In this paper I develop a theory of 'function' and function as a deontic modal word and phenomenon. Kratzer’s account of the semantics for the deontic modals is invoked and using her approach a formal schema for the semantics of 'function'-sentences is proposed. My account of function is a modalized and extended version of Cummins’ systems-type account of function. In the biological and physical sciences, on this account, function is a complex empirical deontic modal property. It is built on (...) the property of X’s doing Y well enough to enable Z, which is implicitly deontic because of the evaluative but nonetheless empirical in its biological and physical applications. This account of function resolves many of the traditional puzzles about biological and physical function, and extends naturally to include the other types of function. With a variant treatment of the semantics, this account is argued also to apply to mathematical function, where it is shown to be interestingly related to Frege’s account of function. (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)

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.

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)

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)

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.

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.

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)

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

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)

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)

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.

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)

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.

The Univalence axiom, due to Vladimir Voevodsky, is often taken to be one of the most important discoveries arising from the Homotopy Type Theory research programme. It is said by Steve Awodey that Univalence embodies mathematical structuralism, and that Univalence may be regarded as ‘expanding the notion of identity to that of equivalence’. This article explores the conceptual, foundational and philosophical status of Univalence in Homotopy Type Theory. It extends our Types-as-Concepts interpretation of HoTT to Universes, and offers (...) an account of the Univalence axiom in such terms. We consider Awodey’s informal argument that Univalence is motivated by the principle that reasoning should be invariant under isomorphism, and we examine whether an autonomous and rigorous justification along these lines can be given. We consider two problems facing such a justification. First, there is a difference between equivalence and isomorphism and Univalence must be formulated in terms of the former. Second, the argument as presented cannot establish Univalence itself but only a weaker version of it, and must be supplemented by an additional principle. The article argues that the prospects for an autonomous justification of Univalence are promising. (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)

InA Theory of Justice, Rawls claims that “to each according to his threat advantage is not a conception of justice.” Although it may indeed seem intuitively plausible that a principle based on “threat advantage” cannot count as a principle of justice, it is an altogether different matter to explain why this is so. The question is especially pressing if one bears in mind that such a principle of bargaining in fact underlies many institutionally regulated interactions. Moreover, to the extent (...) that morality is thought of as a mechanism for guaranteeing mutual advantage in the resolution of conflicts, it may indeed seem necessary that it reflect the bargaining power of the parties (in order to make sure that it is indeed advantageous for all of them). In fact, there is a prominent tradition of social-contract theories (from Hobbes to Gauthier) that work under this assumption and claim to provide an answer to what justice requires as much as Rawls's theory does. So seen, the burden of proof seems to fall rather on the shoulders of those committed to claim both that morality is a mechanism that works to the advantage of all and that it nevertheless requires neutralizing all differences in bargaining power. (shrink)

InA Theory of Justice, Rawls claims that “to each according to his threat advantage is not a conception of justice.” Although it may indeed seem intuitively plausible that a principle based on “threat advantage” cannot count as a principle of justice, it is an altogether different matter to explain why this is so. The question is especially pressing if one bears in mind that such a principle of bargaining in fact underlies many institutionally regulated interactions. Moreover, to the extent (...) that morality is thought of as a mechanism for guaranteeing mutual advantage in the resolution of conflicts, it may indeed seem necessary that it reflect the bargaining power of the parties (in order to make sure that it is indeed advantageous for all of them). In fact, there is a prominent tradition of social-contract theories (from Hobbes to Gauthier) that work under this assumption and claim to provide an answer to what justice requires as much as Rawls's theory does. So seen, the burden of proof seems to fall rather on the shoulders of those committed to claim both that morality is a mechanism that works to the advantage of all and that it nevertheless requires neutralizing all differences in bargaining power. (shrink)

The book discusses the fate of universality and a universal set in several set theories.

Boycott Theory for Palestine aims to advance academic boycott, divestment, and sanctions (BDS) by presenting the fullest and most sophisticated justification for it yet given, demonstrating how the boycott relates to current debates within contemporary political and intellectual life.

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. (shrink)

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)

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.

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)

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

Laws in the special sciences are usually regarded to be non-universal. A theory of laws in the special sciences faces two challenges. (I) According to Lange's dilemma, laws in the special sciences are either false or trivially true. (II) They have to meet the ?requirement of relevance?, which is a way to require the non-accidentality of special science laws. I argue that both challenges can be met if one distinguishes four dimensions of (non-) universality. The upshot is that (...) I argue for the following explication of special science laws: L is a special science law just if (1) L is a system law, (2) L is quasi-Newtonian, and (3) L is minimally invariant. (shrink)

The basic concept of Bentham's moral and political philosophy was public utility. He linked it directly with the concept of the universal interest, which comprises a distinctive partnership of the interests of all members of the community. The ultimate end of government and aim of all of morality is ‘the advancement of the universal interest’. This essay articulates the structure of Bentham's notion of universal interest and locates it in his theory of value.