Based on the computation mode introduced in [13], we deal with the time complexity of computations over arbitrary first-order structures.The main emphasis is on parameter-free computations. Some transfer results for solutions of P versus NP problems as well as relationships to quantifier elimination are discussed. By computation tree analysis using first-order formulas, it follows that P versus NP solutions and other results of structural complexity theory are invariant under elementary equivalence of structures.

We present a model of computation for string functions over single-sorted, total algebraic structures and study some basic features of a general theory of computability within this framework. Our concept generalizes the Blum-Shub-Smale setting of computability over the reals and other rings. By dealing with strings of arbitrary length instead of tuples of fixed length, some suppositions of deeper results within former approaches to generalized recursion theory become superfluous. Moreover, this gives the basis for introducing computational complexity in (...) a BSS-like manner. Relationships both to classical computability and to Friedman's concept of eds computability are established. Two kinds of nondeterminism as well as several variants of recognizability are investigated with respect to interdependencies on each other and on properties of the underlying structures. For structures of finite signatures, there are universal programs with the usual characteristics. For the general case of not necessarily finite signature, this subject will be studied in a separate, forthcoming paper. (shrink)

This paper was motivated by the following two questions which arise in the theory of complexity for computation over ordered rings in the now famous computational model introduced by Blum, Shub and Smale: 1. is the answer to the question P = ?NP the same in every real-closed field?2. if P ≠ NP for , does there exist a problem of which is NP but neither P nor NP-complete ?Some unclassical complexity classes arise naturally in the study of these (...) questions. They are still open, but we could obtain unconditional results of independent interest.Michaux introduced/const complexity classes in an effort to attack question . We show that , answering a question of his. Here A is the class of real problems which are algorithmic in bounded time. We also prove the stronger result: , where PAR stands for parallel polynomial time. In our terminology, we say that is A-saturated and PAR-saturated. We also prove, at the nonuniform level, the above results for every real-closed field. It is not known whether is P-saturated. In the case of the reals with addition and order we obtain P-saturation ). More generally, we show that an ordered -vector space is P-saturated at the nonuniform level ).We also study a stronger notion that we call P-stability. Blum, Cucker, Shub and Smale have shown that fields of characteristic 0 are P-stable. We show that the reals with addition and order are P-stable, but real-closed fields are not.Questions and and the/const complexity classes have some model theoretic flavor. This leads to the theory of complexity over “arbitrary” structures as introduced by Poizat. We give a summary of this theory with a special emphasis on the connections with model theory and we study/const complexity classes from this point of view. Note also that our proof of the PAR-saturation of shows that an o-minimal structure which admits quantifier elimination is A-saturated at the nonuniform level. (shrink)

In this paper we deal with the logical description of complexity classes arising in the real number model of computation introduced by Blum, Shub, and Smale [4]. We adapt the approach of descriptive complexity theory for this model developped in [14] and extend it to capture some further complexity classes over the reals by logical means. Among the latter we find NC R , PAR R , EXP R and some others more.

1. One theory or many? In 2004 a very interesting and readable article by Lenore Blum, entitled “Computing over the reals: Where Turing meets Newton,” appeared in the Notices of the American Mathematical Society. It explained a basic model of computation over the reals due to Blum, Michael Shub and Steve Smale (1989), subsequently exposited at length in their influential book, Complexity and Real Computation (1997), coauthored with Felipe Cucker. The ‘Turing’ in the title of Blum’s article refers of (...) course to Alan Turing, famous for his explication of the notion of mechanical computation on discrete data such as the integers. The ‘Newton’ there has to do to with the well known numerical method due to Isaac Newton for approximating the zeros of continuous functions under suitable conditions that is taken to be a paradigm of scientific computing. Finally, the meaning of “Turing meets Newton” in the title of Blum’s article has another, more particular aspect: in connection with the problem of controlling errors in the numerical solution of linear equations and inversion of matrices,Turing (1948) defined a notion of condition for the relation of changes in the output of a computation due to small changes in the input that is analogous to Newton’s definition of the derivative. The thrust of Blum’s 2004 article was that the BSS model of computation on the reals is the appropriate foundation for scientific computing in general. By way of response, two years later another very interesting and equally readable article appeared in the Notices, this time by Mark Braverman and Stephen Cook (2006) entitled “Computing over the reals: Foundations for scientific computing,” in which the authors argued that the requisite foundation is provided by a quite different “bit computation” model, that is in fact prima facie incompatible with the BSS model. The bit computation model goes back to ideas due to Stefan Banach and Stanislaw Mazur in the latter part of the 1930s, but the first publication was not made until Mazur (1963).. (shrink)

We reduce to a standard circuit-size complexity problem a relativisation of the $P = NP$ question that we believe to be connected with the same question in the model for computation over the reals defined by L. Blum, M. Shub, and S. Smale. On this occasion, we set the foundations of a general theory for computation over an arbitrary structure, extending what these three authors did in the case of rings.

Continuing the paper [7], in which the Blum-Shub-Smale approach to computability over the reals has been generalized to arbitrary algebraic structures, this paper deals with computability and recognizability over structures of infinite signature. It begins with discussing related properties of the linear and scalar real structures and of their discrete counterparts over the natural numbers. Then the existence of universal functions is shown to be equivalent to the effective encodability of the underlying structure. Such structures even have universal functions satisfying (...) the s-m-n theorem and related features. The real and discrete examples are discussed with respect to effective encodability. Megiddo structures and computational extensions of effectively encodable structures are encodable, too. As further variants of universality, universal functions with enumerable sets of program codes and such ones with constructible codes are investigated. Finally, the existence of m-complete sets is shown to be independent of the effective encodability of structures, and the linear and scalar structures are discussed once more, under this aspect. (shrink)

Friendship, Altruism, and Morality, originally published in 1980, gives an account of "altruistic emotions" and friendship that brings out their moral value. Blum argues that moral theories centered on rationality, universal principle, obligation, and impersonality cannot capture this moral importance. This was one of the first books in contemporary moral philosophy to emphasize the moral significance of emotions, to deal with friendship as a moral phenomenon, and to challenge the rationalism of standard interpretations of Kant, although Blum’s "sentimentalism" owes more (...) to Schopenhauer than to Hume. It was a forerunner to care ethics, and feminist ethics more generally; to virtue ethics; and to subsequent influential interpretations of Kant that attempted to room for altruistic emotion and friendship, and other forms of particularism and partialism. In addition, the work has been widely influential in religious studies, political theory, bioethics, and feminist ethics. (shrink)

The essays in this collection examine the moral import of emotion, motivation, judgment, perception, and group identifications, and explore how all these psychic capacities contribute to a morally good life. They examine moral exemplars and the "moral saints" debate, the morality of rescue during the Holocaust, role morality as lying between "personal" and "impersonal" perspectives, Carol Gilligan's theory of women and morality, Iris Murdoch's moral philosophy, and moral responsiveness in young children.

Taking a cue from one of the most (in)famous postmodern thinkers, Friedrich Nietzsche, the essays in this book put forth “experiments” in thought rather than arguments for fixed conclusions. Blum brings John Howard Yoder to the same table with Nietzsche, Michel Foucault, and Jacques Derrida, and provides a provocative glimpse of what the resulting conversation might look like. As Anne Lamott and others have recently insisted, faith is not the opposite of doubt, but of certainty. Blum’s essays explore some of (...) our commonly held ways of talking about knowledge, meaning, commitment, and action. He suggests that some postmodern theoretical work, often dismissed or assumed to be anti-Christian, is well worth bringing into contemporary Anabaptist-Mennonite conversations about discipleship and corporate life. Part of the Polyglossia series, this book is intended for conversation among academics, ministers, and laypersons regarding knowledge, beliefs, and practices of the Christian faith. (shrink)

This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the (...) quantum world of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 61.1 (2000) 59-74 [Access article in PDF] Francesco Patrizi in the "Time-Sack": History and Rhetorical Philosophy * Paul Richard Blum Contemporary theory of history is much concerned with the narrative structure of history, its nature, and its epistemic status. 1 The problem is not only that sources present events mostly wrapped in narrative language but also that temporality is an inherent feature (...) both of the events told and of storytelling. 2 Narrativity and temporality touch upon basic metaphysical and anthropological questions, as Paul Ricoeur has pointed out, if narration is to be understood as self-explanation of a human being in whom "time" occurs as "being-in-time." 3 The following paper cannot claim to contribute to the current debate but presents Francesco Patrizi (1529-97) 4 as a Renaissance philosopher who addressed several of these problems. In discussing his conceptions of history and time, however, it is the aim of this paper only to locate these within his own philosophy. [End Page 59]One of the unresolved problems in the writings of Francesco Patrizi is the difference between his earlier contributions to the humanistic canon and his late philosophical main treatise, Nova de universis Philosophia. The earlier writings conform to the usual humanist literary topics: the political program of a città felice, the treatises on honor, the poetic fury, Petrarch (1553), and then his two dialogues on history (1560) and rhetoric (1562). The two works which followed, the Discussiones peripateticae (1571) and the Poetics (1586), show a characteristic development of humanist thinking, namely, the differentiation of purely philological from essentially philosophical literature.Patrizi's Discussiones peripateticae 5 is a polemic against Aristotle, written from a Platonic viewpoint, but his own philosophy is concealed under a mass of philological material. In an attempt that seeks to be virtually definitive, he cites passages from Aristotle and the Peripatetic tradition in order to point out mistakes and contradictions. It was on this account that Giordano Bruno heaped ridicule on him, calling him "sterco di pedanti." Simply put, he tells us, Patrizi demonstrates "how like he is to an ox or an ass." One cannot say that he has understood Aristotle either well or ill, but merely that he has read him and reread him, cut him up and stitched him together, compared him with a thousand other Greek writers, friends and foes alike, and altogether gone to an immense deal of trouble, not only to no purpose whatsoever but also to our infinite disappointment. Anyone who wishes to see into just what folly and self-regarding vanity pedantic drudgery can plunge and sink should read this book. 6This was one contemporary reaction to Patrizi's attempt to explore all the possibilities of a humanistic style of literary criticism, via the comparison between Plato and Aristotle. 7The Poetics 8 is essentially divided into two quite distinct halves: Della poetica la deca istoriale and Della poetica la deca disputata. The first is a lexicon of [End Page 60] the ancient authors, categories, styles, etc., and the second a series of dissertations on the theory of poetry but these, too, with abundant reference to both ancient and contemporary literature.Finally, and entirely different in style, there is his principal work, the Nova de universis Philosophia (1591). 9 Here the philosopher systematically departs from his accustomed field, ranging from a theory of light (Panaugia), via a discussion on theological principles (Panarchia) and a theory of the soul (Pampsychia) to the Pancosmia, a treatise on cosmology and physics. Even to this work he appends a number of documentary excerpts, and there is no lack of excursions into literary history, but the main part of the work is entirely axiomatic--"methodical"--in approach and argumentative in style.These works of Patrizi represent the development of philosophical humanism in the sixteenth century, a development away from a unified presentation of the problems of the human sciences by the explicit use of the tools of literary rhetoric, and towards the research of philological sources on the one hand and... (shrink)

The question may be asked why many workers are still being paid below subsistence wages and I believe the answer can be found in the confusion over what exactly constitutes a “living wage” and who has the duty to pay these wages. This article therefore clarifies what a living wage is and gives a concrete example of how a living wage can be calculated. To understand who has the obligation to pay living wages I look to the theory of (...) Alan Gewirth on individual and institutional responsibility and the account of Robert Mayer on structural exploitation to argue that all parts of the supply chain have the duty. The final part of this paper willoutline the inclusion of a living wage calculation into corporate codes of conduct to ensure that workers at the end of the supply chain receive living wages. (shrink)

Syncretism is a challenge to modern philosophy, but it was the main characteristic of Giordano Bruno’s thought. This has been made clear by Frances A. Yates, who in interpreting Bruno and Renaissance Hermeticism was not afraid of connecting theories and cultural expressions which on the surface are alien to philosophy. In doing so Yates was congenial to her object of study, as syncretism of theory was no mere side effect of Hermeticism, but had a philosophical aim. This aim can (...) be identified as the desire to connect the world and its general principle, as well as the powers of the human mind, into a philosophical narrative which strives at unifying oppositions and contradictions. (shrink)

The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an (...) integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post–World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly disparate and dispersed field to benefit from the postwar changes in the scientific landscape. (shrink)

This book demonstrates that ancient Christian Gnosticism was an ancient form of cultural criticism in a mythological garb. It establishes that, much like modern forms of critical theory, ancient Gnosticism was set on deconstructing mainstream discourses and cultural premises. Strains of critical theory dealt with include the Frankfurt School, queer theory, and poststructural philosophy. The book documents how in both ancient Gnosticism and modern critical theories issues that used to serve as premises for discussion or as concepts (...) relegated to the realms of the “natural” and the “given” in their respective historical contexts, are transformed into objects of contention. The main aim of this book is to salvage the historical category of Gnosticism from its present scholarly disavowal, if only because Gnosticism, when read as a cultural, and not only a religious phenomenon, presents us an ancient form of culture criticism which would be hard to parallel until (post) modernity. While Hans Jonas remarked many years ago that “something in Gnosticism knocks at the door of our Being and of our twentieth-century Being in particular,” by the 21st century global world this something has already entered and lives with us. We can thus still benefit from another perspective, even if it comes from Mediterranean people who lived almost 2,000 years ago. (shrink)

Contemporary argumentation theory or informal logic is the appropriate logical basis of qualitative inquiry. The communicative principles of cooperation and charity are essential within argumentation theory. An optimal observance of these principles, for strategical reasons for example, is of methodological relevance to qualitative research. In addition, an ethically motivated optimalization of the observance may also enhance methodological quality, especially dialogical intersubjectivity or openness. Moreover, this ethically motivated observance may be supported by a philosophy of life, which may stimulate (...) opting for qualitative inquiry and promote its methodological quality. (shrink)

In The Sovereignty of Good Iris Murdoch suggests that the central task of the moral agent involves a true and loving perception of an- other individual, who is seen as a particular reality external to the agent. Writing in the 1960s she claimed that this dimension of morality had been "theorized away" in contemporary ethics. I will argue today that 20 years later, this charge still holds true of much contemporary ethical theory.

The “diversity” framework the Supreme Court has imposed on affirmative action weakens its justice import in theory and practice. The increasing alignment of wealth with attendance at selective institutions betokens a diminishing quality of student at those institutions. So some of the perceived advantages of affirmative action rely on an increasingly false sense of the quality differences between more and less highly-ranked institutions. Aligning those rankings with the quality of student (and quality of instruction at the different kinds of (...) institution) would have the net effect of benefiting black and Latino students as a group. More generally, improving the quality of education and the standing of less selective higher education institutions is an urgent racial educational justice challenge of the current moment, from which affirmative action diverts attention. (shrink)

Carol Blum's book is an extraordinarily important and beautifully written work for which I have the deepest admiration. No one seriously interested in the French Revolution or in eighteenth-century political language and theory can afford not to read it.

Based on in-depth interviews and fieldwork, this article examines mothers raising kids with invisible, social/emotional/behavioral disabilities to refine feminist theories of mother-blame. The mother-valor/mother-blame binary holds mothers responsible for families and future citizens, maintaining this “natural” care at the center of normative femininity. The author explores how mothers raising such burdensome children understand their experiences and makes three arguments: Fewer mothers are blamed for causing their child's troubles in an era of “brain-blame,” but more are blamed as proximate causes if (...) they do not make unrelenting efforts, paralleling “concerted cultivation,” to resolve them; such mothers often exceed concerted cultivation, as they seize authority, as vigilantes, within educational and medical systems in the midst of turf wars, cost containment, and a resulting proliferation of medication treatments; and this maternal speedup holds mothers accountable for feminizing ties to sons, for policing gender boundaries while policing their own feminine care. In sum, mothers raising invisibly disabled kids may represent the model of maternal valor for an era of public stinginess and extensive medicalization. (shrink)

Zen and the Unspeakable God reevaluates how we study mystical experience. Forsaking the prescriptive epistemological box that has constrained the conversation for decades, ensuring that methodology has overshadowed subject matter, Jason Blum proposes a new interpretive approach—one that begins with a mystic’s own beliefs about the nature of mystical experience. Blum brings this approach to bear on the experiential accounts of three mystical exemplars: Meister Eckhart, Ibn al-ʿArabi, and Hui-neng. Through close readings of their texts, he uncovers the mystics’ own (...) fundamental assumptions about transcendence and harnesses these as interpretive guides to their experiences. The predominant theory-first path to interpretation has led to the misunderstanding and misrepresentation of individual mystical experiences and fostered specious conclusions about cross-cultural comparability among them. Blum’s hermeneutic invites the scholarly community to begin thinking about mystical experience in a new way—through the mystics’ eyes. Zen and the Unspeakable God offers a sampling of the provocative results of this technique and an explanation of its implications for theories of consciousness and our contemporary understanding of the nature of mystical experience. (shrink)

Giordano Bruno was a philosopher in his own right. However, he was famous through the centuries due to his execution as a heretic. His pronouncements against teachings of the Catholic Church, his defence of the cosmology of Nicholas Copernicus, and his provocative personality, all this made him a paradigmatic figure of modernity. Bruno’s way of philosophizing is not looking for outright solutions but rather for the depth of the problems; he knows his predecessors and their strategies as well as their (...) weaknesses, which he exposes satirically. This introduction helps to identify the original thought of Bruno who proudly said about himself: “Philosophy is my profession!” His major achievements concern the creativity of the human mind studied through the theory of memory, the infinity of the world, and the discovery of atomism for modernity. He never held a permanent office within or without the academic world. Therefore, the way of thinking of this “Knight Errant of Philosophy” will be presented along the stations of his journey through Western Europe. (shrink)

Transcententals such as 'being', 'one', 'good', and 'something' are part and parcel of the medieval heritage in Aristotelian philosophy. Since transcendentals must be predicated of every particular thing, they are essential both to argumentation and to metaphysics, specifically to the theory of Platonic Forms. Lorenzo Valla (1407-1457) hence concluded that 'thing' (res) is the only transcendental, distinct from metaphysical universality that applies to God exclusively. Marsilio Ficino (1433-1499) in drawing upon Platonism as entailed in the metaphysics of universals and (...) in theology argued that 'one' must be the transcendental that precedes 'being' – at least in God. Related to that was his epistemological claim (which became popular in Cartesianism) that cognition of external reality is controlled by internal ideas, which in Platonic terms originate in God's ideas. Therefore it seemed logical to Tommaso Campanella (1568-1639) to infer that the first three transcendentals (being, true, good) produce the tri-une God in such a way that these refer to all other properties of things (epistemologically and ontologically). Those approaches were known to Francisco Suárez (1548-1617) who endeavored to keep the semantic and the ontological meaning of transcendentals combined by interpreting Platonic Forms as principles of understanding and of creation. In doing so he developed teachings of Thomas Aquinas. – The Jesuit Suárez is known as a leading Aristotelian of the Second Scholasticism. In this chapter his metaphysics is portrayed as an appropriation and a critique of Renaissance Platonism. (shrink)

Renaissance magic was an attempt to supply Platonism with a philosophy of nature that could compete with Aristotelian physics. It was expected to heal the increasing breach between science and faith. However, the basic presupposition of every magic worldview, the notion of a living universe, favors immanentism and arguably hastened the rise of secularism. Secularism, it should be noted, was not an identifiable set of theories but a process towards modernity with its correspondent philosophical theology. Three different stages in that (...) development can be shown in the philosophical systems of three famous Renaissance magicians: Henry Cornelius Agrippa, Giordano Bruno, and Tommaso Campanella. (shrink)

Politics never became a central intellectual interest of Murdoch’s, but she produced one important and visionary political essay in the ‘50’s, several popular writings on political matters, and a significant chapter in Metaphysics as a Guide to Morals that echoes throughout that book. In the 1958 “House of Theory,” she sees the welfare state as having almost entirely failed to address the deeper problems of capitalist society, including a failure to create the conditions for values she saw as central (...) to the socialist tradition—equality, absence of exploitation, meaningful work, and a sense of community. In Metaphysics as a Guide to Morals, Murdoch abandons the idea that moral ideals provide a guide to constructing a good society. She retains from her earlier work that the individual-moral domain is governed by perfectionism, but society cannot be. ‘Society must be thought of as a bad job to be made the best of’, for example, through the liberal idea of rights. Murdoch had a lifelong engagement with Marxism as a philosophy, introduced to her as a member of the Communist Party in the late ‘30’s and ‘40’s, and continuing through her subsequent long Labour period, and even when she moved to the Right in the Thatcher era. Marx and Marxism were always part of her mental universe, and she continued to work out what she agreed and disagreed with in it. (shrink)

Pantheism, Panpsychism, and secularism? To any historian of ideas still under the die-hard spell of the Enlightenment narrative, this would appear as an unlikely connection.1 If ever the theory of...

L’élaboration d’une théorie de l’objet sert de guide à la doctrine de la science en général, et à l’élaboration formelle du statut de la métaphysique en particulier. L’étude de Paul Richard Blum porte sur l’objet de la métaphysique selon Bartholomaeus Mastrius : l’auteur y dégage les principales positions de Mastrius, débouchant, à la suite de son modèle scotiste, sur une ontologie formelle totalement détachée de la physique, à la différence de la tradition thomiste.The elaboration of the theory of object (...) directs the theory of science in general, and specifically the formal elaboration of the status of metaphysics. Paul Richard Blum’s study deals with the object of metaphysics according to Bartholomaeus Mastrius : the author outlines Mastrius’ principal positions. His metaphysics leads, according to its Scotistic model, to a purely formal ontology, completely severed from physics, contrasting with the Thomistic tradition. (shrink)

Beginning with a focus on the ethical foundations of caregiving in health and expanding towards problems of ethics and justice implicated in a range of issues, this book develops and expands the notion of care itself and its connection to practice. Organised around the themes of culture as a restraint on caregiving in different social contexts and situations, innovative methods in healthcare, and the way in which culture works to position care as part of a rhetorical approach to dependency, responsibility, (...) and justice, The Ethics of Carepresents case studies examining institutional responses to end-of-life issues, the notion of informed consent, biomedicine, indigenous rights and postcolonialism in care and theoretical approaches to the concept of care. Offering discussions from a variety of disciplinary approaches, including sociology, communication, and social theory, as well as hermeneutics, phenomenology, and deconstruction, this book will appeal to scholars across the social sciences with interests in healthcare, medicine, justice and the question of how we think about care as a notion and social form, and how this is related to practice. (shrink)

This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics, a role that has not been taken into account in the standard histories. Radiation was perceived by the main protagonists of matrix and wave mechanics as a central lacuna in these emerging theories and continued to contribute (...) to the theoretical development and conceptual clarification of quantum mechanics. Studying the interplay between quantum mechanics and radiation, the paper provides an account of (a) how quantum mechanics was able to connect to its empirical basis in spectroscopy and (b) how Schrödinger’s equivalence proof emerged from his explorative calculations on the emission of radiation. (shrink)

What reliably characterizes political decisions that serve the common good? Based on insights from ethics and the political sciences, the author develops a theory that integrates procedural and substantive criteria to define the common good. The theory suggests that political decisions serve the common good when they are democratically authorized and do not violate minimum standards in terms of interests and processes.

The history of philosophy has to understand the problems to which past theories are intended as answers,rather than taking the latter as sets of doctrines, which may be correct or mistaken. Examples from theRenaissance are Nicholas of Cusa, Marsilio Ficino, Bernardino Telesio, Girolamo Cardano, and BenedictusPererius: they show that Renaissance thinkers sought for principles of nature in terms of active powers.Whoever denies the validity of such ideas has the burden of proof that alternative theories solve the sameproblems.

This book presents the first detailed account of Werner Heisenberg’s failed attempt to find a theory of everything in the autumn of his career. It further investigates what we can learn from his failure in relation to the search for a final theory of physics, an endeavour that continues to define research in fundamental physics to this day. Thereby it provides the first historically informed contribution to the current debate on post-empirical physics and the state of particle physics.