Despite the growing importance of ‘social value’ as a central feature of research ethics, the term remains both conceptually vague and to a certain extent operationally rigid. And yet, perhaps because the rhetorical appeal of social value appears immediate and self-evident, the concept has not been put to rigorous investigation in terms of its definition, strength, function, and scope. In this article, we discuss how the anthropological concept of liminality can illuminate social value and differentiate and reconfigure its variegated approaches. (...) Employing liminality as a heuristic encourages a reassessment of how we understand the mobilization of ‘social value’ in bioethics. We argue that social value as seen through the lens of liminality can provide greater clarity of its function and scope for health research. Building on calls to understand social value as a dynamic, rather than a static, concept, we emphasize the need to appraise social value iteratively throughout the entire research as something that transforms over multiple times and across multiple spaces occupied by a range of actors. (shrink)

"One of the outstanding authorities on the early days of the Republic, Saul K. Padover offers in this volume a generous sampling of the letters, essays, speeches, discourses, and personal documents--many of them previously unpublished--of the men who made America. Included are extensive selections from the papers and speeches of John Adams, Benjamin Franklin, Alexander Hamilton, Thomas Jefferson, James Madison, and George Washington. There are also copious extracts from the private and public utterances of secondary, but important, figures of the (...) founding days--Samuel Adams, Elbridge Gerry, Patrick Henry, John Dickinson, Oliver Ellsworth, William Paterson, Benjamin Rush, George Wythe, and many others. A number of the speeches made at the Constitutional Convention in 1787 are given in full, and several of the important debates are reproduced. John Dickinson's Letters from an American Farmer in Pennsylvania appear in these pages as well as many of Alexander Hamilton's famous and brief opinions. Also included are John Hancock's speech on the Boston Massacre; Thomas Jefferson's Notes on Virginia; James Madison's Memorial against Religious Assessments; two of the most important of John Marshall's Supreme Court decisions (Marbury vs. Madison and McCulloch vs. Maryland); Robert Morris' Letters on Finance; John Taylor's paper On Aristocracy, and William Paterson's Plan for a Constitution. Taken together, these writings offer in one volume a complete picture of the thinking, the debate, the legal maneuvers, the compromises, the manners, and the morals of the American nation's earliest days. The book provides a sound basic appreciation of the atmosphere in which the Founding Fathers worked and planned and debated with one another. All the many counter-currents that contributed to the building of the Constitution, the stresses to which the young nation was subjected, the rebellion that continued to seethe, the moral climate of the days--these are all recreated in the speeches and writings of America's first patriots. Dr. Padover has bound the selections together with enlightening commentary that enables the reader to understand the exact circumstances of each utterance and brings the particular work into historical perspective."--Jacket. (shrink)

ExcerptMany people assume that the Universal Declaration of Human Rights of 1948 was an exclusively or primarily Western project, imposed on the rest of the world by the European and American powers that emerged victorious from World War II. Harvard Law professor Mary Ann Glendon’s 2001 book, A World Made New: Eleanor Roosevelt and the Universal Declaration of Human Rights, suggests otherwise. It was not the great powers but small powers that pushed hardest for a declaration of rights. And it (...) was often great powers—and one must acknowledge, great powers dominated by people of European ancestry—that did not like the idea of being pushed around by politically and economically weaker inhabitants of the Global South, who were just beginning to emerge from centuries of Western colonialism and other forms of oppression.1. (shrink)

Can an agent's intelligence level be negative? We extend the Legg-Hutter agent-environment framework to include punishments and argue for an affirmative answer to that question. We show that if the background encodings and Universal Turing Machine (UTM) admit certain Kolmogorov complexity symmetries, then the resulting Legg-Hutter intelligence measure is symmetric about the origin. In particular, this implies reward-ignoring agents have Legg-Hutter intelligence 0 according to such UTMs.

Can quantum theory provide examples of metaphysical indeterminacy, indeterminacy that obtains in the world itself, independently of how one represents the world in language or thought? We provide a positive answer assuming just one constraint of orthodox quantum theory: the eigenstate-eigenvalue link. Our account adds a modal condition to preclude spurious indeterminacy in the presence of superselection sectors. No other extant account of metaphysical indeterminacy in quantum theory meets these demands.

The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.

Public health and service delivery programmes, interventions and policies are typically developed and implemented for the primary purpose of effecting change rather than generating knowledge. Nonetheless, evaluations of these programmes may produce valuable learning that helps determine effectiveness and costs as well as informing design and implementation of future programmes. Such studies might be termed ‘opportunistic evaluations’, since they are responsive to emergent opportunities rather than being studies of interventions that are initiated or designed by researchers. However, current ethical guidance (...) and registration procedures make little allowance for scenarios where researchers have played no role in the development or implementation of a programme, but nevertheless plan to conduct a prospective evaluation. We explore the limitations of the guidance and procedures with respect to opportunistic evaluations, providing a number of examples. We propose that one key missing distinction in current guidance is moral responsibility: researchers can only be held accountable for those aspects of a study over which they have control. We argue that requiring researchers to justify an intervention, programme or policy that would occur regardless of their involvement prevents or hinders research in the public interest without providing any further protections to research participants. We recommend that trial consent and ethics procedures allow for a clear separation of responsibilities for the intervention and the evaluation. (shrink)

We construct a machine that knows its own code, at the price of not knowing its own factivity.

Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: “Not without outside help”. This is a paper on the mathematical structure of AGI populations when parent AGIs create child AGIs. We argue that such populations satisfy a certain biological law. Motivated by observations of sexual reproduction in seemingly-asexual species, the Knight-Darwin Law states that it is impossible for one organism to asexually produce another, which asexually produces another, and (...) so on forever: that any sequence of organisms (each one a child of the previous) must contain occasional multi-parent organisms, or must terminate. By proving that a certain measure (arguably an intelligence measure) decreases when an idealized parent AGI single-handedly creates a child AGI, we argue that a similar Law holds for AGIs. (shrink)

Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg- Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer (...) based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures. (shrink)

We define a notion of the intelligence level of an idealized mechanical knowing agent. This is motivated by efforts within artificial intelligence research to define real-number intelligence levels of compli- cated intelligent systems. Our agents are more idealized, which allows us to define a much simpler measure of intelligence level for them. In short, we define the intelligence level of a mechanical knowing agent to be the supremum of the computable ordinals that have codes the agent knows to be codes (...) of computable ordinals. We prove that if one agent knows certain things about another agent, then the former necessarily has a higher intelligence level than the latter. This allows our intelligence no- tion to serve as a stepping stone to obtain results which, by themselves, are not stated in terms of our intelligence notion (results of potential in- terest even to readers totally skeptical that our notion correctly captures intelligence). As an application, we argue that these results comprise evidence against the possibility of intelligence explosion (that is, the no- tion that sufficiently intelligent machines will eventually be capable of designing even more intelligent machines, which can then design even more intelligent machines, and so on). (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.

We present a game mechanic called pseudo-visibility for games inhabited by non-player characters (NPCs) driven by reinforcement learning (RL). NPCs are incentivized to pretend they cannot see pseudo-visible players: the training environment simulates an NPC to determine how the NPC would act if the pseudo-visible player were invisible, and penalizes the NPC for acting differently. NPCs are thereby trained to selectively ignore pseudo-visible players, except when they judge that the reaction penalty is an acceptable tradeoff (e.g., a guard might accept (...) the penalty in order to protect a treasure because losing the treasure would hurt even more). We describe an RL agent transformation which allows RL agents that would not otherwise do so to perform some limited self-reflection to learn the training environments in question. (shrink)

After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning probably will not lead to AGI. We indicate two possible ways (...) traditional reinforcement learning could be altered to remove this roadblock. (shrink)

A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the (...) paradox. (shrink)

Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing a weighted mixture operation. Given a weighted set of agents, their weighted mixture is a new agent whose expected total reward in any environment is the corresponding weighted average of the original agents' expected total rewards in that environment. Thus, if RL agent intelligence is quantified in terms of performance across environments, the weighted mixture's intelligence is (...) the weighted average of the original agents' intelligences. This operation enables various interesting new theorems that shed light on the geometry of RL agent intelligence, namely: results about symmetries, convex agent-sets, and local extrema. We also show that any RL agent intelligence measure based on average performance across environments, subject to certain weak technical conditions, is identical (up to a constant factor) to performance within a single environment dependent on said intelligence measure. (shrink)

The Voluntary Simplicity Movement can be understood broadly as a diverse social movement made up of people who are resisting high consumption lifestyles and who are seeking, in various ways, a lower consumption but higher quality of life alternative. The central argument of this paper is that the Voluntary Simplicity Movement or something like it will almost certainly need to expand, organise, radicalise and politicise, if anything resembling a degrowth society is to emerge in law through democratic processes. In a (...) sentence, that is the 'grass-roots' or 'bottom up' theory of legal and political transformation that will be expounded and defended in this paper. The essential reasoning here is that legal, political and economic structures will never reflect a post-growth ethics of macro-economic sufficiency until a post-consumerist ethics of micro-economic sufficiency is embraced and mainstreamed at the cultural level. (shrink)

In 2011, Hibbard suggested an intelligence measure for agents who compete in an adversarial sequence prediction game. We argue that Hibbard’s idea should actually be considered as two separate ideas: first, that the intelligence of such agents can be measured based on the growth rates of the runtimes of the competitors that they defeat; and second, one specific (somewhat arbitrary) method for measuring said growth rates. Whereas Hibbard’s intelligence measure is based on the latter growth-rate-measuring method, we survey other methods (...) for measuring function growth rates, and exhibit the resulting Hibbard-like intelligence measures and taxonomies. Of particular interest, we obtain intelligence taxonomies based on Big-O and Big-Theta notation systems, which taxonomies are novel in that they challenge conventional notions of what an intelligence measure should look like. We discuss how intelligence measurement of sequence predictors can indirectly serve as intelligence measurement for agents with Artificial General Intelligence (AGIs). (shrink)

One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterates to any desired level of derivative. We first present this material informally, and later discuss how to make it rigorous (a discussion which touches on formal foundations of calculus). We also suggest a finite calculus chain rule (contrary to Graham, Knuth (...) and Patashnik's claim that "there's no corresponding chain rule of finite calculus"). (shrink)

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition result (...) involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which you (...) know.” This definition is non-circular because an AGI, being capable of practical English communication, is capable of understanding the everyday English word “know” independently of how any philosopher formally defines knowledge; we elaborate further on the non-circularity of this circular-looking definition. This elegantly solves the problem that different AGIs may have different internal knowledge definitions and yet we want to study knowledge of AGIs in general, without having to study different AGIs separately just because they have separate internal knowledge definitions. Finally, we suggest how this definition of AGI knowledge can be used as a bridge which could allow the AGI research community to import certain abstract results about mechanical knowing agents from mathematical logic. (shrink)

We provide an intuitive motivation for the hyperreal numbers via electoral axioms. We do so in the form of a Socratic dialogue, in which Protagoras suggests replacing big-oh complexity classes by real numbers, and Socrates asks some troubling questions about what would happen if one tried to do that. The dialogue is followed by an appendix containing additional commentary and a more formal proof.

Recognized as one of the earliest Jewish neo-Platonist writers, Isaac ben Solomon Israeli influenced Muslim, Jewish, and Christian scholars through the Middle Ages. A native of Egypt who wrote in Arabic, Israeli explored definitions of such terms as imagination, sense-perception, desire, love, creation, and “coming-to-be” in his writings. This classic volume contains English translations of Israeli’s philosophical writings, including the _Book of Definitions_, the _Book of Substances,_ and the _Book on Spirit and Soul_. Additionally, _Isaac Israeli_ features a biographical sketch (...) of the philosopher and extensive notes and comments on the texts, as well as a survey and appraisal of his philosophy. Restored to print for the first time in decades, _Isaac Israeli _will be essential reading for students and scholars of medieval philosophy and Jewish studies. (shrink)

Elementary patterns of resemblance notate ordinals up to the ordinal of Pi^1_1-CA_0. We provide ordinal multiplication and exponentiation algorithms using these notations.

Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.

Contemporary education is awakening from a crisis that has held the development of its potential and its relevance at bay for well over a century. Revolutions in science and spirituality are emerging a new relational intelligence that demands commensurate educational paradigms for its blossoming into daily engagements with life and the world around us. At the same time as people are leading increasingly interconnected lives, aware of and often participating in the narratives of people and ecosystems in other parts of (...) the planet, information and communications technologies are increasingly integrating with and serving to mediate the human experience. This article explores the power of this confluence at the current nexus of civilizational demands in the context of increased planetary stresses and destabilizations. The case is made for a thrivable education praxis that draws on these emergent aspects of our developmental potential and emphasizes the importance of functional conviviality as an operational principle of learning for life. (shrink)

Do we live in a computer simulation? I will present an argument that the results of a certain experiment constitute empirical evidence that we do not live in, at least, one type of simulation. The type of simulation ruled out is very specific. Perhaps that is the price one must pay to make any kind of Popperian progress.

We implement a recent characterization of metaphysical indeterminacy in the context of orthodox quantum theory, developing the syntax and semantics of two propositional logics equipped with determinacy and indeterminacy operators. These logics, which extend a novel semantics for standard quantum logic that accounts for Hilbert spaces with superselection sectors, preserve different desirable features of quantum logic and logics of indeterminacy. In addition to comparing the relative advantages of the two, we also explain how each logic answers Williamson’s challenge to any (...) substantive account of determinacy: For any proposition p, what could the difference between “p” and “it’s determinate that p” ever amount to? (shrink)

In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable if and only if it is in the second ambiguous class, if and only if it is eventually annihilated by a certain remainder. We simplify this remainder and give a new proof of the latter equivalence. We then introduce a notion of guessing with an ordinal limit on how often one can change one’s mind. (...) We show that for every ordinal $\alpha$, a guessable set is annihilated by $\alpha$ applications of the simplified remainder if and only if it is guessable with fewer than $\alpha$ mind changes. We use guessability with fewer than $\alpha$ mind changes to give a semi-characterization of the Hausdorff difference hierarchy, and indicate how Wadge’s notion of guessability can be generalized to higher-order guessability, providing characterizations of ${\mathbf{\Delta}}^{0}_{\alpha}$ for all successor ordinals $\alpha\gt 1$. (shrink)

We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

I present an argument that for any computer-simulated civilization we design, the mathematical knowledge recorded by that civilization has one of two limitations. It is untrustworthy, or it is weaker than our own mathematical knowledge. This is paradoxical because it seems that nothing prevents us from building in all sorts of advantages for the inhabitants of said simulation.