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David Ellerman [29]David P. Ellerman [5]
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Profile: David Ellerman (University of California, Riverside)
  1. David Ellerman, A Short Note on the Logico-Conceptual Foundations of Information Theory in Partition Logic.
    A new logic of partitions has been developed that is dual to ordinary logic when the latter is interpreted as the logic of subsets of a fixed universe rather than the logic of propositions. For a finite universe, the logic of subsets gave rise to finite probability theory by assigning to each subset its relative size as a probability. The analogous construction for the dual logic of partitions gives rise to a notion of logical entropy that is precisely related to (...)
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  2. David Ellerman, Category Theory and Universal Models: Adjoints and Brain Functors.
    Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called "internalization through a universal" based on universal mapping properties. A recently developed "heteromorphic" theory (...)
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  3. David Ellerman, Marxism as a Capitalist Tool.
    Just as the two sides in the Cold War agreed that Western Capitalism and Soviet Communism were "the" two alternatives, so the two sides in the intellectual Great Debate agreed on a common framing of questions with the defenders of capitalism taking one side and Marxists taking the other side of the questions. From the viewpoint of economic democracy (e.g., a labor-managed market economy), this late Great Debate between capitalism and socialism was as misframed as would be an antebellum 'Great (...)
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  4. David Ellerman, Does Classical Liberalism Imply Democracy?
    There is a fault line running through classical liberalism as to whether or not democratic self-governance is a necessary part of a liberal social order. The democratic and non-democratic strains of classical liberalism are both present today—particularly in America. Many contemporary libertarians and neo-Austrian economists represent the non-democratic strain. We will take the late James M. Buchanan as a representative of democratic classical liberalism (with assists from the earlier democratic classical liberal philosophers, John Stuart Mill and John Dewey). Unpacking the (...)
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  5. David Ellerman, Four Ways From Universal to Particular: How Chomsky's Language-Acquisition Faculty is Not Selectionist.
    Following the development of the selectionist theory of the immune system, there was an attempt to characterize many biological mechanisms as being "selectionist" as juxtaposed to "instructionist." But this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky's language-acquisition mechanism as all being "selectionist." Yet Chomsky's mechanism (and embryonic development) are significantly different from the selectionist mechanisms of biological evolution or the immune system. Surprisingly, there is a very abstract way using two dual mathematical logics to (...)
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  6. David Ellerman, On Classical Finite Probability Theory as a Quantum Probability Calculus.
    This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. The point is not to (...)
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  7. David Ellerman, Partitions and Objective Indefiniteness.
    Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual (...)
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  8. David Ellerman, Why Delayed Choice Experiments Do NOT Imply Retrocausality.
    There is a fallacy that is often involved in the interpretation of quantum experiments involving a certain type of separation such as the: double-slit experiments, which-way interferometer experiments, polarization analyzer experiments, Stern-Gerlach experiments, and quantum eraser experiments. The fallacy leads not only to flawed textbook accounts of these experiments but to flawed inferences about retrocausality in the context of delayed choice versions of separation experiments.
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  9. David Ellerman (forthcoming). Listen Libertarians!: A Review of John Tomasi's Free Market Fairness. [REVIEW] Conversations in Philanthropy.
    John Tomasi's new book, Free Market Fairness, has been well-received as "one of the very best philosophical treatments of libertarian thought, ever" (Tyler Cowen) and as a "long and friendly conversation between Friedrich Hayek and John Rawls—a conversation which, astonishingly, reaches agreement" (D. McCloskey). The book does present an authoritative state-of-the-debate across the spectrum from right-libertarianism on the one side to high liberalism (that shares some shades of opinion with democratic socialism) on the other side. My point is not to (...)
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  10. David Ellerman (forthcoming). On Concrete Universals: A Modern Treatment Using Category Theory. AL-MUKHATABAT.
    Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...)
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  11. David Ellerman (forthcoming). On Double-Entry Bookkeeping: The Mathematical Treatment. Accounting Education: An International Journal.
    Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ("T-accounts"). That construction was only formulated abstractly in mathematics in the 19th century—even though DEB had been used in the business world for over five centuries. Yet the connection between DEB and the group of differences (here called the "Pacioli group") is still largely unknown both in mathematics and accounting. The precise mathematical treatment of DEB allows clarity on certain conceptual questions and (...)
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  12. David Ellerman (2014). An Introduction to Partition Logic. Logic Journal of the Igpl 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...)
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  13. David Ellerman (2014). On a Fallacy in the Kaldor-Hicks Efficiency-Equity Analysis. Constitutional Political Economy 25 (2):125-136.
    This paper shows that implicit assumptions about the numeraire good in the Kaldor-Hicks efficiency-equity analysis involve a "same-yardstick" fallacy (a fallacy pointed out by Paul Samuelson in another context). These results have negative implications for cost-benefit analysis, the wealth-maximization approach to law and economics, and other parts of applied welfare economics--as well as for the whole vision of economics based on the "production and distribution of social wealth.".
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  14. David Ellerman (2014). On Property Theory. Journal of Economic Issues (3):601–624.
    A theory of property needs to give an account of the whole life-cycle of a property right: how it is initiated, transferred, and terminated. Economics has focused on the transfers in the market and has almost completely neglected the question of the initiation and termination of property in normal production and consumption (not in some original state or in the transition from common to private property). The institutional mechanism for the normal initiation and termination of property is an invisible-hand function (...)
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  15. David Ellerman (2014). Parallel Experimentation: A Basic Scheme for Dynamic Efficiency. Journal of Bioeconomics 16 (3):259–287.
    Evolutionary economics often focuses on the comparison between economic competition and the process of natural selection to select the fitter members of a given population. But that neglects the other "half" of an evolutionary process, the mechanism for the generation of new possibilities that is key to dynamic efficiency. My topic is the process of parallel experimentation which I take to be a process of multiple experiments running concurrently with some form of common goal, with some semi-isolation between the experiments, (...)
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  16. David Ellerman (2013). An Introduction to Logical Entropy and its Relation to Shannon Entropy. International Journal of Semantic Computing 7 (2):121-145.
    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 (...)
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  17. David Ellerman (2010). Inalienable Rights: A Litmus Test for Liberal Theories of Justice. [REVIEW] Law and Philosophy 29 (Sept.):571-599.
    Liberal-contractarian philosophies of justice see the unjust systems of slavery and autocracy in the past as being based on coercion—whereas the social order in modern democratic market societies is based on consent and contract. However, the ‘best’ case for slavery and autocracy in the past were consent-based contractarian arguments. Hence, our first task is to recover those ‘forgotten’ apologia for slavery and autocracy. To counter those consent-based arguments, the historical anti-slavery and democratic movements developed a theory of inalienable rights. Our (...)
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  18. David Ellerman (2010). The Logic of Partitions: Introduction to the Dual of the Logic of Subsets. Review of Symbolic Logic 3 (2):287-350.
    Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of classical "propositional" logic might be the logic of subsets of a given universe set. The propositional interpretation is isomorphic to the special case where the truth and falsity of propositions behave like the subsets of a one-element set. If classical "propositional" logic (...)
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  19. David Ellerman (2010). Workplace Democracy and Human Development: The Example of the Postsocialist Transition Debate. Journal of Speculative Philosophy 24 (4):333-353.
    In the 1990s, a debate raged across the whole postsocialist world as well as in Western development agencies such as the World Bank about the best approach to the transition from various forms of socialism or communism to a market economy and political democracy. One of the most hotly contested topics was the question of the workplace being organized based on workplace democracy (e.g., various forms of worker ownership) or based on the conventional employer-employee relationship. Well before 1989, many of (...)
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  20. Zach VanderVeen, Elinor Ostrom, David Ellerman, Albert W. Dzur, Bruce R. Sievers & Stephen Bloch-Schulman (2010). 1. Front Matter Front Matter. Journal of Speculative Philosophy 24 (4).
     
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  21. David Ellerman (2009). Counting Distinctions: On the Conceptual Foundations of Shannon's Information Theory. Synthese 168 (1):119 - 149.
    Categorical logic has shown that modern logic is essentially the logic of subsets (or “subobjects”). In “subset logic,” predicates are modeled as subsets of a universe and a predicate applies to an individual if the individual is in the subset. 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”. A predicate modeled by a partition π on (...)
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  22. David Ellerman (2007). Adjoints and Emergence: Applications of a New Theory of Adjoint Functors. [REVIEW] Axiomathes 17 (1):19-39.
    Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. A recently developed “heteromorphic” theory about (...)
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  23. David P. Ellerman (2004). Parallel Experimentation and the Problem of Variation. Knowledge, Technology and Policy 16 (4):77-90.
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  24. David Pollard, Paola Parmendola, Linda Brennan, Pierre Desrochers, David Ellerman, Rodrigo Firmino, François Therin, Carl Hausler, Moeketsi Letseka, Rias Wyk, Kalpana David, Jon W. Beard, Andrej Pinter, Daniel Hillyard, John Magney & Kai Jakobs (2003). Book Notes. [REVIEW] Knowledge, Technology and Policy 16 (2):96-145.
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  25. David Ellerman (2001). McGregor's Theory Y Vs. Bentham's Panopticism: Toward a Critique of the Economic Theory of Agency. Knowledge, Technology and Policy 14 (1):34-49.
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  26. David Ellerman (2000). Knowledge-Based Development Assistance. Knowledge, Technology and Policy 12 (4):17-43.
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  27. David Ellerman (1999). The Democratic Firm: An Argument Based on Ordinary Jurisprudence. [REVIEW] Journal of Business Ethics 21 (2-3):111 - 124.
    This paper presents an argument for the democratic (or 'labor-managed') firm based on ordinary jurisprudence. The standard principle of responsibility in jurisprudence ('Assign legal responsibility in accordance with de facto responsibility') implies that the people working in a firm should legally appropriate the assets and liabilities produced in the firm (the positive and negative fruits of their labor). This appropriation is normally violated due to the employment or self-rental contract. However, we present an inalienable rights argument that descends from the (...)
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  28. David Ellerman (1995). Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Rowman and Littlefield.
    Collection of published and unpublished essays covering most of my work up to 1990. Chapters 1 & 2 are about orthodox economics. Chapter 3 is the infamous pseudonymous spoof of Nozick, whose context and reaction is explained in the introduction. Chapter 4 puts the labor theory of property and democratic theory in a Kantian framework of treating persons as ends in themselves (instead of as rentable instruments of production). Chapter 5 shows how to reformulate marginal productivity theory using the fact (...)
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  29. David Ellerman (1992). Property and Contract in Economics: The Case for Economic Democracy. Blackwell.
    From a pre-publication review by the late Austrian economist, Don Lavoie, of George Mason University: -/- "The book's radical re-interpretation of property and contract is, I think, among the most powerful critiques of mainstream economics ever developed. It undermines the neoclassical way of thinking about property by articulating a theory of inalienable rights, and constructs out of this perspective a "labor theory of property" which is as different from Marx's labor theory of value as it is from neoclassicism. It traces (...)
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  30. David P. Ellerman (1988). Category Theory and Concrete Universals. Erkenntnis 28 (3):409 - 429.
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  31. David P. Ellerman (1986). Intentionality and Information Theory. Behavioral and Brain Sciences 9 (1):143.
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  32. David P. Ellerman (1985). On the Labor Theory of Property in Essays on Marx: Value, Property and Ideology. Philosophical Forum 16 (4).
     
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  33. David P. Ellerman (1974). Sheaves of Structures and Generalized Ultraproducts. Annals of Mathematical Logic 7 (2-3):163-195.
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  34. David Ellerman, The Workplace in Deliberative Democratic Theory: A Note on Kant, Mill, and Dewey.
    Early democratic theorists such as <span class='Hi'>Kant</span> considered the effects of being a servant or, in modern terms, an employee to be so negative that such dependent people should be denied the vote. John Stuart Mill and John Dewey also noted the negative effects of the employment relation on the development of democratic habits and civic virtues but rather than deny the franchise to employees, they pushed for workplace democracy where workers would be a member of their company rather than (...)
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