David Ellerman

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.