fallacies

This essay proposes and defends a general thesis concerning the nature of fallacies of reasoning. These in distinctive ways are all said to be deductively invalid. More importantly, the most accurate, complete and charitable reconstructions of these species and specimens of the informal fallacies are instructive with respect to the individual character of each distinct informal fallacy. Reconstructions of the fallacies as deductive invalidities are possible in every case, if deductivism is true, which means that in every case they should be formalizable in an expressively comprehensive formal symbolic deductive logic. The general thesis is illustrated by a detailed examination of Walter Burleigh's paradox in his c. 1323 work, De Puritate Artis Logicae Tractatus Longior (Longer Treatise on the Purity of Logic), as a challenge to the deductive validity of hypothetical syllogism. The paradox has the form, ‹If I call you a swine, then I call you an animal; if I call you an animal, then I speak truly; therefore, if I call you a swine, then I speak truly'. Several solutions to the problem are considered, and the inference is exposed as an instance of the common deductive fallacy of equivocation.     

A Two Dimensional Tense-modal Sortal Logic

We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.     

Women’s Close Friendships across Sexual Orientation: A Comparative Analysis of Lesbian-Heterosexual and Bisexual-Heterosexual Women’s Friendships

Interviews were conducted in close friendship pairs with women who ranged in age from 18 to 52 years at the time of interview. Results suggest that women of different sexual orientation identities had different friendship profiles. Comparisons across friendship type suggest that bisexual-heterosexual friends consistently experienced a shift in friendship dynamic based on the sex of partner for the bisexual friend and were more likely than lesbian-heterosexual friends to integrate their friendship into their social lives. Lesbian-heterosexual friendships were significantly more likely to include an explicit acknowledgment of non-heterosexual identity. Although cross-orientation friendships did not consistently include a feminist/political dimension, when friends also differed in racial identity a feminist/political dimension in the friendship became apparent. In cross-race friendships racial minority identities were explicitly acknowledged even when non-heterosexual identities were not.     

Quantum sortal predicates

Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of counting, to them is associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described. To Patrick Suppes on his 80th birthday.     

从诠释学看墨辩研究的逻辑学范式

This article describes the logic paradigm in the “Mobian” 墨辩 (the debate theory of the Mohist school) investigation from the point of view of hermeneutics, discloses the relationship between the overinterpretation tradition in China and the logic paradigm in the “Mobian” investigation, observes the overinterpretation of the “Mobian” by the creators and supporters of the logic paradigm from Liang Qichao and Hu Shi to the modernists, including mathematical logicians, and analyzes Shen Youding’s reflections on the logic paradigm in his later life. Translated by Huang Deyuan (proofread by Hsiung Ming) from Xueshu Yanjiu 学术研究 (Academic Research Journal), 2005, (1): 49–56     

Argument practices

The move to Postmodernism in argumentation is often predicated on the rejection of the formal basis of argument in logic. While this rejection may be justified, and is widely discussed in the literature, the loss of logic creates problems that a Postmodern theory of argument must address without recourse to logic and its attendant modernist assumptions. This essay argues that conceiving of argument in terms ofpractices will address the key problematics of Postmodernism without abandoning those features of argumentation that make it an important social, cultural and political practice. Implications for both theory and pedagogy are discussed.The author would like to acknowledge the invaluable commentary of, and discussions with, John Lyne, Charles Willard, Steven Fuller, and Ed Schiappa.     

Critical thinking in North America: A new theory of knowledge,learning, and literacy

The pace of change in the world is accelerating, yet educational institutions have not kept pace. Indeed, schools have historically been the most static of social institutions, uncritically passing down from generation to generation outmoded didactic, lecture-and-drill-based, models of instruction. Predictable results follow. Students, on the whole, do not learn how to work by, or think for, themselves. They do not learn how to gather, analyze, synthesize and assess information. They do not learn how to analyze the diverse logic of the questions and problems they face and hence how to adjust their thinking to those problems. They do not learn how to enter sympathetically into the thinking of others, nor how to deal rationally with conflicting points of view. They do not learn to become critical readers, writers, speakers and listeners. They do not learn how to use their native languages clearly, precisely, or persuasively. They do not, therefore, become literate, in the proper sense of the word. Neither do they gain much in the way of genuine knowledge since, for the most part, they could not explain the basis for what they believe. They would be hard pressed to explain, for example, which of their beliefs were based on rational assent and which on simple conformity to what they have been told. They have little sense as to how they might critically analyze their own experience, or identify national or group bias in their own thinking. They are much more apt to learn on the basis of irrational than rational modes of thought. They lack the traits of mind of a genuinely educated person: intellectual humility, courage, integrity, perseverance, and faith in reason.Happily, there is a movement in education today striving to address these problems in a global way, with strategies and materials for the modification of instruction at all levels of education. At its foundation is an emerging new theory of knowledge, learning, and literacy, one which recognizes the centrality of independent critical thinking to all substantial learning, one which recognizes that higher-order, multilogical thinking is as important to childhood as to adult learning, and as important to foundational learning in monological as in multilogical disciplines. This educational reform movement is not proposing an educational miracle cure, for its leading proponents recognize that many social and historical forces must come together before the ideals of the critical thinking movement will become a full academic reality. Schools do not exist in a social vacuum. To the extent that the broader society is uncritical so, on the whole, will be society's schools. Nevertheless, the social conditions necessary for fundamental changes in schooling are increasingly apparent. The pressure for fundamental change is growing. Whether and to what extent these needed basic changes will be delayed or side-tracked, thus requiring new periodic resurgences of this movement, with new, more elaborate articulations of its ideals, goals, and methods — only time will tell.     

Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude

Eight human subjects pressed a lever on a range of variable-interval schedules for 0.25¢ to 35.0¢ per reinforcement. Herrnstein's hyperbola described seven of the eight subjects' response-rate data well. For all subjects, the y-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory; they contradict formal properties of Herrnstein's account and of six other mathematical accounts of single-alternative responding.