This article examines two questions about scientists’ search for knowledge. First, which search strategies generate discoveries effectively? Second, is it advantageous to diversify search strategies? We argue pace Weisberg and Muldoon, “Epistemic Landscapes and the Division of Cognitive Labor”, that, on the first question, a search strategy that deliberately seeks novel research approaches need not be optimal. On the second question, we argue they have not shown epistemic reasons exist for the division of cognitive labor, identifying the errors that led (...) to their conclusions. Furthermore, we generalize the epistemic landscape model, showing that one should be skeptical about the benefits of social learning in epistemically complex environments. (shrink)

This chapter sheds light on a response to experimental philosophy that has not yet received enough attention: the reflection defense. According to proponents of this defense, judgments about philosophical cases are relevant only when they are the product of careful, nuanced, and conceptually rigorous reflection. The chapter argues that the reflection defense is misguided: Five studies (N>1800) are presented, showing that people make the same judgments when they are primed to engage in careful reflection as they do in the conditions (...) standardly used by experimental philosophers. (shrink)

Jennifer Nagel (2010) has recently proposed a fascinating account of the decreased tendency to attribute knowledge in conversational contexts in which unrealized possibilities of error have been mentioned. Her account appeals to epistemic egocentrism, or what is sometimes called the curse of knowledge, an egocentric bias to attribute our own mental states to other people (and sometimes our own future and past selves). Our aim in this paper is to investigate the empirical merits of Nagel’s hypothesis about the psychology involved (...) in knowledge attribution. (shrink)

In this paper, we consider two different attempts to make an end run around the experimentalist challenge to the armchair use of intuitions: one due to Max Deutsch and Herman Cappelen, contending that philosophers do not appeal to intuitions, but rather to arguments, in canonical philosophical texts; the other due to Joshua Knobe, arguing that intuitions are so stable that there is in fact no empirical basis for the experimentalist challenge in the first place. We show that a closer attention (...) to philosophical practices reveal, in turn, that we cannot make sense of these philosophical texts as arguments all the way down; and that our methods are so sensitive to error that even a modest amount of instability is enough to raise deep methodological concerns. (shrink)

This paper argues that higher-order doubt generates an epistemic dilemma. One has a higher-order doubt with regards to P insofar as one justifiably withholds belief as to what attitude towards P is justified. That is, one justifiably withholds belief as to whether one is justified in believing, disbelieving, or withholding belief in P. Using the resources provided by Richard Feldman’s recent discussion of how to respect one’s evidence, I argue that if one has a higher-order doubt with regards to P, (...) then one is not justified in having any attitude towards P. Otherwise put: No attitude towards the doubted proposition respects one’s higher-order doubt. I argue that the most promising response to this problem is to hold that when one has a higher-order doubt about P, the best one can do to respect such a doubt is to simply have no attitude towards P. Higher-order doubt is thus much more rationally corrosive than non-higher-order doubt, as it undermines the possibility of justifiably having any attitude towards the doubted proposition. (shrink)

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)

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)

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)

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.

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, (...) crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

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)

Background: Many people with aphasia and people without brain injury talk to themselves in their heads, i.e., have “inner speech.” Inner speech may be more preserved compared with spoken speech for some people with aphasia and may serve a variety of functions (e.g., emotion regulation), which motivates us to provide a high-fidelity characterization of it. Researchers have used multiple methods to measure this internal phenomenon in the past, which we combine here for the first time in a single study. -/- (...) Aims: We compare performance between individuals with and without aphasia on inner speech tasks that assess inner speech “inthe- moment” to general subjective impressions of inner speech to tease apart the relationship of aphasia severity to inner speech. Methods and Procedures: Twenty people with mild-moderate aphasia and twenty neurotypical controls completed several inner speech tasks, including objective silent rhyme judgements (picture, written, and auditory), subjective reports of inner speech during naming, and subjective rating scales about inner speech experience more generally. -/- Outcomes and Results: In-the-moment inner speech during silent rhyming tasks was associated with aphasia severity only for picture and written rhyming but not auditory rhyming. In-the-moment inner speech reports during silent naming were not associated with aphasia severity, nor were the subjective ratings about general inner speech experience. Individuals with and without aphasia demonstrated a variety of subjective general inner speech experiences, demonstrating heterogeneity of this phenomenon more broadly. -/- Conclusions: Methods of measuring inner speech complement each other and speak to different facets of the inner speech phenomenon, and clinicians and researchers must carefully choose the method(s) that will provide the information about inner speech that they desire. (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)

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

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)

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)

Multiple states are at risk of becoming uninhabitable due to climate change, forcing their populations to flee. While the 1951 Refugee Convention provides the gold standard of international protection, it is only applied to a limited subset of people fleeing their countries, those who suffer persecution, which most people fleeing climate change cannot establish. While many journalists and non-lawyers freely use the term “climate refugees,” governments, and courts, as well as UNHCR and many refugee experts, have excluded most climate refugees (...) from the Convention as a matter of legal interpretation. In our 2015 paper, “Unable to Return in the 1951 Refugee Convention: Stateless Refugees and Climate Change”, we sought to reopen the debate on “climate refugees” by arguing that some climate refugees qualify under the 1951 Convention as it is currently written (even if they are not persecuted): those who are stateless and are unable to return to their country of origin because climate change has rendered it uninhabitable. Our interpretation, however, has been rejected by Goodwin-Gill and McAdam (2021) and by Foster and Lambert (2019), which explicitly responds to our paper. Here, we address and respond to their arguments, and develop a new supplementary one, drawing on the principle of systemic integration, as enshrined in Article 31(3)(c) of the Vienna Convention on the Law of Treaties. (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 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 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)

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)

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.

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)

If we define tradition too hastily we leave to one side the question of what the relevance of tradition is for us. Here the concept of tradition is opened up by considering the different views of it taken by Hannah Arendt, Michael Oakeshott and Alasdair MacIntyre. We see that each has put tradition into a fully developed picture of what our predicament is in modernity; and that each has differed in their assessment of what our relation to tradition is or (...) should be. Arendt sees tradition as something which no longer conditions action, Oakeshott sees tradition as something which conditions all action, and MacIntyre sees tradition as something which should condition right action. In each case, the view of tradition is clearly one element in an attempt to see how the most important constituent elements of human existence – variously called the human condition, human conduct, or human virtue – should be understood in a modernity which is ours because it has put the traditional concept of tradition into question. (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 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 consider an extended notion of reinforcement learning in which the environment can simulate the agent and base its outputs on the agent's hypothetical behavior. Since good performance usually requires paying attention to whatever things the environment's outputs are based on, we argue that for an agent to achieve on-average good performance across many such extended environments, it is necessary for the agent to self-reflect. Thus weighted-average performance over the space of all suitably well-behaved extended environments could be considered a (...) way of measuring how self-reflective an agent is. We give examples of extended environments and introduce a simple transformation which experimentally seems to increase some standard RL agents' performance in a certain type of extended environment. (shrink)

In this paper, we axiomatize the deontic logic in Fusco 2015, which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions (...) Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to ‘lift’ a Kripke frame for a one- dimensional modal logic into two dimensions. (shrink)

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.

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.

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 (...) same argument could be adapted to other media: books beat films, card games beat first-person shooters, parables beat dissertations, etc. We leave it to the reader to decide whether this argument tells us something about classical music, something about Legg-Hutter intelligence, or something about both. (shrink)

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.

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.

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)

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".

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.

This is an appendix containing the stimulus materials for the experiments reported in the paper ‘Salient Alternatives in Perspective.’.

Mathematicians and software developers use the word "function" very differently, and yet, sometimes, things that are in practice implemented using the software developer's "function", are mathematically formalized using the mathematician's "function". This mismatch can lead to inaccurate formalisms. We consider a special case of this meta-problem. Various kinds of agents might, in actual practice, make use of private memory, reading and writing to a memory-bank invisible to the ambient environment. In some sense, we humans do this when we silently subvocalize (...) thoughts about the actions we are taking (at least when the environment we're in is too primitive to probe the contents of our brains). Mathematical function formalizations of agents often ignore this ability. We show that in a general agent-environment framework (of which reinforcement learning is a special case), in a technical sense, such private memories do not enable qualitatively different agent behavior. (shrink)

Few things have impacted our lives as much as science and technology, but how we developed science and civilisation is one of the most challenging questions that has not yet been well explained. Attempting to identify the central driver, leading scientists have highlighted the role of culture, cooperation and geography. They focus thus on broad factors that are important basic preconditions but that we cannot directly influence. To better address the question, this paper integrates evidence from evolutionary biology, cognitive science, (...) methodology, archaeology and anthropology. The paper identifies 9 main preconditions necessary for contemporary science, which include 6 main preconditions for civilisation. Using a kind of quasi-experimental research design we observe that some cultures (experimental groups) met the preconditions while other cultures (control groups) did not. Among the preconditions, we explain how our mind's evolved methodological abilities (to observe, solve problems and experiment) have directly enabled acquiring knowledge about the world and collectively developing increasingly sophisticated methods (such as mathematics and more systematic experimentation) that have enabled science and civilisation. We have driven the major revolutions throughout our history – the palaeolithic technological and agricultural revolutions and later the so-called scientific, industrial and digital revolutions – by using our methodological abilities in new ways and developing new methods and tools, i.e. through methodological revolutions. Viewing our methods as the main mechanism through which we have directly developed scientific and technological knowledge, and thus science and civilisation, provides a new framework for understanding science and the history of science. Viewing humans as homo methodologicus, using an expanding methodological toolbox, provides a nuanced explanation of how we have been directly able to meet our needs, solve problems and develop vast bodies of technological and scientific knowledge. By better understanding the origin and foundations of science, we can better understand their limits and, most importantly, how to push those limits. We can do so especially by addressing the evolved cognitive constraints and biases we face and improving the methods we use. (shrink)

In their paper 'Reward is enough', Silver et al conjecture that the creation of sufficiently good reinforcement learning (RL) agents is a path to artificial general intelligence (AGI). We consider one aspect of intelligence Silver et al did not consider in their paper, namely, that aspect of intelligence involved in designing RL agents. If that is within human reach, then it should also be within AGI's reach. This raises the question: is there an RL environment which incentivises RL agents to (...) design RL agents? (shrink)

For Hans-Georg Gadamer and philosophical hermeneutics, Paul Celan’s poetry and prose have always been decisive in thinking through the possibilities and limitations of language and interpretation. Recently, important hermeneutic research has begun to point to an unavoidable liminal encounter between the body and language in Celan’s texts, which approaches an often-neglected theme in hermeneutic thought: the body and embodied experience. Yet in order for hermeneutics to engage Celan on matters concerning the body, language, and interpretation, it is necessary to understand (...) the profound role that the body and embodied experience plays in Celan’s works. In this essay, I offer three prominent instances of embodiment in Celan’s texts that contribute to such an account. I turn first to his preliminary notes from his 1960 Meridian speech in which he discusses the poem as ‘pneumatic.’ Second, I read Celan’s letter to Hans Bender in 1960 in which poetry is both a tactile Handwerk and a handshake. Third, I engage Celan’s reading notes from two physiology textbooks from 1967 and his poem, “Seelenblind.” While the first two instances affirm the possibility of an embodied encounter with the singularity of the poet, the third instance considers the body as a site of interpretive breakdown. (shrink)

We describe in our own words a visual phenomenon first described by Gallagher and Tsuchiya in 2020. The key to the phenomenon (as we describe it) is to direct one’s left eye at the image of one's left eye, while simultaneously directing one's right eye at the image of one's right eye. We suggest that one would naturally arrive at this phenomenon if one took a sufficiently literal reading of certain words of Socrates preserved in Plato's Alcibiades. We speculate that (...) perhaps Socrates was aware of the visual phenomenon in question. (shrink)

This is a paper about the general theory of measuring or estimating social intelligence via benchmarks. Hernández-Orallo and Dowe described a problem with certain proposed intelligence measures. The problem suggests that those intelligence measures might not accurately capture social intelligence. We argue that Hernández-Orallo and Dowe's problem is even more general than how they stated it, applying to many subdomains of AGI, not just the one subdomain in which they stated it. We then propose a solution. In our solution, instead (...) of using test-cases within the given AGI subdomain to estimate an AI's intelligence, one would use test-cases in an extended subdomain where test-cases have the ability to simulate the AI being tested. Surprisingly, AIs only designed for the original subdomain can be tested with test-cases in the extended subdomain anyway. By extending the subdomain in this way, we might avoid Hernández-Orallo and Dowe's problem. (shrink)

Bilim ve din arasındaki etkileşimler hem tarihsel olarak hem de günümüzde çeşitli ve karmaşıktır. Modeller, verileri anlamlandırmak için faydalı olabilir. Bu makale, bilim-din etkileşimlerini tanımlamak için önerilen dört ana model türünü karşılaştırarak, onların güçlü ve zayıf yönlerini vurgulamaktadır. Bilimsel ve dini bilgiyi ilişkilendirme görevinde 'bütünleyici' modelin en verimli olduğu sonucuna varılmıştır.

Internodons are a formalization of Hennig's concept of species. We present an alternative construction of internodons imposing a tree structure on the genealogical network. We prove that the segments (trivial unary trees) from this tree structure are precisely the internodons. We obtain the following spin-offs. First, the generated tree turns out to be an organismal tree of life. Second, this organismal tree is homeomorphic to the phylogenetic Hennigian species tree of life, implying the discovery of a multi-level tree of life: (...) this phylogenetic tree can be obtained by zooming out from the organismal tree, or conversely, the organismal tree of life can be generated by expanding the phylogenetic nodes into unary trees. Finally, the definition of the organismal tree allows an efficient algorithmic transformation of a given genealogical network into its corresponding phylogenetic species tree of life. The latter will be presented in a separate paper. (shrink)