Starting at the logical level of the logic of partitions, dual to the usual Boolean logic of subsets, the notion of logical entropy, i.e., information as distinctions, is developed as the quantification of the distinctions of partitions—just as probability theory starts with the quantification of elements of subsets. Logical entropy is compared and contrasted with the usual notion of Shannon entropy. Then a semi-algorithmic procedure (from the mathematical folklore) is used to translate the notion of logical entropy at the set (...) level to the corresponding notion of quantum logical entropy at the (Hilbert) vector space level. Examples and some important propositions relate quantum logical entropy to projective measurement and to the Hilbert-Schmidt distance. Overall, the approach demonstrates the logical basis and naturality of this notion of entropy for quantum mechanics. (shrink)

This book presents a new ‘partitional' approach to understanding or interpreting the math of standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM. Since at the set level, partitions are the mathematical tool to represent distinctions and indistinctions (or definiteness and indefiniteness), this approach shows (...) how to interpret the key non-classical QM notion of superposition in terms of (objective) indefiniteness between definite alternatives (as opposed to seeing it as the sum of ‘waves'). Thus, the book develops a new mathematical, or indeed, logical, approach to the century-old problem of interpreting quantum mechanics, ensure it is of interest to philosophers of science as well as mathematicians and physicists. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to (...) go from indefinite to more definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

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 (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy (...) is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement. Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory. (shrink)

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 (...) roots of such ideas in some fascinating and largely forgotten strands of the history of economics. It draws attention to the question of "responsibility" which neoclassicism has utterly lost sight of. It is startlingly fresh in its overall approach, and unusually well written in its presentation. ... It constitutes a better case for its economic democracy viewpoint than anything else in the literature." . (shrink)

The abolition of slavery abolished not only the involuntary ownership of other people (workers) but also voluntary contractual forms of lifetime servitude. But that system of lifetime servitude was replaced by the current system of voluntary renting, hiring, employing, or leasing workers, i.e., the employment system. Hence the name “Neo-Abolitionism” for the idea of abolishing the employer–employee contract in favor of each firm being a workplace democracy. The three arguments against the human rental system are modern versions of old arguments (...) that descend from the Reformation and Enlightenment in the Abolitionist and Democratic Movements. The first argument derives from noting that the old inalienable rights argument based on de facto inalienability of responsibility and decision-making that ruled out the long-term contract of lifetime servitude also applies against the shorterterm contract to rent oneself out. The second argument is the old labor or natural rights theory of private property (in the fruits of one’s labor) that is violated when the employer legally appropriates the positive and negative fruits of the employees working in a firm. And the third argument applies to the firm the democratic arguments against the subjection contract that alienates the rights of self-governance in favor of a democratic contract of delegation. (shrink)

There are fundamentally two mathematical logics. One the Boolean logic of subsets, usually presented today in the special case of propositional logic, which has many sublogics and extensions, the most important being the intuitionistic logic usually modeled by the open subsets of a topological space. The other co-fundamental mathematical logic is the topic of this book, the logic of partitions. We are using ”logic” in a mathematical sense as being about basic mathematical objects, subsets of a universe set or partitions (...) on a universe set.1 Logic, in this mathematical sense, is not about propositions, although, as with any mathematical theory, it involves propositions about the basic objects, e.g., that an element is in a subset or that a distinction is made by a partition. Moreover, by taking the universe set to be the one element set 1, with two subsets ∅ and 1, there is a special case of subset logic, namely propositional logic, that can be interpreted as being about propositions with ∅ representing falsehood and 1 representing truth. (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)

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 (...) second task is to recover that theory and to consider several other applications of the theory. Finally, the liberal theories of justice expounded by John Rawls and by Robert Nozick are briefly examined from this perspective. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper (...) is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunction seeming to be the primary lens. Our topic is a theory showing “where adjoints come from”. The theory is based on object-to-object “chimera morphisms”, “heteromorphisms”, or “hets” between the objects of different categories (e.g., the insertion of generators as a set-to-group map). After showing that heteromorphisms can be treated rigorously using the machinery of category theory (bifunctors), we show that all (...) adjunctions between two categories arise (up to an isomorphism) as the representations (i.e., universal models) within each category of the heteromorphisms between the two categories. The conventional treatment of adjunctions eschews the whole concept of a heteromorphism, so our purpose is to shine a new light on this notion by showing its origin as a het between categories being universally represented within each of the two categories. This heteromorphic treatment of adjunctions shows how they can be split into two separable universal constructions. Such universals can also occur without being part of an adjunction. We conclude with the idea that it is the universal constructions (adjunctions being an important special case) that are really the foundational concepts to pick out what is important in mathematics and perhaps in other sciences, not to mention in philosophy. (shrink)

After Marx, dissenting economics almost always used 'the labour theory' as a theory of value. This paper develops a modern treatment of the alternative labour theory of property that is essentially the property theoretic application of the juridical principle of responsibility: impute legal responsibility in accordance with who was in fact responsible. To understand descriptively how assets and liabilities are appropriated in normal production, a 'fundamental myth' needs to be cleared away, and then the market mechanism of appropriation can be (...) understood. On the normative side, neoclassical theory represents marginal productivity theory as showing that (a metaphorical version of) the imputation principle is satisfied ('people get what they produce') in competitive enterprises. Since that shows the moral commitment of neoclassical economics to the imputation principle, the labour theory of property is presented here as the actual non-metaphorical application of the imputation principle to property appropriation. The property-theoretic analysis at the firm level shows how the neoclassical (and much heterodox) analysis in terms of 'distributive shares' wholly misframed the basic questions. Finally, the paper shows how the imputation principle (modernised labour theory of property) is systematically violated in the present wage labour system of renting persons. The paper can be seen as taking up the recent challenge posed by Donald Katzner for a dialogue between neoclassical and heterodox microeconomics. (shrink)

Democratic ownership in the sphere of economic production is often contrasted with capitalist ownership along the lines of transferability of legal rights, such as profit and governance rights. If capitalist ownership implies full transferability of legal rights in production, democratic ownership anchors legal rights with the current generation of workers in the firm. A worker cooperative is generally considered the best practical proxy for a democratic firm (Ellerman, 2021; Erdal, 2012); however, worker cooperatives remain rare in contemporary economies, while the (...) capitalist form of enterprise continues to dominate the markets despite contrary predictions by intellectual giants like John Stuart Mill. Why did democratic ownership fail to achieve scale? Worker cooperatives are most commonly established from scratch or by fully converting a capitalist firm. In this chapter, we argue that cooperatives have faced challenges because they did not introduce a mechanism that would allow for the gradual conversion of capitalist ownership into democratic ownership. We introduce an alternative proposal that can help scale democratic ownership using the mechanism of leveraged gradual cooperative conversions. In the literature, this solution is described as the “Cooperative ESOP”, since it uses the ESOP leveraged financing mechanism, which is attached to a cooperative vehicle (Ellerman et al., 2022 and Appendix). We argue that the mechanism of gradual and leveraged conversion, with the aid of institutional support, can help democratic ownership grow in our economies and become mainstream. (shrink)

From the 1970’s, there has been almost a half-century of development of employee-owned firms. There has been a wide variety of legal/capital structures that have been tried but too little analysis of which legal forms work or don’t work over the longer term, e.g. the transition from one generation of employee-owners to the next generation of employee owners. This paper provides a critical analysis of the major forms. These include the forms based on common ownership (Yugoslav self-managed firms and the (...) UK EOTs), the older plywood cooperatives in the US Northwest along with the Spanish Sociedades Laborales, and the American Employee Stock Ownership Plans (US ESOPs). Finally, we advocate a variation on the US ESOP model, called the ‘European ESOP’, that seems to avoid some pitfalls and combines the best aspects of the past forms of employee ownership. (shrink)

The name “capitalism” derives from Marx’s false analogy between medieval land ownership and the “ownership of the means of production.” However, unlike medieval land, capital goods can be rented out, e.g., by Frank Knight’s entrepreneur, and then the capital owner does not hold those management or product rights. What then is the characteristic institution in our civilization? It is the voluntary renting of workers. What then is the relationship between Classical Liberalism, the dominant philosophy behind Economics, and a lifetime labour (...) contract? Frank Knight had plenty to say about the doctrine of inalienable rights which disallows such contracts. (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)

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 have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start (...) with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of Sets are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences. (shrink)

Where does the Born Rule come from? We ask: “What is the simplest extension of probability theory where the Born rule appears”? This is answered by introducing “superposition events” in addition to the usual discrete events. Two-dimensional matrices (e.g., incidence matrices and density matrices) are needed to mathematically represent the differences between the two types of events. Then it is shown that those incidence and density matrices for superposition events are the (outer) products of a vector and its transpose whose (...) components foreshadow the “amplitudes” of quantum mechanics. The squares of the components of those “amplitude” vectors yield the probabilities of the outcomes. That is how probability amplitudes and the Born Rule arise in the minimal extension of probability theory to include superposition events. This naturally extends to the full Born Rule in the Hilbert spaces over the complex numbers of quantum mechanics. It would perhaps be satisfying if probability amplitudes and the Born Rule only arose as the result of deep results in quantum mechanics (e.g., Gleason’s Theorem). But both arise in a simple extension of probability theory to include “superposition events”–which should not be too surprising since superposition is the key non-classical concept in quantum mechanics. (shrink)

Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...) a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic. (shrink)

Dramatic changes or revolutions in a field of science are often made by outsiders or 'trespassers,' who are not limited by the established, 'expert' approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.

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 (...) of the market, the market mechanism of appropriation. Does this mechanism satisfy an appropriate normative principle? The standard normative juridical principle is to assign or impute legal responsibility according to de facto responsibility. It is given a historical tag of being "Lockean" but the basis is contemporary jurisprudence, not historical exegesis. Then the fundamental theorem of the property mechanism is proven which shows that if "Hume's conditions" (no transfers without consent and all contracts fulfilled) are satisfied, then the market automatically satisfies the Lockean responsibility principle, i.e., "Hume implies Locke." As a major application, the results in their contrapositive form, "Not Locke implies Not Hume," are applied to a market economy based on the employment contract. It is shown the production based on the employment contract violates the Lockean principle (all who work in an employment enterprise are de facto responsible for the positive and negative results) and thus Hume's conditions must also be violated in the marketplace (de facto responsible human action cannot be transferred from one person to another—as is readily recognized when and employer and employee together commit a crime). (shrink)

Are corporations the problem? Can reforms in the area of corporate responsibility (e.g., more stakeholder governance) lead to any real changes? The goal of the paper is to analyse debates concerning the Citizens United case, corporate personhood, the stakeholder theory, the affected interests principle and, finally, deeper fallacies with respect to the rights of capital embedded in Marxism and conventional economic theories of capital and corporate finance. The last analysis considers another institution at the root of the problems of the (...) current economic system: the renting of human beings in the employment relationship – which has also corrupted the original idea of a corporation that dates back to medieval times. (shrink)

There seems to be two rather different philosophies of aid to development and poverty relief. (1) The progressive/social-democratic approach is for the government or aid agencies to do more and more good things for people. (2) The classical-liberal approach is to change the underlying conditions so that people are empowered to do good things for themselves. In this paper, we analyze Alexis de Tocqueville’s approach to these questions in his First Memoir and his (unfinished) Second Memoir on Pauperism.

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)

ion turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of the direction of parallel lines. This paper developments simple mathematical models of both types of abstraction and shows, for instance, how finite probability theory can be interpreted using #2 abstracts as “superposition (...) events” in addition to the ordinary events. The goal is to use the second notion of abstraction to shed some light on the notion of an indefinite superposition in quantum mechanics. (shrink)

A basic duality arises throughout the mathematical and natural sciences. Traditionally, logic is thought to be based on the Boolean logic of subsets, but the development of category theory in the mid-twentieth century shows the duality between subsets and partitions (or equivalence relations). Hence, there is an equally fundamental dual logic of partitions. At a more basic or granular level, the elements of a subset are dual to the distinctions (pairs of elements in different blocks) of a partition. The quantitative (...) version of subset logic is probability theory (as developed by Boole), and the quantitative version of the logic of partitions is information theory re-founded on the notion of logical entropy. The subset side of the duality uses a one-sample (or one-element) approach, e.g., the mean of a random variable; the partition side uses a two-sample (or pair-of-elements) approach. This paper gives a new derivation of the variance (and covariance) based on the two-sample approach, which positions the variance on the partition and information theory side of the duality and thus dual to the mean. (shrink)

Substance is rivalrous and form is non-rivalrous (in the sense that information can be shared without diminishing one’s own). The recipe to "open the gates to Plato's Heaven" is by minimizing the role of rivalrous substance and maximizing the role of non-rivalrous form. This creates a whole series of different processes, positive feedback processes, vicious or virtuous circles, cumulative circular causality, and increasing returns phenomena, which are analysed in this paper.

This article comments on Isabelle Ferreras’s “Democratizing the Corporation.” The focus is on the conceptual framing, which arguably contains a number of problems that are quite common on the left and are thus doubly deserving of commentary and explanation.

The World Bank, the leading multilateral development agency, begins its mission statement with a dedication to helping people help themselves, and Oxfam, a leading nongovernmental organization (NGO) working on development, states that its “main aim is to help people to help themselves.”1 Perhaps the most successful example of development assistance in modern history was the Marshall Plan, which “did what it set out to do—help people help themselves” (Stern 1997). American of‹cial assistance to developing countries began with Harry Truman’s “Point (...) Four” program in 1949, which was conceived as a worldwide “program of helping underdeveloped nations to help themselves.” 2 John Dewey gave perhaps the best statement of the theme: The best kind of help to others, whenever possible, is indirect, and consists in such modi‹cations of the conditions of life, of the general level of subsistence, as enables them independently to help themselves. (Dewey and Tufts 1908, 390)3 The idea and the rhetoric of “helping people help themselves” has been with us throughout the postwar period of of‹cial development assistance. For instance, we are all familiar with the ancient Chinese saying that if you give people ‹sh, you feed them for a day, but if you teach them how to ‹sh—or rather, if you enable them to learn how to ‹sh— then they can feed themselves for a lifetime.4 There is broad agreement— at least as a statement of high purpose—that helping people help themselves is the best methodology for development assistance in the developing countries as well as for other types of helping relationships. (shrink)

There is a new theory of information based on logic. The definition of Shannon entropy as well as the notions on joint, conditional, and mutual entropy as defined by Shannon can all be derived by a uniform transformation from the corresponding formulas of logical information theory. Information is first defined in terms of sets of distinctions without using any probability measure. When a probability measure is introduced, the logical entropies are simply the values of the probability measure on the sets (...) of distinctions. The compound notions of joint, conditional, and mutual entropies are obtained as the values of the measure, respectively, on the union, difference, and intersection of the sets of distinctions. These compound notions of logical entropy satisfy the usual Venn diagram relationships since they are values of a measure. The uniform transformation into the formulas for Shannon entropy is linear so it explains the long-noted fact that the Shannon formulas satisfy the Venn diagram relations--as an analogy or mnemonic--since Shannon entropy is not a measure on a given set. What is the logic that gives rise to logical information theory? Partitions are dual to subsets, and the logic of partitions was recently developed in a dual/parallel relationship to the Boolean logic of subsets. Boole developed logical probability theory as the normalized counting measure on subsets. Similarly the normalized counting measure on partitions is logical entropy--when the partitions are represented as the set of distinctions that is the complement to the equivalence relation for the partition. In this manner, logical information theory provides the set-theoretic and measure-theoretic foundations for information theory. The Shannon theory is then derived by the transformation that replaces the counting of distinctions with the counting of the number of binary partitions it takes, on average, to make the same distinctions by uniquely encoding the distinct elements--which is why the Shannon theory perfectly dovetails into coding and communications theory. (shrink)

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms that parses an adjunction into two separate parts. Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple category theory and (...) is focused on the interpretation and application of the mathematical concepts. (shrink)

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.

In her recent book Private Government, Elizabeth Anderson makes a powerful but pragmatic case against the abuses experienced by employees in conventional corporations. The purpose of this review-essay is to contrast Anderson’s pragmatic critique of many abuses in the employment relation with a principled critique of the employment relationship itself. This principled critique is based on the theory of inalienable rights that descends from the Reformation doctrine of the inalienability of conscience down through the Enlightenment in the abolitionist, democratic, and (...) feminist movements. That theory was the basis for the abolition of the voluntary slavery or self-sale contract, the voluntary non-democratic constitution (pactum subjectionis), and the voluntary coverture marriage contract in today’s democratic countries. When understood in modern terms, that same theory applies as well against the voluntary self-rental or employment contract that is the basis for our current economic system. (shrink)

ince the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The set notion of a partition is dual to the notion of a subset. Hence the Boolean logic of (...) subsets has a dual logic of partitions. Then the dual progression is from that logic of set partitions to the quantum logic of direct-sum decompositions of a general vector space--which can then be specialized to the direct-sum decompositions of a Hilbert space. This allows the quantum logic of direct-sum decompositions to express measurement by any self-adjoint operators. The quantum logic of direct-sum decompositions is dual to the usual quantum logic of subspaces in the same sense that the logic of partitions is dual to the usual Boolean logic of subsets. (shrink)

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 in their promotion of non-democratic sovereign city-states (startup cities or charter cities). We will take the late James M. Buchanan as a representative of the democratic strain of classical liberalism. Since the (...) fundamental norm of classical liberalism is consent, we must start with the intellectual history of the voluntary slavery contract, the coverture marriage contract, and the voluntary non-democratic constitution (or pactum subjectionis). Next we recover the theory of inalienable rights that descends from the Reformation doctrine of the inalienability of conscience through the Enlightenment (e.g., Spinoza and Hutcheson) in the abolitionist and democratic movements. Consent-based governments divide into those based on the subjects' alienation of power to a sovereign and those based on the citizens' delegation of power to representatives. Inalienable rights theory rules out that alienation in favor of delegation, so the citizens remain the ultimate principals and the form of government is democratic. Thus the argument concludes in agreement with Buchanan that the classical liberal endorsement of sovereign individuals acting in the marketplace generalizes to the joint action of individuals as the principals in their own organizations. (shrink)

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 (...) Debate' between the private or public ownership of slaves. Even though the Great Debate between capitalism and socialism is now in the dustbin of intellectual history, Marxism still plays an important role in sustaining the misframing of the questions so that the defenders of the present employment system do not have to face the real questions that separate that system from a system of economic democracy. In that sense, Marxism has become the ultimate capitalist tool. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u F = {x | F(x)} for a property F(.) could never be self-predicative in the sense of uF ∈ (...) uF. But the mathematical theory of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals – which can be seen as forming the “other bookend” to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato’s Theory of Forms as well as for the idea of a “concrete universal” in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

Liberal thought (in the sense of classical liberalism) is based on the juxtaposition of consent to coercion. Autocracy and slavery were seen as based on coercion whereas today's political democracy and economic 'employment system' are based on consent to voluntary contracts. This paper retrieves an almost forgotten dark side of contractarian thought that based autocracy and slavery on explicit or implicit voluntary contracts. To answer these 'best case' arguments for slavery and autocracy, the democratic and abolitionist movements forged arguments not (...) simply in favour of consent, but arguments that voluntary contracts to legally alienate aspects of personhood were invalid 'even with consent' – which made the underlying rights inherently inalienable. Once understood, those arguments have the perhaps 'unintended consequence' of making the neo-abolitionist case for ruling out today's self-rental contract, the employer-employee contract. The paper has to also retrieve these inalienable rights arguments since they have been largely lost on the Left, not to mention in liberal thought. (shrink)

When this book was first published in 1990, there were massive economic changes in the East and significant economic challenges to the West. This critical analysis of democratic theory discusses the principles and forces that push both socialist and capitalist economies toward a common ground of workplace democratization. This book is a comprehensive approach to the theory and practice of the "Democratic firm" – from philosophical first principles to legal theory and finally to some of the details of financial structure. (...) The argument for economic democracy supports private property, free markets and entrepreneurship for instance, but fundamentally it replaces the employer/employee relationship with democratic membership in the firm. For students, teachers, policy makers and others interested in the application of democracy to the workplace, this book will serve as a manifesto and a standard reference on the topic. (shrink)

Much of the recent discussion in progressive circles [e.g., Stiglitz; Galbraith; Piketty] has focused the obscene mal-distribution of wealth and income as if that was "the" problem in our economic system. And the proposed redistributive reforms have all stuck to that framing of the question. To put the question in historical perspective, one might note that there was a similar, if not more extreme, mal-distribution of wealth, income, and political power in the Antebellum system of slavery. Yet, it should be (...) obvious to modern eyes that redistributions in favor of the slaves, while leaving the institution of owning workers intact, would not address the root of the problem. The system of slavery was eventually abolished in favor of the system we have today which differs in two important respects: the workers are only rented, hired, or employed ; and the rental relationship between employer and employee is voluntary. Today, the root of the problem is the whole institution for the voluntary renting of human beings, the employment system itself, not the terms of the contract or the accumulated consequences in the form of the mal-distribution of income and wealth. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of categories, (...) dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

The short answer is whenever the actual activity of the “cooperative” is not carried out by the members but by employees. The problem is, of course, not in cooperation per se but in the hiring, employing, renting, or leasing of people to carry out the supposedly “cooperative” activities of the “cooperative” (Ellerman, 2021). Consider the case of a typical consumer cooperative. What is the cooperative activity carried out by the consumer‑members? They do not consume cooperatively; that would be a commune (...) or kibbutz. They shop and consume as individuals or as individual families. They do not carry out the activity of the consumer cooperative business—which is conducted by the hired managers and employees of the business. The whole notion of the consumer‑members cooperating together in some joint activity is a beautiful fiction, but a fiction nevertheless. Of course, there may be some overlap between employees and consumers, but we are analyzing functional roles, i.e., the roles people have qua consumers and qua workers. Moreover, the number of consumers will far exceed the number of employees. (shrink)

This essay shows that the principles of classical liberalism (e.g., James Buchanan) do not apply to the firm based on the employer-employee relationship. However, there is a deeper democratic classical liberalism tradition based on inalienable rights, but it rules out the employment or human rental relation.