Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the (...) sum of two squares. In this paper, we analyse a recent proof of this theorem. It is interesting because: it follows all the elements of which Fermat wrote in his outline; it represents a good introduction to all logical nuances and mathematical variants concerning this method of which Fermat spoke. The assertions by Fermat will also be framed inside their historical context. Therefore, the aims of this paper are related to the history of mathematics and to the logic of proof-methods. (shrink)

The work aims to demonstrate that at the heart of Eriugena’s approach to Christian theology there lies a profoundly philosophical interest in the necessity of a cardinal shift in the paradigms of thinking – namely, that from the metaphysical to the dialectical one, which wins him a reputation of the ‘Hegel of the ninth century,’ as scholars in Post-Hegelian Germany called him. The prime concern of Eriugena’s discourse is to prove that the actual adoption of the salvific truth of Christ’s (...) revelation about all humans’ Sonship to God directly depends on the way the truth of God’s Oneness is consistently thought of. It is exactly the dialectic of the universal and particular which allows Eriugena both to tackle the dichotomy between being and non-being and to proceed towards raising a question how the totality of God’s being can be approached so as to let him radically reconsider a predominantly metaphysical view of creation the theological reflection traditionally relies on. According to the dialectical understanding of unity that Eriugena does adhere to, the reality of creation cannot be thought of, and therefore known, otherwise than in the way of being inseparable from the universal Principle of all. This is the Principle abandoned by nothing, unless the mind corrupted by the senses thinks otherwise and, following the metaphysical pattern of dichotomy, improperly sets the creation and its Principle apart. Restoration of the mind to the proper rational motion of recta ratio freed, as Eriugena argues, from the dictates of senses therefore becomes the way of both the epistemological breakthrough to the infinite whole and practical return from the world of finite things to living in the divine reality of creation. The work’s argument is based on the assumption of close affinity between Eriugena’s discourse and that of his Islamic contemporaries, who developed their dialectical ideas within the Mu’tazilah tradition of a philosophically disciplined approach to the truth of God’s Oneness. In particular, al-Nazzam’s engagement with Parmenides’ Periphyseon and his resistance to the danger of a dualistic interpretation of its ontology seem to provoke Eriugena’s innovative approach to Christian theology with a view to suggesting a mode of overcoming dualism as the main obstacle on the way to the Truth revealed. This vision of the meaning of Eriugena’s undertaking allows us not only to better understand the novelty of his approach to Christian theology, but also reconsider some of the key points of his discourse that seem to have become a sort of commonplace in Eriugenian studies: 1. Unlike the prevalent opinion, not the forms of the division of Nature but the modes of interpreting being and non-being are to be understood to constitute the genuine subject-matter of each book of the Periphyseon and, hence, of the five parts of his system. 2. The fourfold division of Nature is to be interpreted not as a basic structure of the system offered by Eriugena, but as a means of introducing dialectic to the body of theology by refuting Augustine’s metaphysical vision of a hierarchical model of the universe and indicating the way of resolution of the cardinally theological contradiction – God does and does not create at the same time. 3. All this gives reason to disagree with a general tendency of associating Eriugena’s work with exploration of the division of God’s Nature and to reinterpret it as an immense anti-division project to be understood as an important turn in the history of Christian thought entirely focused on the truth of God’s Oneness and human life in conformity to it. *** I affirm that this thesis is entirely my own work and has not been submitted for examination in any form elsewhere. (shrink)

All accounts of language acquisition agree that, by around age 4, children’s knowledge of grammatical constructions is abstract, rather than tied solely to individual lexical items. The aim of the present research was to investigate, focusing on the passive, whether children’s and adults’ performance is additionally semantically constrained, varying according to the distance between the semantics of the verb and those of the construction. In a forced‐choice pointing study (Experiment 1), both 4‐ to 6‐year olds (N = 60) and adults (...) (N = 60) showed support for the prediction of this semantic construction prototype account of an interaction such that the observed disadvantage for passives as compared to actives (i.e., fewer correct points/longer reaction time) was greater for experiencer‐theme verbs than for agent‐patient and theme‐experiencer verbs (e.g., Bob was seen/hit/frightened by Wendy). Similarly, in a production/priming study (Experiment 2), both 4‐ to 6‐year olds (N = 60) and adults (N = 60) produced fewer passives for experiencer‐theme verbs than for agent‐patient/theme‐experiencer verbs. We conclude that these findings are difficult to explain under accounts based on the notion of A(rgument) movement or of a monostratal, semantics‐free, level of syntax, and instead necessitate some form of semantic construction prototype account. (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

With Fermat’s Last Theorem finally disposed of by Andrew Wiles in 1994, it’s only natural that popular attention should turn to arguably the most outstanding unsolved problem in mathematics: the Riemann Hypothesis. Unlike Fermat’s Last Theorem, however, the Riemann Hypothesis requires quite a bit of mathematical background to even understand what it says. And of course both require a great deal of background in order to understand their significance. The Riemann Hypothesis was first articulated by Bernhard Riemann in an address (...) to the Berlin Academy in 1859. The address was called “On the Number of Prime Numbers Less Than a Given Quantity” and among the many interesting results and methods contained in that paper was Riemann’s famous hypothesis: all non-trivial zeros of the zeta function, ζ(s) = ∞ n=1 n−s, have real part 1/2. Although the zeta function as stated and considered as a real-valued function is defined only for s > 1, it can be suitably extended. It can, as a matter of fact, be extended to have as its domain all the complex numbers (numbers of the form x + yi, where x and y √ −1) with the exception of 1 + 0i (at which point are real numbers and i =. (shrink)

In this paper we define n+1-valued matrix logic Kn+1 whose class of tautologies is non-empty iff n is a prime number. This result amounts to a new definition of a prime number. We prove that if n is prime, then the functional properties of Kn+1 are the same as those of ukasiewicz's n +1-valued matrix logic n+1. In an indirect way, the proof we provide reflects the complexity of the distribution of prime numbers in the natural series. Further, we introduce (...) a generalization K n+1 * of Kn+1 such that the set of tautologies of Kn+1 is not empty iff n is of the form p , where p is prime and is natural. Also in this case we prove the equivalence of functional properties of the introduced logic and those of n+1. In the concluding part, we discuss briefly a partition of the natural series into equivalence classes such that each class contains exactly one prime number. We conjecture that for each prime number the corresponding equivalence class is finite. (shrink)

Over the past 50 years, rock music has been the prime mover of an emergent national recording industry in Australia. This is a story in turn of increasing size, complexity, diversity, and sophistication, before its ultimate decline into the 21st century. This story has not been told in full previously and this article is a first step to make good this gap in the historical and cultural sociology of popular music. In this study, which has two parts, we survey record (...) labels, recording techniques and forms, and the music that was bought and sold. In Part One we chronicled the emergence of modern record production, the rise of rock music, and the development of a local recording industry in Australia between 1945 and 1970. In Part Two we narrate the rise and fall of Australian local, regional and national rock music cultures and the ebb and flow of independent labels and their labyrinthine relations to the transatlantic centre of the world-system of rock music industry. In particular we focus on four aspects: 1) technological change: the dominance of the vinyl album in the 1970s but its eventual usurpation by cassettes and then compact discs before the ultimate decline of all formats in the rise of the internet and the i-pod; 2) infrastructure: the development of the recording industry as a system of recording studios and record factories; as a system of impresarios and musician management; and also as a system that integrates performance circuits, radio, television, film, and eventually computer, product placement, advertising, and promotion through the cultivation and manipulation of taste markets in consumer culture etc.; 3) business logistics and markets: the tracking of the record labels, their struggles for markets and copyright control, local and global; and 4) musical production and repertoire. Since the digital revolution started eating away firstly and most conspicuously at the recording industry, the 50 years from 1945 to 1995 can now more clearly be seen as the rise and fall of rock music and its major technological form, the vinyl record. This is why we call it ‘the vinyl age’. (shrink)

We say that a ring admits elimination of quantifiers, if in the language of rings, {0, 1, +, ·}, the complete theory of R admits elimination of quantifiers. Theorem 1. Let D be a division ring. Then D admits elimination of quantifiers if and only if D is an algebraically closed or finite field. A ring is prime if it satisfies the sentence: ∀ x ∀ y ∃ z (x = 0 ∨ y = 0 ∨ xzy ≠ 0). Theorem (...) 2. If R is a prime ring with an infinite center and R admits elimination of quantifiers, then R is an algebraically closed field. Let A be the class of finite fields. Let B be the class of 2 × 2 matrix rings over a field with a prime number of elements. Let C be the class of rings of the form $GF(p^n) \bigoplus GF(p^k)$ such that either n = k or g.c.d. (n, k) = 1. Let D be the set of ordered pairs (f, Q) where Q is a finite set of primes and f: Q → A ∪ B ∪ C such that the characteristic of the ring f(q) is q. Finally, let E be the class of rings of the form $\bigoplus_{q \in Q}f(q)$ for some (f, Q) in D. Theorem 3. Let R be a finite ring without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R belongs to E. Theorem 4. Let R be a ring with the descending chain condition of left ideals and without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R is an algebraically closed field or R belongs to E. In contrast to Theorems 2 and 4, we have Theorem 5. If R is an atomless p-ring, then R is finite, commutative, has no nonzero trivial ideals and admits elimination of quantifiers, but is not prime and does not have the descending chain condition. We also generalize Theorems 1, 2 and 4 to alternative rings. (shrink)

A Liouville function is an analytic function $H : C \rightarrow C$ with a Taylor series $\Sigma_{n=1}^\infty x^n/a_n$ such the $a_n\prime s$ form a "very fast growing" sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H.

In lieu of an abstract, here is a brief excerpt of the content:THE STATUS AND FUNCTION OF DIVINE SIMPLENESS IN SUMMA THEOLOGIAE Ia, qq. 2-13 PETER BURNS, S.J. l esuit School of Theology Berkeley, California Introduction I N THE FIRST PART of what follows I hope to do four things: a) to give a brief summary of Aquinas's remarks contained in the third question of the first part of the Summa Theologiae, entitled de Dei simplicitate; b) to outline two diferent (...) ways of interpreting what Aquinas is about when making those remarks; c) to assess which interpretation is better from an exegetical standpoint; d) to assess which interpretation is better from a philosophical standpoint. In the second part my aim will be threefold : a) to trace the way Aquinas derives and uses the concept of divine simpleness in questions 2 through 11 ; b) to examine briefly the relationship between this concept and possible cosmological arguments for the existence of God; and c) to evaluate critically some modern treatments of arguments of the cosmological type in the light of this relationship. I shall not be concerned to show that Aquinas's conclusions in question 2 (the Five Ways) are justified by the arguments he adduces; rather, my concern will be to show that an adequate evaluation of his arguments cannot ignore the function of divine simpleness as a key element therein. I. The Status Of Divinle Simpleness (1) A Summary of S.T. la, 3 At the beginning of question 3 Aquinas lists eight points of inquiry. The first is whether God is a body, that is, composed 1 2 PETER BURNS, S.J. of extended parts. He offers three reasons why he thinks the reply must be negative. Firstly, an unchanging first cause of change, which God is (by la, 2, 3) would appear not to be bodily, since experience offers no examples of bodies causing change without themselves changing. Secondly, to be extended in space implies the potentiality of being divisible, but a primary reality is utterly actual, since absolutely speaking, actuality precedes po~ tentiality, and God is the primary reality. Thirdly, since the soul is nobler than inanimate things, and God is the most excellent of beings, God cannot be any less noble than the soul. But the soul in itself is not bodily but that in virtue of which bodies are what they are. In the next article Aquinas denies that God is composed of matter and form because matter is potential and only exists by participating in some form. In addition, since agents act in virtue of their form, God, as the prime source of activity and being in no way potential, must be considered as being essentially form without composition with matter, Aquinas then asks whether God can be identified with his own essence or nature. Given that matter is the individuating factor in beings composed of matter and form, and that such composition is ruled out in case of God, Aquinas claims that the distinctness of his being must be due to form. Hence God is his own form or nature or essence. In a crucial move in the next article Aquinas identifies God, who is his essence, with his existence, for as an uncaused necessary reality this essence must be self-subsistent. Thus God's nature or essence is necessarily self-instantiating, nor does God participate in existence, but essentially is identical with (the act of) 'existing', Therefore the distinction between essence and existence, between what something is and that it is, does not hold for God. Having daimed that God is his own existence, Aquinas argues that this existence is prior to genus in general and to the genus of substance specifically. So there is no possibility of distinguishing in God genus and difference, nor can God receive predicates as a substance, since this would imply potentiality. Therefore God is DIVINE SIMPLENESS IN SUMMA THEOLOGIAE 3 not composed of substance and accidents. In article 7, Aquinas claims that God is altogether simple. After summing up the previous remarks he makes two general points. Everything composite is subsequent to and dependent on its components, whereas God is the first, uncaused necessary being. Secondly, everything composite is caused, for essentially diverse elements must... (shrink)

Augustin-Louis Cauchy publie une majorité de ses recherches arithmétiques entre 1829 et 1840. Celles-ci ne sont pourtant qu’évoquées dans certaines histoires de la théorie des nombres centrées sur les lois de réciprocité ou sur la théorie des nombres algébriques. Elles y sont décrites comme contenant quelques résultats similaires à ceux de Gauss, Jacobi ou Dirichlet mais de manière incomplète et désordonnée. L’objectif de cet article est de présenter une analyse des textes arithmétiques de Cauchy publiés entre 1829 et 1840 pour (...) montrer qu’ils contiennent au contraire un ensemble cohérent de résultats en lien avec les formes quadratiques \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4p^{\mu }=x^2+ny^2$$\end{document}, où \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} est un nombre premier et \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} un diviseur de \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p-1$$\end{document}. Nous discuterons également la forme particulière de ce corpus et la stratégie utilisée pour retrouver les lignes directrices du travail de Cauchy. Augustin-Louis Cauchy published most of his arithmetical research between 1829 and 1840. These are however only mentioned in some number theory history centered on reciprocity laws or on theory of algebraic numbers. They are described as containing some results similar to those of Gauss, Jacobi and Dirichlet but in a incomplete and disorganized way. The objective of this paper is to present an analysis of Cauchy’s arithmetical texts published between 1829 and 1840 to show that they contain a rather consistent set of results related to quadratic forms \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4p^{\mu } = x ^2 + ny ^2 $$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} is a prime and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} a divisor of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p-1 $$\end{document}. We will also discuss the particular form of this body of texts and the strategy we used to find the guidelines of the work of Cauchy. (shrink)

continent. 1.3 (2011): 149-155. The world is teeming. Anything can happen. John Cage, “Silence” 1 Autonomy means that although something is part of something else, or related to it in some way, it has its own “law” or “tendency” (Greek, nomos ). In their book on life sciences, Medawar and Medawar state, “Organs and tissues…are composed of cells which…have a high measure of autonomy.”2 Autonomy also has ethical and political valences. De Grazia writes, “In Kant's enormously influential moral philosophy, autonomy (...) , or freedom from the causal determinism of nature, became prominent in justifying the human use of animals.”3 One of the oldest uses of autonomy in English is a description of the French civil war from the late sixteenth century: “Others of the…rebellion entred in counsell, whether they ought to admit the King vpon reasonable conditions, specially hauing their autonomy.”4 Life, and in particular human life, and in particular human politics, is well served by the usages of autonomy . What about the rest of reality, however? Should it be thought of, if it's even considered real and mind-independent, as pure stuff for the manipulation or decorative tastes of truly autonomous beings? We tend to think of things such as paperweights and iPhones as mere tools of human design and human use. To use them is to cause them to exist as fully and properly as they can. But according to Martin Heidegger, when a tool such as a paperweight is used, it disappears, or withdraws ( Entzug ). We are preoccupied with copying the page that the paperweight is holding down. We are concerned with an essay deadline, and the paperweight simply disappears into this general project. If the paperweight slips, or if the iPhone freezes, we might notice it. All of a sudden it becomes vorhanden (present-at-hand) rather than zuhanden (ready-to-hand).5 Yet Heidegger is unable to draw a meaningful distinction between what happens to a paperweight when it slips from the book I'm copying from and what happens to the paperweight when it presses on the still resilient pages of the thick paperback itself. Further still and related to this point, even when I am using the paperweight as part of some general task, I am not using the entirety of the paperweight as such. My project itself selects a thin slice of paperweight-being for the purposes of holding down a book. Even when it is zuhanden the paperweight is withdrawn. Graham Harman is the architect of this way of thinking.6 Harman discovered a gigantic coral reef of withdrawn entities beneath the Heideggerian submarine of Da-sein, which itself is operating at an ontological depth way below the choppy surface of philosophy, beset by the winds of epistemology, and infested with the sharks of materialism, idealism, empiricism and most of the other isms that have defined what is and what isn't for the last several hundred years. At a moment when the term ontology was left alone like a piece of well chewed old chewing gum that no one wants to have anything to do with, object-oriented ontology (OOO) has put it back on the table. The coral reef isn't going anywhere and once you have discovered it, you can't un-discover it. And it seems to be teeming with strange facts. The first fact is that the entities in the reef—we call them “objects” somewhat provocatively—constitute all there is: from doughnuts to dogfish to the Dog Star to Dobermans to Snoop Dogg. People, plastic clothes pegs, piranhas and particles are all objects. And they are all pretty much the same, at this depth. There is not much of a distinction between life and non-life (as there isn't in contemporary life science). And there is not much of a distinction between intelligence and non-intelligence (as there is in contemporary artificial intelligence theory). A lot of these distinctions are made by humans, for humans (anthropocentrism). And the concept autonomy has come into play in policing such distinctions. In this essay I shall to try to liberate autonomy for the sake of nonhumans. I shall do so by parsing carefully the title, which is taken from Hakim Bey's work The Temporary Autonomous Zone .8 First we shall explore the term autonomous . Then we shall explore what the full meaning of zone is. Finally, we shall investigate what temporary means. Each of these terms is of great value. An object withdraws from access. This means that its very own parts can't access it. Since an object's parts can't fully express the object, the object is not reducible to its parts. OOO is anti-reductionist. But OOO is also anti-holist. An object can't be reduced to its “whole” either, “reduced upwards” as it were. The whole is not greater than the sum of its parts. So we have a strange irreductionist situation in which an object is reducible neither to its parts nor to its whole. A coral reef is made of coral, fish, seaweed, plankton and so on. But one of these things on its own doesn't embody part of a reef. Yet the reef just is an assemblage of these particular parts. You can't find a coral reef in a parking lot. In this way, the vibrant realness of a reef is kept safe both from its parts and from its whole. Moreover, the reef is safe from being mistaken for a parking lot. Objects can't be reduced to tiny Lego bricks such as atoms that can be reused in other things. Nor can be reduced upwards into instantiations of a global process. A coral reef is an expression of the biosphere or of evolution, yes; but so is this sentence, and we ought to be able to distinguish between coral reefs and sentences in English. The preceding facts go under the heading of undermining . Any attempt to undermine an object—in thought, or with a gun, or with heat, or with the ravages of time or global warming—will not get at the withdrawn essence of the object. By essence is meant something very different from essentialism . This is because essentialism depends upon some aspect of an object that OOO holds to be a mere appearance of that object, an appearance-for some object. This reduction to appearance holds even if that object for which the appearance occurs is the object itself! Even a coral reef can't grasp its essential coral reefness. In essentialism, a superficial appearance is taken for the essence of a thing, or of things in general. In thinking essentialism we may be able to discern another way of avoiding OOO. This is what Harman has christened overmining .? The overminer decides that some things are more real than others: say for example human perception. Then the overminer decides that other things are only granted realness status by somehow coming into the purview of the more real entity. When I measure a photon, when I see a coral reef, it becomes what it is. But when I measure a photon, I never measure the actual photon. Indeed, since at the quantum scale to measure means “to hit with a photon or an electron beam” (or whatever), measurement, perception ( aisthesis ), and doing become the same. What I “see” are deflections, tracks in a diffusion cloud chamber or interference patterns. Far from underwriting a world of pure illusion where the mind is king, quantum theory is one of the very first truly rigorous realisms, thinking its objects as irreducibly resistant to full comprehension, by anything.9 So far we have made objects safe from being swallowed up by larger objects and broken down into smaller objects—undermining. And so far we have made objects safe from being mere projections or reflections of some supervenient entity—overmining. That's quite a degree of autonomy. Everything in the coral reef, from the fish to a single coral lifeform to a tiny plankton, is autonomous. But so is the coral reef itself. So are the heads of the coral, a community of tiny polyps. So is each individual head. Each object is like one of Leibniz's monads, in that each one contains a potentially infinite regress of other objects; and around each object, there is a potentially infinite progress of objects, as numerous multiverse theories are now also arguing. But the infinity, the uncountability, is more radical than Leibniz, since there is nothing stopping a group of objects from being an object, just as a coral reef is something like a society of corals. Each object is “a little world made cunningly” (John Donne).10 We are indeed approaching something like the political valance of autonomy . The existence of an object is irreducibly a matter of coexistence. Objects contain other objects, and are contained “in” other objects. Let us, however, explore further the ramifications of the autonomy of objects. We will see that this mereological approach (based on the study of parts) only gets at part of the astonishing autonomy of things. Yet there are some more things to be said about mereology before we move on. Consider the fact that since objects can't be undermined or overmined, it means that there is strictly no bottom object . There is no object to which all other objects can be reduced, so that we can say everything we want to say about them, hypothetically at least, based on the behavior of the bottom object. The idea that we could is roughly E.O Wilson's theory of consilience .11 Likewise, there is no object from which all things can be produced, no top object . Objects are not emanations from some primordial One or from a prime mover. There might be a god, or gods. Suppose there were. In an OOO universe even a god would not know the essential ins and outs of a piece of coral. Unlike even some forms of atheism, the existence of god (or nonexistence) doesn't matter very much for OOO. If you really want to be an atheist, you might consider giving OOO a spin. If there is no top object and no bottom object, neither is there a middle object . That is, there is no such thing as a space, or time, “in” which objects float. There is no environment distinct from objects. There is no Nature (I capitalize the word to reinforce a sense of its deceptive artificiality). There is no world, if by world we mean a kind of “rope” that connects things together.12 All such connections must be emergent properties of objects themselves. And this of course is well in line with post-Einsteinian physics, in which spacetime just is the product of objects, and which may even be an emergent property of a certain scale of object larger than 10?¹?cm).13 Objects don't sit in a box of space or time. It's the other way around: space and time emanate from objects. How does this happen? OOO tries to produce an explanation from objects themselves. Indeed, the ideal situation would be to rely on just one single object. Otherwise we are stuck with a reality in which objects require other entities to function, which would result in some kind of undermining or overmining. We shall see that we have all the fuel we need “inside” one object to have time and space, and even causality. We shall discover that rather than being some kind of machinery or operating system that underlies objects, causality itself is a phenomenon that floats ontologically “in front of” them. In so doing, we will move from the notion of autonomy and begin approaching a full exploration of the notion of zone , which was promised at the outset of this essay. Since an object is withdrawn, even “from itself,” it is a self-contradictory being. It is itself and not-itself, or in a slightly more expanded version, there is a rift between essence and appearance within an object (as well as “between” them). This rift can't be the same as the clichéd split between substance and accidents , which is the default ontology. On this view, things are like somewhat boring cupcakes with somewhat less boring sugar sprinkles on them of different colors and shapes. But on the OOO view, what is called substance is just another limited slice of an object, a way of apprehending something that is ontologically fathoms deeper. What is called substance and what is called accidence are just on the side of what this essay calls appearance. The rift (Greek, chorismos ) between essence and appearance means that an object presents us with something like what in logic is known as the Liar: some version of the sentence “This sentence is false.” The sentence is true, which means that it is a lie, which means that it is false. Or the sentence is false, which means that it is telling the truth, which means that it is true. Now logic since Aristotle has tried desperately to quarantine such beasts in small backwaters and side streets so that they don't act too provocatively.14 But if OOO holds, then at least one very significant thing in the universe is both itself and not-itself: the object. An object is p ? ¬p. To cope with this fact, we shall need some kind of paraconsistent or even fully dialetheic logic, one that is not allergic to dialetheias (double-truthed things). Yet if we accept that objects are dialetheic, p ? ¬p, we can derive all kinds of things easily from objects. Consider the fact of motion. If objects only occupy one location “in” space at any “one” time, then Zeno's paradoxes will apply to trying to think how an object moves. Yet motion seems like a basic, simple fact of our world. Either everything is just an illusion and nothing really moves at all (Parmenides). Or objects are here and not-here “at the same time.”15 This latter possibility provides the basic setup for all the motion we could wish for. Objects are not “in” time and space. Rather, they “time” (a verb) and “space.” They produce time and space. It would be better to think these verbs as intransitive rather than transitive, in the manner of dance or revolt . They emanate from objects, yet they are not the object. “How can we know the dancer from the dance?” (Yeats).16 The point being, that for there to be a question, there must be a distinction—or there must not be (p ? ¬p).17 It becomes impossible to tell: “What constitutes pretense is that, in the end, you don't know whether it's pretense or not.”18 In this notion of the emergence of time and space from an object we can begin to understand the term zone . Zone can mean belt , something that winds around something else. We talk of temperate zones and war zones. A zone is a place where a certain action is taking place: the zone winds around, it radiates heat, bullets fly, armies are defeated. To speak of an autonomous zone is to speak of a place that a certain political act has carved out of some other entity. Cynically, Tibet is called TAR, the Tibetan Autonomous Region, for this very reason. In this phrase, Region tries to emulate zone : it sounds as if the place has its own rules, but of course, it is very much under the control of China. What action is taking place? “[N]ot something that just is what it is, here and now, without mystery, but something like a quest…a tone on its way calling forth echoes and responses…water seeking its liquidity in the sunlight rippling across the cypresses in the back of the garden.”19 If as suggested earlier there is no functional difference between substance and accidence; if there is no difference between perceiving and doing; if there is no real difference between sentience and non-sentience—then causality itself is a strange, ultimately nonlocal aesthetic phenomenon. A phenomenon, moreover, that emanates from objects themselves, wavering in front of them like the astonishingly beautiful real illusion conjured in this quotation of Alphonso Lingis. Lingis's sentence does what it says, casting a compelling, mysterious spell, the spell of causality, like a demonic force field. A real illusion: if we knew it was an illusion, if it were just an illusion, it would cease to waver. It would not be an illusion at all. We would be in the real of noncontradiction. Since it is like an illusion, we can never be sure: “What constitutes pretense…” A zone is what Lingis calls a level . A zone is not entirely a matter of “free will”: this concept has already beaten down most objects into abject submission. Objects are far more threateningly autonomous, and sensually autonomous, than the Kantian version of autonomy cited in the first paragraph of this essay. A zone is not studiously decided upon by an earnest committee before it goes into action. One of its predominant features is that it is already happening . We find ourselves in it, all of a sudden, in the late afternoon as the shadows lengthen around a city square, giving rise to an uncanny sensation of having been here before. Objects emit zones. Wherever I find myself a zone is already happening, an autonomous zone. It is the nonautonomous zones that are impositions on what is already the case. Or rather, these zones are autonomous zones that exclude and police. They are brittle. Every object is autonomous, but some objects try to maintain themselves through rigidity and brittleness, like (and such as) a police state. Paradoxically, the more rigidly one tries to exclude contradiction, the more virulent become the dialetheias that are possible. I can get around “This sentence is false” by imagining that there are metalanguages that explain what counts as a sentence. Then I can decide that this isn't a real sentence. This is basically Alfred Tarski's strategy, since he invented the notion of metalanguage specifically to cope with dialetheias.20 For example we might claim that sentences such as “This sentence is false” are neither true nor false. But then you can imagine a strengthened version of the Liar such as: “This sentence is not true”; or “This sentence is neither true nor false.” And we can go on adding to the strengthened Liar if the counter-attack tries to build immunity by specifying some fourth thing that a sentence can be besides true, false, and neither true nor false: “This sentence is false, or neither true nor false, or the fourth thing.” And so on.21 It seems as if language becomes more brittle the more it tries to police the Liars of this world. Why? I believe that this increasing brittleness is a symptom of a deep fact about reality. What is this deep fact? Simply that there are objects, that these objects are withdrawn, and that they are walking contradictions. This means indeed that (as Lacan put it) “there is no metalanguage,” since a metalanguage would function as a “middle object” that gave coherency and evenness to the others.22 Since there is no metalanguage, there is no rising above the disturbing illusory play of causality. This may even have political implications: no global critique is therefore possible, and attempts to smooth out or totalize are doomed to fail. To think the zone is to think the notion of temporary , which we shall now begin to discuss in greater detail. The zone is not in time: rather it “times.” But because a zone is an emanation of an object, it is based on a wavering fragility, since objects are p ? ¬p. When an object is born, that means that it has broken free of some other object. An object can be born because it and other objects are fragile. If not, no movement would be possible. Objects contain the seeds of their own destruction, a dialetheic sentence that says something like “This sentence cannot be proved.” Kurt Gödel argues that every true system of propositions contains at least one sentence that the system cannot prove. In order to be true, the system must have a minimum incoherence. To be real, it has to be fragile. Imagine a record player. Now imagine a record called I Cannot Be Played on This Record Player . When you play it on this record player, it produces sympathetic vibrations that cause the record player to shudder apart. No matter how many defense mechanisms you build in, there will always be the possibility of at least one record that destroys the record player.23 That is what being physical is. An object is inherently fragile because it is both itself and not-itself. When the rift between appearance and essence collapses, that is called destruction, ending, death. When an object breaks, several new objects are born. An opera singer sings a loud note in tune with the resonant frequency of a wine glass. (See the movie included below.) The singing is a zone, an autonomous level of intensity, opening a rift between appearance and essence. The glass ripples—for a moment it is nakedly a glass and a not-glass—almost as if it were having an orgasm, a little death. It is caught in the rift of the singing. Then its structure can't handle the coherence of the sound waves, and it breaks. It is incoherence and inconsistency that is the mark of existence, not consistency and noncontradiction. When things break or die, they become coherent. Essence disappears into appearance. I become the memories of friends. A glass becomes a dancing wave. Instantly, there are glass fragments, new temporary autonomous zones. The fragments have broken free from the glass. They are no longer its parts, but emanate their own time and space, becoming perhaps accidental weapons as they bury themselves in my flesh. Thus Hakim Bey's instructions on creating temporary autonomous zones oscillate disturbingly between performance art and politics, circus clowning and revolution. To play with the aesthetic is to play with causality, to rip from the sensual ether emanating from things new regions, new zones. Anarchist politics is the creation of fresh objects in a reality without a top or a bottom object, or for that matter a middle object: Everything in nature is perfectly real including consciousness, there's absolutely nothing to worry about. Not only have the chains of the Law been broken, they never existed; demons never guarded the stars, the Empire never got started, Eros never grew a beard. … There is no becoming, no revolution, no struggle, no path; already you're the monarch of your own skin—your inviolable freedom waits to be completed only by the love of other monarchs: a politics of dream, urgent as the blueness of sky.24 Bey imagines that this is because chaos is a primordial “undifferentiated oneness-of-being.” A Parmenides or a Spinoza or a Laruelle would read this a certain way. Individual objects, or decisions to talk about this rather than that, are just maggot-like things crawling around on the surface of the giant cheese of oneness.25 Yet he also describes chaos as “Primordial uncarved block, sole worshipful monster, inert & spontaneous, more ultraviolet than any mythology.” This image is of an inconsistent object, not of an undifferentiated field. An object, indeed, that can be distinguished from other things. If not, then the first part of The Temporary Autonomous Zone , subtitled “The Broadsheets of Ontological Anarchism,” is a kind of onto-theology. Onto-theology proclaims that some things are more real than others. Bey, however, is writing poetically, and thus ambiguously. We are at liberty to read “undifferentiated oneness-of-being” as something like the irreducibility of a thing to its parts and so forth (undermining and overmining). This certainly seems closer to the language in the following paragraph: “There is no becoming … already you're the monarch of your own skin.”26 On this view, there is no difference between art and politics: “When ugliness, poor design & stupid waste are forced upon you, turn Luddite, throw your shoe in the works, retaliate.” Since Romanticism this has been the war cry of the vanguard artist.27 To say to is to fall prey to the tired axioms of the avant-garde, and we think we know how the game goes. But OOO is not simply a way to advocate “new and improved” versions of this shock-the-bourgeoisie boredom. Bey's text is certainly full enough of that. Rather, since causality as such is aesthetic, and since nonhumans are not that different from humans, the new approach would be to form aesthetic–causal alliances with nonhumans. These alliances would have to resist becoming brittle, whether that brittleness is right wing (authoritarianism) or left wing (the endless maze of critique). No “ism,” especially not the ultimate forms, nihilism and cynicism, is in any sense effective at this point. All forms of brittleness are based on the mistaken assumption that there is a metalanguage and that therefore “Anything you can do, I can do meta.” I will not be listing any approaches here, as Bey does. Such lists and manifestos belong to the vanguardism that no longer works. Why? Not because of some marvelous revolution in human consciousness, but because nonhumans have so successfully impinged upon human social, psychic and aesthetic space. It is the time after the end of the world. That happened in 1945, when a thin layer of radioactive materials was deposited in Earth's crust. Geology now calls it this era the Anthropocene . Ironically, this period, named after humans, is the moment at which even the most thick headed of us make decisive contact with nonhumans, from mercury in our blood to manta rays to magnesium. Richard Dawkins, Pat Robertson and Lady Gaga all have to deal with global warming and mass extinction, somehow. We now live in an Age of Asymmetry marked by a skewed, spiraling relationship between vast knowledge and vast nonhuman things—both become vaster and vaster because of one another and for the same reasons.28 This means that coming up with the perfect attitude or the perfect aesthetic prescription just won't work any more. Even the most hardened anthropocentrist now has to pay through the nose for basic food supplies, and has to use more sunscreen. Whether he knows it or acknowledges it, he is already acting with regard towards nonhumans. There is nothing special to think, no special critique that will get rid of the stains of coexistence. The problem won't fit into the well-established modern boxes, which is why the “mystical,” “spiritual” quality of Bey's prose is welcome. Of course, when I put it this way, you may immediately close off and decide that I am talking about perfect attitudes after all, or something outside of politics, or other ways that the radical left marshals to police its thinking of the nonhuman. Because that is what is really at stake in all this: the nonhuman in its coexistence with the human—bosons, gods, clouds, spirits, lifeforms, experiences, the sunlight rippling across the cypresses. Bey begins to get at this in a Latour litany in the second part of The Temporary Autonomous Zone , “The Assassins”: Pomegranate, mulberry, persimmon, the erotic melancholy of cypresses, membrane-pink shirazi roses, braziers of meccan aloes & benzoin, stiff shafts of ottoman tulips, carpets spread like make-believe gardens on actual lawns—a pavilion set with a mosaic of calligrammes—a willow, a stream with watercress—a fountain crystalled underneath with geometry— the metaphysical scandal of bathing odalisques, of wet brown cupbearers hide-&-seeking in the foliage—“water, greenery, beautiful faces.”29 This will be conveniently dismissed as orientalism. If we're never allowed to escape the crumbling prison of modernity for fear of imperialism there is truly no hope. In a similar way, the fear of anthropocentrism and anthropomorphism is very often staged from a place that just is anthropocentrism .30 Critique turns into ressentiment . An object radiates a zone that is aesthetic and therefore causal. Because objects “time” they are temporary. Not because they exist “in” time that eventually gets the better of them. Their very existence implies the possibility of their non-existence. Since objects are not consistent, they can cease to exist. But nothing, no one, will ever be able to insert a blade between appearance and existence, even thought there is a rift there. Now that's what I call autonomy. NOTES 1. John Cage, Silence: Lectures and Writings (Middletown, CT: Wesleyan University Press, 1973), 96. 2. P. B. Medawar and J. S. Medawar, The Life Science: Current Ideas in Biology (London: Wildwood House, 1977), 8. 3. David DeGrazia, Animal Rights: A Very Short Introduction (Oxford: Oxford University Press, 2002), 5. 4. Antony Colynet, A True History of the Civil Warres in France (London, 1591), 480. 5. Martin Heidegger, Being and Time , tr. Joan Stambaugh (Albany, N.Y: State University of New York Press, 1996) 62–71. 6. Graham Harman, Tool-Being: Heidegger and the Metaphysics of Objects (Peru, IL: Open Court, 2002). 7. Hakim Bey, The Temporary Autonomous Zone (Brooklyn: Autonomedia, 1991). 8. Graham Harman, The Quadruple Object (Ripley: Zero Books, 2011), 7–18. 9. This is not the place to get into an argument about quantum theory, but I have argued that quanta also do not endorse a world that I can't speak about because it is only real when measured. This world is that of the reigning Standard Model proposed by Niels Bohr and challenged by De Broglie and Bohm (and now the cosmologist Valentini, among others). See Timothy Morton, “Here Comes Everything: The Promise of Object-Oriented Ontology,” Qui Parle 19.2 (Spring–Summer, 2011), 163–190. 10. John Donne, Holy Sonnets 15, in The Major Works: Including Songs and Sonnets and Sermons , ed. John Carey (Oxford: Oxford University Press, 2009). 11. Edward O. Wilson, Consilience: The Unity of Knowledge (New York: Knopf, 1998). 12. Martin Heidegger, What Is a Thing? (Washington: Regnery, 1968), 243. 13. Albert Einstein, Relativity: The Special and the General Theory (London: Penguin, 2006); Petr Horava, “Quantum Gravity at a Lifshitz Point,” arXiv:0901.3775v2 [hep-th]. 14. Graham Priest, In Contradiction (Oxford University Press, 2006), passim: the most notable recent quarantine officers have been Tarski, Russell, and Frege. 15. Priest, In Contradiction , 172–181. 16. William Butler Yeats, “Among School Children,” Collected Poems , ed. Richard J. Finneran (New York: Scribner, 1996). 17. Paul de Man, “Semiology and Rhetoric,” Diacritics 3.3 (Autumn, 1973), 27–33 (30). 18. Jacques Lacan, Le seminaire, Livre III: Les psychoses (Paris: Editions de Seuil, 1981), 48. See Slavoj Zizek, The Parallax View (Cambridge, Mass.: MIT Press, 2006), 206. 19. Alphonso Lingis, The Imperative (Bloomington: Indiana University Press, 1998), 29. 20. Priest, In Contradiction , 9–27. 21. See Graham Priest and Francesco Berto, “ Dialetheism ,” The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), ed. Edward N. Zalta. 22. Jacques Lacan, Écrits: A Selection , tr. Alan Sheridan (London: Tavistock, 1977), 311. 23. The analogy can be found at length in Douglas Hofstadter, “Contracrostipunctus,” Gödel, Escher, Bach: An Eternal Golden Braid (New York: Basic Books, 1999), 75–81. 24. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 25. This is closest to the language of François Laruelle in Philosophies of Difference: A Critical Introduction to Non-Philosophy (New York: Continuum, 2011) 179. 26. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 27. Peter Bürger, Theory of the Avant Garde (Minneapolis: University of Minnesota Press, 1984). 28. For further discussion see Timothy Morton, “From Modernity to the Anthropocene: Ecology and Art in the Age of Asymmetry,” The International Social Science Journal 209 (forthcoming). 29. Bey, “ The Assassins ,” Temporary Autonomous Zone . 30. Timothy Morton, The Ecological Thought (Cambridge, Mass.: Harvard University Press, 2010), 75–76. (shrink)

The coterie of commentators represented in the present volume include some of the clearest voices for Heidegger’s way of thinking among the second and third generations of American Heidegger scholars. Two of the contributors, who are also the volume’s editors, have just published a new translation of Einführung in die Metaphysik, an event that would appear to be one of the reasons for the project published here. Its thirteen essays are organized under three headings: the question of being, Heidegger and (...) the Greeks, and Politics and Ethics. The first part begins with Thomas Sheehan’s “prolegomenon to a fresh reading of Introduction to Metaphysics ” from the perspective of Heidegger’s later ruminations on Ereignis, “what brings about being,” that is “the opening of a clearing in which entities can appear as this or that”. Professor Sheehan’s discussion is both comprehensive of Heidegger’s major concepts and comprehensible to the beginning student. For specialists, the essay challenges the standing interpretation of one of the recurring topics in Heidegger scholarship, the so-called Kehre in which his way of thinking is said to have been implicated. According to Charles Guignon, Introduction to Metaphysics “undertakes the task of recovering the earliest ways of understanding Being for the purpose of revitalizing our contemporary understanding” of Being. He distinguishes in Heidegger’s thinking an “event ontology” that contrasts with the “ substance ontology” of metaphysics in effect since the classic Greek philosophers. Professor Guignon’s comments focus on Heidegger’s understanding of the early Greek concept of phusis and “how such a notion is illuminating in trying to make sense of things that the substance ontology fails to make intelligible”. He observes that history “provides a prime example of an entity whose Being is that of phusis”. Such an interpretation of phusis is in striking contrast to the standard understanding of phusis as physical nature. Later, in part 2, Susan Schoenbohm continues the discussion of Heidegger’s interpretation of phusis, noting that, according to Heidegger, in its fundamental sense, phusis does not mean nature but rather “the emerging, for the fist time, of something out of no determination at all.” It is “a name for the emerging of the originary difference of determination and no determination”, and, as such, must for certain reasons itself be “determinately ambiguous”. For Heidegger, she observes, phusis and Being are the same. Richard Polt, who is one of the volume’s editors, attempts “to lay the foundation for an adequate interpretation of Heidegger’s ‘Nothing’” in the context of the question brought into philosophical focus and prominence by Lebiniz: Why is there something instead of nothing? He notes that “the closest antecedents of Heidegger’s Nothing are to be found in nineteenth-century thought”, but that there are resonances of the topic as Heidegger treats it to be found in Eastern thought as well. In both traditions, “the question of Nothing forms part of the question of Being”, and that “precisely because Nothing is Being’s other, the question of Nothing is included in the question of Being”. Professor Polt points out the rich history of the notion of Nothing in Heidegger’s way of thinking. “We have found,” he writes, “that Heidegger uses ‘Nothing’ to refer to a wide variety of phenomena, including inauthenticity, uncanniness, death, guilt, meaninglessness, and the withdrawal of Be-ing”. He concludes that Heidegger’s Introduction to Metaphysics does not contain a “‘doctrine’ of Nothing,” but rather should be understood as “a voyage and a provocation, not a treatise”, adding that “Heidegger himself did not always view the text as a success”, which may account for why he chose not to publish it for nearly twenty years after first presenting it in public. Daniel Dahlstrom sees Heidegger’s text as “an introduction to the end of metaphysics and [the] beginning of a new way of thinking.” He suggests that Heidegger is in search of understanding “what it means to say that something is at all”. The author’s focus is on Heidegger’s interpretation of the sense of logos in pre-Socratic philosophy. Professor Dahlstrom examines what he terms the “logical prejudice” in Western philosophy as Heidegger construes it and attempts to show why, for Heidegger, such a way of understanding the relation between thinking and being “is understandable but not inevitable”, but, regrettably, “disables thinking about being”. According to the author, Heidegger discovers among the pre-Socratics an understanding of thinking that is “more rigorous and original than judgmental or propositional thinking”. On Dahlstrom’s assessment, Introduction to Metaphysics is, in fact, an introduction to logic. Part 1 of the Companion concludes with a refreshingly challenging analysis of “a complication in Heidegger’s theory of language and its consequences” for his way of thinking about being as a whole. In his text, Dieter Thomä sets out to “turn the tables and claim that shortcomings in both the early and late thinking of Heidegger can be pointed out by means of the Introduction to Metaphysics … in the respective conceptions of language”. He uses “an approach that takes Heideggerian arguments as incentives for a way of thinking that leads beyond him”. Focusing on the philosophical possibility of the declaration “I am,” that is “indexical being”, Professor Thomä discusses changes in Heidegger’s view of language from Being and Time to the Introduction, which he claims, by the way, “is not to be regarded as one of Heidegger’s strongest texts,” in particular “[i]n terms of systematic cohesion and unity”: “The tone of the book is uneven, changing among bold appeals, philological details, simple mistakes and bold arguments”. Thomä’s discussion of Heidegger’s concept of naming is respectful of and fully conversant with the texts, without, however, being reverential in tone, a feature that unaccountably has characterized so much Heidegger scholarship. (shrink)

Je lui ai associÉ un court extrait d'une revue de questions portant sur le même thème. Implicit memory is revealed when previous experiences facilitate perf on a task that does not require conscious or intentional recollection of those expces. Explicit memory is revealed when perf on a task requires conscious recolelction of previous expces. Il s'agit de defs descriptives qui n'impliquent pas l'existence de deux systs de mÉmo sÉparÉs. Historiquement Descartes est le premier ˆ faire mention de phÉnomènes de mÉmo (...) implicites, Leibniz, Maine de Biran, Bergson en ont Également parlÉ. Korsakoff (1889) avec ses travaux sur les amnÉsiques montre qu'ils sont capables d'utiliser de l'info qu'ils ont acquises dans des Épisodes rÉcents sans pour autant manifester le moindre souvenir de l'Épisode. L'interprÉtation de ces phÉnomènes Était alors que ça renvoyait ˆ des traces en mÉmoire trop tÉnues pour accèder jusqu'au champ de la conscience. Cette interprÉtation va pouvoir être ÉcartÉe par les travaux rÉcents. Thorndike a Également conduit un nbre important de travaux sur MI. Les trauvaux un peu plus rÉcents ont montrÉ qu'un apprentissage antÉrieur pouvait faciliter une perfce sans qu'il y ait ref explicite à l'Épisode d'apprentissage. On a montrÉ aussi l'effet de stimuli subliminaux, qui en tant que tels ne peuvent pas être rappelÉs consciemment, mais qui influencent la conduite ou les jugts ultÉrieurs. Par ex, la prÉsentation de formes sur des temps très courts qui excluent la possibilitÉ d'une perception consciente influence significativement lechoix de formes dans une pÉreuve ultÉrieure de choix forcÉs où les sjts doivent indiquer la forme qu'il prÉfère entre deux. Ils choisissent prÉfÉrentiellement celles qui leur ont ÉtÉ prÉsentÉes de manière subliminale. De même Bargh et al. ont montrÉ que des sjts soumis de manière subliminale ˆ des mots hostiles portent ultÉrieurement des jugts plus nÉgatifs sur une personne target. Il ya Également eu des travaux sur l'apprsge ou le condt without awareness en particulier apprsge implicite de règles de grammaire (ie le sjt peut construire de nouvelles phrases conformes ˆ la syntaxe de celles qui lui ont ÉtÉ prÉsentÉes sans pour autant petre capables d'noncer les règles de grammaire qu'il utilise) Rem: N'est ce pas un pbe de typemÉtacognition??? Enfin, tous les travaux sur le priming sont des elts en faveur de MI: Facilitation in the processing of a stimulus as a function of a recent encounter with the same stimulus. Type de perfce sur lesquels les effets de priming ont ÉtÉ dÉmontrÉs: -T‰ches de dÉcision lexicale: Le sjt doit dire si la cha"ne de caractères qu'on lui prÉsente est un mot ou pas: Le temps de latence est beaucoup plus court si la cha"ne a dÉjˆ ÉtÉ prÉsentÉe une première fois. -Mesures de temps d'identification de mots en rpÉsentation tachitoscopiques -ComplÉmentation de mots: les sjts ont tendance ˆ complÉter pour crÉer les mots qui leur ont ÉtÉ prÉsentÉs antÉrieurement. L'intÉrêt pour le paradigme de priming se retouve chez les gens qui s'intÉressent ˆ: -reconnaissance de mots et organisation lexicale. les effets de priming permettent de faire des hyps sur l'accès lexical et la reprÉsentation. -M. Épisodique: travux sur les amnÉsiques qui ne se souviennent pas qu'on vient de leur prÉsenter des mots mais qui manifestent une mÉmoire implicite lorsqu'on leur fait faire de la complÉmentation de mots. DISSOCIATION ENTRE M.I. ET M EXPLICITE 1-Si de nombreux travaux montrent que la M explicite est influencÉe par le travail d'Élaboration (profondeur de traitement) en jeu pendant la première phase d'Étude des stimuli, il semble que la MI ne le soit pas. 2-Le changt de modalitÉ (par ex auditif -> visuel) entre la phase d'Étude et la phase de test provoque une attÉnuation importante de l'effet de priming si le test est un test de MI mais pas si c'est un test de ME. 3-Les effets de primings persistent assez largement sur plusieurs jours ce qui n'est pas le cas des perfces ˆ une Épreuve de reconnaissance. 4-Les perfces sur des tests de MI ne semblent pas influencÉes par des manipulations d'interfÉrences proactives ou rÉtroactives dont on sait qu'elles influencent les perfces en ME. 5-Absce de corrÉlation entre perfces ˆ des tests de reconnaissance et perfces ˆ une Épreuve de complÉmentation de mots. SIMILARITES ENTRE PRIMING ET REMEMBERING 1- A certaines conditions les durÉes de rÉtention on des effets parallèles sur les effets de priming et les mesures de ME (REm: en partie contradictoire avec 3 ci dessus) 2-La manipulation du contexte de la liste lors de la phase d'Étude affecte ˆ la fois les perfces en reconnaissance et en identification de mots. 3- ME et MI sont influencÉes par des associations nouvellement acquises entre des paires de mots non reliÉes (Rem: contradictoires avec 4 ci dessus ??) 4- Rem: Le contraire de 1 du pt "dissociation" !!!! dans une manip particulière 5-Johnston et al. ont montrÉ que des mots identifÉs plus rapidement Étaient plus svt jugÉs comme 'old' dans une t‰che de reconnaissance que les mots identifiÉs plus lentement. Il n'est pas exclu que les phÉnomènes que l'on interprètent comme relevant de MI soient parfois de la ME involontaire cad des cas o les cues fournis dans le test conduisent ˆ un souvenir involontaire mais totalement conscient. LES INTERPRETATIONS THEORIQUES DE MI 1-Les effets de priming sur des test de MI sont attribuables ˆ l'activation temporaires de reprÉsentations ou structures de K prÉ-existantes . Cette activation est supposÉe avoir lieu de manière automatique, indÉpendamment des processus d'Élaboration nÉcessaires pour Établir de nouvelles traces Épisodiques. 2- les difÉrences entre ME et MI sont dues ˆ la nature et aux relations entre les processus d'encodage et de rÉcupÉration. Une version de cette approche est celle qui s'appuie sur la distinction entre processus dirigÉs par les donnÉes et processus dirigÉs par les concepts. Ces derniers reflètent des activitÉs initiÉes par le sjt comme l'Élaboration, l'organisation et la reconstruction, c'est sur ce type de processus que reposerait la ME alors que la MI reposerait sur des processus data-driven. 3-ME et MI renvoient ˆ des systs sous jacents diffÉrents. Pour Cohen & Squire (1984), la ME est supportÉe par une M DECLARATIVE , syst qui est en jeu dans la formation de nouvelles reprÉsentations. La MI repose sur un syst PROCEDURAL dans lequel la M se manifeste par des modifications on line de procÉdures ou opÉrations de traitement. Le syst de M Épisodique est vu comme la base pour le souvenir explicite d'evts rÉcents tandis que la M sÉmantique est responsable des perfces sur des tests de MI. Chacune de ces approches est conforme ˆ certaines des donnÉes recueillies mais pas ˆ d'autres. (shrink)

We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. (...) We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit. (shrink)

We study effectively inseparable prelattices $\wedge, \vee$ are binary computable operations; ${ \le _L}$ is a computably enumerable preordering relation, with $0{ \le _L}x{ \le _L}1$ for every x; the equivalence relation ${ \equiv _L}$ originated by ${ \le _L}$ is a congruence on L such that the corresponding quotient structure is a nontrivial bounded lattice; the ${ \equiv _L}$ -equivalence classes of 0 and 1 form an effectively inseparable pair of sets). Solving a problem in we show, that (...) if L is an e.i. prelattice then ${ \le _L}$ is universal with respect to all c.e. preordering relations, i.e., for every c.e. preordering relation R there exists a computable function f reducing R to ${ \le _L}$, i.e., $xRy$ if and only if $f\left{ \le _L}f\left$, for all $x,y$. In fact ${ \le _L}$ is locally universal, i.e., for every pair $a{ < _L}b$ and every c.e. preordering relation R one can find a reducing function f from R to ${ \le _L}$ such that the range of f is contained in the interval $\left\{ {x:a{ \le _L}x{ \le _L}b} \right\}$. Also ${ \le _L}$ is uniformly dense, i.e., there exists a computable function f such that for every $a,b$ if $a{ < _L}b$ then $a{ < _L}f\left{ < _L}b$, and if $a{ \equiv _L}a\prime$ and $b{ \equiv _L}b\prime$ then $f\left{ \equiv _L}f\left$. Some consequences and applications of these results are discussed: in particular for $n \ge 1$ the c.e. preordering relation on ${{\rm{\Sigma }}_n}$ sentences yielded by the relation of provable implication of any c.e. consistent extension of Robinson’s system R or Q is locally universal and uniformly dense; and the c.e. preordering relation yielded by provable implication of any c.e. consistent extension of Heyting Arithmetic is locally universal and uniformly dense. (shrink)