Suppose that T is an equational theory of groups or of rings. If T is finitely axiomatizable, then there is a least number μ so that T can be axiomatized by μ equations. This μ can depend on the operation symbols that occur in T. In the 1960s, Tarski and Green completely determined the values of μ for arbitrary equational theories of groups and of rings. While Tarski and Green announced the results of their collaboration in 1970, the only fuller (...) publication of their work occurred as part of a seminar led by Tarski at Berkeley during the 1968–69 academic year. The present paper gives a full account of their findings and their proofs. (shrink)

We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provide an example of a lattice which fails to be inherently nonfinitely based but whose equational theory is not finitely axiomatizable.

This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies (...) in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text. (shrink)

Steroid hormone receptors are ligand‐inducible transcription factors that exhibit potent effects on gene expression in living cells. Precise dissection of their mode of action at the molecular level can best be carried out in functional cell‐free systems. This article will describe the benefits of such systems and review their development up to the recent establishment of steroid receptor‐dependent in vitro transcription. Subsequent advances in our knowledge of receptor function arising from the exploitation of this powerful experimental tool will be described. (...) Particular emphasis will be placed upon two key problems: the role of steroid hormone in receptor action and the mechanisms by which steroid receptors activate gene transcription. (shrink)

ABSTRACT Benjamin Page's thoughtful critique of my book, The Illusion of Public Opinion, strives to reassure readers that all is well—despite the book's extensive documentation of measurement‐error artifacts in numerous public opinion surveys. Page's own careful polling practices are not followed outside of elite academic survey centers. Moreover, even in such well‐run surveys, the respondents are often ignorant of the issues being probed. The fact that nonrandom reasons of some sort must be determining on‐the‐spot survey responses may allow us to (...) call the respondents “rational” in a loose sense. But the responses still don't represent actual opinions about the specific policy issues being probed—let alone well‐informed answers. Finally, while Page argues that measurement errors are most likely random, and should cancel out in the aggregate, the “miracle of aggregation” doesn't occur when the form, wording, and context of questions varies from survey to survey. And even when wording and context are held constant, the respondents' understanding of the same words can vary dramatically or subtly over time, due to new political events and their changing interpretation. (shrink)

Microphysical laws are time reversible, but macrophysics, chemistry and biology are not. This paper explores how this asymmetry arises due to the cosmological context, where a non-local Direction of Time is imposed by the expansion of the universe. This situation is best represented by an Evolving Block Universe, where local arrows of time emerge in concordance with the Direction of Time because a global Past Condition results in the Second Law of Thermodynamics pointing to the future. At the quantum level, (...) the indefinite future changes to the definite past due to quantum wave function collapse events. (shrink)

The American Journal of Bioethics, Volume 12, Issue 5, Page 8-9, May 2012.

This chapter responds to claims that causal closure of the underlying microphysics determines brain outcomes as a matter of principle, even if we cannot hope to ever carry out the needed calculations in practice. The reductionist position is that microphysics alone determines all, specifically the functioning of the brain. Here I respond to that claim in depth, claiming that if one firstly takes into account the difference between synchronic and diachronic emergence, and secondly takes seriously the well established nature of (...) biology in general and neuroscience in particular, downward causation enables genuine causal powers to occur at higher emergent levels in biology and that causal closure is in reality an interlevel affair involving even social levels. (shrink)

In their new indictments of global neoliberalism and the economic profession's culpability in its harms, Dani Rodrik and Joseph Stiglitz press the case for reconstructed globalization that generates benefits for all and not just for corporate and financial elites. Both books are deeply consistent with the insights of Karl Polanyi, who had identified the inherent contradictions of the project to create what he called a self-regulating economy. Like Polanyi, Rodrik and Stiglitz are attentive to the inadequacies of neoliberalism, and both (...) emphasize the capture of the state and international economic policy by elites, who have turned their backs on those left behind. While Stiglitz emphasizes that the profession knows how to fix the problem by applying modern Keynesian insights, Rodrik emphasizes the inherent epistemic limitations facing economists. Indeed, his arguments about development policy reflect the insights of Friedrich Hayek into the limits of economic expertise. (shrink)

A biogenetic structural explanation is offered for the cross‐culturally common mystical experience called portalling, the experience of moving from one reality to another via a tunnel, door, aperture, hole, or the like. The experience may be evoked in shamanistic and meditative practice by concentration upon a portalling device (mirror, mandala, labyrinth, skrying bowl, pool of water, etc.). Realization of the portalling experience is shown to be fundamental to the phenomenology underlying multiple reality cosmologies in traditional cultures and is explained in (...) terms of radical re‐entrainment of the neurological systems mediating experience in the brain. Phenomenological experiments with mirror portalling devices from both the Tibetan and the Tsimshian religious traditions are reported. (shrink)

The causal closure of physics is usually discussed in a context free way. Here I discuss it in the context of engineering systems and biology, where strong emergence takes place due to a combination of upwards emergence and downwards causation. Firstly, I show that causal closure is strictly limited in terms of spatial interactions because these are cases that are of necessity strongly interacting with the environment. Effective Spatial Closure holds ceteris parabus, and can be violated by Black Swan Events. (...) Secondly, I show that causal closure in the hierarchy of emergence is a strictly interlevel affair, and in the cases of engineering and biology encompasses all levels from the social level to the particle physics level. However Effective Causal Closure can usefully be defined for a restricted set of levels, and one can experimentally determine Effective Theories that hold at each level. This does not however imply those effective theories are causally complete by themselves. In particular, the particle physics level is not causally complete by itself in the contexts of solid state physics, digital computers, or biology. Furthermore Inextricably Intertwined Levels occur in all these contexts. (shrink)

Physics and chemistry underlie the nature of all the world around us, including human brains. Consequently some suggest that in causal terms, physics is all there is. However, we live in an environment dominated by objects embodying the outcomes of intentional design (buildings, computers, teaspoons). The present day subject of physics has nothing to say about the intentionality resulting in existence of such objects, even though this intentionality is clearly causally effective. This paper examines the claim that the underlying physics (...) uniquely causally determines what happens, even though we cannot predict the outcome. It suggests that what occurs is the contextual emergence of complexity: the higher levels in the hierarchy of complexity have autonomous causal powers, functionally independent of lower level processes. This is possible because top-down causation takes place as well as bottom-up action, with higher level contexts determining the outcome of lower level functioning and even modifying the nature of lower level constituents. Stored information plays a key role, resulting in non-linear dynamics that is non-local in space and time. Brain functioning is causally affected by abstractions such as the value of money and the theory of the laser. These are realised as brain states in individuals, but are not equivalent to them. Consequently physics per se cannot causally determine the outcome of human creativity, rather it creates the possibility space allowing human intelligence to function autonomously. The challenge to physics is to develop a realistic description of causality in truly complex hierarchical structures, with top-down causation and memory effects allowing autonomous higher levels of order to emerge with genuine causal powers. (shrink)

It has been just over 100 years since the birth of Alan Turing and more than 65 years since he published in Mind his seminal paper, Computing Machinery and Intelligence. In the Mind paper, Turing asked a number of questions, including whether computers could ever be said to have the power of “thinking”. Turing also set up a number of criteria—including his imitation game—under which a human could judge whether a computer could be said to be “intelligent”. Turing’s paper, as (...) well as his important mathematical and computational insights of the 1930s and 1940s led to his popular acclaim as the “Father of Artificial Intelligence”. In the years since his paper was published, however, no computational system has fully satisfied Turing’s challenge. In this paper we focus on a different question, ignored in, but inspired by Turing’s work: How might the Artificial Intelligence practitioner implement “intelligence” on a computational device? Over the past 60 years, although the AI community has not produced a general-purpose computational intelligence, it has constructed a large number of important artifacts, as well as taken several philosophical stances able to shed light on the nature and implementation of intelligence. This paper contends that the construction of any human artifact includes an implicit epistemic stance. In AI this stance is found in commitments to particular knowledge representations and search strategies that lead to a product’s successes as well as its limitations. Finally, we suggest that computational and human intelligence are two different natural kinds, in the philosophical sense, and elaborate on this point in the conclusion. (shrink)

In this paper, we explore the architecture of downward causation on the basis of three central cases. We set out by answering the question of how top-down causation is possible in the universe. The universe is not causally closed, because of irreducible randomness at the quantum level. What is more, contextual effects can already be observed at the level of quantum physics, where higher levels can modify the nature of lower-level elements by changing their context, or even creating them. As (...) one moves up through higher levels, contextual effects on lower levels occur on various scales within nature, which is crucial in biology in general and the brain in particular. We then argue that there are important logical downward causes.objects have causal effects on material-energetic systems. It can be shown that abstract objects have measurable effects on lower levels, which needs to be accounted for by successful explanations of real phenomena such as intentional action. Intentional action has the form of deductive causation from logical structures to human agency. Without this assumption, we would not be warranted in believing that our physical theories latch onto a universe that is essentially the way we discover it to be. Denying top-down causation on account of the idea that the universe permits only bottom-up constitution of wholes from lower-level elements leads to undermining the very possibility of knowledge and science. Thus, it can be rejected as a global form of explanation. We sketch a model for mind-body interaction according to which the various levels of a human organism together enable the emergence of mental top-down effects. They are necessary conditions for the emergence of human mindedness. Once it is clear that downward causation is a widespread natural phenomenon, the apparent mystery of mental causation is, in principle, solved. (shrink)

ABSTRACT Critics of Converse’s agenda‐setting 1964 essay underexplored the seemingly technical issue of measurement error. Down this road not taken lie serious questions about the evidence for both of Converse’s main theses. First, a thorough reexamination of the exact questions posed to a mass sample of the electorate and to an elite sample of congressional candidates suggests that the mass/elite difference in ideological constraint reported by Converse could be, in significant part, a measurement‐error artifact caused by differences in question form. (...) Furthermore, the vagueness and ambiguity of the questions not only calls into question the plausibility of Converse’s main thesis—lack of ideological constraint among the public—but of his subsidiary thesis: that, measured over time, members of the public had such unstable political opinions that they might best be considered “nonattitudes.”. (shrink)

ABSTRACT Critics of Converse’s agenda‐setting 1964 essay underexplored the seemingly technical issue of measurement error. Down this road not taken lie serious questions about the evidence for both of Converse’s main theses. First, a thorough reexamination of the exact questions posed to a mass sample of the electorate and to an elite sample of congressional candidates suggests that the mass/elite difference in ideological constraint reported by Converse could be, in significant part, a measurement‐error artifact caused by differences in question form. (...) Furthermore, the vagueness and ambiguity of the questions not only calls into question the plausibility of Converse’s main thesis—lack of ideological constraint among the public—but of his subsidiary thesis: that, measured over time, members of the public had such unstable political opinions that they might best be considered “nonattitudes.”. (shrink)

There has been much controversy over weak and strong emergence in physics and biology. As pointed out by Phil Anderson in many papers, the existence of broken symmetries is the key to emergence of properties in much of solid state physics. By carefully distinguishing between different types of symmetry breaking and tracing the relation between broken symmetries at micro and macro scales, I demonstrate that the emergence of the properties of semiconductors is a case of strong emergence. This is due (...) to the existence of quasiparticles such as phonons. Furthermore time dependent potentials enable downward causation as in the case of digital computers. Additionally I show that the processes of evolutionary emergence of living systems is also a case of strong emergence, as is the emergence of properties of life out of the underlying physics. A useful result emerges: standard physics theories and the emergent theories arising out of them are all effective theories that are equally valid. (shrink)

Plato pays little attention to the third class in his ideal city, regarding them as raw material on which the Guardians exercise their art. But modern criticism is interested in them, for upon their treatment and opportunities our judgement of Plato's city partly depends. They are the great mass of the people, and centuries of Christian equalitarianism have made us regard their welfare as an important criterion of the city's value.

William Harper presents five reasons for concluding that God should be referred to exclusively in male terms. To the contrary, I argue that: (1) by devaluating the feminine gender, Harper is guilty of the same reductionist and dichotomous thinking as his protagonists, (2) Harper’s view of God is contrary to “the Biblical example,” and (3) Harper’s position rests on a number of logical confusions. I conclude that Harper’s view should be rejected by both men and women of Christian convictions.