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Samuel Alexander [40]Samuel Allen Alexander [11]Samuel A. Alexander [5]
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Samuel Allen Alexander
Ohio State University (PhD)
  1.  71
    Space, Time and Deity.Samuel Alexander - 1920 - London,: Macmillan.
  2.  83
    Space, time, and Deity: the Gifford lectures at Glasgow 1916-1918.Samuel Alexander - 1920 - New York: Dover Publications.
  3. AGI and the Knight-Darwin Law: why idealized AGI reproduction requires collaboration.Samuel Alexander - 2020 - Agi.
    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 (...)
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  4. Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents.Samuel Alexander - 2019 - Journal of Artificial General Intelligence 10 (1):24-45.
    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 (...)
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  5. Measuring the intelligence of an idealized mechanical knowing agent.Samuel Alexander - 2020 - Lecture Notes in Computer Science 12226.
    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 (...)
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  6.  13
    SPINOZA & TIME.Samuel Alexander - 2016 - Wentworth Press.
    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 (...)
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  7. The Archimedean trap: Why traditional reinforcement learning will probably not yield AGI.Samuel Allen Alexander - 2020 - Journal of Artificial General Intelligence 11 (1):70-85.
    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 (...)
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  8. Pseudo-visibility: A Game Mechanic Involving Willful Ignorance.Samuel Allen Alexander & Arthur Paul Pedersen - 2022 - FLAIRS-35.
    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 (...)
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  9. The Basis of Realism.Samuel Alexander - 1914 - [Oxford University Press].
  10. Strengthening Consistency Results in Modal Logic.Samuel Alexander & Arthur Paul Pedersen - 2023 - Tark.
    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 (...)
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  11. Reward-Punishment Symmetric Universal Intelligence.Samuel Allen Alexander & Marcus Hutter - 2021 - In AGI.
    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.
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  12. Measuring Intelligence and Growth Rate: Variations on Hibbard's Intelligence Measure.Samuel Alexander & Bill Hibbard - 2021 - Journal of Artificial General Intelligence 12 (1):1-25.
    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 (...)
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  13. Formal differential variables and an abstract chain rule.Samuel Alexander - 2023 - Proceedings of the ACMS 23.
    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 (...)
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  14.  33
    Beauty and other forms of value.Samuel Alexander - 1933 - New York,: Crowell.
  15. A Machine That Knows Its Own Code.Samuel A. Alexander - 2014 - Studia Logica 102 (3):567-576.
  16. Short-circuiting the definition of mathematical knowledge for an Artificial General Intelligence.Samuel Alexander - 2020 - Cifma.
    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 (...)
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  17. Universal Agent Mixtures and the Geometry of Intelligence.Samuel Allen Alexander, David Quarel, Len Du & Marcus Hutter - 2023 - Aistats.
    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 (...)
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  18. Big-Oh Notations, Elections, and Hyperreal Numbers: A Socratic Dialogue.Samuel Alexander & Bryan Dawson - 2023 - Proceedings of the ACMS 23.
    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.
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  19.  92
    Voluntary Simplicity and the Social Reconstruction of Law: Degrowth from the Grassroots Up.Samuel Alexander - 2013 - Environmental Values 22 (2):287-308.
    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 (...)
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  20.  32
    Philosophical and literary pieces.Samuel Alexander - 1939 - Westport, Conn.,: Greenwood Press. Edited by John Laird.
  21. A type of simulation which some experimental evidence suggests we don't live in.Samuel Alexander - 2018 - The Reasoner 12 (7):56-56.
    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.
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  22. An axiomatic version of Fitch’s paradox.Samuel Alexander - 2013 - Synthese 190 (12):2015-2020.
    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 (...)
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  23. Infinite graphs in systematic biology, with an application to the species problem.Samuel A. Alexander - 2013 - Acta Biotheoretica 61 (2):181--201.
    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 (...)
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  24. A purely epistemological version of Fitch's Paradox.Samuel Alexander - 2012 - The Reasoner 6 (4):59-60.
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  25. Mathematical shortcomings in a simulated universe.Samuel Alexander - 2018 - The Reasoner 12 (9):71-72.
    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.
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  26. Knowledge-of-own-factivity, the definition of surprise, and a solution to the Surprise Examination paradox.Alessandro Aldini, Samuel Allen Alexander & Pierluigi Graziani - 2022 - Cifma.
    Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal characterisations of the surprise notion, (...)
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  27. Self-referential theories.Samuel A. Alexander - 2020 - Journal of Symbolic Logic 85 (4):1687-1716.
    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.
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  28. Arithmetical algorithms for elementary patterns.Samuel A. Alexander - 2015 - Archive for Mathematical Logic 54 (1-2):113-132.
    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.
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  29. Fast-Collapsing Theories.Samuel A. Alexander - 2013 - Studia Logica (1):1-21.
    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.
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  30. Legg-Hutter universal intelligence implies classical music is better than pop music for intellectual training.Samuel Alexander - 2019 - The Reasoner 13 (11):71-72.
    In their thought-provoking paper, Legg and Hutter consider a certain abstrac- tion of an intelligent agent, and define a universal intelligence measure, which assigns every such agent a numerical intelligence rating. We will briefly summarize Legg and Hutter’s paper, and then give a tongue-in-cheek argument that if one’s goal is to become more intelligent by cultivating music appreciation, then it is bet- ter to use classical music (such as Bach, Mozart, and Beethoven) than to use more recent pop music. The (...)
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  31. Self-graphing equations.Samuel Alexander - manuscript
    Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.
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  32. Guessing, Mind-Changing, and the Second Ambiguous Class.Samuel Alexander - 2016 - Notre Dame Journal of Formal Logic 57 (2):209-220.
    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. (...)
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  33. This sentence does not contain the symbol X.Samuel Alexander - 2013 - The Reasoner 7 (9):108.
    A suprise may occur if we use a similar strategy to the Liar's paradox to mathematically formalize "This sentence does not contain the symbol X".
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  34. Biologically Unavoidable Sequences.Samuel Alexander - 2013 - Electronic Journal of Combinatorics 20 (1):1-13.
    A biologically unavoidable sequence is an infinite gender sequence which occurs in every gendered, infinite genealogical network satisfying certain tame conditions. We show that every eventually periodic sequence is biologically unavoidable (this generalizes König's Lemma), and we exhibit some biologically avoidable sequences. Finally we give an application of unavoidable sequences to cellular automata.
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  35. Moral Order and Progress an Analysis of Ethical Conceptions.Samuel Alexander - 1889 - K. Paul, Trench, Trübner, & Co..
     
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  36. Formulas for Computable and Non-Computable Functions.Samuel Alexander - 2006 - Rose-Hulman Undergraduate Mathematics Journal 7 (2).
  37. Natural Piety.Samuel Alexander - 1921 - Hibbert Journal 20:609.
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  38. Ptolemaic and Copernican Views of the Place of Mind in the Universe.Samuel Alexander - 1909 - Hibbert Journal 8:47-66.
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  39. A paradox related to the Turing Test.Samuel Alexander - 2011 - The Reasoner 5 (6):90-90.
  40.  3
    Art and instinct.Samuel Alexander - 1927 - Philadelphia: R. West.
  41. Art and the Material: The Adamson Lecture for 1925.Samuel Alexander - 1925 - Manchester University Press.
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  42. Artistic creation and cosmic creation.Samuel Alexander - 1928 - London,: H. Milford.
     
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  43. Disruptive social innovation for a low-carbon world.Samuel Alexander - 2014 - In David Humphreys & Spencer S. Stober (eds.), Transitions to sustainability: theoretical debates for a changing planet. Common Ground Publishing LLC.
     
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  44.  3
    Locke.Samuel Alexander - 1908 - Port Washington, N.Y.,: Kennikat Press.
  45. Spinoza: An Address in Commemoration of the Tercentenary of Spinoza Birth.Samuel Alexander - 1933 - Manchester University Press.
  46.  3
    Spinoza and time.Samuel Alexander - 1921 - London,: G. Allen & Unwin.
    Excerpt from Spinoza and Time The Arthur Davis Memorial Lecture was founded in 1917, under the auspices of the Jewish Historical Society of England, by his collaborators in the translation of "The Service of the Synagogue," with the object of fostering Hebraic thought and learning in honour of an unworldly scholar. The Lecture is to be given annually in the anniversary week of his death, and the lectureship is to be open to men or women of any race or creed, (...)
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  47. Spinoza.Samuel Alexander - 1933 - [Manchester]: Manchester university press.
     
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  48.  16
    Space, time.Samuel Alexander - 1966 - London,: Macmillan.
  49.  84
    The First-Order Syntax of Variadic Functions.Samuel Alexander - 2013 - Notre Dame Journal of Formal Logic 54 (1):47-59.
    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.
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  50.  1
    Review of On Truth by George Mivart. [REVIEW]Samuel Alexander - 1889 - Mind 14 (55):420-425.