This is Chapter 11 in my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
Finding the Markets in the Math: Arbitrage and Optimization Theory
June 1, 2024 by
This is Chapter 10 from my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
One of the fundamental insights of mainstream neoclassical economics is the connection between competitive market prices and the Lagrange multipliers of optimization theory in mathematics. Yet this insight has not been well developed. In the standard theory of markets, competitive prices result from the equilibrium of supply and demand schedules. But in a constrained optimization problem, there seems to be no mathematical version of supply and demand functions so that the Lagrange multipliers would be seen as equilibrium prices. How can one “find the markets in the math” so that Lagrange multipliers will emerge as equilibrium market prices?
Category Theory as the Theory of Concrete Universals
June 1, 2024 by
This is Chapter 8 of my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
This essay deals with a connection between a relatively recent (1940s and 1950s) field of mathematics, category theory, and a hitherto vague notion of philosophical logic usually associated with Plato, the self-predicative universal or concrete universal. Consider the following example of “bad Platonic metaphysics.”
Given all the entities that have a certain property, there is one entity among them that exemplifies the property in an absolutely perfect and universal way. It is called the “concrete universal.” There is a relationship of “participation” or “resemblance” so that all the other entities that have the property “participate in” or “resemble” that perfect example, the concrete universal.
All of this and much more “bad metaphysics” turns out to be precisely modeled in category theory.
The Semantics Differentiation of Minds and Machines
June 1, 2024 by
This is Chapter 7 from my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
The watershed event in the philosophy of mind (particularly as it relates to artificial intelligence or AI) during the last decade was John Searle’s 1980 article “Minds, Brains and Programs.” This chapter was written about the same time and independently of Searle’s but it was updated in 1985 to take Searle’s work into account. Searle’s exposition was based on his now-famous “Chinese Room Argument”—an intuition pump that boils down to a nontechnical explanation of the difference between syntax (formal symbol manipulation) and semantics (using symbols based on their intended interpretation). Searle argues, in opposition to “hard AI,” that computers can at best only simulate but never duplicate minds because computers are inherently syntactical (symbol manipulators) while the mind is a semantic device.
The syntax-semantics distinction is hardly new; it was hammered out in philosophical logic during the first part of this century and it is fundamental in computer science itself. The purpose of our paper is to analyze the minds-machines question using simple arguments based on the syntax-semantics distinction from logic and computer science (sans “Chinese Room”). I arrive at essentially the same results as Searle—with some simplification and sharpening of the argument for readers with some knowledge of logic or computer science.
Double-Entry Bookkeeping: Mathematical Formulation and Generalization
June 1, 2024 by
This is Chapter 6 from my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
The essay on double-entry bookkeeping (DEB) is intellectually interesting for several reasons in spite of the well-known soporific aspects of bookkeeping. Several of the essays in the volume explicitly employ the analogy between additive and multiplicative operations (i.e., the common group-theoretic properties of additive groups of numbers and multiplicative groups of nonzero numbers). For instance, given the system of multiplying whole numbers or integers, there is no operation inverse to multiplication (i.e., there is no division). But there is a standard method of enlarging the system to allow division. Consider pairs of whole numbers a/b (with b ¹ 0) and define multiplication in the obvious way: (a/b)(c/d) = (ac)/(bd). These ordered pairs of integers are the “fractions” and they allow the operation of division (“multiply by the reciprocal”).
Now substitute addition for multiplication. We start with the additive system of positive numbers along with zero (i.e., the non-negative numbers) where is no inverse operation to addition (i.e., there is no subtraction). To enlarge the domain of non-negative numbers to include subtraction, consider ordered pairs [a // b] and define addition in the analogous way: [a // b] + [c // d] = [a+c // b+d]. This enlarged system of additive operations on ordered pairs of non-negative numbers allows subtraction (“add on the reversed pair”). The origin of the intellectual trespassing into DEB was the observation that these ordered pair were simply the T-accounts of DEB.
Aside from illustrating the interplay of additive-multiplicative themes, the essay illustrates one of the most astonishing examples of intellectual insulation between disciplines, in this case, between accounting and mathematics. Double-entry bookkeeping was developed during the fifteenth century and was first recorded as a system by the Italian mathematician Luca Pacioli in 1494. Double-entry bookkeeping has been used as the accounting system in market-based enterprises of any size throughout the world for several centuries. Incredibly, however, the mathematical basis for DEB is not known, at least not in the field of accounting.
Are Marginal Products Created ex Nihilo?
June 1, 2024 by
This is Chapter 5 from my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
When an orthodox economist considers the principle of people getting the fruits of labor, he or she will invariably interpret it in terms of marginal productivity. The orthodox claim is that under the conditions of competitive equilibrium, each unit of labor “gets what it produces.” Well-meaning capitalist liberals emphasize that actual capitalism may be neither competitive nor in equilibrium, and in any case, there are enormous difficulties in measuring the “marginal product of each factor of production.” In other words, they accept that interpretation of marginal productivity theory in principle but fuss about its applicability in practice.
The Kantian Person/Thing Principle in Political Economy
June 1, 2024 by
This is Chapter 4 in my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
Ethical theories can be broadly grouped into utilitarian theories and rights-based theories. Modern economics is so thoroughly utilitarian that most economists would be hard-pressed to cite the application of a rights-based argument to economic institutions. Yet the normative principles outlined in the first two chapters, the labor theory of property and the de facto theory of inalienability, are squarely within the rights-based tradition. The democratic principle of self-determination is also a closely allied rights-based theory [see Ellerman 1992].
The Libertarian Case for Slavery (A Spoof on Nozick)
June 1, 2024 by
This is Chapter 3 from my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
Liberalism is living a lie. It pretends that the contract to sell all of one’s labor, the self-enslavement contract, is an invalid contract beyond the pale while the contract to sell one’s labor piecemeal (by the hour, day, month, or year) is a perfectly valid contract above reproach. The self-enslavement contract is one of the skeletons in liberalism’s intellectual closet. Defenders of liberal capitalism are quick to accept even the most superficial arguments against voluntary slavery just to shove the issue back in the closet—just so long as the arguments do not carry over to the current contract to rent oneself out, the employer-employee contract. Who wants to be seen as, in effect, defending voluntary slavery by showing how most arguments against the self-sale contract are baseless (aside from one “J. Philmore”)?
Myth and Metaphor in Orthodox Economics
June 1, 2024 by
This is Chapter 2 from: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
Discussion of the fundamental questions of political economy is today almost completely clouded and distorted by a number of basic myths and metaphors. Deconstruction is necessary before constructive discussions can begin. The myths and metaphors are concerned with basic conceptions about property and contract, not with prices and markets. As layer upon layer of distortions are removed, new facts and new perspectives on old facts will emerge. These facts have fairly direct normative implications, but the disagreements and controversies are about the facts, not about norms or prescriptions.
Trespassing against the Happy Consciousness of Orthodox Economics
June 1, 2024 by
This is Chapter 1 in my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.
This first chapter addresses the problems of trespassing involved in understanding the arguments presented in the first five “controversial” chapters of the collection. These chapters challenge the whole idea of the employer-employee relationship that is the institutional basis for our present version of a private-property market economy. The problems of trespassing against fundamental orthodoxy in the social and moral sciences are of a completely different order of magnitude than the problems of trespassing in the natural and mathematical sciences.