ABSTRACT In 1933 Gödel introduced an axiomatic system, currently known as S4, for a logic of an absolute provability, i.e. not depending on the formalism chosen ([God 33]). The problem of finding a fair provability model for S4 was left open. The famous formal provability predicate which first appeared in the Gödel Incompleteness Theorem does not do this job: the logic of formal provability is not compatible with S4. As was discovered in [Art 95], this defect of the formal provability (...) predicate can be bypassed by replacing hidden quantifiers over proofs by proof polynomials in a certain finite basis. The resulting Logic of Proofs enjoys a natural arithmetical semantics and provides an intended provability model for S4, thus answering a question left open by Gödel in 1933. Proof polynomials give an intended semantics for some other constructions based on the concept of provability, including intuitionistic logic with its Brouwer- Heyting- Kolmogorov interpretation, ?-calculus and modal ?-calculus. In the current paper we demonstrate how the intuitionistic propositional logic Int can be directly realized by proof polynomials. It is shown, that Int is complete with respect to this proof realizability. (shrink)

We define a novel interpretation R of second order arithmetic into Explicit Mathematics. As a difference from standard D-interpretation, which was used before and was shown to interpret only subsystems proof-theoretically weaker than T 0 , our interpretation can reach the full strength of T 0 . The R-interpretation is an adaptation of Kleene's recursive realizability, and is applicable only to intuitionistic theories.

A natural realist approach to the philosophy of arithmetic is defended by way of considering and arguing against contemporary attempts to solve Paul Benacerraf's dilemma . The first horn of the dilemma concerns the existence of abstract mathematical objects, which seems necessitated by a desire for a unified semantics. Benacerraf adopts an extensional semantics whereby the reference of terms for natural numbers must be abstract objects. The second horn concerns a desirable causal constraint on knowledge, according to which "for X (...) to know that S is true requires some causal relation to obtain between X and the referents of the names, predicates, and quantifiers of S". Within the philosophical tradition, Benacerraf's dilemma crystallizes the tension between realists and empiricists . It is shown that natural realism and naturalism meet. ;Both horns of the dilemma are amended.objects are conceived along conceptualist lines such that their existence is not mind-independent. The causal constraint is refined by drawing upon the work of Mark Steiner . Natural realism is the notion that the truth-values of arithmetical statements are recognition-transcendent. Natural realism explains why one and only one arithmetic is applicable. It is in some sense discovered, which is captured by the idea that arithmetical statements have truth-values even if one is not able to adduce what they are. ;It is argued that with proper emendation, like that of Philip Kitcher , empiricism as envisioned by J. S. Mill is defensible. Furthermore, the epistemology of arithmetical knowledge is divided into two tiers. The first principles of arithmetic are acquired by causal interaction with physical objects. As Kitcher has shown, empiricism functions at the first-tier. The a priori is revised such that arithmetical knowledge generated from the first-tier is considered non-empirical. ;It is argued that pragmatists' indispensability argument, once qualified, allows that arithmetic's applicability is one reason to consider natural realism for that domain . Furthermore, this thesis provides a case where aspects of Hilary Putnam's early and later views are rendered consistent. By way of utilizing both Putnam's writing in favour of realism , and those that break with them , it is suggested that he should not have abandoned his earlier view. In a nutshell, the realization of knowledge can depend upon agents' values, methods, and so on, without forcing the abandonment of realism . Putnam's early view sets the criteria for when one can be a realist about a given domain. (shrink)

We describe a short model-theoretic proof of an extended normal form theorem for derivations in predicate logic which implies in PRA a normal form theorem for the arithmetic derivations . Consider the Gentzen-type formulation of predicate logic with invertible rules. A derivation with proper variables is one where a variable b can occur in the premiss of an inference L but not below this premiss only in the case when L is () or () and b is its eigenvariable. Free (...) variables of such derivation are eigenvariables and free variables of its last sequent. Then any sequent derivable in predicate logic has a cut-free derivation with proper variables where the main formula of any antecedent rule is underivable. The proof is by a simple modification of the construction of a countermodel of the formula from the open branch of its canonical proof-search tree. It extends to intuitionistic and higher order systems. The proof of the corresponding normalization theorem outlined in [8] uses the passage to the infinitary derivations enriched by finitary derivations. The normal form after a modification to make it decidable can be considered as a realization of Gentzen's idea stated at the end of [2], that his notion of reduction for arithmetic can be extended to other fields of mathematics. (shrink)

The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality. The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A. More precisely, there exists a function f on the formulas of the language of T such that T + B C implies T + A f.The interpretability (...) logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna ''s axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88]. [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP. The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98]. (shrink)

We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s (...) Paradox in this framework. Furthermore, we define explicit and implicit self-reference in paradoxes in the incompleteness phenomena. (shrink)

The provability logic of a theory $T$ is the set of modal formulas, which under any arithmetical realization are provable in $T$. We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$. We make an analogous modification for interpretability logics. We first study provability logics with restricted realizations and show that for various natural candidates of $T$ and restriction set $\Gamma$, the result is the logic of linear frames. However, for (...) the theory Primitive Recursive Arithmetic (PRA), we define a fragment that gives rise to a more interesting provability logic by capitalizing on the well-studied relationship between PRA and I$\Sigma_1$. We then study interpretability logics, obtaining upper bounds for IL(PRA), whose characterization remains a major open question in interpretability logic. Again this upper bound is closely related to linear frames. The technique is also applied to yield the nontrivial result that IL(PRA) $\subset$ ILM. (shrink)

The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of philosophy (deepening Heidegger’s destruction of it from (...) the pre-Socratics to the Pythagoreans). Husserl’s phenomenology and Heidegger’s derivative “fundamental ontology” as well as his later doctrine after the “turn” are the starting point of the research as established and well known approaches relative to the newly introduced conception of ontomathematics, even more so that Husserl himself started criticizing his “Philosophy of arithmetic” as too naturalistic and psychological turning to “Logical investigations” and the foundations of phenomenology. Heidegger’s “Aletheia” is also interpreted ontomathematically: as a relation of locality and nonlocality, respectively as a motion from nonlocality to locality if both are physically considered. Aristotle’s ontological revision of Plato’s doctrine is “destructed” further from the pre-Socratics' “Logos” or Heideger’s “Language” (after the “turn”) to the Pythagoreans “Numbers” or “Arithmetics” as an inherent and fundamental philosophical doctrine. Then, a leap to contemporary physics elucidates the essence of ontomathematics overcoming the Cartesian abyss inherited from Plato’s opposition of “ideas” versus “things”, and now unifying physics and mathematics, particularly allowing for the “creation from nothing” instead of the quasi-scientific myth of the “Big Bang”. Furthermore, ontomathematics needs another interpretation of arithmetic, propositional logic and set theory in the foundations of mathematics, where the latter two ones are both identified with Boolean algebra, and the former is considered to be a “half of Boolean algebra” in the exact meaning to be equated to it after doubling by a dual anti-isometric counterpart of Peano arithmetic. That unified algebraic realization of the foundations of mathematics is related to Hilbert mathematics in both “narrow and wide senses” where the latter is isomorphic to the qubit Hilbert space, thus underlying all the physical world by the newly introduced substance of quantum information being physically dimensionless and generalizing classical information measured in bits. The substance of information, whether classical or quantum, visualizes the way of the unification of physics and mathematics by merging their foundations in Hilbert arithmetic and Hilbert mathematics: thus how ontomathetics is a “first philosophy”. The relation of ontomathematics to the Socratic “human problematics”, furthermore being fundamental for Western philosophy in Modernity, is discussed. Ontomathematics implies its “substitution” by abstract information (or by “subjectless choice” relevant to it), thus “obliterating the human outline on the ocean beach sand” (by Michel Foucault’s metaphor). A reflection back from the viewpoint of mathematic to Western philosophy as the philosophy of locality ends the study. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

The ‘Turing barrier’ is an evocative image for 0′, the degree of the unsolvability of the halting problem for Turing machines—equivalently, of the undecidability of Peano Arithmetic. The ‘barrier’ metaphor conveys the idea that effective computability is impaired by restrictions that could be removed by infinite methods. Assuming that the undecidability of PA is essentially depending on the finite nature of its computational means, decidability would be restored by the ω-rule. Hypercomputation, the hypothetical realization of infinitary machines through relativistic (...) and quantium models, would thus be capable of breaking the Turing barrier. The speculation is unfounded in principle, apart from issues of physical realizability: The point is that the ω-rule does not cope with all objects entailing the undecidability of PA. As long as the system is consistent, the computational boundary can be established by paradox-like constructions, such as Gödel-Rosser’s and Yablo’s, which are refractory to infinite induction, and do stand as the barrier’s buttresses. (shrink)

The Gödel–Artemov framework offered a formalization of the Brouwer–Heyting–Kolmogorov semantics of intuitionistic logic via classical proofs. In this framework, the intuitionistic propositional logic IPC is embedded in the modal logic S4, S4 is realized in the Logic of Proofs LP, and LP has a provability interpretation in Peano Arithmetic. Self-referential LP-formulas of the type ‘t is a proof of a formula ϕ containing t itself’ are permitted in the realization of S4 in LP, and if such formulas are indeed (...) involved, it is then necessary to use fixed-point arithmetical methods to explain intuitionistic logic via provability. The natural question of whether self-referentiality can be avoided in realization of S4 was answered negatively by Kuznets who provided an S4-theorem that cannot be realized without using directly self-referential LP-formulas. This paper studies the question of whether IPC can be embedded in S4 and then realized in LP without using self-referential formulas. We consider a general class of Gödel-style modal embeddings of IPC in S4 and by extending Kuznetsʼ method, show that there are IPC-theorems such that, under each such embedding, are mapped to S4-theorems that cannot be realized in LP without using directly self-referential formulas. Interestingly, all double-negations of tautologies that are not IPC-theorems, like ¬¬, are shown to require direct self-referentiality. Another example is found in IPC→, the purely implicational fragment of IPC. This suggests that the BHK semantics of intuitionistic logic is intrinsically self-referential. (shrink)

In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an Mkrtychev semantics. Motivation and (...) intuition for FOLP can be found in Artemov and Yavorskaya [4], and are not fully discussed here.This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with. (shrink)

The dissertation studies the mathematical strength of strict constructivism, a finitistic fragment of Bishop's constructivism, and explores its implications in the philosophy of mathematics. ;It consists of two chapters and four appendixes. Chapter 1 presents strict constructivism, shows that it is within the spirit of finitism, and explains how to represent sets, functions and elementary calculus in strict constructivism. Appendix A proves that the essentials of Bishop and Bridges' book Constructive Analysis can be developed within strict constructivism. Appendix B further (...) develops, within strict constructivism, the essentials of the functional analysis applied in quantum mechanics, including the spectral theorem, Stone's theorem, and the self-adjointness of some common quantum mechanical operators. Some comparisons with other related work, in particular, a comparison with S. Simpson's partial realization of Hilbert's program, and a discussion of the relevance of M. B. Pour-El and J. I. Richards' negative results in recursive analysis are given in Appendix C. ;Chapter 2 explores the possible philosophical implications of these technical results. It first suggests a fictionalistic account for the ontology of pure mathematics. This leaves a puzzle about how truths about fictional mathematical entities are applicable to science. The chapter then explains that for those applications of mathematics that can be reduced to applications of strict constructivism, fictional entities can be eliminated in the applications and the puzzle of applicability can be resolved. Therefore, if strict constructivism were essentially sufficient for all scientific applications, the applicability of mathematics of mathematics in science would be accountable. The chapter then argues that the reduction of mathematics to strict constructivism also reduces the epistemological question about mathematics to that about elementary arithmetic. The dissertation ends with a suggestion that a proper epistemological basis for arithmetic is perhaps a mixture of Mill's empiricism and the Kantian views. (shrink)

This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, i.e. Dialectica and Diller-Nahm interpretation as well as Kreisel's modified realization, together with their Troelstra-style hybrids, are applied to constructive as well as (...) classical systems of arithmetic, analysis, and set theory. They yield relative consistency and conservativity results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations. Prerequisites are: familiarity with classical and intuitionistic predicate logic, basics of computability theory, Gödel's incompleteness theorems. (shrink)

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the (...) evaluation of major foundational approaches by a careful examination of two case studies: a partial realization of Hilbert’s program due to Simpson [1988], and predicativism in the extended form due to Feferman and Schütte. -/- Shore [2010, 2013] proposes that equivalences in reverse mathematics be proved in the same way as inequivalences, namely by considering only omega-models of the systems in question. Shore refers to this approach as computational reverse mathematics. This paper shows that despite some attractive features, computational reverse mathematics is inappropriate for foundational analysis, for two major reasons. Firstly, the computable entailment relation employed in computational reverse mathematics does not preserve justification for the foundational programs above. Secondly, computable entailment is a Pi-1-1 complete relation, and hence employing it commits one to theoretical resources which outstrip those available within any foundational approach that is proof-theoretically weaker than Pi-1-1-CA0. (shrink)

In 1902 there arrived in Jena a letter from Russell laying out a proof that shattered Frege’s confidence in logicism, which is widely taken to be the doctrine according to which every truth of arithmetic is re-expressible without relevant loss as a provable truth about a purely logical object. Frege was persuaded that Russell had exposed a pathology in logicism, which faced him with the task of examining its symptoms, diagnosing its cause, assessing its seriousness, arriving at a treatment option, (...) and making an estimate of future prospects. The symptom was the contradiction that had crept into naïve set theory in the form of the set that provably is and is not its own member. The diagnosis was that it is caused by Basic Law V of the Grundgesetze (Frege, In: Grundgesetze der Arithmetik: Begrifsschriftlich abgeleitet, Jena: Herman Pohle, 1893/1903. Translated into English as Basic Laws of Arithmetic, also edited by Philip A. Ebert and Marcus Rossberg, with Crispin Wright, Oxford: Oxford University Press, 2013). Triage answers the question, “How bad is it?” The answer was that the contradiction irreparably destroys the logicist project. The treatment option was nil. The disease was untreatable. In due course, the prognosis turned out to be that a scaled-down Fregean logic could have an honourable life as a theory inference for various domains of mathematical discourse, but not for domains containing the logical objects required for logicism. Since there aren’t such objects, there aren’t such domains. On the face of it, Frege’s logicist collapse is astonishing. Why wouldn’t he have repaired the fault in Law V and gone back to the business of bringing logicism to an assured realization? In the course of our reflections, we will have nice occasion to consider the good it might have done Frege to have booked some time with Aristotle had he been able to. By the time we’re finished, we’ll have cause to think that in the end the Russell might well have begged the question against Frege. (shrink)

continent. 1.4 (2011): 242—252. Introduction The following two works were produced by visual artist Jonas Staal and writer Vincent W.J. van Gerven Oei during a visit as artists in residence at The Bag Factory, Johannesburg, South Africa during the summer of 2010. Both works were produced in situ and comprised in both cases a public intervention conceived by Staal and a textual work conceived by Van Gerven Oei. It was their aim, in both cases, to produce complementary works that could (...) be read “through each other,” in which the movement of artistic construction would be imitated by textual deconstruction and vice versa. Both works deal with the way in which capital, apartheid, and monumentality are interwoven in South-African society. The Missing Link addresses a monument for democracy, erected on the premises of a private corporation running both an amusement park and the Apartheid Museum franchise. The textual intervention accompanying this public intervention investigates the limits of the inclusiveness of the anti-discrimination section in the South-African constitution, itself a monumental work of democracy. The Monument for the Distribution of Wealth deals with the history and eventual dissolution of a monumental square, commemorating the Soweto Uprising, in one of the poorest townships of Johannesburg. The history accompanying this public dismemberment of memory is equally fragmented, which is expressed by the many voices recounting uncertain and perhaps even irrelevant “facts” about the genius loci, the way in which the memorial space has actually entered into the memory of the inhabitants surrounding it. Next to their individual practices, Staal and Van Gerven Oei have worked together on a number of projects ever since 2007, including several art residencies. Their work involves an investigation of the different interfaces between art, politics, and public space in media ranging from theater and public interventions, to video installations and (co-authored) textual works. The Missing Link Missing Link (1) Missing Link (2) Missing Link (3) Intervention on the monument entitled The Seven Pillars of the Constitution , part of the Apartheid Museum in Johannesburg, South Africa. The Seven Pillars represent the constitutional values propagated in South Africa since the abolition of the apartheid regime. The monument and museum were built by the Gold Reef Resorts corporation, which is also responsible for the theme park and casino next to it. By placing the word “capitalism” on the wall surrounding the museum, the capitalist system and the constant social divisions that it implies are interpreted as sophistic continuations of apartheid politics. Through the capitalist system, apartheid is still operational within South African society. Whereas during the apartheid regime, the separation clearly ran along race divisions, in the current, “democratic” system, the same actual separation is sustained without it being an explicit element of the foundations of the country, i.e. the constitution. This intervention foregrounds the constant role of capitalism is both periods. At the same time the intervention acknowledges that contemporary Western artisthood is a mirror of the privileges that are offered by the capitalist system, and the type of artist that it produces. The intervention initiates a critical discourse concerning the capitalist system situated within the disaster of capitalism itself, in other words: through the desire to break with the presumption that art would be able to operate outside the capitalist system and to confirm that art—and the artist himself—is in fact modeled on this system. The public intervention by Staal was supplemented by a textual intervention by Van Gerven Oei: a proposition to alter the seventeenth amendment of the South African constitution. Even though the anti-discrimination legislation in South-Africa is one of the most stringent and inclusive in the world, one factor—wealth—remains outside its scope, thus continuing the schisms along racial lines produced during the apartheid regime: §9.3. The state may not unfairly discriminate directly or indirectly against anyone on one or more grounds, including race, gender, sex, pregnancy, marital status, ethnic or social origin, colour, sexual orientation, age, disability, religion, conscience, belief, culture, language, birth, and wealth. Monument for the Distribution of Wealth Intervention concerning the June 16 Memorial Acre in Central Western Jabavu, one of the poorest townships of Johannesburg. The monument comprises a park on which different are placed recalling an important protest the black population against the former apartheid regime. In 1976, from a school adjacent to the park, they started a massive protest against the introduction of Afrikaans in the school curriculum. The police reacted violently, and shot several hundreds of students. The construction of the June 16 Memorial Acre was started in 2005, and from the start was the paragon of corruption. Coordinated by local politicians, some family members of the protest leader from 1976 gained control of the realization of the monument, outside the regulation through external institutions. The available budget of 41 million rand (at that time well over 5 million euro) was largely embezzled. In the meantime, the monument has become fully dilapidated and defaced. The park has become overgrown with weeds and covered in a layer of dirt, and the local population is slowly plundering the square to use the material for the construction and decoration of their own houses. The Monument for the Distribution of Wealth develops the dynamics already existent around the June 16 Memorial Acre. Without obtaining official permission in advance, several local inhabitants were hired to break down the monument, sort the materials, and offer it to the neighborhood. Thus, the redistribution of wealth after the fall of the apartheid regime is finally taking place, albeit from the mere remains of the capital that was once invested in the community. The words “monument” and “for free” are spray-painted on the stacks of material, both in English and Zulu, as these are locally the most common languages. Van Gerven Oei supplemented Staal’s public intervention with an account of the history of the monument based on a series of interviews. The account clarifies how the different interests within the protest 1976 are reflected in the exceeding decay of the park, and how in the end those interests were represented by the June 16 Memorial Acre. Monument for the Distribution of Wealth 1: Removing stones Monument for the Distribution of Wealth 3: Pulling down statues Monument for the Distribution of Wealth 4: Offering the material Monument for the Distribution of Wealth 5: Offering the material Monument for the Distribution of Wealth 6 The next day A Fragmentary History of the Monument for the Distribution of Wealth, Formerly Known as the June 16 Memorial Acre in Central Western Jabavu, Soweto Vincent W.J. van Gerven Oei The following text, based on interviews and online research aims to provide parts of a history of the park in front of Morris Isaacson High School in Central Western Jabavu, Soweto. The idea for the transformation of the park into a memorial site has its source in the events of June 16, 1976: the start of the the student uprising in Soweto. The development of the park was started in the early 1980s, and the actual transformation into a memorial site, the June 16 Memorial Acre, was initiated in 2005. Over the last few years, several monumental additions have been made to the park: A marble monument with three pillars was revealed on June 16, 2006. A sculpture of a book and several billboards on June 16, 2008. A sculpture of student leader Tsietsi Mashinini on June 16, 2010. The park was transformed into the Monument for the Distribution of Wealth on August 3, 2010. According to the entry “Youth Struggle” on the website South African History Online, the Bantu Education Act was introduced in 1953 . In 1954 , Dr Verwoerd, Minister of Native Affairs, stated: “What is the use of teaching the Bantu child mathematics when it cannot use it in practice? That is quite absurd.” According to the entry “Soweto uprising” on Wikipedia, the Afrikaans Medium Decree was issued in 1974 , forcing all black schools to use Afrikaans and English in a 50-50 mix as languages of instruction. The Regional Director of Bantu Education (Northern Transvaal Region), J.G. Erasmus, told Circuit Inspectors and Principals of Schools that from January 1, 1975 , Afrikaans had to be used for mathematics, arithmetic, and social studies from standard five (7th grade). English would be the medium for general science and practical subjects. Indigenous languages would be used for religion instruction, music, and physical culture. According the entry “Soweto uprising” on Wikipedia, on April 30, 1976 , students from the Orlando West Junior School in Soweto went on strike, refusing to go to school. Their example was followed by other schools in Soweto. A student from Morris Isaacson High School, Toboho “Tsietsi” Mashinini, proposed a meeting on June 13, 1976 to discuss further action. According to Weizmann Hamilton’s article “The Soweto Uprising 1976,” which appeared in the September 1986 edition of Inqaba Ya Basebenzi (Fortress of the Revolution), on June 13, 1976 , the South African Students’ Movement called a meeting at the Donaldson Community Center in Orlando. 300-400 Students representing 55 schools decided to hold a mass demonstration on June 16. According to Brian Mokhele, member of the Joint Community Safety Forum, Dr Edelstein was the first victim of the Soweto uprising and killed the day before the march on June 15, 1976 . Edelstein was an administrator at the pass office in Jabavu and gave golf courses to the local community. Edelstein was put in a garbage bin and pierced by pickaxes. The garbage bin was left at the very spot of the murder for many years. A few years ago, a child was beheaded at the same spot, and the basketball court next to it has been abandoned since. According to Marcus Neustetter, founder of the Trinity Session, this story is untrue. According the entry “Soweto uprising” on Wikipedia, on June 16 , Tsietsi Mashinini led students from Morris Isaacson High School to join up with others who walked from Naledi High School. A crowd of between 3,000 and 10,000 eventually ended up near Orlando High School. According to Raymond Marlowe, a local photographer, Tsietsi Mashinini was heading the march. According to the entry “Hector Pieterson” on Wikipedia, Dr Edelstein died on June 16, 1976 , stoned to death by mob and left with a sign around his neck proclaiming “Beware Afrikaaners.” The first child to die that day was called Hastings Ndlovu. According to Pat Motsiri, Orlando West is claiming struggle heritage through the Hector Pieterson Museum, while Hector Pieterson was from Jabavu. According to Pat Motsiri, his generation effectively struggled between 1980 and 1991, forcing the release of Nelson Mandela and negotiations with the apartheid regime while the 1976-generation was safely in exile. Nevertheless, this has not been recognized in any monument. After the abolition of apartheid, the generation from 1976 returned from exile, occupied important government and ANC positions, creating an abundance of 1976 memorials and refusing to acknowledge that this was only possible because of the younger generation’s struggle. He calls this a generational conflict. According to Archibald Dlamini, the park officer responsible for the Memorial Acre, he started working for the municipality in 1978. In 1981/82 , Isaac Makhele from Pimville, who used to work in the cemetery business, was the first developer of the park. It used to be just a normal park until City Parks decided to develop the Memorial Acre in 2006. In 2007 the work was stopped by the community. According to Brian Mokhele, he left the country in 1989 after he participated in the riots of 1986. But when he returned in 1999 he found that nothing had changed. He says that they were promised to be protected by the Constitution, but that reality is different. The police uses fear to suppress them so that they don’t come out to talk openly. He has been arrested twice, both times harassed and tortured by the police, but in the end always released without indictment. He says that this is their way to threaten communities to back off from politics. According to Moses, who is sitting outside rolling a joint, Brian knows everything. He tells Brian to tell me everything he knows. According to Brian Mokhele, Tsietsi Mashinini was possibly murdered in 1990 during his exile in New York. Two weeks before he was supposed to return to South Africa, his papers in order, he was found dead under mysterious circumstances. His coffin was sealed when he was buried. According to Pat Motsiri, he came up with the idea for the Memorial Acre in 2003 . He submitted the documents for the proposal to the council, which sidelined him as soon as the budget came out in 2005 . According to Brian Mokhele, there was on estimation R 41,000,000 spent to redesign the park and turn it into the Memorial Acre. The millions were divided by Amos Masondo, the mayor of Soweto, the local councilor Bongani D. Zondi, and the director of the city of Johannesburg, Pat Lephunya. They were dividing the money between several contractors: Tsietsi Mashinini’s brothers were involved in the development of the park, they got the tender to do the green areas, the landscaping. Construction was done by other companies, some did the paving, the toilets, etc. EMBA, a private company appointed by the municipality was in control of the money flow, but the money was quickly gone. According to Raymond Marlowe, the contractor bought a BMW with the money. According to Archibald Dlamini, the Mashinini brothers got the tender, so the space would look more like the other places around in Soweto. It was agreed that after they were done, they would return the property to the municipality. They did whatever they could do. According to Mafaisa, a member of the Jabavu business community, he was one of the contractors for the landscaping and the pavement under Mpho Mashinini, one of the brothers. He says that I should contact Mavi for information on Mpho. According to Poi Stuurman, a local youth worker, Mafaisa is one of the guys who ran away with the money. According to Mavi, Mpho Mashinini was never a contractor. The contracts were organized by Sbu Butelezi, the former head of the Gauteng Department for Public Works. The June 16 Foundation and the Mashinini brothers will be the beneficiaries of the park when it is finished. According to Brian Mokhele, City Parks did not accept the Memorial Acre because it was not finished. The rest of the year, the unfinished park is not maintained, as should have happened. This was done deliberately so that in the end they can just clean the whole thing up and have a reason to redo the whole park. According to Brian Mokhele, the Mashinini brothers now work for the government. People that manipulate for money purposes always come from the government’s side. Because the park was left unfinished, the people from the neighborhood are taking away the stones to decorate their own homes with. According to Archibald Dlamini, because City Parks doesn’t accept responsibility of the park, he officially has nothing the guard, except for his cottage, which is municipal property. The thieves come at night and destroy the park, but he cannot do anything because he is sleeping. According to the website of the Thanda Foundation on June 16, 2006 a bronze statue of Hector Pieterson, the first child to die in the 1976 protests, made by Kobus Hattingh and Jacob Maponyane was unveiled in the Maponya Mall in Soweto. The statue is sculpted after the famous image shot by Sam Nzima of Mbuyisa Makhubo carrying the dead body of the boy. The sculpture was sponsored by the Thanda Foundation, founded by the Swedish entrepreneur Dan Olofsson and South-African entrepreneur Matthews Phosa. According to the official website of the City of Johannesburg, the Memorial Acre and Artwork were unveiled in 2006. According to a blog post on sowetouprisings.com, the Memorial Acre was still under development on July 24, 2006. According to Archibald Dlamini, City Parks only cleans up the park once a year just before the June 16 celebrations. Everybody is waiting for the Mashinini brothers to finish their job. The last time he talked with them was in 2007 . According to a sign on the school grounds of the Morris Isaacson High School, the June 16 Trail will be finished in 2008 . According to a blog post on sowetouprisings.com, the Memorial Acre contains another monument erected in Tsietsi’s honor. The monument was created as part of the Sunday Times Heritage Public Art program. Its physical form resembles a giant book which symbolizes the crisis in education experienced in 1976. On the face of the book is the map of the route taken by the students from Morris Isaacson High School in Central Western Jabavu to Phefeni Junior Secondary in Orlando West (currently the site of the Hector Pieterson Museum), while the back cover of the ‘book’ is inscribed with a tribute to Tsietsi Mashinini. The monument was revealed on June 16, 2008 . According to Marcus Neustetter, the billboards on the Memorial Acre were part of a school project realized in 2008. Following several workshops, the students from different high schools along the June 16 Trail were invited to work with artists on the billboards, while the neighborhood community was invited to watch the process during the festivities on June 15 and 16, 2008 . The billboards were supposed to be removed because of construction works on the Memorial Acre, which never ended up happening. According to Brian Mokhele, the former toilet facilities were converted into a house for the park officer. This park officer has been working for city parks for more than 12-15 years, but does nothing here, because the park, including the new toilet buildings, is not finished. The government is now moving around looking for people to take this job because they stopped it. They confronted everybody who was going in and chased them away. According to John, in 2009 , some girls, around 16 or 17 years old, were raped by four men who had been drinking in a local shebeen. When the bar quit they said that they would go home by car, but instead raped the girls on the Memorial Acre nearby. This happened in the unfinished toilets, because the doors couldn’t be closed. According to Brian Mokhele, there used to be some fences around the park because of the construction work that was eventually stopped, but these were also stolen. According to Archibald Dlamini, people from the neighborhood started about two and a half years ago, and the last piece was stolen near the end of 2009 . Sometimes he would catch someone with a roll of fence, and then use it for his own cottage. According to the official website of the City of Johannesburg, a statue of Tsietsi Mashinini by Johannes Pokhela was revealed on June 16, 2010 , “Youth Day.” According to Shirley Makutoane, deputy principal of Isaac Morrison High School, the statue of Tsietsi Mashinini, funded by the June 16 Foundation, has temporarily been placed within the school perimeter. The statue will be moved to the Memorial Acre when it will be finished, in 2011 . According to Brian Mokhele, beside the June 16 Foundation, there is also a June 16 Memorial Acre Foundation. Both foundations are quarreling about the money involved in the Memorial Acre project. Nobody knows who’s involved in them. According to Marcus Neustetter, the June 16 Foundation consists of people that were part of 1976 protest movement, local government officials, representatives of the Hector Pieterson Museum, and the council. According to students from the Isaac Morrison High School, the statue of Tsietsi Mashinini is on the school ground because on the Memorial Acre it would be vandalized by youths from White City, an adjacent neighborhood. Accorcing to Brian Mokhele, the statue of Tsietsi should eventually be mounted on the Memorial Acre. It is wrong that the statue is in the school at the moment, because it is not a public school. He wants the statues to depict the massiveness of the force that was coming into Soweto after the protests. According to Brian Mokhele, City Parks, City of Jo’burg, City Lights, and SAPS are making some sort of plan to take the plan back. They want to remove the trees from the Memorial Acre, and redesign the Memorial Acre into a relaxing park, without political content. They want to depoliticize the square. In doing so,they will have their own employment and not use local workforces. According to Brian Mokhele, the community wants to remove the monuments, amphitheater, and sculptures from the Memorial Acre because they do not resemble anything. The sculptures should be depicting the truth of what happened, because the Memorial Acre is a political heritage site. He wants to involve the people that actually participated in the struggle to make the monument so that everyone can enjoy it and get a better understanding of the struggle heritage. Therefore, he proposes collective ideology in which everyone has a say. This would prevent future vandalization of the monument. According to Pat Motsiri, the sculptures must depict the event around June 16, 1976. Like the story of Dr Edelstein, who was pierced by pickaxes, forced into a garbage bin and burned alive. According to Jonas Staal, the Memorial Acre should be destroyed, its elements stacked on pallets, thus forming the Monument for the Distribution of Wealth . According to Mafaisa, his men can do the work quickly. He has about twenty men working under him. (shrink)

Husserl’s lifelong interest in Kant eventually becomes a preoccupation in his later years when he finds his phenomenology in competition with Neokantianism for the title of transcendental philosophy. Some issues that Husserl is concerned with in Kant are bound up with the works of Lambert. Kant believed that the role played by principles of sensibility in metaphysics should be determined by a “general phenomenology” on which Lambert had written. Kant initially believed that man is capable only of symbolic cognition, not (...) intellectual intuition. Lambert saw an increasing need in mathematics for symbolic cognition as exemplified in his proofs of the irrationality of π and e. Kant takes from Leibniz and Lambert an unrestricted notion of construction, allowing him to view mathematics as constructing its concepts in intuition, while Lambert’s proofs convince him that all mathematical problems are eventually solvable. Husserl criticizes Kant’s intuitionism for its inadequate accommodation of meaning to intuition, which he redresses with his theory of categorial intuition. This may improve on Kant’s intuition of the axiom of parallels but not so clearly on his spatial intuition. Husserl opposes Kant’s view of space as the form of outer intuition with his own view of it as the form of things. Husserl’s exploration of the geometry of visual space, which involves his earliest uses of epoché and reduction, converges however with Hilbert’s logical analysis of Kantian spatial intuition in leading to Euclidean spatial judgments. Hilbert’s analysis leads him to affirm the solvability of all well posed mathematical problems, a thesis complicated by the outbreak of logical paradoxes. Untroubled by such paradoxes, Husserl develops a supramathematics of all possible deductive systems whose completeness implicitly would also provide solutions of all such problems. Husserl’s full transcendental turn coincides with his realization that in effecting his Copernican turn, Kant was really the first to detect the “secret longing” of modern philosophy for a phenomenological clarification of being. Husserl now finds that Kant’s transcendental deductions presuppose a pure ego not adequately analyzed by Kant that survives the phenomenological reduction. Husserl’s idealism leads him to develop his own intuitionism, which adds to Kant’s, a “method of clarification” of mathematical concepts intended to clarify difficult impossibility proofs, but neither Husserl nor Kant base arithmetic on time. Husserl’s critique of the room left in Kant’s idealism, for things in themselves, leads to his own monadological solution of the problem of intersubjectivity. Husserl’s final judgment on Kant is that his form of transcendental idealism did not enable him to achieve absolute subjectivity through a genuine transcendental reduction. (shrink)

Are the laws of nature among the eternal truths that, according to Descartes, are created by God? The basis of those laws is the immutability of the divine will, which is not an eternal truth, but a divine attribute. On the other hand, the realization of those laws, and in particular, the quantitative consequences to be drawn from them, depend upon the eternal truths insofar as those truths include the foundations of geometry and arithmetic.

LetA H be the Herbrand normal form ofA andA H,D a Herbrand realization ofA H. We showThere is an example of an (open) theory ℐ+ with function parameters such that for someA not containing function parameters Similar for first order theories ℐ+ if the index functions used in definingA H are permitted to occur in instances of non-logical axiom schemata of ℐ, i.e. for suitable ℐ,A In fact, in (1) we can take for ℐ+ the fragment (Σ 1 0 (...) -IA)+ of second order arithmetic with induction restricted toΣ 1 0 -formulas, and in (2) we can take for ℐ the fragment (Σ 1 0,b -IA) of first order arithmetic with induction restricted to formulas VxA(x) whereA contains only bounded quantifiers.On the other hand, $$PA^2 \vdash A^H \Rightarrow PA \vdash A,$$ wherePA 2 is the extension of first order arithmeticPA obtained by adding quantifiers for functions andA∈ℒ(PA). This generalizes to extensional arithmetic in the language of all finite types but not to sentencesA with positively occurring existential quantifiers for functions. (shrink)

A variant of the notion of symmetric constructive realizability is introduced where the information about the symmetric constructive truth or falsity of an arithmetical formula is expressed by a single natural number. The methods of transformations of such a realization to the realizations of known kinds and those of reverse transformations are given. The formal arithmetical system based on such a realizability is investigated.

Nelson has presented a constructive arithmetic with a negation opera- tion () dierent from the ordinary intuitionistic one . In [5] he presents a variant of Kleene's realization semantics for intuitionistic arithmetic, and proves that relative to this interpretation the arithmetic language with { has the same expressive power as the usual intuitionistic one, and fact certain theories of arithmetic incorporating his negation are equivalent to corresponding systems of intuitionistic arithmetic. A Fitch style natural deduction formulation ) of the (...) pure rst order logic that may be extracted, from Nelson's work may be obtained from that for intuitionistic rst order logic by rst dropping the intuitionistic rule of negation intro- duction and then adding rules guaranteeing the De Morgan equivalences, their quantier analogues, and the equivalence of anegated implication with the conjunction of its antecedent and the negation of its consequent. Given the De Morgan equivalences, conjunction and the existential quantier may he treated as dened operators. (shrink)

In his “Begriffsschrift, a Formalized Language of Pure Thought Modelled upon the Language of Arithmetic,” published in 1879, Frege attributes his approach to Leibniz’ idea of a “lingua characteristica.” And it can be said that, in the field of logic and the foundations of mathematics, he indeed achieved the realization of the essential aspects of Leibniz’ program.

This paper is devoted to the reconstruction of the implicit logic of Plato’s Par-menides. The reconstructed logic, F, makes it possible to form a new semi-intuitionistic system of logic of predicates, FN. The axioms of Peano Arithmetic (PA) and an axiom of infinity follow from FN. Therefore, FN can be seen as a new attempt at the realization of Frege’s logicist program. Some very strong systems can be seen as other variants of FN, e.g. Leśniewski’s ontology. The hypothesis from (...) Parmenides II contains proof of the existence of the two highest principles, i.e. the One and the Dyad, their mutual relationship, their relations to other things, and the reasoning regarding the mutual relationship follows some exact formal rules. Six types of Plato’s negation of a predicate are defined. The system is a first-order logic with non-classical negation of a predicate (local negation) that is non-definable by classical sentential negation. Therefore, the implicit logic of Plato’s Parmenides differs from classical syllogistics (formed in the Łukasiewicz’s style) as well as from the classical predicate calculus. (shrink)

Research in the fields of pragmatics has highlighted important differences in speech act realisation strategies and the perception of contextual variables across lingua-cultures. This particularly applies for requests, which are potentially face-threating acts and important expressions of cultural behaviour, as their performance is influenced by culturally-embedded perspectives on rights and obligations. Although some languages have been widely investigated in terms of request realisation, such as English, little research has been done on Italian. This study examines request realisation strategies in Italian, (...) in terms of Head Acts and request perspective, and the impact of the sociopragmatic factors of social distance and weight of imposition of the request on strategy choice amongst eight Italian speakers, by means of open-ended roleplays. The data was analysed by using a coding scheme based on Blum-Kulka and Olshtain and revealed that the Italian speakers where more influenced by social distance, which in turn impacted on the choice of request perspective. They were shown to prefer using hearer-orientation, which reflected in the verb conjugation of the Head Acts, since this perspective allows them to do relational work with the hearer, by either addressing the recipient with the familiar tu or with the formal lei. (shrink)

The article argues that the structure of self-realisation is bipolar, and that genuine self-realisation should be conceptualised as a phenomenon of connectedness manifesting itself simultaneously in both a horizontal and a vertical dimension. As a relation between individual self-assertion and self-exposition on the one hand and ideals and values in relation to individually transcending horizons of meaning on the other hand, genuine self-realisation develops through different self-organisational levels, with the relational character of the self being transformed in ways corresponding to (...) the level of its self-organisation. 2012 APA, all rights reserved). (shrink)

Arithmetical cognition is the result of enculturation. On a personal level of analysis, enculturation is a process of structured cultural learning that leads to the acquisition of evolutionarily recent, socio-culturally shaped arithmetical practices. On a sub-personal level, enculturation is realized by learning driven plasticity and learning driven bodily adaptability, which leads to the emergence of new neural circuitry and bodily action patterns. While learning driven plasticity in the case of arithmetical practices is not consistent with modularist theories (...) of mental architecture, it can be enriched by the theory of neural reuse. According to neural reuse, cerebral regions are reused to contribute to multiple neural circuits in functionally constrained ways throughout ontogeny. By hypothesis, learning driven plasticity is complemented by learning driven bodily adaptability, which suggests that there is an interesting functional relationship between finger gnosis, finger counting, and arithmetical practices. The emerging perspective on enculturated arithmetical cognition will be complemented by considerations on associated developmental and acquired disorders, namely developmental dyscalculia and acquired acalculia. The upshot is that we need to take the cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturation into account in order to arrive at a better understanding of the phylogenetic and ontogenetic conditions of arithmetical cognition. (shrink)

Multiple realisation prompts the question: how is it that multiple systems all exhibit the same phenomena despite their different underlying properties? In this paper I develop a framework for addressing that question and argue that multiple realisation can be reductively explained. I illustrate this position by applying the framework to a simple example – the multiple realisation of electrical conductivity. I defend my account by addressing potential objections:contra Polger and Shapiro, Batterman, and Sober, I claim that multiple realisation is commonplace, (...) that it can be reductively explained, but that it requires asui generisreductive explanatory strategy. (shrink)

S’il y a bien une urgence à prendre en charge la crise écologique, comme le reconnaît Arne Naess, on ne voit cependant pas bien de prime abord dans quelle mesure le traitement de cette urgence supposerait une réforme ontologique, une nouvelle philosophie de la nature, et encore moins pourquoi, si l’on se tourne vers le versant éthique de la pensée de Naess, il faudrait s’en remettre, en dernier ressort, à un principe de réalisation de soi. Les réformes pratiques, la modification (...) de nos condui... (shrink)

When conceived as an empirical claim, it is natural to wonder how one might test the hypothesis of multiple realization. I consider general issues of testability, show how they apply specifically to the hypothesis of multiple realization, and propose an auxiliary assumption that, I argue, must be conjoined to the hypothesis of multiple realization to ensure its testability. I argue further that Bechtel and Mundale go astray because they fail to appreciate the need for this auxiliary assumption. (...) †To contact the author, please write to: Department of Philosophy, University of Wisconsin–Madison, 5185 Helen C. White Hall, 600 North Park Street, Madison, WI 53706; e‐mail: [email protected]. (shrink)

Pattern parametrisation has the potential to address the inefficiencies and environmental concerns associated with traditional pattern construction practices dominating both industry and academia. However, its adoption is still limited due to a lack of realisation despite its presence in CAD technical applications for decades. This has impeded its ability to shift the pattern industry and academia to a more efficient and sustainable paradigm. Using mixed methods and a three-phased quasi-experimental design, this study aims to enhance the realisation of pattern parametrisation (...) across various industry and academic settings and assess participants’ behavioural intentions to adopt it. Findings from a convenience sample of 40 UK-based participants, analysed using Kirkpatrick’s (1994) model, indicate increased recognition and intention to adopt pattern parametrisation, as evidenced by participants identifying its diverse applications and aspiring to integrate it into their future goals. This study contributes to theory and has practical applications for both academia and industry. (shrink)

This book argues that the ability to integrate biological and psychological levels of understanding is inhibited by two important issues. Ideas about the autonomic nervous system are integrated with those from the author's previous text A Basic Theory of Neuropsychoanalysis.

Patient autonomy is a fundamental principle in end of life decision making. However, its realisation may take a variety of forms. Discourse analysis was conducted in a qualitative interview study of 19 physicians. The physicians made use of three different discourses, each of which contained a specific understanding of patient autonomy and a physician’s proper activities in the context of end of life decision making.

This article addresses the question raised by the Anthropocene of rethinking the concept of autonomy which, in the conditions of the new geological epoch, is subject to a crisis of legitimation. It explores the ‘strong hypothesis’ according to which nature is a necessary condition of our qualitative experience of the world and a constitutive relation of autonomy defined as the self-realisation of individual identity. With this aim in mind, the article attempts to rethink the concept of recognition in order to (...) conceive a recognising attitude of nature in the form of love of nature as a form of adequate recognition. Rethinking recognition can serve as foundation of an ‘objective’ theory of autonomy, that is, a theory that explains how nature can be defined as a condition and constitutive relation of autonomy. The article, therefore, proposes to reformulate the concept of autonomy as the self-realisation of an ecological or environmental identity in the form of the self-realisation of an ecological ethos, that is, an attitude of respect and care for nature. This enquiry, ultimately, is a contribution to the task of rethinking the basis of our conceptions of autonomy and freedom in the Anthropocene, so that the idea of autonomy can legitimately constitute the central value of the social transformation that is needed to face the ecological crisis. (shrink)