David Ellerman

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.

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.

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.

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.

Saunders Mac Lane famously remarked that "Bourbaki just missed" formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre--which then had to wait until Daniel Kan's 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms within a category, i.e., homomorphisms. When Samuel's treatment is reconsidered in view of the treatment of adjoints using heteromorphisms or hets (object-to-object morphisms between objects in different categories), then he, in effect, isolated the concept of a left representation solving a universal mapping problem. When dualized to obtain the concept of a right representation, the two halves only need to be united to obtain an adjunction. Thus Samuel was only a now-simple dualization away for formulating adjoints in 1948. Apparently, Bodo Pareigis' 1970 text was the first and perhaps only text to give the heterodox "new characterization" (i.e., heteromorphic treatment) of adjoints. Orthodox category theory uses various relatively artificial devices to avoid formally recognizing hets--even though hets are routinely used by the working mathematician. Finally we consider a "philosophical" question as to whether the most important concept in category theory is the notion of an adjunction or the notion of a representation giving a universal mapping property (where adjunctions arise as the special case of a bi-representation of dual universal mapping problems).

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, with benchmarking comparisons made between the experiments, and with the "migration" of discoveries between experiments wherever possible to ratchet up the performance of the group. The thesis is that parallel experimentation is a fundamental dynamic efficiency scheme to enhance and accelerate variation, innovation, and learning in contexts of genuine uncertainty or known ignorance. Within evolutionary biology, this type of parallel experimentation scheme was developed in Sewall Wright's shifting balance theory of evolution. It addressed the rather neglected topic of how a population on a low fitness peak might eventually be able to go "downhill" against selective pressures, traverse a valley of low fitness, and then ascend a higher fitness peak. The theme of parallel experimentation is used to recast and pull together dynamic and pluralistic theories in economics, political theory, philosophy of science, and social learning.

Two aspects of the fine Flecha-Cruz paper can be usefully elaborated. The Mondragon cooperatives differ not only from capitalist firms but also from most other cooperatives in the doctrine of the 'priority of labor over capital' which means that the people working in any sort of cooperative will be members and will not be rented as employees. Also the Mondragon system of internal capital accounts solves the equity-structure problem that has plagued many modern cooperatives structured as non-profits or traditional worker cooperatives with 'membership shares'.

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."

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 Reformation and Enlightenment which argues that the self-rental contract, like the self-sale or voluntary slavery contract, is inherently invalid. The key intuition of the inalienable rights theory is that one cannot in fact voluntarily transfer de facto responsibility for one's actions to another person. One can only voluntarily co-operate with another person, but then one is de facto jointly responsible for the results. Just as the legal authorities legally reconstruct the criminous employer and employee as a partnership with shared responsibility, so justice demands that every firm be legally reconstructed as a partnership of all who work (working employers and employees) in the enterprise, i.e., as a democratic firm.

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).

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.

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. Yet the market also provides a laissez-faire mechanism: when the legal authorities do not intervene, then the initial right is, in effect, assigned to the first seller and the terminal liability to the last buyer. But does this mechanism satisfy the juridical principle of responsibility: assign de jure responsibility in accordance with de facto responsibility? The fundamental theorem states that if all transfers are covered by voluntary contracts and all contracts are fulfilled, then the laissez-faire mechanism satisfies the responsibility principle.Une théorie de la propriété se doit d’expliquer entièrement le cycle de vie du droit de propriété: les conditions de son émergence, de son transfert et de sa résiliation. La théorie économique s’est focalisée sur les mécanismes de transferts sur le marché et a presque totalement négligé la question de l’émergence et de la réalisation de la propriété dans les phénomènes de production et de consommation. Pourtant, le marché fournit également un mécanisme de laissez-faire: lorsque les autorités légales s’abstiennent d’intervenir, le droit initial est affecté au premier vendeur et la responsabilité terminale au dernier acheteur. Néanmoins, ce mécanisme satisfait-il le principe juridique de responsabilité? A savoir, assigner une responsabilité de jure en accord avec le principe de responsabilité de facto? En effet, le théorème fondamental exprime qui si tous les transferts s’effectuent par des contrats volontaires, et que tous les contrats sont remplis, alors le principe du laissez-faire satisfait le principe de responsabilité.

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

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.

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.

Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) 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 notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) 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 partitions to the quantum logic of direct-sum decompositions (i.e., the vector space version of a set partition) of a general vector space--which can then be specialized to the direct-sum decompositions of a Hilbert space. This allows the logic to express measurement by any self-adjoint operators rather than just the projection operators associated with subspaces. In this introductory paper, the focus is on the quantum logic of direct-sum decompositions of a finite-dimensional vector space (including such a Hilbert space). The primary special case examined is finite vector spaces over ℤ₂ where the pedagogical model of quantum mechanics over sets (QM/Sets) is formulated. In the Appendix, the combinatorics of direct-sum decompositions of finite vector spaces over GF(q) is analyzed with computations for the case of QM/Sets where q=2.

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

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 to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics.

John Tomasi's new book, Free Market Fairness, has been well-received as "one of the very best philosophical treatments of libertarian thought, ever" and as a "long and friendly conversation between Friedrich Hayek and John Rawls—a conversation which, astonishingly, reaches agreement". The book does present an authoritative state-of-the-debate across the spectrum from right-libertarianism on the one side to high liberalism on the other side. My point is not to question where Tomasi comes down with his own version of "market democracy" as a remix of Hayek and Rawls. My point is to use his sympathetic restatements of views across the liberal spectrum to show the basic misframings and common misunderstandings that cut across the liberal-libertarian viewpoints surveyed in the book. As usual, the heart of the debate is not in the answers to carefully framed questions, but in the framing itself.

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 Claude Shannon's entropy. In this manner, the new logic of partitions provides a logico-conceptual foundation for information-theoretic entropy or information content.

Early democratic theorists such as Kant 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 an employee. In spite of the continuing prevalence of the employment relation and the lack of workplace democracy, this topic now seems to be something of a "third rail" in deliberative democratic theory

The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement.

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.

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 along with a new concept to abstractly model the functions of a brain.

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 make the distinction between genuinely selectionist mechanisms and what are better called "generative" mechanisms. This note outlines that distinction.