We consider two axioms of second-order arithmetic. These axioms assert, in two different ways, that infinite but narrow binary trees always have infinite paths. We show that both axioms are strictly weaker than Weak König's Lemma, and incomparable in strength to the dual statement (WWKL) that wide binary trees have paths.

The work of Roshdi Rashed has set a landmark in many senses, but perhaps the most striking one is his inexhaustible thrive to open new paths for the study of conceptual links between science and philosophy deeply rooted in the interaction of historic with systematic perspectives. In the present talk I will focus on how a framework that has its source in philosophy of logic, interacts with some new results on the foundations of mathematics. More precisely, the main objective of (...) my brief remarks is to discuss some claims of the late Hintikka who brought forward the idea that a game-theoretical interpretation of the Axiom of Choice yields its meaning “evident”. More precisely I will show that if we develop Per Martin-Löf’s demonstration of the axiom within a dialogical setting, the claim of Hintikka can be upheld. However, the dialogical demonstration, shows that, contrary to the expectations of Hintikka, the meaning that the game-theoretical setting provides to the Axiom is compatible with constructivist rather than with classical tenets. (shrink)

This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. An (...) overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

We investigate the provability or nonprovability of certain ordinary mathematical theorems within certain weak subsystems of second order arithmetic. Specifically, we consider the Cauchy/Peano existence theorem for solutions of ordinary differential equations, in the context of the formal system RCA 0 whose principal axioms are ▵ 0 1 comprehension and Σ 0 1 induction. Our main result is that, over RCA 0 , the Cauchy/Peano Theorem is provably equivalent to weak Konig's lemma, i.e. the statement that every infinite {0, 1}-tree (...) has a path. We also show that, over RCA 0 , the Ascoli lemma is provably equivalent to arithmetical comprehension, as is Osgood's theorem on the existence of maximum solutions. At the end of the paper we digress to relate our results to degrees of unsolvability and to computable analysis. (shrink)

The Nash axiom is a basic property of consistency in choice. This paper proposes weaker versions of the axiom and examines their logical implications. In particular, we demonstrate that weak Nash axioms are useful to understand the relationship between the Nash axiom and the path independence axiom. We provide an application of weak Nash axioms to the no-envy approach. We present a possibility result and an impossibility result.

The present study compares the philosophy of Leibniz with Heidegger’s thought, in particular his analysis of the principium reddendae rationis sufficientis, the so-called principle of reason: nihil est sine ratione. Early on, the author notes that this version of what Leibniz referred to, in 1686, in a letter to Antoine Arnauld as “my great principle” was for Leibniz merely a “vulgar axiom,” the fundamental form of which “[is that] whereby one can always account for why something has happened this (...) way rather than in some other way”. Heidegger, for his part, finds philosophical meat precisely in the modifying phrase “[in] this way rather than in some other way,” not in the traditional “axiom” that “nothing is without a reason”. Although Leibniz does not give the principium in its pure form in the text cited by Cristin, we are to understand that it is a metaphysical principle, not a logical principle. It is not, however, the principle of causality, which demands an answer to the question about why things are, but rather an ontological principle, which shows that and how things are as they are and not otherwise. The foundation of things, which is expressed in Leibniz’s “great principle,” is like the rose spoken of in a line from Johannes Scheffler’s Cherubinischer Wandersmann that Heidegger admired so much: “The rose is without a ‘why’; it blooms because [weil] it blooms”. Like the rose, the nature of the foundation is not gained by asking “Why?” Yet how can that be? What is more fundamental than asking about etiology, reasons, or grounds? In Der Satz vom Grund [The Principle of Ground], a lecture course from 1955/56, Heidegger replies: “The Why [Warum] looks for [sucht] the foundation. The While [Weil] brings about [bringt] the foundation”. Incidentally, when Heidegger makes a noun from the adverb “weil” in this text, he restores the original meaning of the adverb, which is an abbreviated form of “dieweil,” meaning a span of time. In so doing, he points to the temporal nature of the foundation. We can now better understand how, for Heidegger, the principle of the foundation should not be understood as a proposition or utterance, but rather as something like a tempo marking that leads thinking along its path. (shrink)

Name der Zeitschrift: Internationales Jahrbuch für philosophische Anthropologie Jahrgang: 7 Heft: 1 Seiten: 245-258.

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is (...) translatable to a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

This chapter provides a historical account of the transformation of pregnancy through philosophical theory and legal practice. What has remained seemingly consistent across history, though, is the lack of rights a pregnant woman can enjoy. Whilst it may manifest differently across time and place, unfortunately misogynistic attitudes persist, and this is reflected in the continual degrading of the gestator (and gestation), which is reinforced by certain philosophical theorising and technological advancement. We thus urge caution in making philosophical claims about the (...) epistemic transformation in pregnancy, given the epistemic (and other) injustices already faced by pregnant people. We recognise that there are transformations that occur because of pregnancy, but we argue that there ought not be with respect to the pregnant person's autonomy, agency, and control over their bodies. Through an analysis of legal cases, we can see that the practice falls out of line with the theory regarding how pregnant people are treated. But perhaps it is both the theory and the practice that need to change so as to bring them in line. How we theorise about pregnancy is intertwined with our cultural views, our technological advancements, and our medical and legal practices, requiring multi-disciplinary study for a more holistic overview. In this chapter, we contribute to this endeavour by bringing some such strands together, regarding the transformation that pregnancy is, that pregnancy makes, and that pregnancy has had historically, in philosophy, and in legal practice. (shrink)

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, (...) and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to (...) embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

In the context of indivisible public objects problems (e.g., candidate selection or qualification) with “separable” preferences, unanimity rule accepts each object if and only if the object is in everyone’s top set. We establish two axiomatizations of unanimity rule. The main axiom is resource monotonicity, saying that resource increase should affect all agents in the same direction. This axiom is considered in combination with simple Pareto (there is no Pareto improvement by addition or subtraction of a single object), (...) independence of irrelevant alternatives, and either path independence or strategy-proofness. (shrink)

Since the beginning of the 20th century, philosophers of science have asked, "what kind of thing is a scientific theory?" The logical positivists answered: a scientific theory is a mathematical theory, plus an empirical interpretation of that theory. Moreover, they assumed that a mathematical theory is specified by a set of axioms in a formal language. Later 20th century philosophers questioned this account, arguing instead that a scientific theory need not include a mathematical component; or that the mathematical component need (...) not be specified by a set of axioms in a formal language. We survey various accounts of scientific theories entertained in the 20th century -- removing some misconceptions, and clearing a path for future research. (shrink)

The Law of Inertia plays a key role in the scheme of constructive axioms for the General Theory of Relativity. A new formulation of this law which avoids the circularity problems inherent in previous formulations is presented. The empirical status of this law and the manner in which it provides a non-conventional foundation for the Law of Motion and the definition of physical forces is established. First, quite general path structures are discussed which are not defined at the outset (...) in terms of geodesic paths and which require for their description only the local differential topological structure. Secondly, a number of theorems are presented which serve as purely local differential topological criteria for singling out from among the general path structures the geodesic ones that represent the inertial structure of spacetime. (shrink)

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation (...) to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality. (shrink)

We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindelöf property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. [Formula: see text] as “almost finite”, while the latter allows one to treat uncountable sets like e.g. [Formula: see text] (...) as “almost countable”. This reduction of the uncountable to the finite/countable turns out to have a considerable logical and computational cost: we show that the aforementioned lemmas, and many related theorems, are extremely hard to prove, while the associated sub-covers are extremely hard to compute. Indeed, in terms of the standard scale (based on comprehension axioms), a proof of these lemmas requires at least the full extent of second-order arithmetic, a system originating from Hilbert–Bernays’ Grundlagen der Mathematik. This observation has far-reaching implications for the Grundlagen’s spiritual successor, the program of Reverse Mathematics, and the associated Gödel hierarchy. We also show that the Cousin lemma is essential for the development of the gauge integral, a generalization of the Lebesgue and improper Riemann integrals that also uniquely provides a direct formalization of Feynman’s path integral. (shrink)

In 1970, K. Kunen, working in the context of Kelley–Morse set theory, showed that the existence of a nontrivial elementary embedding j:V→V is inconsistent. In this paper, we give a finer analysis of the implications of his result for embeddings V→V relative to models of ZFC. We do this by working in the extended language , using as axioms all the usual axioms of ZFC , along with an axiom schema that asserts that j is a nontrivial elementary embedding. (...) Without additional axiomatic assumptions on j, we show that that the resulting theory is weaker than an ω-Erdös cardinal, but stronger than n-ineffables. We show that natural models of ZFC+BTEE give rise to Schindler’s remarkable cardinals. The approach to inconsistency from ZFC+BTEE forks into two paths: extensions of ZFC+BTEE+Cofinal Axiom and ZFC+BTEE+¬Cofinal Axiom, where Cofinal Axiom asserts that the critical sequence is cofinal in the ordinals. We describe near-minimal inconsistent extensions of each of these theories. The path toward inconsistency from ZFC+BTEE+¬Cofinal Axiom is paved with a sequence of theories of increasing large cardinal strength. Indeed, the extensions of the theory ZFC +“j is a nontrivial elementary embedding” form a hierarchy of axioms, ranging in strength from Con to the existence of a cardinal that is super-n-huge for every n, to inconsistency. This hierarchy is parallel to the usual hierarchy of large cardinal axioms, and can be used in the same way. We also isolate several intermediate-strength axioms which, when added to ZFC+BTEE, produce theories having strengths in the vicinity of a measurable cardinal of high Mitchell order, a strong cardinal, ω Woodin cardinals, and n-huge cardinals. We also determine precisely which combinations of axioms, of the form result in inconsistency. (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. Cuts................................................................................................ ..............39 2.4. Humean Events............................................................................................43 2.5. (...) Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams............................................................................................ ..454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)

This is an in-depth study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that (...) are grasped through geometrical or intelligible intuition. -/- Accordingly, this study classifies Fichte’s philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the Wissenschaftslehre itself may be read as an attempt at a new philosophical mathesis, or “mathesis of the mind.” -/- “This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched.” Professor Dr. Marco Ivaldo -/- “This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the Wissenschaftslehre and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious.” Professor Dr. Emmanuel Cattin. (shrink)

We present a temporal logic of branching time with four primitive operators: |$\exists {\mathcal {C}}$| – it may change whether; |$\forall {\mathcal {C}} $| – it must change whether; |$\exists \Box $| – it may be endlessly unchangeable that; and |$\forall \Box $| – it must be endlessly unchangeable that. Semantically, operator |$\forall {\mathcal {C}}$| expresses a change in the logical value of the given formula in every state that may be an immediate successor of the one considered, while |$\exists (...) {\mathcal {C}}$| expresses a change in the logical value of the given formula in some state that is a possible immediate successor. |$\forall {\mathcal {C}} $| and |$\exists {\mathcal {C}}$| are not normal operators, they are not mutually definable and have unusual properties: |$\forall {\mathcal {C}} A\leftrightarrow \forall {\mathcal {C}} \neg A$| and |$\exists {\mathcal {C}} A \leftrightarrow \exists {\mathcal {C}} \neg A$| are axioms. Operators |$\exists \Box $| and |$\forall \Box $| express endless unchangeability in some and all paths, respectively. Our axiomatization contains two infinitary rules that allow one to obtain |$\exists \Box A$| from infinitely many combinations of formulas with |$A, \neg, \forall {\mathcal {C}}, \land $|⁠, and to get |$\forall \Box A$| from infinitely many combinations of formulas with |$A, \neg, \exists {\mathcal {C}}, \land $|⁠. We show that our formalism is complete by presenting a bridge between our logic and logic |$\textsf {UB}$|⁠, which is a fragment of |$\textsf {CTL}$| in which until operators does not occur. (shrink)

In the framework of ethical social choice theory, sustainability is justified by efficiency and equity as ethical axioms. These axioms correspond to the Suppes–Sen grading principle. In technologies that are productive in a certain sense, the set of Suppes–Sen maximal utility paths is shown to equal the set of non-decreasing and efficient paths. Since any such path is sustainable, efficiency and equity can thus be used to deem any unsustainable path as ethically unacceptable. This finding is contrasted with (...) results that seem to indicate that an infinite number of generations cannot be treated equally. (shrink)

The so-called weak König's lemma WKL asserts the existence of an infinite path b in any infinite binary tree . Based on this principle one can formulate subsystems of higher-order arithmetic which allow to carry out very substantial parts of classical mathematics but are Π 2 0 -conservative over primitive recursive arithmetic PRA . In Kohlenbach 1239–1273) we established such conservation results relative to finite type extensions PRA ω of PRA . In this setting one can consider also a (...) uniform version UWKL of WKL which asserts the existence of a functional Φ which selects uniformly in a given infinite binary tree f an infinite path Φf of that tree. This uniform version of WKL is of interest in the context of explicit mathematics as developed by S. Feferman. The elimination process in Kohlenbach [10] actually can be used to eliminate even this uniform weak König's lemma provided that PRA ω only has a quantifier-free rule of extensionality QF-ER instead of the full axioms of extensionality for all finite types. In this paper we show that in the presence of , UWKL is much stronger than WKL: whereas WKL remains to be Π 2 0 -conservative over PRA, PRA ω ++ UWKL contains full Peano arithmetic PA. We also investigate the proof–theoretic as well as the computational strength of UWKL relative to the intuitionistic variant of PRA ω both with and without the Markov principle. (shrink)

§1. Iterated Gödelian extensions of theories. The idea of iterating ad infinitum the operation of extending a theory T by adding as a new axiom a Gödel sentence for T, or equivalently a formalization of “T is consistent”, thus obtaining an infinite sequence of theories, arose naturally when Godel's incompleteness theorem first appeared, and occurs today to many non-specialists when they ponder the theorem. In the logical literature this idea has been thoroughly explored through two main approaches. One is (...) that initiated by Turing in his “ordinal logics” and taken very much further in Feferman's work on transfinite progressions, which also introduced the more general study of extensions by reflection principles, of which consistency statements are a special case. This approach starts from an assignment of theories to ordinal notations, and extracts sequences of theories through a suitable choice of a path in the set of ordinal notations. The second approach, illustrated in particular by the work of Schmerl and Beklemishev, starts instead from a suitably well-behaved primitive recursive well-ordering, which is used to define a sequence of theories. This second approach has led to precise results about the relative proof-theoretical strength of sequences of theories obtained by iterating different reflection principles. The Turing-Feferman approach, on the other hand, lends itself well to an investigation in qualitative and philosophical terms of the relevance of such iterated reflection extensions to mathematical knowledge, in particular because of two developments associated with this approach. (shrink)

By , we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. is defined to be plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of , there exists a countable model M′ of whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and sets (...) not in the second-order part of M. By combining this fact with a certain forcing argument over universal trees, we obtain the following result : if proves X!Y with arithmetical, so does . We also discuss several improvements of this results. (shrink)

One cannot really speak of a school of personalistic economists. Moreover, there is a wide gulf between the economic philosophy of the personalists and the mathematical context of economic science. Since the thirties, philosophers such as Alexandre Marc, Jacques Maritain, Emmanuel Mounier and many others have been searching, on the basis of a personalistic view of man, for a `third way' between individualistic capitalism and statist socialism , but there was seldom interest from the side of the scientific economists.Fortunately, there (...) are some notable exceptions. François Perroux, Kenneth Boulding, Ernst Schumacher, Serge Christophe Kolm, and Amartya Sen are economists who, in various ways, have attempted to bridge the gulf between the personalistic view of man and economic rationality. By carrying out an immanent critique of some of the standard economic assumptions, they opened a path for a normative economics that was clearly distinct from a purely positive economics as well as from Pareto's welfare economics. One can affix various labels to these attempts: humanistic economics , socio-economics , moral economics . In what follows, I shall interpret these attempts as initiatives in the direction of a personalistic economics. I would also situate the current research in `economics and ethics', which is becoming part of the mainstream of economic thought, and which has received official recognition with the recent Nobel prize award to Sen, within this tendency towards a more personalistic economics.Attention to moral feelings, human rights, altruistic motives, justice and solidarity, non-profit organizations, etc., contribute to situating the economic problem in a field where economics, politics and ethics no longer function as three distinct domains but where their interaction is central.Yet does this interactive economics fit into a personalistic way of thinking? Is a generalized system theory not more attractive? System theory has a different focus than personalistic economics. System theory considers the axioms of system equilibrium and sustainable growth as the ultimate horizon, whereas a personalist sees them as merely important conditions for a good society and economy. However refined it may be, system theory views the person from an external point of view, while the personalist refers to the internal experience of human freedom and meaning as something that transcends and regulates the system's functionality.One could object that neo-classical economists do not use system theory as their point of departure. In their eyes, system equilibrium is the result of the utility-maximizing behaviour of individuals. These individuals subjectively determine what their preferences are and then act accordingly. Is this openness for a free, utility-maximizing actor — where there is room for both material and immaterial, egoistic and altruistic preferences — not sufficient to speak of a personalistic economics ? If this were true, then the discourse of personalism would be more or less superfluous.I take the term `personalistic economics' to refer to a normative economics that does not simply reconstruct the problem of efficient allocation as an individual or social problem of utility, but in the first instance as a problem of human dignity and social justice. To reduce the problem of human choice to a problem of subjective utility is in itself a far-reaching normative standpoint. As soon as one realizes this, there is no reason to exclude other normative assumptions, such as personalistic ones. (shrink)

In this paper I propose a cognitive interpretation of the emergence of monotheism. I first distinguish between two fundamentally different conceptions of representation: one intuitive, which favors an analog model of rational cognition, and one discursive, which favors a digital model. While both Hellenism and Judaism may have been instrumental in setting civilization on the path to reason and law, it is the discursive or digital conception of God as a single universal Judge, I argue, that provides the foundational (...) axiom of the moral logic of the Hebrew Scriptures. That is, in monotheism, God came to be represented differently. (shrink)

The concept of the dialogical soul proposed by Joseph Ratzinger is a contemporary attempt to describe the anthropology of humanity in terms of basic, fundamental theological concepts. Epistemological approach of the dialogic soul is not about the division, but co-existence in the concept of humanity significantly different anthropological concepts. Modern neuroscience, although following completely different paths of knowing is currently concerning an important issue "of the embodied mind". Such a holistic effort to discover the truth about the man, though carried (...) out on completely different epistemological platforms, however, have some points in common. The difficulty in finding a common language for the dialogue in this field can be overcome and lead to dialogue, which is extremely difficult but doable. We must, however, at the beginning formulate certain fundamental axioms that define class concepts used in different areas of scientific activity. The concept of dialogical soul of Ratzinger’s now exceeds the barrier of scientific paradigms axioms. It does not stop on the vision of human oneself, but recognition of one in the area of relationships and makes room for a substantial dialogue with the world of modern science. (shrink)

A complete list of Finsler, Scott and Boffa sets whose transitive closures contain 1, 2 and 3 elements is given. An algorithm for deciding the identity of hereditarily finite Scott sets is presented. Anti-well-founded sets, i. e., non-well-founded sets whose all maximal ∈-paths are circular, are studied. For example they form transitive inner models of ZFC minus foundation and empty set, and they include uncountably many hereditarily finite awf sets. A complete list of Finsler and Boffa awf sets with 2 (...) and 3 elements in their transitive closure is given. Next the existence of infinite descending ∈-sequences in Aczel universes is shown. Finally a theorem of Ballard and Hrbáček concerning nonstandard Boffa universes of sets is considerably extended. (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)

In lieu of an abstract, here is a brief excerpt of the content:400 KANT'S MISREPRESENTATIONS OF HUME'S PHILOSOPHY OF MATHEMATICS IN THE PROLEGOMENA In 1783, Immanuel Kant published the following reflections upon the philosophy of mathematics of David Hume, words which have colored all subsequent interpretations of the letter's work: Hume being prompted to cast his eye over the whole field of a priori cognitions in which human understanding claims such mighty possessions (a calling he felt worthy of a philosopher) (...) heedlessly severed from it a whole, and indeed its most valuable, province, namely, pure mathematics ; for he imagined its nature or, so to speak, the state constitution of this empire depended on totally different principles, namely, on the law of contradiction alone; and although he did not divide judgments in this manner formally and universally as I have done here, what he said was equivalent to this: that mathematics contains only analytical, but metaphysics synthetical, a priori propositions. In this he was mistaken, and the mistake had a decidedly injurious effect upon his whole conception. But for this, he would have extended his question concerning the origin of our synthetical judgments far beyond the metaphysical concept of causality and included in it the possibility of mathematics a priori also, for this latter he must have assumed to be equally synthetical. And then he could not have based his metaphysical propositions on mere experience without subjecting the axioms of mathematics equally to experience, a thing which he was far too acute to do. The good company in which metaphysics would thus have been brought would have saved it from the danger of a contemptuous illtreatment, or the thrust intended for it must have reached mathematics, which was and could not have been Hume's intention. Thus that acute 401 man could have been led into considerations which must needs be similar to those that now occupy us, but would have gained inestimably by his inimitably elegant style. In other words, Hume failed to notice that mathematics, despite its a priori character, is synthetic. It was thus easy for him to conclude that all a priori judgments are analytic, and that therefore metaphysics (conceived of as synthetic ¿ priori judgments) is impossible. Now what considerations led Kant himself to the opposite conclusion, that mathematics is synthetic despite being a priori? Let's consider Kant's own words in a typical passage: Just as little is any principle of geometry analytical. That a straight line is the shortest path between two points is a synthetical proposition. For my concept of straight contains nothing of quantity, but only a quality. The concept 'shortest' is therefore altogether additional and cannot be obtained by any analysis of the concept 'straight line.' Here, too, intuition must come to aid us. It alone makes the synthesis possible. I should like the reader now to compare the following passage from Hume's Treatise of Human 2 Nature, Book I, Part II, Section IV: 'Tis true, mathematicians pretend they give an exact definition of a right line, when they say, it is the shortest way betwixt two points. But in the first place, I observe, that this is more properly the discovery of one of the properties of a right line, than a just definition of it. For I ask any one, if upon mention of a right line he thinks not immediately on such a particular appearance, and if 'tis not by accident only that he considers this property? A right line can be comprehended alone; but this definition is unintelligible 402 without a comparison with other lines, which we conceive to be more extended. In common life 'tis establish 'd as a maxim, that the streightest way is always the shortest; which wou'd be as absurd as to say, the shortest way is always the shortest, if our idea of a right line was not different from that of the shortest way betwixt two points. Style and terminology apart, I defy the reader to distinguish between these two arguments and their conclusions. Hume argues that 'The shortest distance between two points is a straight line' is no definition; furthermore he says almost explicitly that 'There is a longer distance between two points than a straight line... (shrink)

Although written more than 2,500 years ago and within a radically different culture, the Tao Te Ching's concepts and teachings have become more influential in the West than ever before. Laozi, the Chinese sage and founder of Taoism, sets out a path (tao) that allows us to tune in to the nature of the universe. His axioms are intended to help us achieve transcendence and a life of integrity and balance: they explore the importance of male and female complementary (...) qualities while praising self-knowledge and criticizing rational understanding. Among his insights are the beliefs that flexibility and suppleness are superior to rigidity and strength, and that self-absorption and self-importance are vain and destructive. This illustrated edition of a classic work is an essential addition to any home library of the world's classic philosophical texts. (shrink)

It is the aim of this paper to trace, firstly, how far Epicurus is indebted to pre-Socratic physiology regarding the axiom of nihil ex nihilo, which the Samian philosopher accepts in toto; secondly to prove that physics, with this axiom as a ground, is a requisite for a both natural and mental framework where ἀταραξία can be achieved. In the first part of this writing, the aforementioned principle is presented as a struggle against myth, for a new interpretative (...) structure of the world. Afterwards, a path is defined, that goes from Parmenides and Melissus of Samos, as a necessary conceptual link, to the first ancient atomism. In the second part of this research effort, the role of atomistic materialistic physics is presented as an essential explanatory foundation for achieving, in the Epicurean way, a happy life without fear or mental disturbance. Accordingly, the study of nature, and the rational assumption of its conclusions, becomes a tool for soul care. (shrink)

1. Setting off: An introduction. 1.1. A measure of motivation. 1.2. Computable mathematics. 1.3. Reverse mathematics. 1.4. An overview. 1.5. Further reading -- 2. Gathering our tools: Basic concepts and notation. 2.1. Computability theory. 2.2. Computability theoretic reductions. 2.3. Forcing -- 3. Finding our path: Konig's lemma and computability. 3.1. II[symbol] classes, basis theorems, and PA degrees. 3.2. Versions of Konig's lemma -- 4. Gauging our strength: Reverse mathematics. 4.1. RCA[symbol]. 4.2. Working in RCA[symbol]. 4.3. ACA[symbol]. 4.4. WKL[symbol]. 4.5. (...) [symbol]-models. 4.6. First order axioms. 4.7. Further remarks -- 5. In defense of disarray -- 6. Achieving consensus: Ramsey's theorem. 6.1. Three proofs of Ramsey's theorem. 6.2. Ramsey's theorem and the arithmetic hierarchy. 6.3. RT, ACA[symbol], and the Paris-Harrington theorem. 6.4. Stability and cohesiveness. 6.5. Mathias forcing and cohesive sets. 6.6. Mathias forcing and stable colorings. 6.7. Seetapun's theorem and its extensions. 6.8. Ramsey's theorem and first order axioms. 6.9. Uniformity -- 7. Preserving our power: Conservativity. 7.1. Conservativity over first order systems. 7.2. WKL[symbol] and II[symbol]-conservativity. 7.3. COH and r-II[symbol]-conservativity -- 8. Drawing a map: Five diagrams -- 9. Exploring our surroundings: The world below RT[symbol]. 9.1. Ascending and descending sequences. 9.2. Other combinatorial principles provable from RT[symbol]. 9.3. Atomic models and omitting types -- 10. Charging ahead: Further topics. 10.1. The Dushnik-Miller theorem. 10.2. Linearizing well-founded partial orders. 10.3. The world above ACA[symbol]. 10.4. Still further topics, and a final exercise. (shrink)

It is shown that the evolution of physics canin several regards be described by elements of``regression'', i.e., that within a certaintradition of ideas one begins with theconstruction of most ``plausible'' statements(axioms) at hand, and then ``works onselfbackwards'' with respect to developmental terms.As a consequence of this strategy, the furtherwork proceeds along such a ``regressive'' path,the more one arrives at concepts andrelationships which are unexpected or evencounter-intuitive in terms of our everydayexperiences. However, a comparable phenomenology is wellknown from studies on (...) states of consciousness.In particular, the evolutionary logic of theconstructions of major ``cognitive invariances''in physics, which is in part due to everincreasing rates of data processing, ismirrored in a logic of states of consciousnesswhich deviate from a ``normal'' state of dailyroutine along increasing levels of centralnervous arousal. Examples are given from the evolution ofphysics, and future perspectives are brieflyoutlined on the basis thereof. (shrink)

A continuum is here a primitive notion intended to correspond precisely to a path-connected subset of the usual euclidean space. In contrast, however, to the traditional treatment, we treat here continua not as pointsets, but as irreducible entities equipped only with a partial ordering ≤ interpreted as parthood. Our aim is to examine what basic topological and geometric properties of continua can be expressed in the language of ≤, and what principles we need in order to prove elementary facts (...) about them. Surprisingly enough ≤ suffices to formulate the very heart of continuity (=jumpless and gapless transitions) in a general setting. Further, using a few principles about ≤ (together with the axioms of ZFC), we can define points, joins, meets and infinite closeness. Most important, we can develop a dimension theory based on notions like path, circle, line (=one-dimensional continuum), simple line and surface (=two-dimensional continuum), recovering thereby in a rigorous way Poincaré's well-known intuitive idea that dimension expresses the ways in which a continuum can be torn apart. We outline a classification of lines according to the number of circles and branching points they contain. The ordering (C,≤) is a topped and bottomed, atomic, almost dense and complete partial ordering, weaker than a lattice. Continuous transformations from C to C are also defined in a natural way and results about them are proved. (shrink)

The inquiry will attempt to answer several questions about: a) the cognitive status of philosophy according to Kant; b) the possibility of distinguishing philosophy from other forms of knowledge, with particular reference to specifically named scientific cognitions; c) the consequences connected with the necessity of thinking of philosophy in its relation to an ulterior dimension with respect to that of science, which is, according to Kant, the dimension of wisdom. Philosophy, according to Kant, is a rational cognition, yet different from (...) mathematics. Philosophy is a rational cognition from concepts, and therefore makes a discursive use of reason in accordance with concepts. Mathematics is instead a rational cognition from the construction of concepts, and therefore makes intuitive use of reason through the construction of concepts. The construction of a concept implies necessarily the capacity and the possibility of exposing in the intuition the corresponding object and to express it through a representation which is universally valid “for all possible intuitions that belong under the same concept”. It is precisely the fact that it is a cognition that proceeds along the construction of concepts which makes mathematics a stable and certain discipline, accompanied by evident proofs founded upon definitions, axioms and demonstrations that no rational cognition that proceeds with mere concepts can possess. It is for this reason that philosophy, in contrast with mathematics and whatever else is in some manner reducible to mathematics, may not be learned; for the fact that philosophy, understood as a scientific discipline in the same way in which all scientific disciplines are to be understood, really doesn’t exist. Philosophy is not a discipline in the sense in which all the other scientific disciplines are, because philosophy, for Kant, “is a mere idea of apossible science that precisely as an idea of a possible science is nowhere given in concreto”. If one may effectively speak about philosophy as a science, this does not constitute the moment in which philosophy finally reaches completion in itself. What Kant underscores is that at this level philosophy is only a science, that is, knowledge which, as much as it is fundamentally stable and certain, does not succeed in any case in obtaining that which constitutes instead, the most important and irreducible element of philosophy: “the relation of all cognition to the essential ends of human reason”. The philosopher is not for Kant simply a technician of reason, in that his aim is not solely that of ability, the completeness of knowledge and its systematic organisation. Rather, he aspires to something which goes beyond the merely cognitive dimension, and that Kant calls “wisdom”. Even knowing that science is the only available path, philosophy knows also that science cannot satisfy itself. In this sense philosophy presents itself as a science of limits and finds precisely in this determination the difference of all particular scientific disciplines, and, at one and the same time, of all pseudocognitive attitudes which are programmatically presented as independent from and alternative to science. (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)

We introduce a new formulation of the axiom of dependent choice, which can be viewed as an abstract termination principle that in particular generalises recursive path orderings, the latter being fundamental tools used to establish termination of rewrite systems. We consider several variants of our termination principle, and relate them to general termination theorems in the literature.

We propose an adynamical, background independent approach to quantum gravity and unification whereby the fundamental elements of Nature are graphical units of space, time and sources. The transition amplitude for these elements of “spacetimesource” is computed using a path integral with discrete Gaussian graphical action. The unit of action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical relations so that (...) it contains a non-trivial null space, and J is then restricted to the column space of K which ensures it is distributed in a divergence-free fashion over the spacetime defined by the element. This rule for the relational construct of K and J is our proposed fundamental axiom of physics and results in a self-consistency relationship between sources, the spacetime metric, and the stress-energy-momentum content of the element, rather than a dynamical law for time-evolved entities. In its most general form, the set of fundamental elements employed by lattice gauge theory contains scalar fields on nodes and links, and vector fields on nodes. To complete the fundamental set, we propose the addition of scalar fields on plaquettes and vector fields on links. We use this approach via modified Regge calculus to correct proper distance in the Einstein-deSitter cosmology model yielding a fit of the Union2 Compilation supernova data that matches ɅCDM without having to invoke accelerating expansion or dark energy. (shrink)

continent. 2.2 (2012): 76–81 Comments on Eugene Thacker’s “Cosmic Pessimism” Nicola Masciandaro Anything you look forward to will destroy you, as it already has. —Vernon Howard In pessimism, the first axiom is a long, low, funereal sigh. The cosmicity of the sigh resides in its profound negative singularity. Moving via endless auto-releasement, it achieves the remote. “ Oltre la spera che piú larga gira / passa ’l sospiro ch’esce del mio core ” [Beyond the sphere that circles widest / (...) penetrates the sigh that issues from my heart]. 1 The axiomatic sigh of the pessimist is in a way the pure word of philosophy, a thought that thinks without you, speaks where you are not. The live pneumatic form of the soul’s eventual exit from the dead body’s mouth, the sigh restores consciousness to the funeral of being, to the passing away that is existence. Pessimism speaks in piercing aphorisms because first it sighs. “Beyond the sphere passeth the arrow of our sigh. Hafiz! Silence.” 2 … pessimism is guilty of that most inexcusable of Occidental crimes—the crime of not pretending it’s for real. To the pessimist, the ‘real’ world—the world on whose behalf we are expected to wake up in the morning—is a ceaseless index of its own unreality. The pessimist’s day is not an illumined space for the advancement of experience and action, but a permanently and inescapably reflective zone, the vast interior of a mirror where each thing is only insofar as it is, at best, a false image of itself. Within this speculative situation, inside the doubleness of the mirror, pessimism splits into two paths, false and true, one that tries to fix pessimism (establish a relation with the mirror) and decides in favor of the apparent real, and another that totally falls for pessimism (enters the mirror) and communes with the greater reality of the unreal. These two paths are distinguished by their relation to pessimism’s guilt vis-à-vis the world’s reality-project. The first form, that which remains pessimism for the world and puts on a smiling face, stays guilty to itself (i.e. unconscious) and thus turns hypocritical, becoming at once the pessimism of the commoner who really just wants things to be better for himself and the pessimism of the elite who wants to critically refashion reality in his own image. The general form of this worldly, hypocritical pessimism is the impulse to ‘make the world a better place’, which is the global mask under which the world is diurnally made worse. The second form, that which follows pessimism away from the world and ceases to put on a smiling face, refuses guiltiness as itself theessential Occidental mode of pretense and turns honest, becoming at once the intelligent pessimism required of all ordinary action and the radical pessimism necessary for self-knowledge: seeing that no one is capable of doing good. The general form of this universal, honest pessimism is the impulse not to worry, to give up and embrace dereliction, which is the only real way the world is actually improved. Where worldly pessimism is the engine productive of interminably warring secular and sacred religions (good-projects), universal pessimism strives hopelessly for the paradise of a supremely instantiated pessimus: things are getting so bad that there is no longer any time for them to get worse; things are so constantly-instantly worst that this is BEST. Cosmic pessimism is the mode of universal pessimism which can yet discourse with the world, which has not chosen silence and can spread the inconceivably BAD NEWS in an orderly form ( kosmos ) that the world can understand (if it wanted to). … the result of a confusion between the world and a statement about the world. That is what the world is (the result of a confusion between the world and a statement about the world). … a generalized misanthropy without the anthropos. Pessimism crystallizes around this futility—it is its amor fati , rendered as musical form. Pessimism’s love of fate is a blind love, a love of the blindness of being human in a cosmos conceived around the human’s eclipse, a heavy levitation in the contradictory space between the inescapability of its having been and the impossibility of its will-be. Pessimism’s song of futility is a sensible way of loving fate, with a minimum of eros, by means of a kind of matrimonial love of the fatal. As music, pessimism stays open to the irreparable and the inexorable without the binding of affirmation, in the apparent absence of the radical, infinitely surplus will that absolute amor fati seems to require. Crying, laughing, sleeping—what other responses are adequate to a life that is so indifferent? “Unless a man aspires to the impossible, the possible that he achieves will scarcely be worth the trouble of his achieving it. We should aspire to the impossible, to absolute and infinite perfection [….] The apocatastasis is more than a mystical dream: it is a norm of action, it is a beacon for high deeds [….] For true charity is a species of invasion [….] It is not charity to rock and lull our fellow men to sleep in the inertia and heaviness of matter, but rather to arouse them to anguish and torment of spirit.” 3 … the impossibility of ever adequately accounting for one’s relationship to thought. “The paroxysm of interior experience leads you to regions where danger is absolute, because life which self-consciously actualizes its roots in experience can only negate itself [….] There are no arguments [….] On the heights of despair, the passion for the absurd is the only thing that can still throw a demonic light on chaos [….] I live because the mountains do not laugh and the worms do not sing .” 4 It took three attempts before she was fully decapitated, all the while she continued, perhaps miraculously, to sing. According to the earliest account of Cecilia’s martyrdom, the beheading turns out worse. After not severing her head in three strokes, “the cruel executioner left her half dead” (seminecem eam cruentus carnifex dereliquit). 5 Cecilia’s effortlessly powerful endurance of the three strokes—a fitting icon for pessimism as an art of dereliction—demonstrates the “passivity and absence of effort [….] in which divine transcendence is dissolved.” 6 There’s a ghost that grows inside of me, damaged in the making, and there’s a hunt sprung from necessity, elliptical and drowned. Where the moving quiet of our insomnia offers up each thought, there’s a luminous field of grey inertia, and obsidian dreams burnt all the way down. Like words from a pre-waking dream. There is no reason to think that they are not. NOTES 1. Dante Alighieri. Vita Nuova . ed. and trans. Dino S. Cervigni and Edward Vasta. Notre Dame: University of Notre Dame Press. 1995. 41:10. 2. Hafiz of Shiraz. The Divan . trans. H. Wilberforce Clarke. London: Octagon Press. 1974. 10.9. 3. Miguel de Unamuno. The Tragic Sense of Life in Men and Nations . trans. Anthony Kerrigan. Princeton: Princeton University Press. 1972. 305-6. 4. E.M. Cioran. On the Heights of Despair . trans. Ilinca Zarifopol-Johnston. Chicago: University of Chicago Press. 1992. 9-10. 5. Giacomo Laderchi. S. Caeciliae Virg[inis] et Mart[yris] Acta. . . Rome. 1723. 38. 6. Georges Bataille. On Nietzsche . trans. Bruce Boone. London: Continuum. 2004. 135. See Nicola Masciandaro. “ Half Dead: Parsing Cecilia .” A Commentary on Eugene Thacker’s "Cosmic Pessimism" Gary J. Shipley Pessimism is the refusal to seek distraction, the refusal to remodel failure into a platform for further (doomed) possibilities, the refusal of comfort, the acceptance of the sickness of healthy bodies, the cup of life overflowing with cold vomit. If, as Ligotti suggests when discussing Invasion of the Body Snatchers , 1 humans prefer the anxieties of their familiar human lives to the contentment of an alien one, then the pessimist, we could argue, represents some perverted combination of the two, preferring (presuming he has a choice) the defamiliarization of human life to the contentment of its unquestioned mundanity. The quasi-religious state of mind that Wittgenstein would mention on occasion, that of “feeling absolutely safe,” 2 is a state the pessimist could only imagine being approximated by death, or perhaps some annihilative opiate-induced stupor. This Wittgensteinian commingling of certainty and faith looks every bit the futile gesture, a mere rephrasing of collapse or partial collapse. The only certainty open to the pessimist is that of the toxic formula of life itself—a formula known and lacuna-free. Certainty, far from being the gateway to deliverance, becomes the definitive impediment; and the possibility of salvation, as long as it remains, becomes crucially reliant on postulations of ignorance, epistemic gaps, a perennial incompleteness: “the perfect safety of wooed death […] the warm bath of physical dissolution, the universal unknown engulfing the miniscule unknown.” 3 The height of Leibniz’s Panglossian insanity nurtured the idea that our knowing everything—via the universal calculus—could be accurately described a triumph, as opposed to a nightmare in which our every futility is laid bare. Stagnancy and boredom are perhaps two of the greatest ills of Western civilisation, and the most potent pessimism tells you that you’re stuck with both. The most we can hope for, by way of salvation, is to throw open our despair to the unknown. The fact that Schopenhauer’s pessimism stopped short of morality and allowed him to play the flute, as Nietzsche complained, highlights the predicament of a man who despite having adorned nothingness with a smiling face still found himself alive. The demand here is that it be felt: a cross-contamination of intellect and emotion. The safety net of numerous parentheses makes for a failed philosophy, rather than a philosophy of failure. Depressives make bad pessimists, because, unless they choose to die, living will always infect them with necessities of hope, forcing them to find something, anything (all the various “as ifs”) to make existence tolerable. For as Cioran observed, while “[d]epressions pay attention to life, they are the eyes of the devil, poisoned arrows which wound mortally any zest and love of life. Without them we know little, but with them, we cannot live.” 4 And even when cured of our depressions we’ll find ourselves consumed, eaten alive by the hyper-clinical (borderline autistic) mania that replaces them: a predicament captured all too clearly in the microscriptual fictions of Robert Walser, where spectral men and women stifle their depressive madness with protective comas of detail, their failed assimilations buried beneath thick crusts of remote data. Like Beckett’s Malone their stories may have ended, but cruelly their lives have not. Pessimism is an extraneous burden (a purposeless weight) that makes everything else harder to carry, while at the same time scooping it out and making it lighter. If pessimism had a sound it would be the harsh non-noise of tinnitus—the way that every person would hear themselves if they refused their distractions long enough to listen: a lungless scream from the extrasolar nothing of the self. The music of pessimism—if indeed we can imagine such a thing—is the reverberating echo of the world’s last sound, conjectured but never heard, audible only in its being listened for. The one consolation of this hollow paradox of audibility being, that “he will be least afraid of becoming nothing in death who has recognized that he is already nothing now.” 5 The pessimist suffers a derangement of the real, a labyrinthitis at the nucleus of his being: he’s the stumbling ghost relentlessly surprised that others can see him. If Cioran’s refusal is manifested in sleep (when even saying ‘no’ is too much of a commitment), then Pessoa’s resides in the dreams inside that sleep. Pessoa chooses to exploit the fact that he’s being “lived by some murmuring non-entity both shadowy and muddied” 6 by growing more voids to live him. His is a Gnostic breed of sleep, “sleeping as if the universe were a mistake,” 7 a sleep that dreams through Thacker’s cosmic pessimism (“a pessimism of the world-without-us.”, “the unhuman orientation of deep space and deep time” 8 ), through the critical error of there being anything at all when there could be nothing. The metaphysical pessimist is someone who, however well life treats them, still desires to wake from it, as from the poisonous air of a bad dream. Pessimism is a paradox of age, being simultaneously young and old; its youth residing in a refusal to accept the authority of existence (its rich history, its inherent beneficence), a refusal to “get over” the horror of what it sees with its perpetually fresh eyes, and its maturity in the unceremonious disposal of the philosophical playthings (those futile architectures) of adolescence. As Thacker remarks: “Pessimism abjures all pretenses towards system—towards the purity of analysis and the dignity of critique.” 9 A sentiment shared with Pessoa, who duly categorizes those that choose to enact this futile struggle: “The creators of metaphysical systems and of psychological explanations are still in the primary stage of suffering.” 10 If the pessimist has shared a womb with anyone, it’s with the mystic and not the philosopher. As Schopenhauer tells us: “The mystic is opposed to the philosopher by the fact that he begins from within, whereas the philosopher begins from without. […] But nothing of this is communicable except the assertions that we have to accept on his word; consequently he is unable to convince.” 11 The crucial difference between the mystic and the pessimist is not the latter’s impassivity and defeatism, but his unwillingness/inability to contain in any way the spread of his voracious analyticity, his denial of incompleteness, his exhaustive devotion to failure. The truth of our predicament, though heard, is destined to remain unprocessed. Like the revelations of B.S. Johnson’s Haakon (“We rot and there’s nothing that can stop it / Can’t you feel the shaking horror of that?” 12 ) the pessimist’s truths are somehow too obvious to listen to, as if something inside us were saying, “Of course, but haven’t we gotten over that?” Pessimism is simple and ugly, and has no desire to make itself more complex or more attractive. The true moral pessimist knows that the Utilitarian’s accounts will always be in the red. He can see that for all his computational containments, his only honest path is a negative one, and that such a path has but one logical destination: that of wholesale human oblivion. Thacker notes how at the core of pessimism lies the notion of “the worst,” through which death is demoted by the all-pervasive suffering of a life that easily eclipses its threat. And so with doom made preferable to gloom, death begins to glint with promise, “like beauty passing through a nightmare.” 13 But even among pessimists suicide is, for the most part, thought to be an error. Schopenhauer, for instance, regarded suicide a mistake grounded in some fundamentally naïve disappointment or other. Pessoa too thought suicide an onerous escape tactic: “To die is to become completely other. That’s why suicide is a cowardice: it’s to surrender ourselves completely to life.” 14 There is a call here to be accepting of and creative with the puppetry of your being, an insistence that it’s somehow a blunder to attempt to hide in death from the horrors you find inlife. 15 Tied up with this perseverance is the slippery notion of the good death, for maybe, as Blanchot warns, suicide is rarely something we can hope to get right, for the simple reason that “you cannot make of death an object of the will.” 16 “Even in cases where the entire corpus of an author is pessimistic, the project always seems incomplete,” 17 and this is not simply because the project itself belies something yet to be disclosed, but because the project itself is a thing waiting. It waits on a cure it knows will not come, but for which it cannot do anything (as long as it continues to do anything) but wait. NOTES 1. See Thomas Ligotti. The Conspiracy Against the Human Race . New York: Hippocampus Press. 2010. 91. 2. Ludwig Wittgenstein. “A Lecture on Ethics.” Philosophical Review . (74) 1. 1965. 8. 3. Vladimir Nabokov. Pale Fire . New York: Vintage. 1989. 221. 4. E. M. Cioran. The Book of Delusions . trans. Camelia Elias. Hyperion. 5.1. (2010): 75. 5. Arthur Schopenhauer. The World as Will and Representation. vol. 2 . trans. E .F J. Payne. New York: Dover. 1966. 609. 6. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 67. 7. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 35. 8. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 68. 9. Ibid. 73. 10. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 341. 11. Arthur Schopenhauer. The World as Will and Representation. vol. 2 . trans. E .F J. Payne. New York: Dover. 1966. 610-11. 12. B.S Johnson. “You’re Human Like the Rest of Them.” in Jonathan Coe. Like a Fiery Elephant: The Story of B.S. Johnson . London: Picador. 2004. 177. 13. Fernando Pessoa. The Book of Disquiet . trans. Richard Zenith. London: Penguin. 2002. 415. 14. Ibid. 199. 15. “Suicide is, after all, the opposite of the poem.” Anne Sexton. No Evil Star: Selected Essays, Interviews and Prose . ed. Steven Gould Axelrod. Ann Arbor: University of Michigan Press. 1985. 92. 16. Maurice Blanchot. The Space of Literature . trans. Ann Smock. Lincoln: University of Nebraska Press. 1989. 105. 17. Eugene Thacker. “Cosmic Pessimism.” continent. . 2.2 (2012): 75. (shrink)

Towards the end of their reign, the logical positivists found themselves in bitter disagreement as to what extent the methods and axioms of the natural sciences can be justified by our abilities to grunt and point. What began as a project to epistemically ground the natural sciences ended as an argument about cavemen. Although such a story might be a good one, the consensus, among the positivists’ rivals and the positivists themselves, seemed to be that ahead lay a difficult road (...) indeed if grunts clarify physics. Understandably, that road would be one not traveled, and so our weary fact-warriors walked off elsewhere, leaving the detritus in their path and the rest of the world to deal with the consequences. And consequences there were. Take the current, popular idea that the natural sciences need not be governed by moral concerns; or if they do, such moral governance only need be justified by appeals to governmental, technological or, happily in this most learned of eras, divine authority. Although we may not be able to connect such popular ideas directly to the positivist program, it is nevertheless no great leap to say that their program was motivated in strong ways by a blind acceptance of the abilities of technological advancement and the triumphant march of the natural sciences. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Infinitesimal Differences: Controversies between Leibniz and his ContemporariesFrançoise Monnoyeur-BroitmanUrsula Goldenbaum and Douglas Jesseph, editors. Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Berlin-New York: Walter de Gruyter, 2008. Pp. vi + 327. Cloth, $109.00.Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected (...) to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt.Many of us know and probably have used the Leibnizian formula: to calculate the area under a curve; this book considers the origin, nature, method, and metaphysics of this formula. The most fascinating question discussed in it is the fiction introduced to define the infinitesimal calculation: in his mature period, Leibniz himself referred to his calculus as “a well-founded fiction.” We learn that he gradually gave up the idea of an actual infinite in favor of describing infinitely small quantities. As a result, the quantities became fictive and finite or indefinite instead of real and infinite, and the process of calculation shifted towards mathematics rather than metaphysics.In the first essay, Richard Arthur compares the calculus of Leibniz and Newton and demonstrates how it was based for both on the development of continuously varying quantity. He also shows how the understanding of this quantity derived from the Archimedean axiom that excludes the existence of actual infinite quantity. Ursula Goldenbaum next demonstrates how Hobbes, with his conatus considered as point and instant, had a direct impact on the Leibnizian conception of continuity; to confirm her interpretation, she includes at the end of her article the “Marginalia or Leibniz comments” on Hobbes. Samuel Levey establishes a connection between the notion of the infinitesimal as a “well-founded fiction” and the law of continuity, arguing that the law of continuity, understood as an extension of Archimedes’ principle, gives a finite foundation to the infinitesimal calculation. O. Bradley Bassler discusses the idea of the differential in terms of infinitely small quantities and the use of proportions between infinitely small and finite quantities in order to measure [End Page 527] the infinitely small; here, differentials are also presented as fictions. Fritz Nagel discusses the methodological sophistication of the calculus and its opponents. His main questions concern the different grades of infinity, quantities regarded as zero, and the infinitesimal as a fiction that can be calculated. Douglas Jesseph considers the reality of the infinitesimal and the “well-founded fiction,” showing how Leibniz methodically constructs infinitesimal quantities without reality by returning to Hobbes’ notion of conatus. Hobbes is, for Jesseph, the initiator of these infinitely small quantities without existence.A second group of essays examines the connection between algebra and geometry in the calculus. Philip Beeley demonstrates how John Wallis, on the path of Cavalieri’s method of the indivisibles, found a way to transform geometric problems into sums of arithmetic sequences. Siegmund Probst expresses the different phases in the discovery of the Leibnizian method. He mentions that Leibniz coined the term ‘infinitesimal’ in 1673, and points out that he did not need the method of indivisibles to find a curve from its given arc, but only a series expansion using differences of higher order. Emily Grosholz looks at how, thanks to his algebraic and geometrical notations of curves, Leibniz could formulate the equation of his infinitesimal calculus. According to Grosholz, Leibniz exploits the ambiguity of notations in order to express the geometrical and dynamical aspect of the calculus. Herbert Breger underlines the novelty and abstract nature of Leibniz’s new method of calculation, showing how the theory of infinitesimals became an algebraic calculus independent of geometry.A final group of articles studies the relationship between the calculus and Leibniz’s physics. François Duchesneau shows how the differential and integral calculus provided a model for the integrative laws of Leibniz’s... (shrink)