Our aim is to solve a quite old question on the difference between expandability and compact expandability. Toward this, we further investigate the logic of countable cofinality.

Consider the set of inferences that are acceptable to use in all our theory building endeavors. Call this set of inferences the universal theory building toolkit, or just ’the toolkit’ for short. It is clear that the toolkit is tightly connected to logic in a variety of ways. Beall, for example, has argued that logic just is the toolkit. This paper avoids making a stand on that issue and instead investigates reasons for thinking that, logic or not, the toolkit is (...) substructural. It is presented as a dialogue for the simple reason that it summarizes a range of dialogues on this subject that the author has had with various folks over the past few years. The method I use to investigate the toolkit is inspired in both philosophical and technical details by Alasdair Urquhart’s work on semantics for relevance logics from the early 1970s. (shrink)

We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite useful for formulating categoricity-like questions regarding powers below the cardinality of a theory. We prove, for universal theories T, that if T is κ-unique for one uncountable κ, then it is κ-unique for every uncountable κ; in particular, it (...) is categorical in powers greater than the cardinality of T. (shrink)

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies the axioms iff it embeds into a first order algebra. Importantly, our argument is modular and also works for, e.g., the positive existential algebras and the quantifier-free algebras. We also explain the relationship to theories, and indicate how to add in function (...) symbols. (shrink)

. Toward a universal theory of criminal law: Rethinking the comparative and international project. Criminal Justice Ethics: Vol. 27, No. 1, pp. 53-66.

Recent findings about the capabilities of smart animals such as corvids or octopi and novel types of artificial intelligence, from social robots to cognitive assistants, are provoking the demand for new answers for meaningful comparison with other kinds of intelligence. This book fills this need by proposing a universal theory of intelligence which is based on causal learning as the central theme of intelligence. The goal is not just to describe, but mainly to explain queries like why one kind of (...) intelligence is more intelligent than another, whatsoever the intelligence. Shiny terms like "strong AI," "superintelligence," "singularity" or "artificial general intelligence" that have been coined by a Babylonian confusion of tongues are clarified on the way. (shrink)

Michael Uljens; The Idea of a Universal Theory of Education—an Impossible but Necessary Project?, Journal of Philosophy of Education, Volume 36, Issue 3, 16 Dec.

We apply the theory of partial algebras, following the approach developed by Van Alten, to the study of the computational complexity of universal theories of monotonic and normal modal algebras. We show how the theory of partial algebras can be deployed to obtain co-NP and EXPTIME upper bounds for the universal theories of, respectively, monotonic and normal modal algebras. We also obtain the corresponding lower bounds, which means that the universal theory of monotonic modal algebras is co-NP-complete and (...) the universal theory of normal modal algebras is EXPTIME-complete. It also follows that the quasi-equational theory of monotonic modal algebras is co-NP-complete. While the EXPTIME upper bound for the universal theory of normal modal algebras can be obtained in a more straightforward way, as discussed in the paper, due to its close connection to the equational theory of normal modal algebras with the universal modality operator, the technique based on the theory of partial algebras is applicable to the study of universal theories of algebras corresponding to a wide range of logics with intensional operators, where no such connection is available. (shrink)

Michael Uljens; The Idea of a Universal Theory of Education—an Impossible but Necessary Project?, Journal of Philosophy of Education, Volume 36, Issue 3, 16 Dec.

Current disputes over the nature and purpose of the university are rooted in a philosophical divide between theory and practice. Academics often defend the concept of a university devoted to purely theoretical activities. Politicians and wider society tend to argue that the university should take on more practical concerns. I critique two typical defenses of the theoretical concept—one historical and one based on the value of pure research—and show that neither the theoretical nor the practical concept of a university accommodates (...) all the important goals expected of university research and teaching. Using the classical pragmatist argument against a sharp division between theory and practice, I show how we can move beyond the debate between the theoretical and practical concepts of a university, while maintaining a place for pure and applied research, liberal and vocational education, and social impact through both economic applications and criticism aimed at promoting social justice. (shrink)

We show that if a countable structure M in a finite relational language is not cellular, then there is an age-preserving $N \supseteq M$ such that $2^{\aleph _0}$ many structures are bi-embeddable with N. The proof proceeds by a case division based on mutual algebraicity.

We study the computational complexity of the universal theory of residuated ordered groupoids, which are algebraic structures corresponding to Nonassociative Lambek Calculus. We prove that the universal theory is co $$\textsf {NP}$$ -complete which, as we observe, is the lowest possible complexity for a universal theory of a non-trivial class of structures. The universal theories of the classes of unital and integral residuated ordered groupoids are also shown to be co $$\textsf {NP}$$ -complete. We also prove the co $$\textsf (...) {NP}$$ -completeness of the universal theory of classes of residuated algebras, algebraic structures corresponding to Generalized Lambek Calculus. (shrink)

A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

This thesis examines the prospects for mechanical procedures that can identify true, complete, universal, first-order logical theories on the basis of a complete enumeration of true atomic sentences. A sense of identification is defined that is more general than those which are usually studied in the learning theoretic and inductive inference literature. Some identification algorithms based on confirmation relations familiar in the philosophy of science are presented. Each of these algorithms is shown to identify all purely universal theories (...) without function symbols. It is demonstrated that no procedure can solve this universal theory inference problem in the more usual senses of identification. The question of efficiency for theory inference systems is addressed, and some definitions of limiting complexity are examined. It is shown that several aspects of obvious strategies for solving the universal theory inference problem are NP-hard. Finally, some non-worst case heuristic search strategies are examined in light of these NP-completeness results. These strategies are based upon an isomorphism between clausal entailments of a certain class and partition lattices, and are applicable to the improvement of earlier work on language acquisition and logical inductive inference. (shrink)

This volume addresses the role value judgments play in science. It is my contention that a particular research programme in modern physical cosmology rests crucially on a value judgment. Before making my case, let me introduce the following abbreviations for the following propositions.

Literature and Character Education in Universities presents the potential of literary and philosophical texts for character education in modern universities. The book engages with theoretical and practical aspects of character development in higher education, combining conceptual discussion of the role of literature in character education with applied case studies from university classrooms. Character education within the academic context of the university presents unique challenges and opportunities. Literature and Character Education in Universities presents perspectives from academics in Europe, the USA and (...) Asia, offering unique insights into the ways that engaged reading and discussion of core texts can promote the development of intellectual and moral virtues. Chapters draw on a wide range of texts from Confucius' Analects to J. D. Salinger's The Catcher in the Rye, focusing on themes such as truthfulness, self-knowledge, prudence, tolerance, friendship, and humility. Literature and Character Education in Universities will be of real use to researchers, academics and postgraduates in the fields of higher education, philosophy, and literature. It should be essential reading for university educators interested in character development and advocates of literary education in modern universities. (shrink)

The reason for physics’ failure to find a final theory of the universe is examined. Problems identified are: the lack of unequivocal definitions for its fundamental elements (time, length, mass, electric charge, energy, work, matter-waves); the danger of relying too much on mathematics for solutions; especially as philosophical arguments conclude the universe cannot have a mathematical basis. It does not even need the concept of number to exist. Numbers and mathematics are human inventions arising from the human predilection for measurement. (...) Following Aristotle, a single fundamental cause is proposed to explore the efficacy of using pure non-mathematical philosophy to explain the universe, contrary to current quantum physical views. The cause is taken as Time, which is then defined, surprisingly leading automatically to a definition of a three-dimensional space answering the question into what can a universe be placed (space before space seems non-sensical). This enables the philosophical arguments to derive a universal rule giving clear-cut descriptions (definitions) of force (both gravitational and electromagnetic), motion, energy, and particles. The formation of atomic nuclei and atomic properties together with an unexpected role for neutrinos follow. In particular, a Popper-test can be prepared by introducing the concept of measurement to allow the philosophy arguments to be tested in another discipline - mathematics. The solution agrees with human physical observations to a remarkable degree of accuracy, automatically explaining and predicting values for Planck’s and the fine-structure constants. Although mathematical, it is included as confirming the efficacy of philosophy in attaining a final theory. (shrink)

Category theory is often treated as an algebraic foundation for mathematics, and the widely known algebraization of ZF set theory in terms of this discipline is referenced as “categorical set theory” or “set theory for category theory”. The method of algebraization used in this theory has not been formulated in terms of universal algebra so far. In current paper, a _universal algebraic_ method, i.e. one formulated in terms of universal algebra, is presented and used for algebraization of a ground mereological (...) system described as “quantitative” (QMS) and of the standard set theories built upon it. The QMS is algebraized by using abelian generalized groups (AGGs) generalizing both abelian groups and Boolean algebras. To algebraize set theory, the AGG are enriched with operators to produce _extensional algebras_ (EA) of Tarskian “Boolean algebras with operators” type. EAs explicate the intuition of set theory’ universes (of discourse). The axiomatic set theory presented in this paper, named _extension theory_, previously went through an intuitive phase of development during its use by the author in computer science projects, where it served as the basis for development of a foundational data science framework and an extensional model of natural languages also outlined here. (shrink)

Scientists from various disciplines have begun to focus attention on the psychology and biology of human morality. One research program that has recently gained attention is universal moral grammar (UMG). UMG seeks to describe the nature and origin of moral knowledge by using concepts and models similar to those used in Chomsky's program in linguistics. This approach is thought to provide a fruitful perspective from which to investigate moral competence from computational, ontogenetic, behavioral, physiological and phylogenetic perspectives. In this article, (...) I outline a framework for UMG and describe some of the evidence that supports it. I also propose a novel computational analysis of moral intuitions and argue that future research on this topic should draw more directly on legal theory. (shrink)

Any empirical physical theory must have implications for observable events at the scale of everyday life, even though that scale plays no special role in the basic ontology of the theory itself. The fundamental physical scales are microscopic for the “local beables” of the theory and universal scale for the non-local beables. This situation creates strong demands for any precise quantum theory. This paper examines those constraints, and illustrates some ways in which they can be met.

In the The Undivided Universe, David Bohn and Basil Hiley present a radically different approach to quantum theory.

Kojman, M. and S. Shelah, The universality spectrum of stable unsuperstable theories, Annals of Pure and Applied Logic 58 57–72. It is shown that if T is stable unsuperstable, and 1 [brvbar]T[brvbar], T stable and κ<κ then there is a universal tree of height κ + 1 in cardinality λ.

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory.Our emphasis will be on various approaches toward (more or less naively formed)universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.

In the original publication of the article, the authors name were abbreviated as “D. Shkatov” and “C. J. Van Alten”. However it should be “Dmitry Shkatov” and “Clint J. Van Alten”. The original article has been corrected.

University of Keele, England This article analyzes the strategies and means by which universalist claims about human nature become successful in science. Of specific interest are the conditions under which claims of this sort are taken to be inherently superior to those which are particularistic or context-specific (a hierarchy of values which we term "universality bias"). We trace the birth of universalists claims in neglected fields, their growth through methodological agreements and the use of invisible referents, and their roots in (...) multiple audiences with different evaluation criteria. Our analysis complements philosophical and political critiques of theories about human nature and demonstrates the historical specificity of universalist claims. (shrink)

A Theory of Universal Democracy empowers cultures and communities across the world to custom design democracy in consonance with their traditional values. For example, the book makes concrete proposals for Muslim countries to democratize their constitutions without accepting Western values and without violating the principles of Islamic law. More importantly, Universal Democracy further develops the idea of Free State, which the author first presented in his previous book, The Extinction of Nation-States (Kluwer, 1996). The proposed fusion of Universal Democracy and (...) Free State is designed to revolutionize the classical theory of government and to offer a new paradigm that accommodates both universality and uniqueness. Scholars, teachers and students of international law, constitutional law, legal theory, and Islamic law will find this book a source of valuable ideas. (shrink)

In the post-Apartheid era South Africa’s universities have faced serious questions about the quality of their student learning in the face of near impossible challenges. The University of Cape Town, widely seen as the country’s leading higher education institution, has shown remarkable resilience, however, in the range of initiatives it has launched to support and enhance student learning. These initiatives, designed with a common purpose, are of course intended to work together so that their effects might be compounded and realized (...) in enhanced student learning outcomes. Drawing substantially on the power of compounding (which is itself redolent of the claim made by complexity theory that relations and emergence are crucial concepts), complexity theory offers unique insights into how and why things change – and also into how and why things remain largely the same or inexorably grind towards failure. The networked initiatives undertaken by the University of Cape Town constitute a case of learning refurbishment that is also well explained and understood in terms of complexity theory. This paper draws on concepts from complexity theory both to understand how learning might be enhanced in higher education institutions in severely straitened circumstances and to offer insights for education leaders and policy-makers in this domain. (shrink)

Let T be a complete first-order theory over a finite relational language which is axiomatized by universal and existential sentences. It is shown that T is almost trivial in the sense that the universe of any model of T can be written $F \overset{\cdot}{\cup} I_1 \overset{\cdot}{\cup} I_2 \overset{\cdot}{\cup} \cdots \overset{\cdot}{\cup} I_n$ , where F is finite and I 1 , I 2 ,...,I n are mutually indiscernible over F. Some results about complete theories with ∃∀-axioms over a finite relational (...) language are also mentioned. (shrink)

Cosmology as Weltanschauung is as old as the world. Cosmology as a physical discipline, however, is a child of this century, born in 1917, when Albert Einstein and Willem de Sitter first applied the theory of general relativity to the space-time of the entire universe. When did the child come of age and become a fully-fledged science? A popular myth shared by many practitioners holds that this did not happen until 1965, when the discovery of the 2.7K cosmic microwave background (...) radiation validated the concept of the hot big bang. Earlier accomplishments culminating in the 1965 event include the derivation of evolving relativistic models by Alexander Friedmann and George Lemaître, Edwin Hubble’s discovery of the redshift-magnitude relationship and George Gamow’s theory of the primordial nucleosynthesis containing the prediction of the microwave background left from the hot and dense past of the universe. This linear development is thrown into sharper relief in textbooks, by referring to an inarticulate.. (shrink)

This book offers an original hypothesis capable of unifying evolution in the physical universe with evolution in biology; herewith it lays the conceptual foundations of ?transdisciplinary unified theory?. The rationale for the hypothesis is presented first; then the theoretical framework is outlined, and thereafter it is explored in regard to quantum physics, physical cosmology, micro- and macro-biology, and the cognitive sciences (neurophysiology, psychology, with attention to anomalous phenomena as well). The book closes with a variety of studies, both by the (...) author and his collaborators, sketching out the implications of the hypothesis in regard to brain dynamics, cosmology, the concept of space, phenomena of creativity, and the prospects for the elaboration of a mature transdisciplinary unified theory. The Foreword is written by philosopher of science Arne Naess, and the Afterword is contributed by neuroscientist Karl Pribram. (shrink)

General theory of law (general jurisprudence, allgemeine Rechtslehre) has often claimed to deal with general or universal concepts, i.e., concepts which are deemed to be common to any legal system whatsoever. At any rate, this is the classic determination of such a field of study as provided by John Austin in the nineteenth century—a determination, however, which deserves careful analysis. In what sense, indeed, can one assert that some legal concepts are common to different legal systems? And, above all, in (...) what sense can one assert that some concepts are common to different languages and cultures? My paper sets out to discuss such questions—although, obviously, they are too complicated to be answered in a single paper. The first section reconstructs the Austinian argument for general jurisprudence by placing it in its historical context. The second section tries to apply to legal concepts some suggestions derived from the contemporary debate on conceptual relativism. The third section, returning to the Austinian problem, comes to the following conclusion: Even if conceptual relativism were true and there were no general or universal legal concepts, this would not invalidate in any way the didactic and scientific value of (general) theory of law. (shrink)

This chapter takes a naturalized approach to the philosophy of science using evidence from cognitive psychology and from the history of science. It first describes the problem of the theory ladenness of perception. Then it provides a general top-down/bottom-up framework from cognitive psychology that is used to organize and evaluate the evidence for theory ladenness throughout the process of carrying out science (perception, attention, thinking, experimenting, memory, and communication). The chapter highlights both the facilitatory and inhibitory role of theory in (...) the scientific process. Both the historical record and the evidence from cognitive psychology suggest that the top-down factors have their greatest impact when the bottom-up information is weak or degraded. There is a short discussion of the normative implications of the material in the chapter for carrying out science. (shrink)