This research, focusing on the 'Oracle Bone Script' of Anyang City, China, holds significant academic value. It delves into the discovery of oracle bones and their use for divination and sacrifice during the Shang Dynasty, shedding light on the social, political, economic, and cultural aspects of the time, as well as local wisdom. The study investigates the connection between oracle bones and the lives and society of the local people in Anyang, including the construction of identity (...) and the utilization of oracle bones' value. The main findings of the study, titled 'Oracle Bone Script Culture of Anyang, China,' highlight the inseparable link between 'self-identity construction' and 'value utilization of inheritance.' These two elements interact to shape a distinctive oracle bone culture that mirrors the self-identity of the people of Anyang. The research's academic significance lies in its exploration of ancient cultural identity and its provision of crucial educational and informational value for the cultural development policies of various countries. (shrink)

When presented with a situation involving an agent’s choice between alternative actions, a moral oracle says what the agent is allowed to do. The oracle bases her advice on some moral theory, but the nature of that theory is not known by us. The moral oracle’s test consists in determining whether a series of questions to the oracle can be so constructed that her answers will reveal which of two given types of theories she adheres to. (...) The test can be applied to moral theories in order to determine if they differ in their recommendations for action. Based on this test, a terminology is developed to specify different forms and degrees of distinguishability between moral theories, or types of theories, in terms of their recommendations for action. In conclusion, the test is applied to consequentialism and utilitarianism. (shrink)

We consider the following problem for various infinite-time machines. If a real is computable relative to a large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it already computable? We show that the answer is independent of ZFC for ordinal Turing machines with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite-time Turing machines, unresetting and (...) resetting infinite-time register machines, and α-Turing machines for countable admissible ordinals α. (shrink)

The object of this paper is to explain a certain type of construction which occurs in priority proofs and illustrate it with two examples due to Lachlan and Harrington. The proofs in the examples are essentially the original proofs; our main contribution is to isolate the common part of these proofs. The key ideas in this common part are due to Lachlan; we include several improvements due to Harrington, Soare, Slaman, and the author.Our notation is fairly standard. If X (...) is an r.e. set, Xs is the finite set of elements enumerated in X before step s. if Ф is a recursive functional, Фs is the approximation to Ф at step s; it only queries the oracle about numbers xi and iless-than-or-equals, slantx; and right-pointing angle bracketx0,...,xk−1right-pointing angle bracket is an increasing function of each of its arguments. Sets are sometimes identified with their characteristic functions. Wj isthe jth r.e. set. Xc is the complement of X. (shrink)

In this article we find some sufficient and some necessary ${\Sigma^1_1}$ -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from the point of view of a model of arithmetic. These internal arguments are (...) used in conjunction with Pabion’s theorem that ensures that certain oracles are coded in a sufficiently saturated model of arithmetic. Examples of applications are provided for the theories of dense linear orders and of discrete linear orders. These results are then generalised to other ω-categorical theories and theories with a unique countable recursively saturated model. (shrink)

Historians of science and religion have given little attention to how historical‐critical scholarship influenced perceptions of the relationship between science and religion in the nineteenth century. However, the so‐called “cofounders” of the “conflict thesis,” the idea that science and religion are fundamentally and irrevocable at odds, were greatly affected by this literature. Indeed, in his two‐volume magnum opus, A History of the Warfare of Science with Theology in Christendom (1896), Andrew D. White, in his longest and final chapter of his (...) masterpiece, traced the development of the “scientific interpretation” of the Bible. In this article, I argue that developments in biblical criticism had a direct impact on how White constructed his historical understanding of the relationship between science and religion. By examining more carefully how biblical criticism played a significant role in the thought of White and other alleged cofounders of the conflict thesis, this article hopes to relocate the origins, development, and meaning of the science–religion debate at the end of the nineteenth century. (shrink)

We consider the relationship between the computational complexity classes NP and EL . Taking into account the inclusion or incomparability of these classes, the existence or nonexistence of immune sets in their differences, and the existence or nonexistence of sparse sets in the differences, there are exactly 24 different cases for their relationship. We show that 16 cases are impossible in the real nonrelativized world as well as in any relativized world. Each of the remaining 8 cases is realizable in (...) appropriate relativized worlds. Further we examine which of the 8 cases is most probably for a random oracle. (shrink)

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

We consider implicit definability over the natural number system $\mathbb{N},+,\times,=$. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of $\mathbb{N}$ which are not explicitly definable from each other. The second theorem says that there exists a subset of $\mathbb{N}$ which is not implicitly definable but belongs to a countable, explicitly definable set of subsets of $\mathbb{N}$. Previous proofs of these theorems have used finite- or infinite-injury priority constructions. (...) Our new proof is easier in that it uses only a nonpriority oracle construction, adapted from the standard proof of the Friedberg jump theorem. (shrink)

With 500+ papers and 20+ books spanning many scientific disciplines, Mark Burgin has left an indelible mark and legacy for future explorers of human thought and information technology professionals. In this paper, I discuss his contribution to the evolution of machine intelligence using his general theory of information (GTI) based on my discussions with him and various papers I co-authored during the past eight years. His construction of a new class of digital automata to overcome the barrier posed by (...) the Church–Turing Thesis, and his contribution to super-symbolic computing with knowledge structures, cognizing oracles, and structural machines are leading to practical applications changing the future landscape of information systems. GTI provides a model for the operational knowledge of biological systems to build, operate, and manage life processes using 30+ trillion cells capable of replication and metabolism. The schema and associated operations derived from GTI are also used to model a digital genome specifying the operational knowledge of algorithms executing the software life processes with specific purposes using replication and metabolism. The result is a digital software system with a super-symbolic computing structure exhibiting autopoietic and cognitive behaviors that biological systems also exhibit. We discuss here one of these applications. (shrink)

It is shown that if A and C are sets of degrees uniformly recursive in 0' with $\mathbf{0} \nonin \mathscr{C}$ then there is a degree b with b' = 0', b ∪ c = 0' for every c ∈ C, and $\mathbf{a} \nleq \mathbf{b}$ for every a ∈ A ∼ {0}. The proof is given as an oracle construction recursive in 0'. It follows that any nonrecursive degree below 0' can be joined to 0' by a degree strictly (...) below 0'. Also, if $\mathbf{a ' and a" = 0" then there is a degree b such that a ∪ b = 0' and a ∩ b = 0. (shrink)

An oracle A is low-for-speed if it is unable to speed up the computation of a set which is already computable: if a decidable language can be decided in time $t(n)$ using A as an oracle, then it can be decided without an oracle in time $p(t(n))$ for some polynomial p. The existence of a set which is low-for-speed was first shown by Bayer and Slaman who constructed a non-computable computably enumerable set which is low-for-speed. In this (...) paper we answer a question previously raised by Bienvenu and Downey, who asked whether there is a minimal degree which is low-for-speed. The standard method of constructing a set of minimal degree via forcing is incompatible with making the set low-for-speed; but we are able to use an interesting new combination of forcing and full approximation to construct a set which is both of minimal degree and low-for-speed. (shrink)

In [20] Krajíček and Pudlák discovered connections between problems in computational complexity and the lengths of first-order proofs of finite consistency statements. Later Pudlák [25] studied more statements that connect provability with computational complexity and conjectured that they are true. All these conjectures are at least as strong as $\mathsf {P}\neq \mathsf {NP}$ [23–25].One of the problems concerning these conjectures is to find out how tightly they are connected with statements about computational complexity classes. Results of this kind had been (...) proved in [20, 22].In this paper, we generalize and strengthen these results. Another question that we address concerns the dependence between these conjectures. We construct two oracles that enable us to answer questions about relativized separations asked in [19, 25] (i.e., for the pairs of conjectures mentioned in the questions, we construct oracles such that one conjecture from the pair is true in the relativized world and the other is false and vice versa). We also show several new connections between the studied conjectures. In particular, we show that the relation between the finite reflection principle and proof systems for existentially quantified Boolean formulas is similar to the one for finite consistency statements and proof systems for non-quantified propositional tautologies. (shrink)

Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. A corollary to this is that there is a Δn+10 basic sequence with respect to which no Δn0 real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.

The human brain has some capabilities that the brains of other animals lack. It is to these distinctive capabilities that our species owes its dominant position. Other animals have stronger muscles or sharper claws, but we have cleverer brains. If machine brains one day come to surpass human brains in general intelligence, then this new superintelligence could become very powerful. As the fate of the gorillas now depends more on us humans than on the gorillas themselves, so the fate of (...) our species then would come to depend on the actions of the machine superintelligence. But we have one advantage: we get to make the first move. Will it be possible to construct a seed AI or otherwise to engineer initial conditions so as to make an intelligence explosion survivable? How could one achieve a controlled detonation? To get closer to an answer to this question, we must make our way through a fascinating landscape of topics and considerations. Read the book and learn about oracles, genies, singletons; about boxing methods, tripwires, and mind crime; about humanity's cosmic endowment and differential technological development; indirect normativity, instrumental convergence, whole brain emulation and technology couplings; Malthusian economics and dystopian evolution; artificial intelligence, and biological cognitive enhancement, and collective intelligence. (shrink)

A set $B\subseteq\mathbb{N}$ is called low for Martin-Löf random if every Martin-Löf random set is also Martin-Löf random relative to B . We show that a $\Delta^0_2$ set B is low for Martin-Löf random if and only if the class of oracles which compress less efficiently than B , namely, the class $\mathcal{C}^B=\{A\ |\ \forall n\ K^B(n)\leq^+ K^A(n)\}$ is countable (where K denotes the prefix-free complexity and $\leq^+$ denotes inequality modulo a constant. It follows that $\Delta^0_2$ is the largest arithmetical (...) class with this property and if $\mathcal{C}^B$ is uncountable, it contains a perfect $\Pi^0_1$ set of reals. The proof introduces a new method for constructing nontrivial reals below a $\Delta^0_2$ set which is not low for Martin-Löf random. (shrink)

In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power that is needed to learn finite families of structures. In particular, we prove that, if a family of structures is both finite and learnable, then any oracle which computes the Halting set is able to achieve such a learning. On the other hand, we (...) construct a pair of structures which is learnable but no computable learner can learn it. (shrink)

Both Socrates and Mozi are said in Plato’s dialogues and in the Mozi respectively to have claimed that they are living a sort of life following superhuman “intention”: Socrates according to the Delphic oracle, and Mozi the intention of heaven. Some modern philosophers show discomfort with their “superstitious” attitudes, taking the claims literally as a kind of groundless devotion, while others conjecture “sensible” purposes to understand the mystic elements as providing moral lessons. This paper, by responding to these modern (...) revisions of their doctrines, aims at highlighting the necessity of their (re-)introductions of superhuman perspectives to their inquiries. Through examining the similarities in Plato’s and Mohists’ demonstrations, the suggestion made will be that despite countless incommensurable features, heaven’s intention for Mohists offers a fundamental philosophical basis which enables them to develop arguments by means of sharp dichotomies, what is right or wrong, in the same way that Socrates in the Apology and in the Hippias Minor does for the development of Plato’s constructive endeavour beyond his Socratic a/euporetic legacy. Not only are their practices dependent on the presupposition of the existence of a perspective beyond humans, but also the reality of that perspective is established though their own investigative practices. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Human Goodness: Pragmatic Variations on Platonic ThemesCatherine E. MorrisonHuman Goodness: Pragmatic Variations on Platonic Themes by Paul Schollmeier Cambridge: Cambridge University Press, 2006. Pp. x + 302. $80.00, cloth.This is a book about spirits—human, godly, ghostly, and alcoholic. Paul Schollmeier's Human Goodness: Pragmatic Variations on Platonic Themes explores how humble humans act morally in an absurd world. Schollmeier contends that the Socratic spirit, or daimon, of self-knowledge and (...) hypothesis testing provides the foundation for a deeply human moral philosophy. It is, in Schollmeier's elegant phrasing, daimonic rather than eudaimonic, joining Aristotle and Plato with William James, as well as contributions from the ghosts of David Hume and Immanuel Kant and a few rounds of whiskey. Spirits abound! Mixing Socratic skepticism with Jamesian empiricism, Schollmeier argues that we act best when we apply general principles held as opinion (not as certain knowledge), and tested through experience, to our particular situation. When these opinions yield fruit, we find ourselves less at the whim of our capricious surroundings; when they do not, we are obliged to recognize the provisional nature of our opinions and change them. The ends of these day-to-day activities reflect a far grander cosmological order, one we ignore to our mortal (and moral) peril. It is by engaging in this intellectual activity that we are made happy, and it is in measured pursuit of this happiness that we are virtuous. Our actions are neither absolutely true nor perfect. They are instead the best that we can do. And for a reviewer attempting to encapsulate a finely nuanced book in a small space, this is comforting advice indeed. [End Page 190]The book begins with a puzzle: The curious twin claims in Plato's Apology that, true to the Delphic oracle's proclamation, Socrates is both wise and knows nothing. The key to this apparent paradox, Schollmeier contends, is the difference between divine knowledge, "ultimate, nonhypothetical knowledge of final causes" (6), and human knowledge, which is hypothetical only. Schollmeier marshals William James to argue that as humans, we encounter objects of knowledge perceptually; even our concepts are fashioned from this meager material. Without access to divine knowledge, humans must test hypotheses and assume that they are true only provisionally.James's (and Hume's) emphasis on the passions as the foundation for action, however, gives Schollmeier pause. In order to construct a moral philosophy that avoids absolutism but remains objective, Schollmeier argues for a harmony between the intellectual and the passional that is ultimately rational, our Socratic daimon. We are neither gods nor animals. Should we surrender rationality to desire, Schollmeier warns in concert with Socrates, our already fragile perceptual knowledge will be further distorted by fickle emotion. It is precisely because our grasp on the world is so tenuous that we must pay heed to cool intellect rather than hot passion.Such skepticism of our claim to know might make one hesitant to engage in the enigmatic world—but we have no choice! In order to find our hybrid daimon, both Socratic and pragmatic, Schollmeier suggests rhetoric as the methodology best suited to serving practical knowledge because it eschews certainty in favor of probability and acknowledges that the hypotheses on which we act are tentative and revisable. To this end, Schollmeier highlights the enthymeme and argument by example as the two techniques that best suit the nature of our hypothetical knowledge, and he urges a return to philodoxy, the love of opinion.Giving up our claim to certainty need not be a dismal proposition. Having established his methodology, Schollmeier begins building a moral philosophy that embraces an ontology of change and contends that our happiness provides us with stability in the form of a rational teleology. The objects of our human happiness are fleeting and changeable, so happiness cannot be static but is, rather, an activity that is its own end, "an activity that is an intellectual inquiry" (78). Our happiness is contingent on our ability to hypothetically determine, in our particular setting, our function and then fulfill this role to the best of our abilities. Depending on the setting, it may be dancing, parenting, or simply a lively... (shrink)

This paper defines natural hierarchies of function and relation classes □i,kc and Δi,kc, constructed from parallel complexity classes in a manner analogous to the polynomial-time hierarchy. It is easily shown that □i−1,kp □c,kc □i,kp and similarly for the Δ classes. The class □i,3c coincides with the single-valued functions in Buss et al.'s class , and analogously for other growth rates. Furthermore, the class □i,kc comprises exactly the functions Σi,kb-definable in Ski−1, and if Tki−1 is Σi,kb-conservative over Ski−1, then □i,kp is (...) completely parallelizable. All functions in □i,kc are Σi,kb-definable in Rki; this suffices to show that if the known Σi,kb conservativity between R3i and S3i−1 extends to R2i and S2i−1, then NC = NC1 relative to an oracle in PH. We prove a KPT-style witnessing theorem for Ski using constantly many rounds of □i,kc interactive computation, and thus show that if Ski ≡ Rki+1 then the bounded arithmetic hierarchy collapses, provably in Ski. (shrink)

The automation of many repetitive or dangerous human activities yields numerous advantages. In order to automate a physical task that requires a finite series of sequential steps, the translation of those steps in terms of a computational procedure is often required. Even apparently menial tasks like following a cooking recipe may involve complex operations that can’t be perfectly described in formal terms. Recently, several studies have explored the possibility to model cooking recipes as a computational procedure based on a set (...) of instructions. This vision is the foundation for the construction of robotics kitchen, as Moley. These kitchen robots have shown promising results. Moley, for instance, is the very first example of a new generation of bioinspired robotics, based on the reproduction of particular movement, cooking, through artificial arms and hands. It is entirely different from the current appliances present in our domestic domain because Moley is able to manipulate ingredients and interact with kitchen equipment in order to prepare a dish autonomously. Nonetheless, they have also shown several limitations. In particular, Moley is an entirely autonomous robot in a structured environment in which it knows precisely the object position and manipulates the ingredients based on a list of instructions and a training phase made by Machine Learning. In this contribution we contend that these limitations arise from an essential mismatch between computational procedures, as originally described by Turing in his seminal 1936 paper, and recipes. Computational procedures have been originally created to observe and modify formal symbols with formal operators. Thus, they are independent from time and they are ideally executed in a closed environment, in which the computer directly produces all the relevant changes required to produce the intended result. Recipes, instead, are followed in an open environment, in which, while time goes by, changes happen independently from the cook’s intervention: the cook puts the butter on the pan, starts the fire and then waits until the butter is melted. To operate effectively in the open environment a kitchen robot must couple computational procedures with sensors, e.g a sensor which provides a time signal. These sensors are de facto oracles for the procedures and yet are required to bridge the gap from the formal to the physical world. (shrink)

In his Republic Plato considers grasping the unity of mathematics as the ultimate goal of the mathematical studies in which the future philosopher-rulers must engage before they turn to philosophy. How the unity of mathematics is supposed to be understood is not explained, however. This book argues that Plato conceives of the unity of mathematics in terms of the mutually benefiting links between its branches, just as he conceives of the unity of the state outlined in the Republic in terms (...) of the common benefit for all citizens. Evidence for this view is provided by a discussion of his conception of astronomy as a propedeutic to philosophy, which can be best understood as hinting at a historically possible link between fourth-century-BC astronomy and solid geometry. The monograph also includes a detailed discussion of two well-known stories about Plato: not only he motivated Greek mathematicians to solve a difficult problem in solid geometry with his interpretation of a Delphic oracle given to the inhabitants of the island of Delos but he also posed the question which led to the development of the astronomical theory of homocentric spheres. It is argued that these stories are best understood as fictional episodes in Plato's life, constructed from passages in his works. (shrink)

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages and modern-day programming. This book (...) concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses-natural deduction-is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. Part II "Formal Syntactic Proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. Part III "Formal Semantic Disproof" shows you how to construct mathematical counterexamples to shoe that proof is impossible. Jape can check the counterexamples you build. Part IV " Program Specification and Proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web. (shrink)

The infinite time Turing machine analogue of Post's problem, the question whether there are semi-decidable supertask degrees between 0 and the supertask jump 0∇, has in a sense both positive and negative solutions. Namely, in the context of the reals there are no degrees between 0 and 0∇, but in the context of sets of reals, there are; indeed, there are incomparable semi-decidable supertask degrees. Both arguments employ a kind of transfinite-injury construction which generalizes canonically to oracles.

Cosmopolitanism seeks a political ethics of world togetherness and a political aesthetics that can contribute to this task critically and imaginatively. Regarding political ethics, I explore the world as a “cosmopolitan mind” composed of “dialogic voices” and threatened by neoliberalism, neofascism, and other nihilistic “oracles.” I also construct a criterion for determining which public artworks (1) resist oracles and (2) help us imagine a “cosmopolitan democracy” and its political ethics. The latter includes the concordance of three ethico-political virtues—solidarity, heterogeneity, and (...) fecundity (creating new voices through the interplay among other voices)—and must appeal to different peoples worldwide. I also examine how this political ethics and aesthetics can be applied to nonhuman life and non-sentient formations in a non-anthropocentric manner; indeed, how the cosmos in its entirety and plurality can also be thought of as voices and participants in the cosmopolitan mind and its artistic expression. Moreover, I contend that my ontology of dialogic voices and proposed public art criterion, like the cosmopolitan mind itself, are “events” or “becomings.” This means that there can never be an articulation of the ontology that is final nor a public art criterion that could curtail the imaginative reach of art. (shrink)

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, (...) which assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)

We consider questions related to the rigidity of the structure R, the PTIME-Turing degrees of recursive sets of strings together with PTIME-Turing reducibility, pT, and related structures; do these structures have nontrivial automorphisms? We prove that there is a nontrivial automorphism of an ideal of R. This can be rephrased in terms of partial relativizations. We consider the sets which are PTIME-Turing computable from a set A, and call this class PTIMEA. Our result can be stated as follows: There is (...) an oracle, A, relative to which the PTIME-Turing degrees are not rigid . Furthermore, the automorphism can be made to preserve the complexity classes DTIMEA for all k 1, or to move any DTIMEA for n 2. From the existence of such an automorphism we conclude as a corollary that there is an oracle A relative to which the classes DTIME are not definable over R. We carry out the corresponding partial relativization for the many-one degrees to construct an oracle, A, relative to which the PTIMA-many-one degrees relative to A have a nontrivial automorphism, and one relative to which the lattice of sets in PTIMEA under inclusion have a nontrivial automorphism. The proof is phrased as a forcing argument; we construct the set A to meet a particular collection of dense sets in our notion of forcing. Roughly, the dense sets will guarantee that if A meets these sets and we split A into two pieces, A0 and A1, in a simple way, and then switching the roles of A0 and A1 in all computations from A will produce an automorphism of the ideal of PTIMA-degrees below A. We force A0 and A1 to have different PTIME-Turing degree; this will then make the automorphism nontrivial. An appropriately generic set A is constructed using a priority argument. (shrink)

Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are (...) likewise irrelevant, since diagonalization can cover any amount of value assignments. This should not be construed as a restriction of computing power: Turing’s uncomputability is not a ‘barrier’ to be broken, but simply an effect of the expressive power of consistent programming systems. (shrink)

We consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this is localised (...) in open domains of spatial regions and the result of this process is a family of different ZFC models. Random forcing, as in set theory, corresponds precisely to the random influence on the system of external stimuli, and the principles of reflection of set theory explain the conscious internal reaction of the system. We also develop the conscious Turing machines which have their external ZFC environment and the dynamics is encoded in the random forcing changing models of ZFC in which Turing machines with oracles are formulated. The construction is applied to cooperating families of conscious agents which, due to the reflection principle, can be reduced to the implementation of certain concurrent games with different levels of self-reflection. (shrink)

The human brain has some capabilities that the brains of other animals lack. It is to these distinctive capabilities that our species owes its dominant position. Other animals have stronger muscles or sharper claws, but we have cleverer brains. If machine brains one day come to surpass human brains in general intelligence, then this new superintelligence could become very powerful. As the fate of the gorillas now depends more on us humans than on the gorillas themselves, so the fate of (...) our species then would come to depend on the actions of the machine superintelligence. But we have one advantage: we get to make the first move. Will it be possible to construct a seed AI or otherwise to engineer initial conditions so as to make an intelligence explosion survivable? How could one achieve a controlled detonation? To get closer to an answer to this question, we must make our way through a fascinating landscape of topics and considerations. Read the book and learn about oracles, genies, singletons; about boxing methods, tripwires, and mind crime; about humanity's cosmic endowment and differential technological development; indirect normativity, instrumental convergence, whole brain emulation and technology couplings; Malthusian economics and dystopian evolution; artificial intelligence, and biological cognitive enhancement, and collective intelligence. This profoundly ambitious and original book picks its way carefully through a vast tract of forbiddingly difficult intellectual terrain. Yet the writing is so lucid that it somehow makes it all seem easy. After an utterly engrossing journey that takes us to the frontiers of thinking about the human condition and the future of intelligent life, we find in Nick Bostrom's work nothing less than a reconceptualization of the essential task of our time. (shrink)

It is consistent that each union of many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter , the cofinality of the reduced ultrapower is greater than . The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.

Les pratiques et les discours philosophiques sous l'empire romain ont été largement inspirés par le langage des cultes à mystères. Depuis la période grecque classique, la pensée philosophique antique a assimilé et réélaboré la terminologie de ces cultes afin d'exprimer l'accès au savoir philosophique, le parcours de la connaissance et l'acquisition d'une 'révélation' réservée aux seuls initiés. Au fil des siècles, le langage platonicien, pétri de références aux cultes à mystères, devient le socle commun de la plupart des lettrés, quelle (...) que soit leur appartenance religieuse, païenne ou chrétienne. Dans une approche d'histoire des religions, la réflexion sur les catégories et leurs usages, tant dans les sources que dans l'historiographie, est inséparable de la construction de la discipline elle-même. Quel est dès lors l'impact de l'historiographie dans l'appréciation des rapports entre cultes à mystères et philosophie? Ensuite, dans quelle mesure les discours et pratiques philosophiques ont-ils été nourris par le lexique mystérique et par les rituels de ces cultes? Des textes réputés avoir partie liée avec les mystères, mais passablement négligés jusqu'ici, sont scrutés en détail--les fragments de Numénius, les Oracles Chaldaïques et plus généralement les expressions respectives des écoles philosophiques. Inversement, des pratiques rituelles mystériques sont susceptibles de révéler l'influence des réflexions philosophiques. Au fil des études, ce volume interroge la relation entre cultes à mystères et philosophies selon une double perspective, émique et étique, la seule qui puisse fournir des éclaircissements sur ce problème."--Page 4 of cover. (shrink)

The property common to three kinds of paradoxes (logical, semantic, and cultural) is the underlying presence of an exclusive disjunction: even when it is put to a check by the paradox, it is still invoked at the level of implicit discourse. Hence the argumentative strength of paradoxical propositions is derived. Logical paradoxes (insolubilia) always involve two contradictory, mutually exclusive, truths. One truth is always perceived to the detriment of the other, in accordance with a succession which is endlessly repetitive. A (...) check is put on the principle of the excluded middle by the logical paradoxes, because self-reference leads to an endlessly repeating circle, out of which no resolution is conceivable. Logical paradoxes are to be compared with the `objective ambiguity' prevalent in oracles (Gallet, 1990). Semantic paradoxes are contextually-determined occurrences, whose resolution at the metalinguistic level is made possible by the discovery of a middle term. They express a wilful ambiguity, in which the interlocutor is invited to take an active part in the construction of sense, since what must be found is the unexpected sense thanks to which A and not-A can be asserted simultaneously. Cultural paradoxes play about doxa (`common sense') and openly challenge common opinion because of their character as inopinata (`unexpected'). My aim is to show that even cultural paradoxes hide sometimes a flaw of argumentation similar to logical or semantic paradox; they too imply an exclusive disjunction leading to the disappearance of the middle terms. Finally, basing myself on the theory of topoi (Anscombre and Ducrot, 1983), a tentative resolution of the cultural paradoxes will be suggested. (shrink)

The technical contribution of this paper is threefold.First we show how to encode functionals in a ‘flat’ applicative structure by adding oracles to untyped λ-calculus and mimicking the applicative behaviour of the functionals with an impredicatively defined reduction relation. The main achievement here is a Church-Rosser result for the extended reduction relation.Second, by combining the previous result with the model construction based on partial equivalence relations, we show how to extend a λ-closed simple type structure to a model of (...) the polymorphic λ-calculus.Third, we specialize the previous result to a counter model against a simple minimization. This minimization is realized by a bar recursive functional, which contrasts the results of Spector and Girard which imply that the bar recursive functions are exactly those that are definable in the polymorphic λ-calculus. As a spin-off, we obtain directly the non-conservativity of the extensions of Gödel's T with bar recursion, fan functional, and Luckhardt's minimization functional, respectively. For the latter two extensions these results are new. (shrink)

One-sided classifiers are computable devices which read the characteristic function of a set and output a sequence of guesses which converges to 1 iff the set on the input belongs to the gven class. Such a classifier istwo-sided if the sequence of its output in addition converges to 0 on setsnot belonging to the class. The present work obtains the below mentionedresults for one-sided classes (= Σ0 2 classes) with respect to four areas: Turing complexity, 1-reductions, index sets and measure.There (...) are one-sided classes which are not two-sided. This can have two reasons: (1) the class has only high Turing complexity. Then there are some oracles which allow to construct noncomputale two-sided classifiers. (2) The class is difficult because of some topological constraints and then there are also no nonrecursive two-sided classifiers. For case (1), several results are obtainedto localize the Turing complexity of certain types of one-sided classes.The concepts of 1-reduction, 1-completeness and simple sets is transferred to one-sided classes: There are 1-complete classes and simple classes, but no class is at the same time 1-complete nd simple.The one-sided classes have a natural numbering. Most of the common index sets relative to this numbering have the high complexity Π1 1: the index set of the class {0,1}∞, the index set of the equality problem and the index set of all two-sided classes. On the other side the index set of the empty class has complexity Π0 2; Π0 2 and Σ0 2 are the least complexities any nontrivial index set can have.Lusin showed that any one-sided class is measurable. Concerning the effectiveness of this measure, it is shown that a one-sided class has recursive measure 0 if it has measure 0, but that thre are one-sided classes having measure 1 without having measure 1 effectively. The measure of a two-sided class can be computed in the limit. (shrink)

The following is excerpted from Sean Gurd’s translation of Euripides’ Hippolytus published with Uitgeverij this year. Though he was judged “most tragic” in the generation after his death, though more copies and fragments of his plays have survived than of any other tragedian, and though his Orestes became the most widely performed tragedy in Greco-Roman Antiquity, during his lifetime his success was only moderate, and to him his career may have felt more like a failure. He was regularly selected to (...) have his plays performed in the annual festival of Dionysus at Athens. But the plays were performed in a competition, and in the competitions he lost and lost, winning first place only five times in a career that spanned more than forty years. His corpus reads like the remains of a life spent trying to get a few things right and never being quite satisfied: scenes and schematized combinations of elements recur again and again, each time slightly changed. Hippolytus itself is an example: it contains two scenes in which a sick or dying character lies on a couch or a stretcher and is surrounded by silence and grief; he had experimented with such scenes in Alcestis, and would work with them again in Herakles and Orestes. Nor, judging from appearances, was he immune to the desire to score a hit, or to satisfy the audiences and the judges at the competition. Hippolytus is a rewrite of another Hippolytus, performed several years earlier, which scandalized the audience and certainly did not take first place. In that earlier Hippolytus (called by later writers Hippolytus Veiled), Euripides fashioned a Phaedra who was neither ashamed of loving her stepson nor incapable of taking steps to satisfy her desire. The forwardness of her approach to Hippolytus so outraged him that he covered his head with a robe (hence the play’s later title). Euripides liked to write energetic and self-confident women like this. He staged his Medea in 431, just three years before he revised Hippolytus, and in it the jilted title character murders her children in revenge for Jason’s new marriage to a more politically advantageous wife. Another flop: the play came in third of three. Evidently the judges did not like their women showing agency, especially when the consequences were transgressive. “The ornament of women,” wrote another great Athenian a little earlier, “is silence.”i Euripides’ Medea and his first Phaedra had other decorations. So three years after Medea crashed and burned and some time after the first Hippolytus suffered the same fate, he produced another Hippolytus play with a different setting and story. How could this one not have been a reaction to the failure of the first? “Second thoughts are always better,” he has one of his characters say, as though he were offering an apology for his first thoughts on the same story. In this new version, Phaedra is suicidally ashamed of her love, choosing to die rather than have it discovered, and willing to bring down her beloved Hippolytus in the service of the same end. Now it is Phaedra herself who covers her head in shock and horror at her desire. Only an intermediary, a slave of the house and an old crone with her fingers in all sorts of illicit pots, communicates Phaedra’s secret – against orders – and in consequence brings about the demise of two resolutely moral figures. It worked. For his tale of two well-born nobles with an unswerving commitment to moral action, destroyed by the meddling of a slave (and by the hostility of some particularly uncaring divinities), the judges crowned Euripides winner. It was the first time he had won, after almost thirty years of work. *** What Hippolytus wants more than anything else, as he protests with outrage just before leaving Trozen for the last time, is the benefit of due process – oaths, witnesses, an investigation that would reveal who really lusted after whom. Ironic, given that in the first Hippolytus, as far as we can make out, he did get a trial – but too late, and Theseus’ successful processing of Hippolytus failed to prevent his death. I cannot help hearing in the second Hippolytus’ complaints the anger of his authorial semblable who lost year after year by a process of judging that might have seemed brutal to him. Judges took no cognizance of how he worked, how long or hard or why; they just voted, and Euripides lost. But then I hear, in the fate of the first Hippolytus, an even grimmer commentary. Processed or not, we lose. We run aground. At the very least, this might cast a darker shadow on the business of watching or reading a play: in that twilight, things move too fast to make a fair assessment and, in any case, the reasonably high definition of what you see and hear belies the truth of indistinction, the multiplicities just below the surface. Watching is a constrained activity, a form of captivity, but reading is plastic. This translation was begun to supply the script for an audio version of the play, recorded in the spring of 2012, and here and there it sacrifices literalness for sayability and the voices and passions of the actors on that occasion. But it was finished to be read, and engineered to create a reading caught between the poles of specificity and non-specificity that the play itself conjures and relies on at its generative core. Thus two texts: the one clear, perhaps overprecise, respectably modern in its presentation, and the other ancient, a reasonable approximation of the classical reading process, and indistinct in vital ways. Like early modern dramatic texts, the exact provenance and original function of the scripts that have made it down to us are unknown. We do know that the ultimate survival of Hippolytus was thanks to its wide-spread use as a school text. But its relation to the first performance in 428 BCE is a matter only of speculation. Euripides presumably had a fair copy before production began; it was probably modified during rehearsals. The actors may have had copies, too (probably the young men who served in the chorus did not). The chor?gos, a wealthy Athenian who paid for the production, might have been presented with or just made sure to get his hands on a high-quality text, to commemorate the play’s success. Fans might have been able to buy copies. Any one of these sources might have provided the ultimate progenitor of our text. Several of them might have, in fact, if later editors compared and conflated traditions. The plays toured extensively in the Greek-speaking world, and were restaged as repertoire for centuries afterwards. In the process they were subjected to enough modifications by producers and actors that in the later fourth century the Athenian statesman Lycurgus had a law passed prohibiting performances at Athens from deviating from the official “city” text of the tragedies (which he had commissioned). It is unlikely that the city text was the last word; but it marks an important moment in Athens’ role in their dissemination, since after this the major sites of textual curatorship moved overseas, to Alexandria, Pergamum, Rome, Antioch, Constantinople. Any single text of any single play is thus no more than a moment of clarity and stability, crossed and subtended by multiple vectors of change, including that of textual flux (from Euripides’ first drafts to the latest printed text) and that of Euripides’ life work as a writer, in the light of which the Hippolytus is just one attempt to produce something exactly right, to win the prize or finally satisfy himself or prove to himself that all this longing for perfection was a waste of time. I am intrigued by the possibility that a single text might somehow serve as a lens onto this wider zone of indistinction, representing a small region clearly but nonetheless containing a blurred image of the whole, like a Leibnizian monad. After all, no text is a witness: it is, rather, a perception and a performance, and what every Hippolytus must perform is the awkward overlay of singular and plural, social practise and subliminal drive, that structures the tragedy. Modern critical editions can do this by juxtaposing a (relatively) clean and simple text with a textual apparatus reporting variants and theorizing the relationship between textual instantiations. A translation lacks the resolution to catch the fine variations which feed into the construction of an apparatus. But there are other means to hand. Guessing at the exact words of the original text is always just that – guessing – though Hippolytus is less problematic than plays like Iphigenia at Aulis. But we can make a pretty secure guess at what such a text looked like. Texts read by fifth-century readers were fundamentally different from what is presented in the best medieval MSS and printed in modern publications. The texts of Euripides’ time and for many centuries afterwards did not indicate word division with spaces (or by any other means) and were extremely sparing in punctuation, often avoiding it altogether. There was only one “case” of letters – what we call “capitals.” Musical sections were inscribed as though they were prose, without line endings to reflect their rhythm or their rhetorical structure. There was no indication of the speakers within a dramatic text, either. The earliest surviving dramatic texts, which come from over a century after Euripides’ death and a time which was much more elaborate and precise in its textual culture, indicated speaker-change with a little line or paragraphos below the line and a double-point [:] at its end. This convention almost certainly does not date back to Euripides’ own time; it may not even date to Lycurgus. In any case, such indications were understood to be readers’ marks: they did not have the same authority as the text and they were subject to readers’ revisions. At least ideationally, if not in concrete and distinguishable fact, a dramatic text was understood as containing no indication of speaker-change (and certainly none of who was saying what). The reader had to figure that out for him-/herself. The clear, legible, easy texts we are accustomed to reading are the fabrications of medieval and modern reading cultures. The first text, then, presents the translation as the text would have been in the mid-fourth century, perhaps decades after Euripides’ death. The second text processes Hippolytus, makes sense of it and makes it “readable.” That is: too distinct, dangerously so. It gets in your way, conjures fantoms, tries to make you see. Fragments of the Hippolytus Veiled, otherwise almost entirely lost, are juxtaposed with similar passages in the text – not to suggest a reconstruction, but a dialogue and a complex set of reassessments. I have not tried to represent the full variety of textual variants, but I have signalled where, for one reason or another, the text is soft and different editions propose excisions or changes. The two texts must be read together: you, reader, form the bridge between the distinctly seen and the indistinct invisible. You, in the end, will be its mask. *** illsandhateddiseaseswhatcanidoforyouwhatshouldinotdohereisthelightandthebrightairyoursickbedisnowout s idethehouseyoureverywordwastocomeherebutyouwillrushbacktoyourbedroomagainyoufadequicklyyoudelig htinnothingyoudislikewhatyouhaveyoulovewhatyoudontitsbettertobesickthantendthesickthefirstissimpleto the secondattachesheartspainandhandsworkeveryhumanlifeispainfulthereisnoendtotoildarknesshidesbehindclo udswhateverisdearerthanlifeweproveunhappyloversofwhatshineshereforlackofknowledgeofanotherlifethere isnoproofforthingsbeneaththeearthonlystoriessustainus liftmybodystraightenmyheadthebondsofmylimbsareloosenedtakemyhandsandmypalearmsthishatistooheavy formyheadtoweartakeitoffspreadmyhairovermyshoulders couragechilddonttossandturnsoviolentlyyouwillbearyoursicknessmoreeasilywithpeaceandanoblemindallmort alssuffer aiaiiwanttodrinkpurewaterfromadewyspringiwanttoliebackandrestunderthetreesinsomegrassymeadowchildw hycrydontsaythesethingsnearthecrowdhurlingwordsmountedonmadness sendmetothemountainiwillgototheforestwherebeastkillingdogspressthespotteddeergodsilongtoshouttothedo gstoshootthethessalianjavelinpastmyblondhairtoholdthebarbeddartinmyhandwhythisanxietychildwhatdoyouc areabouthuntingwhydoyoulustforflowingspringstheresahillwithwaterjustnexttothetowerwecangetyouadrinkt h ereartemismistressofthesaltlakeandthecoursethunderingwithhorseshoovesiwishiwereonyourplainsbreakings t uds whythrowthesefrenziedwordsaboutjustnowyouweresettingoutforthemountaintohuntandnowyoulongforhorses onthewavelesssand thesethingsneedanoracletotellwhichgodreinsyouinanddrivesyoufromyoursenseschild whathaveidonehowfarhaveibeendrivenfromgoodthoughtsiwascrazyiwascursedbysomepowerpheupheualasn ursecovermyheadagainimashamedofwhativesaidcovermeatearmovesdownfrommyeyeanditembarrassesm eithurtstostraightenourmindanditisterribletobeinsanebesttodiebeforeyoubecomelucidagain illcoveryoubutwhenwilldeathcovermeimoldivelearnedalotmortalsshoulddrinkoffriendshipmoderatelynotfrom th edeepestmarrowofthesoulamindslovecharmsshouldbeeasytoundoorthrustawayortiemoretightlyitisaverydiffic ultweightforonesoultolaborovertwopeopleasiamwrackedbypainforhertoomuchdisciplinecausesmoreharmthan pleasureandwarswithhealthipraisetoomuchlessthannothinginexcessandthewiseagreewithme *** Scene 1 Enter Phaedra and the Nurse; the former is recumbent on a couch while the latter bustles about her with gestures that might be those of a caregiver or a guard. NURSE Ills and hated diseases! What can I do for you? What should I not do? Here is the light, and the bright air; your sick bed is now outside the house. Your every word was to come here, but you will rush back to your bedroom again. You fade quickly. You delight in nothing. You dislike what you have. You love what you don’t. It’s better to be sick than tend the sick – the first is simple. To the second attaches heart’s pain and hand’s work. Every human life is painful. There is no end to toil. Darkness hides behind clouds whatever is dearer than life. We prove unhappy lovers of what shines here for lack of knowledge of another life. There is no proof for things beneath the earth. Only stories sustain us. PHAEDRA Lift my body, straighten my head: the bonds of my limbs are loosened. Take my hands and my pale arms. This hat is too heavy for my head to wear. Take it off, spread my hair over my shoulders. NURSE Courage, child; don’t toss and turn so violently. You will bear your sickness more easily with peace and a noble mind. All mortals suffer. PHAEDRA Aiai. I want to drink pure water from a dewy spring. I want to lie back and rest under the trees in some grassy meadow. NURSE Child, why cry? Don’t say these things near the crowd, hurling words mounted on madness. PHAEDRA Send me to the mountain. I will go to the forest where beast-killing dogs press the spotted deer. Gods! I long to shout to the dogs, to shoot the Thessalian javelin past my blond hair, to hold the barbed dart in my hand. NURSE Why this anxiety, child? What do you care about hunting? Why do you lust for flowing springs? There’s a hill with water just next to the tower; we can get you a drink there. PHAEDRA Artemis, mistress of the salt lake and the course thundering with horse’s hooves: I wish I were on your plains breaking studs! NURSE Why throw these frenzied words about? Just now you were setting out for the mountain to hunt – and now you long for horses on the waveless sand. These things need an oracle to tell which god reins you in and drives you from your senses, child. PHAEDRA What have I done? How far have I been driven from good thoughts? I was crazy, I was cursed by some power. Pheu pheu. Alas. Nurse, cover my head again. I’m ashamed of what I’ve said. Cover me – a tear moves down from my eye and it embarrasses me. It hurts to straighten your mind and it is terrible to be insane. Best to die before you become lucid again. NURSE I’ll cover you. But when will death cover me? I’m old; I’ve learned a lot. Mortals should drink of friendship moderately, not from the deepest marrow of the soul. A mind’s love-charms should be easy to undo, or thrust away, or tie more tightly. It is a very difficult weight for one soul to labor over two people, as I am wracked by pain for her. Too much discipline causes more harm than pleasure and wars with health. I praise “too much” less than “nothing in excess,” and the wise agree with me. ***. (shrink)

Translated by Drew S. Burk and Anthony Paul Smith. Excerpted from Struggle and Utopia at the End Times of Philosophy , (Minneapolis: Univocal Publishing, 2012). THE END TIMES OF PHILOSOPHY The phrase “end times of philosophy” is not a new version of the “end of philosophy” or the “end of history,” themes which have become quite vulgar and nourish all hopes of revenge and powerlessness. Moreover, philosophy itself does not stop proclaiming its own death, admitting itself to be half dead (...) and doing nothing but providing ammunition for its adversaries. With our sights set on clearing up this nuance, we differentiate philosophy as an institutional entity, and the philosophizability of the World and History, of “thought-world,” which universalizes the narrow concept of philosophy and that of “capital.” We also give an eschatological and apocalyptical cause to this end, of “times” or “ages” rather than those of philosophical practice. Last but not least, it is the Future itself in the performativity of its ultimatum that determines this end times, reversing these times from the Identity the Future accorded to it, withdrawing the thought-world from the lie of its death. Why this style of axioms and oracles, these more or less subtle distinctions, old and debased, with an appeal to the ultimata , to end times and last words? We fight to give, parallel to the concept of Hell, its new theoretical position, for its philosophical return and its non-philosophical transformation. No more so than any other word, Hell is not a metaphor here, just the Principle of Sufficient World. Every man, no doubt, has his “hell” readily available, connivance, control, conformism, domestication, schooling, alienation, extermination, exploitation, oppression, anxiety, etc. We have our little list that the Contemporaries established in the previous century in the same way one used to construct lists of virtues and vices or honors and wealth. They invented it for us without knowing it, for us-the-Futures who have as our responsibility to invent its use. In the Christian and Gnostic tradition, the struggle of the End Times takes place “on earth.” The most sophisticated of believers have it taking place in Heaven as well, above all in Heaven. The various kinds of gnosis imagine infinite falls and vertiginous highs, the vertigo of salvation. On Earth as in Heaven, a hell is available. The Marxists have the law of profit and the control of production, the class struggle Capital imposes on man. The Nietzscheans, the dull grumble of the struggle in the foundations of World and History, the domestication of man, the society of control. The phenomenologists, the capture of being, the most superficial amongst them, the age of suspicion. But all of these “hells” are taken from World, History, Society, and Religion. What we call Hell is no longer of the order of these specific and total intra-worldly generalities, it is both more singular and more universal, no longer being at all of the same order, it is the determinant Identity of these small hells strung out through history but unified here in the name of the last Humaneity. It is even found within the French idiom for hell [ enfer ], en-fer literally means “in-irons.” We are as much “in-irons” as we are “alive” [ en-Vie ]. We believe in Hell but as non-philosophers and it is even because we are non-philosophers that we can believe in it outside of any sort of religion. Hell is less mythological than ideological, it combines philosophizability with universal capital. Under what form? A single term could work for them without being a metaphor or something they would participate in by analogy, a more innovative and conjectural term than control, more universal than profit. It would denote the growing and permanent extortion of a surplus-value of communication, of speed and of urgency in change, in productivity and in work, in the pressure of images and slogans. It would be worse than solicitation, more tenacious than capture, more active and persecutory than control, softer and more insidious than a frontal attack, just as perverse as questioning and accusation, less brutal and offensive than extermination, less ritualized than inquisition, it would be soft and dispersed, instantaneous and vicious, it would be a crime without declared violence. Collusion and conformism, it would be afraid to show itself. Related to rumor, from which it borrows its infinite and tortuous ways. It is harassment. As a modernized form of Hell, perhaps harassment has a long future in front of it, of innocent torture, slow assassination, in short the fall, but radical with no way of recovering and which tolerates only salvation. THE PHILOSOPHICAL PAST OF NON-PHILOSOPHY Non-philosophy is thus Man as the utopian identity of the philosophical form of the World, a utopia destined to transform it. We still have to understand these equations, in particular that of the being-uni-versed from Man, and this book adheres to this by re-exposing non-philosophy in a different way via one of its new possibilities. It uses this opportunity to once again take up formulations that lead to objections answering certain external critics, as well as revisiting diverging interpretations specific to non-philosophers. A portion of this book is devoted to going through these theories via a strict or “lengthy” presentation of non-philosophy, and its defense against more expeditious solutions. This work of rectification is the occasion, merely the occasion, for refocusing non-philosophy on Man (the “Man-in-person,” “Humaneity”), and in a more innovative manner, on its utopian vocation established since the book Future Christ . As for this “occasion,” it is quite obvious. A school of posture, not to say a school of thought, supposes a minimum of closure from the most liberating of knowledge, a heritage, its utilization, and its no less certain dispersal. Within its development, a variety of interpretations will no doubt appear, deviations that are as much normalizations, and a struggle against this multiplication of divergent tendencies. These are perhaps not inevitable evils, especially here, merely a normal development according to the twisting paths of history. But the problem is made worse by the fact that this school of non-philosophers is that of utopia. Not the former attempts devoted to commenting on the worst authoritarian and criminal forms of the past and the present, but utopia as the determinant principle for human life, or to put it another way, of the Future as an irreducible presupposition of (for) thinking the World and History. Non-philosophers are engaged in an aleatory navigation between the respect for the most rigorous utopia, whose rules are not that of the reproductive imagination but those from the Future determining imagination itself, as well as the temptations, diversions, and remorse of history. Little by little, we will begin to understand that the Future as we understand it no longer has any temporal consistency or positive content, without being an empty form or a nothingness, but that it is foreclosed to past and present History, just as it is foreclosed to the place of places, the World, and that it is the only method for establishing the practice of thinking in a non-imaginary instance. Because it is the World and History that are imaginary and have a terrible materiality, it is not necessarily utopia. We will overlap two objectives here: the defense of non-philosophy against the (non-) philosophers that we are, only occasionally, and the introduction of philosophy to a rigorous future. Together they set out to definitively render, without any possible return to philosophical conformism or towards the facilities of the past and present, the non-philosophical enterprise understood as utopia or uchronia. Imagination and speculation, left to themselves and thus undistinguished, are quite good for participating in the grand game of History but have little value or worse for the Future which is unimaginable and unintelligible and must be maintained as such. MAN-IN-PERSON AS SUSPENSION OF THE PHILOSOPHICAL CHORA The point where philosophical resistance is concentrated is without a doubt the invention of the Name-of-Man, first name, oracular as much as axiomatic, of the determining cause for the non-philosophical posture. And that which concentrates the differends is the style of non-philosophy as identity that possesses the dual aspect, of discipline and of the oeuvre, of the theorem and of the oracle. But the real difficulty in understanding the simplicity of non-philosophy is profoundly hidden in the depths of philosophy itself. Because philosophy, from Parmenides to Derrida, even Levinas, continues to be a divided gesture, without a veritable immanence, transforming its thematic contents of transcendence in also forgetting to transform the operative transcendence in the element from which the ontology of surface is established which we will call, in memory of Plato, the chorismos. The general effect of the chora literally gives place to philosophy, demanding binding and sutures to which we will once and for all “oppose” the Man-in-person, his power of cloning, and his future being. All philosophy contains a hinter-philosophy in which it deploys its operations and weaves its tradition like an understudy of a topographical nature and in the best of cases being itself topological. Philosophy as well consists of two levels, its pre-ontological operative conditions on the one hand, and its superficial theme on the other, it too has its presupposed, but is not aware of it or erases it within the unity of appearance named Logos. Rightly, the Logos, and its flash or lightning nature, possesses a “dark precursor,” the chora, which is as much a virtual image, and philosophy, dazzled by its own lightning flash, seems to completely forget about it at the same time it sets itself up within it. Non-philosophy risks taking this same path, of confusing what it believes to be the real with its phantom double, contenting itself to working on the thematic level of philosophy, not its surface objects and its idle chatter (we stopped talking about this a long time ago and in any case they are merely simple materials for inducing a work of transformation), but the transcendence-form of its objects. In the end it risks, through precipitation, taking back up the heritage of philosophy, a heritage of a misunderstood presupposed, even more profound than the play of transcendences. This is what the imperative of the radicality of immanence meant, to treat immanence in an immanent manner, not to make a new object out of it. And from here we get non- (philosophy) and its refusal of the Platonic chorismos , symbol of all abstraction, and thus all transcendental appearance. There are no illusions. The message will leave a heritage in tattered pieces and interpretations. But it was difficult not to dispute the differend to its core. There will be complete confusion of the multiple, possible, and necessary effectuations of non-philosophy with its interpretations. The non-philosophical or human freedom of philosophical effectuation and the philosophical freedom of interpretation. Effectuations demand non-philosophy to return to zero from the point of view of its philosophical material and thus also but within these limits the formulation of its axioms , but in no way providing from the outset divergent interpretations of the aforementioned axioms. They are divergent because they do not take into account the material from which these axioms are derived within non-philosophy, and because they do not see themselves as symptoms of another vision of the World. The utterances of non-philosophy are not mathematical theorems and pure axioms, they merely have a mathematical aspect . They are, by their extraction or origin, mathematical and transcendental. And by their determined function in-Real, within non-philosophy, they are identically in-the-last-Humaneity entities which have an aspect of an axiom and an aspect of interpretation (or an oracular aspect as we say) that attempts (sometimes it is ourselves who provide the occasion) to isolate and transform, in complete freedom of interpretation. There will be an opportunity to complain about the complex character of the language of non-philosophy, an idiom saturated with classical references, sophisticated in a contemporary way. Its freedom of decision up against the whole of philosophy demands these effects of “complication” and “privatization,” as the saying goes. But it also demands fighting against the drift [ dérive ] of the pedagogical-all and the mediatic-all that leads philosophy into the shallow depths of opinion, which is the site of its impossible death. The noble idealism of “pop-philosophy” has been consumed into a “philo-reality;” against this we propose philo-fiction. Parricide, which is at the bottom of these interpretations and which we can judge as being quite fertile, although it has informed tradition, only takes place once or within one lone meaning. In regards to Parmenides, it was possible; Plato introduced the Other as non-being and language, bringing into existence the philosophical system of the World, but is it possible to repeat it again with the same fecundity in regards to non-philosophy, this time in introducing (non) religion or (non) art, still mixing them without taking into account this mixture, alternatively as a philosophical or religious resentment? If philosophy begins via a crime, it is no doubt obliged to continue down similar pathways, to the effect that the crimes of philosophy, once the founding crime has been committed, are a reaction of self-defense. It is undoubtedly from this that we get Marx’s declaration that history begins by tragedy and repeats itself or ends in farce. The preservation of rigor and fecundity is, in every respect, a psychologically difficult task within a theory such as non-philosophy. Having posited an essential objective of liberation in regards to philosophy and its services, one has often understood this objective as an authorization of providing particular interpretations of its axioms and ends up obliterating their scope. This ends up confusing, on one hand, two kinds of freedoms in regards to non-philosophy, the freedom of its interpretations and the freedom of its effectuations. On the other hand, any defense of “principles” against precipitated interpretations is immediately taxed with a will to orthodoxy, a prohibitive objection when we are dealing with, as is the case here, a heretical theory of thought. Nevertheless, it is time to stop confusing heresy as the cause of thought with an ideology of heresies, which is certainly not at all our object, but rather a form of normalization. As for the “disciplinary” aspect, which is not the only aspect, it demands something other than philosophical “answers to objections,” a precision in the definition and use of its procedures in the formation of utterances, since non-philosophy is neither a supplementary doctrine interior to philosophy nor a vision of the world but one whose priority is a “vision of Man,” or rather Man as “vision” that implies a theory and a practice of philosophy. In the end, struggle is only one aspect of non-philosophy, not its whole or telos, struggle coming only from its materiality. In particular, if the discipline of non-philosophy is inseparable from struggle, it is not a question of reducing the monomaniacal obsession of its “marching orders.” This would reduce its complexity and kill its indivisibility, deploying it in a “long march” and a form of Maoization whose philosophical presuppositions no longer have any pertinence here, a case of the One and the Two, which are now cloned and no longer tied together. More generally, non-philosophy is a complex thought composed of a multitude of aspects, which is to say, unilateral interpretations, of a philosophical origin but reduced by their determination in-the-last-instance . The “liberalism” of non-philosophy is merely one of the aspects of which it is capable, not an essence. Similarly, it is only capable of having a “Maoist” aspect. Let us generalize. The weakness of non-philosophy is due to a specific cause, the determination-in-the-last-Humaneity of a subject for the World. Everything that has a right to the philosophical city can be said about it in turn and in a retaliatory mode since Man contributes nothing of himself that Man takes from the World. We can consider non-philosophy as being pretentious, absurd, idealistic, empty, materialistic, formalistic, contradictory, modern, post-modern, Zen, Buddhist, Marxist; it endures or tolerates, perhaps “appeals” to, or at least renders possible, sarcasms, ironies, and insults without even talking about the misunderstandings, partly for the same reason as psychoanalysis. All of this goes beyond simple “deviations.” They are its aspects, which is to say, its “unilateral” philosophical interpretations in both senses of the word, being either sufficient coming from the mouth of philosophers, or reduced to their absolute dimension of sufficiency and totality in the mouths of non-philosophers, and both times due to the weakness and strength of Man-in-person as their determination only in-the-last-instance. The non-philosopher is certainly not a Saint Paul fantasizing about a new Church. The non-philosopher is either a (Saint) Sebastian whose flesh is pierced with as many arrows as there are Churches, or a Christ persecuted by a Saint Paul. What is engaged in here is the practice of retaliation. A negative rule of the non-philosophical ethics of outlawed discussion by way of argumentation (the sufficient is you, the orthodox one is always you, you are the fashionable one, and when a master you are someone else) that is founded on the confusion of effectuations of non-philosophy and of its overall interpretations. Retaliation is the law but as with any too-human law, it must acquire a dimension that displaces it, or rather emplaces it and takes away its authority but not all of its effectiveness. If the non-philosopher is only authorized by himself, which is to say by philosophy but limited by the Real-of-the-last-instance, its critique of other non-philosophers can merely be retaliatory under the same conditions, only by the Real limited in-the last-instance. THE TREE OF PHILOSOPHICAL SAINTLINESS The thematic horizon or material of these debates is in the relationships between philosophy, religion as gnosis, and non-philosophy. It is inevitable, regarding non-philosophers in general (whether they are non-philosophers by name or simply its neighbors) that we often end up evoking Marx’s Holy Family and imagining, arranged on the neighboring branches of the tree of philosophy and annexed, sometimes abusively, to non-philosophy, authors who would quite evidently and quite rightly refuse this label. So it is that we find, for example, a Saint Michel, a Saint Alain, a Saint Gilles 1 without even mentioning the youngest who aspire as well to the freedom of “saintliness” and who make their muted voices heard here. If there is a Holy Family of non-philosophers, it extends completely beyond these three, provided that the sectarian spirit can save us. This book is organized in the following manner: To begin, in order to recall the essential part of the problematic, we have organized a Summary of Non-Philosophy , a vade-mecum of notions and basic problems, in a classical style. Secondly, there is Clarifications On the Three Axioms of Non-Philosophy , designed to posit their proper use as much as to elucidate their meaning. Thirdly, an analysis of Philosophizability and Practicity , both being extreme constituents of philosophical material or the contents of the third axiom. Fourthly, the heart of this work: Let us Make a Tabula Rasa of the Future or of Utopia as Method . Fifthly, we have a theoretical outline of a non-institutional utopia, The International Organization of Non-Philosophy, L’Organisation Non-Philosophique Internationale, (ONPHI) already created in practice but under the conditions of possibility and functioning from which here we put into question “de jure,” thus not without a perplexity concerning “facts,” in any case, without the capability of “getting to the bottom of things.” Sixthly, an essay characterizing The Right and the Left of Non-Philosophy , a brief topology of several philosophizing and normalizing positions of proponents or tenants of this problematic. Seventhly, Rebel in the Soul: A Theory of Future Struggle , a systematic discussion starting from a confrontation of non-philosophical gnosis and non-religious gnosis to the extent that they pose, posed or perhaps still will pose themselves as rivals to non-philosophy in a mixture of fidelity and infidelity. Despite the fact that it can also be read as putting non-philosophy into perspective: it pits against a standard Platonism two contemporary appropriations of Gnosticism. On the basis of the paradigm of Man who never ceases to come as the Future-in-person, each one of these moments strives to reestablish not the “true” non-philosophy and its orthodoxy, but the minimal conditions to respect in order to allow for its maximum fecundity. And in order to bring about one of the last possibilities of its development, making explicit Humaneity as a utopia-for-the-World. In introducing these considerations in the form of a “testament” and “ultimatum,” we want to indicate two things: First, that this is the last time we will intervene in order to caution non-philosophers against the temptation of returning and looking backwards towards philosophy. Only a disillusioned nostalgia for the former World and its traditions barely remain permissible to us.… Secondly, that non-philosophy is also a sort of ultimatum for considering one’s life and transforming one’s thought from the perspective of a uni-version rather than a conversion. Man as future is this ultimatum in action, not an impatient self-proclaimed genius, and philosophy is his testament. It is obviously the ultimatum that determines this testament as “old” with a view towards a life that is, itself, non-testamentary. In and of itself, the “old” can never bear a veritable eschaton. Thus, this book intersects according to the logic of this paradigm, under the sign of the ultimate or “last” as future, philosophy as testament and cautionary note for maintaining the non-philosophical oeuvre as “future” or “utopian.” We will see that between these two dimensions it cradles a theory of struggle. In the end, this book envisions non-philosophers in multiple ways. It inevitably sees them as subjects of knowledge, most often academics insofar as life in the world demands, but above all as close relatives of three great human types. The analyst and political militant are quite obvious, for non-philosophy is close to psychoanalysis and Marxism insofar as it transforms the subject in transforming philosophy. Here again, one must have a sense not of certain nuances but of aspects (of the interpretations, albeit unilateralized) and not in order to construct a simple proletarization or militarization of thought as theory. To be rigorous, rather than authoritarian or spiteful, is its task. And lastly, non-philosophy is a close relative of the spiritual but definitely not the spiritualist. Those who are spiritual are not at all spiritualists, for the spiritual oscillate between fury and tranquil rage, they are great destroyers of the forces of Philosophy and the State, which are united under the name of Conformism. They haunt the margins of philosophy, gnosis, mysticism, science fiction and even religions. Spiritual types are not only abstract mystics and quietists; they are heretics for the World. The task is to bring their heresy to the capacity of utopia, and their utopia to the capacity of the paradigm. NOTES We will recognize allusions, and sometimes references, to closely related or distant themes, but which are related, in the work of Michel Henry, Alain Badiou and via the representative of “non-religious” gnosis of a Platonic origin, in Gilles Grelet. It goes without saying that these discussions are current and local, neither concerning the ensemble of doctrines nor prejudging the eventual evolution of certain amongst them. This concerns defining certain proximities with non-philosophy (rather than adversaries which in some sense they are) and typological and emblematic differends (rather than conflicts with a certain author). (shrink)

Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing, the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. (...) Though less well known than his other work, Turing's 1938 Princeton PhD thesis, "Systems of Logic Based on Ordinals," which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This book presents a facsimile of the original typescript of the thesis along with essays by Andrew Appel and Solomon Feferman that explain its still-unfolding significance. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science. (shrink)

Social constructionist claims are surprising and interesting when they entail that presumably natural kinds are in fact socially constructed. The claims are interesting because of their theoretical and political importance. Authors like Díaz-León argue that constitutive social construction is more relevant for achieving social justice than causal social construction. This paper challenges this claim. Assuming there are socially salient groups that are discriminated against, the paper presents a dilemma: if there were no constitutively constructed social kinds, the causes (...) of the discrimination of existing social groups would have to be addressed, and understanding causal social construction would be relevant to achieve social justice. On the other hand, not all possible constitutively socially constructed kinds are actual social kinds. If an existing social group is constitutively constructed as a social kind K, the fact that it actually exists as a K has social causes. Again, causal social construction is relevant. The paper argues that (i) for any actual social kind X, if X is constitutively socially constructed as K, then it is also causally socially constructed; and (ii) causal social construction is at least as relevant as constitutive social construction for concerns of social justice. For illustration, I draw upon two phenomena that are presumed to contribute towards the discrimination of women: (i) the poor performance effects of stereotype threat, and (ii) the silencing effects of gendered language use. (shrink)

In The Construction of Social Reality, John Searle argues that there are two kinds of facts--some that are independent of human observers, and some that require..

Niche construction theory highlights the active role of organisms in modifying their environment. A subset of these modifications is the developmental niche, which concerns ecological, epistemic, social and symbolic legacies inherited by organisms as resources that scaffold their developmental processes. Since in this theory development is a situated process that takes place in a culturally structured environment, we may reasonably ask if implicit cultural biases may, in some cases, be responsible for maladaptive developmental niches. In this paper we wish (...) to argue for an affirmative answer. In order to do so, we first propose to conceptualize implicit bias as embodied perceptual habits, and then proceed to show that these habits are at least partially responsible for maladaptive developmental niches of children with Down syndrome and autism. With this framework we thus hope to bring together two fields of research that haven’t been explicitly connected: implicit bias and niche construction theory. Linking these two theories may bring benefits both to implicit bias researchers, who can extend this concept to characterize other sets of processes as biased, as well as to niche construction theorists, who will have a useful theoretical tool to diagnose maladaptive features of niches brought about by sociocultural biases. (shrink)

We propose a conceptual model that maps the causal pathways relating biological evolution to cultural change. It builds on conventional evolutionary theory by placing emphasis on the capacity of organisms to modify sources of natural selection in their environment (niche construction) and by broadening the evolutionary dynamic to incorporate ontogenetic and cultural processes. In this model, phenotypes have a much more active role in evolution than generally conceived. This sheds light on hominid evolution, on the evolution of culture, and (...) on altruism and cooperation. Culture amplifies the capacity of human beings to modify sources of natural selection in their environments to the point where that capacity raises some new questions about the processes of human adaptation. Key Words: adaptation; altruism; cooperation; evolutionary psychology; gene-culture coevolution; human evolution; human genetics; niche construction; sociobiology. (shrink)

The existence of objective knowledge and the possibility of communicating it by means of language have traditionally been taken for granted by educators. Recent developments in the philosophy of science and the historical study of scientific accomplishments have deprived these presuppositions of their former plausibility. Sooner or later, this must have an effect on the teaching of science. In this paper I am presenting a brief outline of an alternative theory of knowing that takes into account the thinking organism''s cognitive (...) isolation from reality. This orientation was proposed by Vico at the beginning of the 18th century, disregarded for two hundred years, and then propounded independently by Piaget as a developmentally grounded constructivist epistemology. The paper focuses specifically on the adaptive function of cognition, Piaget''s scheme theory, the process of communication, and the subjective perspective on social interaction. In the concluding section it then suggests some of the consequences the shift of epistemological presuppositions might have for the practice of teaching. (shrink)