Background Design thinking is a tool for generating and exploring ideas from multiple stakeholders. We used DT principles to introduce students to the ethical implications of organ transplantation. Students applied DT principles to propose solutions to maximise social justice in liver transplant allocation. Methods A 150 min interactive workshop was integrated into the longitudinal ethics curriculum. Following a group didactic on challenges of organ donation in the USA supplemented by patient stories, teams of students considered alternative solutions to optimise fairness (...) of organ distribution and ethical implications of changing the current model. Facilitators led students through DT steps of empathy, defining the team’s point of view, ideating on potential solutions, prototyping a specific idea and testing the idea through oral presentation, with questions and answers by peers and faculty. The curriculum was evaluated with presurveys and postsurveys including quantitative and open-ended items. Results 100 first year medical students participated. Before the session, 75.3% of students had no practical experience with DT. Following participation, students reported an increased understanding of the current liver transplant allocation system and an increased appreciation of shortcomings of the current organ allocation system. After the session, 73.8% of students felt that DT could be used to approach complex health system problems. Discussion Students participating in a DT workshop displayed improved knowledge and attitudes toward organ transplantation and DT. In this pilot study, DT showed promise as a student-led approach emphasising collaboration and creativity in ethics curricula in medical education. (shrink)

A recent fMRI study by Webb et al. (Cortical networks involved in visual awareness independent of visual attention, Proc Natl Acad Sci U S A 2016;113:13923–28) proposes a new method for finding the neural correlates of awareness by matching atten- tion across awareness conditions. The experimental design, however, seems at odds with known features of attention. We highlight logical and methodological points that are critical when trying to disentangle attention and awareness.

The higher order approach to consciousness attempts to build a theory of consciousness from the insight that a conscious state is one that the subject is conscious of. There is a well-known objection1 to the higher order approach, a version of which is fatal. Proponents of the higher order approach have realized that the objection is significant. They have dealt with it via what David Rosenthal calls a “retreat” (2005b, p. 179) but that retreat fails to solve the problem.

[[This was written as a commentary on Ned Block 's paper "On A Confusion about a Function of Consciousness" . It appeared in _Behavioral_ _and Brain Sciences_ 20:148-9, 1997, and also in the collection _The Nature of Consciousness: Philosophical Debates_ edited by Block, Flanagan, and Guzeldere. ]].

David Friedman attacks deontological or principled libertarianism from a utilitarian point of view. The present essay is an attempt to refute his critique of this philosophy, and to cast aspersions on the utilitarian version of libertarianism he favors.

This paper argues that the “Canberra Plan” picture of physicalistic reduction of mind--a picture shared by both its proponents and opponents, philosophers as diverse as David Armstrong, David Chalmers Frank Jackson, Jaegwon Kim, Joe Levine and David Lewis--neglects ground (Fine, 2001, 2012). To the extent that the point of view endorsed by the Canberra Plan has an account of the physical/functional ground of mind at all, it is in one version trivial and in another version implausible. In (...) its most general form, the point of view of the Canberra Plan is committed to unacceptably treating indexical or name-related facts as part of the ultimate physical/functional ground of the mental. (shrink)

A milestone in Wittgenstein scholarship, this collection of essays ranges over a wide area of the philosopher's thought, presenting divergent interpretations of his fundamental ideas. Different chapters raise many of the central controversies that surround current understanding of the Tractatus, providing an interplay that will be particularly useful to students. Taken together, the essays present a broader and more comprehensive view of Wittgenstein's intellectual interests and his impact on philosophy than may be found elsewhere.The thirteen chapters treat topics from both (...) periods of Wittgenstein's work: More than half are devoted to his early thought, the Tractatus Logico-Philosophicus of 1921, reflecting a growing interest today among philosophers in reexamining this seminal book, while three chapters treat the Philosophical Investigations, published posthumously in 1953. The remaining chapters discuss such "nonstandard" topics as philosophy of religion, aesthetics, and anthropology.Contents: The Early Wittgenstein and the Middle Russell, Kenneth Blackwell; Frege and Wittgenstein, Michael Dummett; Wittgenstein and the Theory of Types, Hide Ishiguro; The So-called Realism of Wittgenstein's Tractatus, Brian McGuinness; The Logical Independence of Elementary Propositions, David Pears; The Rise and Fall of the Picture Theory, Peter Hacker; The Picture Theory and Wittgenstein's Later Attitude to It, Erik Stenius; Wittgenstein's Early Philosophy of Mind, Anthony Kenny; A Theory of Language?, G. E. M. Anscombe; Im Anfang war die Tat, Peter Winch; Wittgenstein's Full Stop, D. Z. Phillips; Quote: Judgments from Our Brain, Paul Ziff; Wittgenstein and the Fire Festivals, Frank Cioffi, Index.Irving Block is Associate Professor in the Philosophy Department at The University of Western Ontario. (shrink)

Wu Ch'eng (1249-333) was the most innovative Confucian scholarteacher during the Mongol epoch in China, and his thought is a bridge between thinkers of the Sung und Ming eras. Having experienced the Mongol takeover in his thirties and the abrogation of the examination system, which blocked the traditional route to an official career, Wu was at first associated with Sung loyalists and did not serve the Yuan rulers until he was over sixty (in the National College and the Hanlin Academy). (...) Even then, his affinities for Taoism and individualistic strains in Confucian thought set him at odds with those who reestablished the examination system in the early fourteenth century. He was also one of the first scholars to question the legitimacy of the conquest dynasties. Wu pursued a scholarly vision that bore fruit in his searching classical commentaries, educational policies, and philosophical essays stressing intellectual enlightenment. This study of Wu's life and career examines his flirtations with official service, his disagreements with the educational establishment at the capital and locally, and how these experiences shaped his outlook. (shrink)

This introduction explains the logic of bringing together the perspectives of Hyman Minsky and Karl Polanyi to analyze processes of financialization. Although Minsky and Polanyi have very different intellectual trajectories, there are important complementarities in their approaches. The introduction also explains the focus of the three papers in this special section written by Kurtuluş Gemici, Lucas Kirkpatrick, and David Woodruff.

One of the foremost scientists and thinkers of our time, David Bohm worked alongside Oppenheimer and Einstein. In Science, Order and Creativity he and physicist F. David Peat propose a return to greater creativity and communication in the sciences. They ask for a renewed emphasis on ideas rather than formulae, on the whole rather than fragments, and on meaning rather than mere mechanics. Tracing the history of science from Aristotle to Einstein, from the Pythagorean theorem to quantum mechanics, (...) the authors offer intriguing new insights into how scientific theories come into being, how to eliminate blocks to creativity and how science can lead to a deeper understanding of society, the human condition and the human mind itself. Science, Order and Creativity looks to the future of science with elegance, hope and enthusiasm. (shrink)

This is a charming and engaging book that combines careful attention to the phenomenology of experience with an appreciation of the psychology and neuroscience of perception. In some of its aimsfor example, to show problems with a rigid version of a view of visual perception as an inverse optics process of constructing a static 3-D representation from static 2-D information on the retina--it succeeds admirably. As No points out, vision is a process that depends on interactions between the perceiver and (...) the environment and involves contributions from sensory systems other than the eye. He is at pains to note that vision is not passive. His analogy with touch is to the point: touch involves skillful probing and movement, and so does vision, although less obviously and in my view less centrally so. This much is certainly widely accepted among vision scientistsalthough mainstream vision scientists (represented, for example, by Stephen Palmers excellent textbook²) view these points as best seen within a version of the inverse optics view that takes inputs as non-static and as including motor instructions (for example, involving eye movements and head movements).³ The kind of point that No raises is viewed as important at the margins, but as not disturbing the main lines of the picture of vision that descendswith many changesfrom the pioneering work of David Marr in the 1980s (and before him, from Helmholtz). But No shows little interest in mainstream vision science, focusing on non-mainstream ideas in the science of perception, specifically ideas from the anti-representational psychologist J.J. Gibson, and also drawing on Wittgenstein and the phenomenology tradition. There is a sense throughout the book of revolution, of upsetting the applecart. This is a review from the point of view of the applecart. (shrink)

Is conceptual analysis required for reductive explanation? If there is no a priori entailment from microphysical truths to phenomenal truths, does reductive explanation of the phenomenal fail? We say yes . Ned Block and Robert Stalnaker say no.

One of the foremost scientists and thinkers of our time, David Bohm worked alongside Oppenheimer and Einstein. In _Science, Order and Creativity_ he and physicist F. David Peat propose a return to greater creativity and communication in the sciences. They ask for a renewed emphasis on ideas rather than formulae, on the whole rather than fragments, and on meaning rather than mere mechanics. Tracing the history of science from Aristotle to Einstein, from the Pythagorean theorem to quantum mechanics, (...) the authors offer intriguing new insights into how scientific theories come into being, how to eliminate blocks to creativity and how science can lead to a deeper understanding of society, the human condition and the human mind itself. _Science, Order and Creativity_ looks to the future of science with elegance, hope and enthusiasm. (shrink)

In a recent article, James Van Cleve joins a growing throng who have argued that Hilary Putnam's model-theoretic argument (and his "just more theory" response) begs the question against those who hold externalist theories of reference. Van Cleve has misinterpreted Putnam's argument. Putnam does not demand that the statements which make up the causal theory of reference must, themselves, do the reference-fixing. That would be question-begging. Rather, Putnam's argument is a "reductio", which can only be blocked with a theory of (...) reference that is both substantive and plausible. Putnam argues that there is no interpretation of "causality" that meets both conditions. (shrink)

This book uses different perspectives on argumentation to show how we create arguments, test them, attack and defend them, and deploy them effectively to justify beliefs and influence others. David Zarefsky uses a range of contemporary examples to show how arguments work and how they can be put together, beginning with simple individual arguments, and proceeding to the construction and analysis of complex cases incorporating different structures. Special attention is given to evaluating evidence and reasoning, the building blocks of (...) argumentation. Zarefsky provides clear guidelines and tests for different kinds of arguments, as well as exercises that show student readers how to apply theories to arguments in everyday and public life. His comprehensive and integrated approach toward argumentation theory and practice will help readers to become more adept at critically examining everyday arguments as well as constructing arguments that will convince others. (shrink)

In this chapter I seek to provide a theoretical defense of workplace democracy that is independent from and outside the lineage of Marxist and communist theory. Common to the council movements, anarcho- syndicalism and many other forms of libertarian socialism was the idea “that workers’ self- management was central.” Yet the idea of workers’ control has not been subject to the same theoretical development as Marx’s theory, not to mention capitalist economic theory. This chapter aims to contribute at a theoretical (...) level by providing a justification and defense of self- managed workplaces that is independent of the particular historical tradition of the council movements. There is a clear and definitive case for workplace democracy based on first principles that descends to modern times through the Reformation and Enlightenment in the abolitionist, democratic and feminist movements. By the twentieth century, the arguments had been scattered and lost – like the bones of some ancient beast scattered in a desert – partly due to misconceptions, mental blocks and misinterpretations embodied in Marxism, liberalism and economic theory. When one has worked through some of these intellectual roadblocks, then one may be better able to reassemble the case for workplace democracy from well- known first principles developed in the abolitionist, democratic and feminist movements. (shrink)

In two papers, Ned Block has argued that representationalists have trouble with the empirical discovery that differences in the degree of visual attention to an object can lead to a difference in h...

David McNeill, a pioneer in the ongoing study of the relationship between gesture and language, here argues that gestures are active participants in both speaking and thinking. He posits that gestures are key ingredients in an “imagery-language dialectic” that fuels speech and thought. The smallest unit of this dialectic is the growth point, a snapshot of an utterance at its beginning psychological stage. In _Gesture and Thought,_ the central growth point comes from a Tweety Bird cartoon. Over the course (...) of twenty-five years, the McNeill Lab showed this cartoon to numerous subjects who spoke a variety of languages, and a fascinating pattern emerged. The shape and timing of gestures depends not only on what speakers see but on what they take to be distinctive; this, in turn, depends on the context. Those who remembered the same context saw the same distinctions and used similar gestures; those who forgot the context understood something different and changed gestures or used none at all. Thus, the gesture becomes part of the growth point—the building block of language and thought. _Gesture and Thought _is an ambitious project in the ongoing study of how we communicate and how language is connected to thought. (shrink)

Scholars such as Renaud Barbara and Bernhard Waldenfels and Regula Giuliani have emphasized time’s central role in Merleau-Ponty’s philosophy, and Michael Kelly has shown how the Phenomenology’s “Temporality” chapter already broaches his later ontological concerns. I deepen our understanding of this temporal–ontological nexus by showing how Merleau-Ponty’s temporal ontology in fact erupts even earlier in the Phenomenology, as an underlying theme that unifies part two, on “The Perceived World,” as leading into the “Temporality” chapter. I do this via a close (...) study of the chapter, “The Thing and the Natural World,” first explicating some profound but easily overlooked points about time implied in Merleau-Ponty’s initial remarks on the constancy of form and size. I then closely analyze his study of color constancy in relation to his central source, David Katz’s The World of Colour, to show how color leads him to conceptualize things as what I call “time-things”—and more generally to conceptualize things, the world, and nature, as being in such a way that temporality is ingredient in their being. This leads to some implications for his temporal ontology. (shrink)

In Grimes v. Kennedy Krieger Institute (KKI), the Maryland Court of Appeals, while noting that U.S. federal regulations include risk standards for pediatric research, endorses its own risk standards. The Grimes case has implications for the debate over whether the minimal risk standard should be interpreted based on the risks in the daily lives of most children (the objective interpretation) or the risks in the daily lives of the children who will be enrolled in a given study (the subjective interpretation). (...) The court's use of the objective interpretation to block studies like the KKI study protects individual children who are worse off than the average child. Unfortunately, this approach also may block research intended to improve the lives of these same individuals. A similar dilemma arises in the context of multinational research, suggesting that a "modified objective standard," proposed to address this dilemma in the multinational setting, may offer a framework for addressing the dilemma in the context of pediatric research as well. (shrink)

In Section I, I clarify turning point issues in the Phillips and Block debate about whether there is unconscious perception. These include questions about whether uptake of certain visual information is an individual or person level accomplishment, as required for genuine unconscious _perceiving_. Section II takes up a recent reorientation proposed in Block ( 2017 ) towards the question of whether there is unconscious perceiving, where we are to look for the pervasive role of unconscious perceiving in, perhaps (...) especially, the online control of everyday reaching and grasping. I point out that while this may well be a helpfully different approach to explore, it does not evade the central questions and challenges familiar from the prior debate between Phillips and Block. Section III reviews an approach summarized in Dehaene ( 2014 ), drawing from a range of measures of neural activity. Dehaene provides evidence of quite rich non-conscious perceptual system responses, some arguably individual or person level. But in a fairly thin or fragile way, absent taking up, in higher level assessment, the information encoded in initial visual response. Or that is the interpretation I argue for, in relating the Dehaene account to the Phillips and Block debate, in a way that illuminates the Phillips and Block discussions. An Appendix provides an overview of debates in the literature about the Goodale and Milner Two Visual Systems Hypothesis, that Block ( 2017 ) makes central appeal to. (shrink)

I argue that we can get evidence for the temporal ontology of the universe simply by looking at the time. The argument is an extension of the ‘epistemic objection’ towards Growing Block theories.

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...) necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks. (shrink)

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We provide a sound and complete algorithm for computing explanatory factors (...) with respect to a given context, and demonstrate its flexibility and competitive performance against state of the art alternatives on various tasks. (shrink)

Before the early 1990s, accounts of classical American philosophy paid relatively little attention to the work and intellectual contributions of women philosophers. However, as early as 1991, a number of contemporary feminist philosophers and historians began to devote more focused attention to women philosophers whose intellectual achievements had been marginalized or forgotten. One woman philosopher whose contributions have still gone unnoticed is that of American logician, mathematician, and color theorist Christine Ladd-Franklin. This paper argues that Ladd-Franklin's feminist efforts to increase (...) the opportunities for women in professional academia were influenced not only by her work as a woman scientist and her reading of feminist literature but also by her understanding of pragmatism and her interaction with Charles Peirce. Specifically, Ladd-Franklin's arguments to increase academic research positions for women and her criticisms of male-only scientific societies point out how discrimination on the basis of gender violates Peirce's first rule of reason that one ought not block the road to inquiry and expose the unscientific nature of gender discrimination by contrasting the pragmatic meaning of acquiring a doctorate with the institutional practice of barring women from making intellectual contributions by denying them professorial positions. (shrink)

The various problems associated with co-authorship of research articles have attracted much attention in recent years. We believe that this growing awareness is a very welcome development. However, we will argue that the particular and increasing importance of authorship and the harmful implications of current practices of research authorship for junior researchers have not been emphasised enough. We will use the case of our own research area to illustrate some of the pitfalls of current publishing practices—in particular, the impact on (...) the evaluation of one’s work in the area of employment or funding. Even where there are explicit guidelines, they are often disregarded. This disregard, which is often exemplified through the inflation of co-authorship in some research areas, may seem benign to some of us; but it is not. Attribution of co-authorship for reasons other than merit in relation to the publication misrepresents the work towards that publication, and generates unfair competition. We make a case for increasing awareness, for transparency and for more explicit guidelines and regulation of research co-authorship within and across research areas. We examine some of the most sensitive areas of concern and their implications for researchers, particularly junior ones, and we suggest several strategies for future action. (shrink)

Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite (...) probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |U|² from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions.". (shrink)

Physicists have suggested what I call symmetry fundamentalism: the view that symmetries are fundamental aspects of physical reality and that these aspects are more fundamental than what one might ordinarily think of as the fundamental building blocks of the world, such as elementary particles. The goal of this paper is to develop an ontology for classical particle mechanics that provides a precise instance of symmetry fundamentalism.

Several authors have argued that non-extreme probabilities used in special sciences such as chemistry and biology can be objective chances, even if the true microphysical description of the world is deterministic. This article examines an influential version of this argument and shows that it depends on a particular methodology for defining the relationship between coarse-grained and fine-grained events. An alternative methodology for coarse-graining is proposed. This alternative methodology blocks this argument for the existence of emergent chances, and makes better sense (...) of two well-known subjects of philosophical discussion: the Miners Puzzle and Simpson’s Paradox. (shrink)

In Science, Order and Creativity, David Bohm and F. David Peat argue that science has lost its way in recent years and needs to go beyond a narrow and fragmented view of nature and embrace a wider holistic view that restores the importance of creativity and communication for all humanity - not just scientists. The result of a close collaboration by one of the 20th century's greatest physicists and thinkers, David Bohm, with leading science writer F. (...) class='Hi'>David Peat, provides a rare combination of profound reflection and clear exposition that can be appreciated by anyone concerned with science and its importance in our lives. This new edition includes a new preface and an extended additional chapter by Peat which draws upon further discussions with David Bohm before the latter's death in 1992. A fascinating diagnosis and considered proposal for a cure for science's ills, it is also very accessible entry point to the work of David Bohm. Bohm and Peat contend that science has lost its bearings in the last century in favour of a narrow, abstracted, fragmented approach to nature and reality. Tracing the history of science, Bohm and Peat offer intriguing new insights into how scientific theories come into being, how to eliminate blocks of creativity and how science can lead to a deeper understanding of society, the human condition and the human mind itself. (shrink)

Ned BlockÕs influential distinction between phenomenal and access consciousness has become a staple of current discussions of consciousness. It is not often noted, however, that his distinction tacitly embodies unargued theoretical assumptions that favor some theoretical treatments at the expense of others. This is equally so for his less widely discussed distinction between phenomenal consciousness and what he calls reflexive consciousness. I argue that the distinction between phenomenal and access consciousness, as Block draws it, is untenable. Though mental states (...) that have qualitative character plainly differ from those with no mental qualities, a mental stateÕs being conscious is the same property for both kinds of mental state. For one thing, as Block describes access consciousness, that notion does not pick out any property that we intuitively count as a mental stateÕs being conscious. But the deeper problem is that BlockÕs notion of phenomenal consciousness, or phenomenality, is ambiguous as between two very different mental properties. The failure to distinguish these results in the begging of important theoretical questions. Once the two kinds of phenomenality have been distinguished, the way is clear to explain qualitative consciousness by appeal to a model such as the higher-order-thought hypothesis. Ó 2002 Elsevier Science . All rights reserved. (shrink)

A sensible quality is a perceptible property, a property that physical objects (or events) perceptually appear to have. Thus smells, tastes, colors and shapes are sensible qualities. An egg, for example, may smell rotten, taste sour, and look cream and round.1,2 The sensible qualities are not a miscellanous jumble—they form complex structures. Crimson, magenta, and chartreuse are not merely three different shades of color: the first two are more similar than either is to the third. Familiar color spaces or color (...) solids capture, to a greater or lesser extent, these relations between the colors. The same goes for sensible qualities perceived in other modalities: middle C, high C, and D are not merely three different notes, and the taste of lemons, oranges, and sugar cubes are not merely three different tastes. How can this structure of appearance be explained? One idea is that sensible qualities are of two sorts: basic and derived. The basic sensible qualities are the building blocks from which the derived sensible qualities can be.. (shrink)

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting (...) it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). (shrink)

According to John Rawls, self-respect is the most important of the primary goods and is essential for the construction of the just society. Self-respect, however, remains a concept which is inadequately theorised, being closely linked to other concepts such as dignity, shame, pride, autonomy and security. Most usually self-respect is considered to be just the self-reflection of the respect we receive from others. In this paper I argue that self-respect consists of both a self-evaluative and a social reflexive element. Using (...) Darwall’s distinction between two types of respect as a building block, I argue that it is worth considering self-respect as having three dimensions. Broadly these are human recognition, status recognition and appraisal. (shrink)

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean logic (...) of subsets is the normalized counting measure of the subsets (events). Thus logical entropy is a measure on the set of ordered pairs, and all the compound notions of entropy (join entropy, conditional entropy, and mutual information) arise in the usual way from the measure (e.g., the inclusion-exclusion principle)--just like the corresponding notions of probability. The usual Shannon entropy of a partition is developed by replacing the normalized count of distinctions (dits) by the average number of binary partitions (bits) necessary to make all the distinctions of the partition. (shrink)