Homotopy Type Theory (HoTT) is a putative new foundation for mathematics grounded in constructive intensional type theory that offers an alternative to the foundations provided by ZFC set theory and category theory. This article explains and motivates an account of how to define, justify, and think about HoTT in a way that is self-contained, and argues that, so construed, it is a candidate for being an autonomous foundation for mathematics. We first consider various questions that a foundation for mathematics might (...) be expected to answer, and find that many of them are not answered by the standard formulation of HoTT as presented in the ‘HoTT Book’. More importantly, the presentation of HoTT given in the HoTT Book is not autonomous since it explicitly depends upon other fields of mathematics, in particular homotopy theory. We give an alternative presentation of HoTT that does not depend upon ideas from other parts of mathematics, and in particular makes no reference to homotopy theory (but is compatible with the homotopy interpretation), and argue that it is a candidate autonomous foundation for mathematics. Our elaboration of HoTT is based on a new interpretation of types as mathematical concepts, which accords with the intensional nature of the type theory. 1 Introduction2 What Is a Foundation for Mathematics? 2.1 A characterization of a foundation for mathematics 2.2 Autonomy3 The Basic Features of Homotopy Type Theory 3.1 The rules 3.2 The basic ways to construct types 3.3 Types as propositions and propositions as types 3.4 Identity 3.5 The homotopy interpretation4 Autonomy of the Standard Presentation?5 The Interpretation of Tokens and Types 5.1 Tokens as mathematical objects? 5.2 Tokens and types as concepts6 Justifying the Elimination Rule for Identity7 The Foundations of Homotopy Type Theory without Homotopy 7.1 Framework 7.2 Semantics 7.3 Metaphysics 7.4 Epistemology 7.5 Methodology8 Possible Objections to this Account 8.1 A constructive foundation for mathematics? 8.2 What are concepts? 8.3 Isn’t this just Brouwerian intuitionism? 8.4 Duplicated objects 8.5 Intensionality and substitution salva veritate9 Conclusion 9.1 Advantages of this foundation. (shrink)

Homotopy Type Theory is a proposed new language and foundation for mathematics, combining algebraic topology with logic. An important rule for the treatment of identity in HoTT is path induction, which is commonly explained by appeal to the homotopy interpretation of the theory's types, tokens, and identities as spaces, points, and paths. However, if HoTT is to be an autonomous foundation then such an interpretation cannot play a fundamental role. In this paper we give a derivation of path induction, motivated (...) from pre-mathematical considerations, without recourse to homotopy theory. (shrink)

Homotopy Type Theory is a putative new foundation for mathematics grounded in constructive intensional type theory that offers an alternative to the foundations provided by ZFC set theory and category theory. This article explains and motivates an account of how to define, justify, and think about HoTT in a way that is self-contained, and argues that, so construed, it is a candidate for being an autonomous foundation for mathematics. We first consider various questions that a foundation for mathematics might be (...) expected to answer, and find that many of them are not answered by the standard formulation of HoTT as presented in the ‘HoTT Book’. More importantly, the presentation of HoTT given in the HoTT Book is not autonomous since it explicitly depends upon other fields of mathematics, in particular homotopy theory. We give an alternative presentation of HoTT that does not depend upon ideas from other parts of mathematics, and in particular makes no reference to homotopy theory, and argue that it is a candidate autonomous foundation for mathematics. Our elaboration of HoTT is based on a new interpretation of types as mathematical concepts, which accords with the intensional nature of the type theory. 1 Introduction2 What Is a Foundation for Mathematics?2.1 A characterization of a foundation for mathematics2.2 Autonomy3 The Basic Features of Homotopy Type Theory3.1 The rules3.2 The basic ways to construct types3.3 Types as propositions and propositions as types3.4 Identity3.5 The homotopy interpretation4 Autonomy of the Standard Presentation?5 The Interpretation of Tokens and Types5.1 Tokens as mathematical objects?5.2 Tokens and types as concepts6 Justifying the Elimination Rule for Identity7 The Foundations of Homotopy Type Theory without Homotopy7.1 Framework7.2 Semantics7.3 Metaphysics7.4 Epistemology7.5 Methodology8 Possible Objections to this Account8.1 A constructive foundation for mathematics?8.2 What are concepts?8.3 Isn’t this just Brouwerian intuitionism?8.4 Duplicated objects8.5 Intensionality and substitution salva veritate9 Conclusion9.1 Advantages of this foundation. (shrink)

The Hole Argument is primarily about the meaning of general covariance in general relativity. As such it raises many deep issues about identity in mathematics and physics, the ontology of space–time, and how scientific representation works. This paper is about the application of a new foundational programme in mathematics, namely homotopy type theory, to the Hole Argument. It is argued that the framework of HoTT provides a natural resolution of the Hole Argument. The role of the Univalence Axiom in the (...) treatment of the Hole Argument in HoTT is clarified. (shrink)

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: The erasure of one bit of information in a computational device is necessarily accompanied by a generation of kTln2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. John Norton (2005) and Owen Maroney (2005) both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers (...) a method that he claims instantiates the operation Reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences (assuming the second law of thermodynamics). We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'Reset', and thereby recover the quantitative form of Landauer's Principle. (shrink)

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: The erasure of one bit of information in a computational device is necessarily accompanied by a generation of kTln2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. John Norton and Owen Maroney both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers a method (...) that he claims instantiates the operation Reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences. We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'Reset', and thereby recover the quantitative form of Landauer's Principle. (shrink)

Among the most interesting features of Homotopy Type Theory is the way it treats identity, which has various unusual characteristics. We examine the formal features of “identity types” in HoTT, and how they relate to its other features including intensionality, constructive logic, the interpretation of types as concepts, and the Univalence Axiom. The unusual behaviour of identity types might suggest that they be reinterpreted as representing indiscernibility. We explore this by defining indiscernibility in HoTT and examine its relationship with identity. (...) We argue that identity types are a primitive component of HoTT and cannot be reduced to indiscernibility. (shrink)

When considering controversial thermodynamic scenarios such as Maxwell's demon, it is often necessary to consider probabilistic mixtures of states. This raises the question of how, if at all, to assign entropy to them. The information-theoretic entropy is often used in such cases; however, no general proof of the soundness of doing so has been given, and indeed some arguments against doing so have been presented. We offer a general proof of the applicability of the information-theoretic entropy to probabilistic mixtures of (...) macrostates, making clear the assumptions on which it depends, in particular a probabilistic version of the Kelvin statement of the Second Law. We briefly discuss the interpretation of our result. (shrink)

The Univalence axiom, due to Vladimir Voevodsky, is often taken to be one of the most important discoveries arising from the Homotopy Type Theory research programme. It is said by Steve Awodey that Univalence embodies mathematical structuralism, and that Univalence may be regarded as ‘expanding the notion of identity to that of equivalence’. This article explores the conceptual, foundational and philosophical status of Univalence in Homotopy Type Theory. It extends our Types-as-Concepts interpretation of HoTT to Universes, and offers an account (...) of the Univalence axiom in such terms. We consider Awodey’s informal argument that Univalence is motivated by the principle that reasoning should be invariant under isomorphism, and we examine whether an autonomous and rigorous justification along these lines can be given. We consider two problems facing such a justification. First, there is a difference between equivalence and isomorphism and Univalence must be formulated in terms of the former. Second, the argument as presented cannot establish Univalence itself but only a weaker version of it, and must be supplemented by an additional principle. The article argues that the prospects for an autonomous justification of Univalence are promising. (shrink)

Homotopy type theory is a new branch of mathematics that connects algebraic topology with logic and computer science, and which has been proposed as a new language and conceptual framework for math- ematical practice. Much of the power of HoTT lies in the correspondence between the formal type theory and ideas from homotopy theory, in par- ticular the interpretation of types, tokens, and equalities as spaces, points, and paths. Fundamental to the use of identity and equality in HoTT is the (...) powerful proof technique of path induction. In the ‘HoTT Book’ this principle is justified through the homotopy interpretation of type theory, by treating identifications as paths and the induction step as a homotopy between paths. This is incompatible with HoTT being an au- tonomous foundation for mathematics, since any such foundation must be able to justify its principles without recourse to existing areas of mathemat- ics. In this paper it is shown that path induction can be motivated from pre-mathematical considerations, and in particular without recourse to ho- motopy theory. This makes HoTT a candidate for being an autonomous foundation for mathematics. (shrink)

Where does the road to reality lie? This fundamental question is addressed in this collection of essays by physicists and philosophers, inspired by the original ideas of Sir Roger Penrose, the English mathematical physicist and philosopher of science. The topics range from black holes and quantum information to the very nature of mathematical cognition itself. *** Librarians: ebook available on ProQuest and EBSCO [Subject: Philosophy, Physics, Mathematics, Cosmology].

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: The erasure of one bit of information in a computational device is necessarily accompanied by a generation of kT ln 2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. John Norton (2005) and Owen Maroney (2005) both argue that Landauer's Principle has not been shown to hold in general, and (...) Maroney offers a method that he claims instantiates the operation reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences (assuming the second law of thermodynamics). We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'reset', and thereby recover the quantitative form of Landauer's Principle. (shrink)

Reissued here in its corrected second edition of 1864, this essay by John Stuart Mill argues for a utilitarian theory of morality. Originally printed as a series of three articles in Fraser's Magazine in 1861, the work sought to refine the 'greatest happiness' principle that had been championed by Jeremy Bentham, defending it from common criticisms, and offering a justification of its validity. Following Bentham, Mill holds that actions can be judged as right or wrong depending on whether they (...) promote happiness or 'the reverse of happiness'. Although attracted by Bentham's consequentialist framework based on empirical evidence rather than intuition, Mill separates happiness into 'higher' and 'lower' pleasures, arguing for a weighted system of measurement when making and judging decisions. Dissected and debated since its first appearance, the essay is Mill's key discussion on the topic and remains a fundamental text in the study of ethics. (shrink)

This volume argues for a new image of science that understands both natural and social phenomena to be the product of mechanisms, casting the work of science as an effort to understand those mechanisms. Glennan offers an account of the nature of mechanisms and of the models used to represent them in physical, life, and social sciences.

Philosophers of science typically associate the causal-mechanical view of scientific explanation with the work of Railton and Salmon. In this paper I shall argue that the defects of this view arise from an inadequate analysis of the concept of mechanism. I contrast Salmon's account of mechanisms in terms of the causal nexus with my own account of mechanisms, in which mechanisms are viewed as complex systems. After describing these two concepts of mechanism, I show how the complex-systems approach avoids certain (...) objections to Salmon's account of causal-mechanical explanation. I conclude by discussing how mechanistic explanations can provide understanding by unification. (shrink)

Stuart Kauffman here presents a brilliant new paradigm for evolutionary biology, one that extends the basic concepts of Darwinian evolution to accommodate recent findings and perspectives from the fields of biology, physics, chemistry and mathematics. The book drives to the heart of the exciting debate on the origins of life and maintenance of order in complex biological systems. It focuses on the concept of self-organization: the spontaneous emergence of order widely observed throughout nature. Kauffman here argues that self-organization plays (...) an important role in the emergence of life itself and may play as fundamental a role in shaping life's subsequent evolution as does the Darwinian process of natural selection. Yet until now no systematic effort has been made to incorporate the concept of self-organization into evolutionary theory. The construction requirements which permit complex systems to adapt remain poorly understood, as is the extent to which selection itself can yield systems able to adapt more successfully. This book explores these themes. It shows how complex systems, contrary to expectations, can spontaneously exhibit stunning degrees of order, and how this order, in turn, is essential for understanding the emergence and development of life on Earth. Topics include the new biotechnology of applied molecular evolution, with its important implications for developing new drugs and vaccines; the balance between order and chaos observed in many naturally occurring systems; new insights concerning the predictive power of statistical mechanics in biology; and other major issues. Indeed, the approaches investigated here may prove to be the new center around which biologicalscience itself will evolve. The work is written for all those interested in the cutting edge of research in the life sciences. (shrink)

In this work, Mill reflects on the struggle between liberty and authority and defends the view that “the only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others.” He questions the justification for the limits of freedom of conscience and religion, freedom of speech, freedom of action, and the nature of liberalism itself. This new Broadview Edition demonstrates the ways in which Mill’s intellectual landscape differed (...) markedly from our own, while also drawing attention to the reasons why the work remains relevant and essential reading in the present day. Appendices include antecedents to Mill’s work, critical discussions by his contemporaries, and related writings by Mill. Please note: Broadview offers two separate editions of On Liberty. The Kahn edition is particularly relevant to readers who are interested in how the work is situated in the history of political philosophy, whereas the Alexander edition is recommended to those most interested in the work’s Victorian literary and social contexts. (shrink)

From the operation of the universe to DNA, the brain and the economy, natural and social frequently describe their activity as being concerned with discovering mechanisms. Despite this fact, for much of the twentieth century philosophical discussions of the nature of mechanisms remained outside philosophy of science. The Routledge Handbook of Mechanisms and Mechanical Philosophy is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising over (...) thirty chapters by a team of international contributors the _Handbook_ is divided into four parts: Historical Perspectives on Mechanisms The Nature of Mechanisms Mechanisms and the Philosophy of Science Disciplinary Perspectives. Within these sections central topics and problems are examined, including the rise of mechanical philosophy in the seventeenth century; mechanisms as parts and wholes and their interactive powers; mechanisms and laws and regularities; how mechanisms are discovered and explained; dynamical systems theory; and disciplinary perspectives from physics, chemistry, biology, biomedicine, ecology, neuroscience and the social and political sciences. Essential reading for students and researchers in philosophy of science and philosophy the _Handbook _will also be of interest to those in related fields, such as metaphysics, philosophy of psychology and history of science. (shrink)

A fascinating exploration of the very essence of life itself sheds new light on the order and evolution in complex life systems and defines and explains autonomous agents and work within the contexts of thermodynamics and information theory, setting the stage for a dramatic technological revolution. 50,000 first printing.

At Home in the Universe presents and extends the intellectual core ofKauffman's earlier book The Origins of Order (OUP 1993) for any intelligentgeneral reader can understand and appreciate. The reader is very effectivelyinvited into Kauffman's vision and thought processes, in one of the moreexhilarating and important books of popular science.

Faced with the absurdity of continued climate inaction, more people are becoming morally outraged about the projections of human suffering and loss due to global warming impacts. This article draws from the work of Albert Camus to examine human responses to absurdity through rebellion and how this can be applied to understand the notion of climate rebellion. Focusing on Camus’ works The Rebel and The Plague, as well as his speech “The Human Crisis”, I examine the conditions of climate injustice (...) that present the grounds for climate rebellion, what becoming a climate rebel might mean, the importance of solidarity in climate rebellion, and lastly how Camus’ value of limitation might inform ethical responses to minimize climate-related harm. (shrink)

In this book, Stuart Hampshire argues that no individual and no modern society can avoid conflicts between incompatible moral interests.

Machine generated contents note: -- Chapter 1. A Short View of Ignorance -- Chapter 2. Finding Out -- Chapter 3. Limits, Uncertainty, Impossibility, and Other Minor Problems -- Chapter 4. Unpredicting -- Chapter 5. The Quality of Ignorance -- Chapter 6. Ignorance in Action: Case Histories -- Chapter 7. Ignorance beyond the Lab.

Since the Harvard Committees bold and highly successful attempt to redefine death in 1968 (Harvard Ad Hoc committee, 1968), multiple controversies have arisen. Stimulated by several factors, including the inherent conceptual weakness of the Harvard Committees proposal, accumulated clinical experience, and the incessant push to expand the pool of potential organ donors, the lively debate about the definition of death has, for the most part, been confined to a relatively small group of academics who have created a large body of (...) literature of which this issue of the Journal of Medicine and Philosophy is an example. Law and public policy, however, have remained essentially unaffected. This paper will briefly review the multiple controversies about defining death in an attempt to explain why they have and will remain unresolved in the academic community and have even less chance of being understood and resolved by politicians, legislators, and the general public. Considering this, we will end by suggesting the probable course of public policy and clinical practice in the decades ahead. (shrink)

This is the introduction to the Routledge Companion to Thought Experiments.

Explores the possiblity and process of evolution beyond the standard and established scientific principles.

"The pursuit of science by professional scientists every day bears less and less resemblance to the perception of science by the general public. It is not the rule-based, methodical system for accumulating facts that dominates the public view. Rather it is the idiosyncratic, often bumbling search for understanding in mostly uncharted places. It is full of wrong turns, cul-de-sacs, mistaken identities, false findings, errors of fact and judgment-and the occasional remarkable success. The widespread but distorted view of science as infallible (...) originates in an education system that teaches nothing but facts using very large, very frightening textbooks, and is spread by media that report on discoveries but almost never on process. It is further reinforced by politicians who pay for it and want to use it to determine policy and therefore want it right and, worst of all, sometimes by scientists who learn early on that talking too much about failures and not enough about successes can harm their careers. Failure, then, is a book that seeks to make science more appealing by exposing its faults. In this sequel to Ignorance, Stuart Firestein shows us that scientific enterprise is riddled with failures, and that this is not only necessary but good. Failure reveals how science got its start, when humans began to use a process-trial and error-as a kind of recipe that includes a hefty dose of failure. It gives the non-scientifically trained public an insider's view of how science is actually done, with the aim of making it accessible, comprehensible, and entertaining."--Publisher description. (shrink)

Mechanism is undoubtedly a causal concept, in the sense that ordinary definitions and philosophical analyses explicate the concept in terms of other causal concepts such as production and interaction. Given this fact, many philosophers have supposed that analyses of the concept of mechanism, while they might appeal to philosophical theories about the nature of causation, could do little to inform such theories. On the other hand, methods of causal inference and explanation appeal to mechanisms. Discovering a mechanism is the gold (...) standard for establishing and explaining causal connections. This fact suggests that it might be possible to provide an analysis of causation that appeals to mechanisms. (shrink)

My aim in this paper is to make a case for the singularist view from the perspective of a mechanical theory of causation, and to explain what, from this perspective, causal generalizations mean, and what role they play within the mechanical theory.

This book is the first comprehensive report and analysis of the Dutch euthanasia experience over the last three decades. In contrast to most books about euthanasia, which are written by authors from countries where the practice is illegal and therefore practised only secretly, this book analyzes empirical data and real-life clinical behavior. Its essays were written by the leading Dutch scholars and clinicians who shaped euthanasia policy and who have studied, evaluated and helped regulate it. Some of them have themselves (...) practised euthanasia. The book will contribute to the world literature on physician-assisted death by providing a comprehensive examination of how euthanasia has been practised and how it has evolved in one specific national and cultural context. It will greatly advance the understanding of euthanasia among both advocates and opponents of the practice. (shrink)

Fetal pain has long been a contentious issue, in large part because fetal pain is often cited as a reason to restrict access to termination of pregnancy or abortion. We have divergent views regarding the morality of abortion, but have come together to address the evidence for fetal pain. Most reports on the possibility of fetal pain have focused on developmental neuroscience. Reports often suggest that the cortex and intact thalamocortical tracts are necessary for pain experience. Given that the cortex (...) only becomes functional and the tracts only develop after 24 weeks, many reports rule out fetal pain until the final trimester. Here, more recent evidence calling into question the necessity of the cortex for pain and demonstrating functional thalamic connectivity into the subplate is used to argue that the neuroscience cannot definitively rule out fetal pain before 24 weeks. We consider the possibility that the mere experience of pain, without the capacity for self reflection, is morally significant. We believe that fetal pain does not have to be equivalent to a mature adult human experience to matter morally, and so fetal pain might be considered as part of a humane approach to abortion. (shrink)

In this highly relevant and important contribution to the debate on the future of the welfare state, Stuart White reconsiders the principles of economic citizenship appropriate to a democratic society, and explores the radical implications of these principles for public policy.

Ultimately we will only understand biological agency when we have developed a theory of the organization of biological processes, and science is still a long way from attaining that goal. It may be possible nonetheless to develop a list of necessary conditions for the emergence of minimal biological agency. The authors offer a model of molecular autonomous agents which meets the five minimal physical conditions that are necessary (and, we believe, conjointly sufficient) for applying agential language in biology: autocatalytic reproduction; (...) work cycles; boundaries for reproducing individuals; self-propagating work and constraint construction; and choice and action that have evolved to respond to food or poison. When combined with the arguments from preadaptation and multiple realizability, the existence of these agents is sufficient to establish ontological emergence as against what one might call Weinbergian reductionism. Minimal biological agents are emphatically not conscious agents, and accepting their existence does not commit one to any robust theory of human agency. Nor is there anything mystical, dualistic, or non-empirical about the emergence of agency in the biosphere. Hence the emergence of molecular autonomous agents, and indeed ontological emergence in general, is not a negation of or limitation on careful biological study but simply one of its implications. (shrink)

Ethicists and economists commonly assume that if A is all things considered better than B, and B is all things considered better than C, then A is all things considered better than C. Call this principle Transitivity. Although it has great conceptual, intuitive, and empirical appeal, I argue against it. Larry S. Temkin explains how three types of ethical principle, which cannot be dismissed a priori, threaten Transitivity: (a) principles implying that in some cases different factors are relevant to comparing (...) A to C than to comparing A to B or B to C; (b) principles of limited scope; (c) principles implying that morally relevant differences in degree can amount to differences in kind. My counterexamples employ a principle of type (c): pleasures and pains enormously different in intensity differ in kind. Temkin has also endorsed this type of counterexample, using arguments based on earlier drafts of this paper. (shrink)

FOE, some time much has been said, in England and on the Continent, concerning " Positivism " and " the Positive Philosophy." Those phrases, which during ...

This is a book about two stories of education. In one story there is a vocabulary of means, efficiency, bureaucracy, inspection and science; in the other, one of autonomy, democracy, emancipation and action research. One is the story of positivist managerialist approaches to education, the other is the story of reflective teaching. This book displaces both of these stories. By applying the techniques of deconstruction, Stuart Parker overturns the assumptions common to both of these positions and, in doing so, (...) jettisons some widely cherished beliefs about education, autonomy and rationality. Moving beyond current debates, this book articulates a new manifesto for education in postmodernity and highlights the implications for educational practices and institutions. (shrink)

Attempts to ‘naturalize’ phenomenology challenge both traditional phenomenology and traditional approaches to cognitive science. They challenge Edmund Husserl’s rejection of naturalism and his attempt to establish phenomenology as a foundational transcendental discipline, and they challenge efforts to explain cognition through mainstream science. While appearing to be a retreat from the bold claims made for phenomenology, it is really its triumph. Naturalized phenomenology is spearheading a successful challenge to the heritage of Cartesian dualism. This converges with the reaction against Cartesian thought (...) within science itself. Descartes divided the universe between res cogitans, thinking substances, and res extensa, the mechanical world. The latter won with Newton and we have, in most of objective science since, literally lost our mind, hence our humanity. Despite Darwin, biologists remain children of Newton, and dream of a grand theory that is epistemologically complete and would allow lawful entailment of the evolution of the biosphere. This dream is no longer tenable. We now have to recognize that science and scientists are within and part of the world we are striving to comprehend, as proponents of endophysics have argued, and that physics, biology and mathematics have to be reconceived accordingly. Interpreting quantum mechanics from this perspective is shown to both illuminate conscious experience and reveal new paths for its further development. In biology we must now justify the use of the word “function”. As we shall see, we cannot prestate the ever new biological functions that arise and constitute the very phase space of evolution. Hence, we cannot mathematize the detailed becoming of the biosphere, nor write differential equations for functional variables we do not know ahead of time, nor integrate those equations, so no laws “entail” evolution. The dream of a grand theory fails. In place of entailing laws, a post-entailing law explanatory framework is proposed in which Actuals arise in evolution that constitute new boundary conditions that are enabling constraints that create new, typically unprestatable, Adjacent Possible opportunities for further evolution, in which new Actuals arise, in a persistent becoming. Evolution flows into a typically unprestatable succession of Adjacent Possibles. Given the concept of function, the concept of functional closure of an organism making a living in its world, becomes central. Implications for patterns in evolution include historical reconstruction, and statistical laws such as the distribution of extinction events, or species per genus, and the use of formal cause, not efficient cause, laws. (shrink)

In this fascinating read, Kauffman concludes that the development of life on earth is not entirely predictable, because no theory could ever fully account for the limitless variations of evolution. Sure to cause a stir, this book will be discussed for years to come and may even set the tone for the next "great thinker.".

One way of increasing the supply of vital organs without violating the dead donor rule is to declare death on cardiopulmonary criteria after withdrawing life support. The question then is how quickly death may be declared.

Cognitive agents, whether human or computer, that engage in natural-language discourse and that have beliefs about the beliefs of other cognitive agents must be able to represent objects the way they believe them to be and the way they believe others believe them to be. They must be able to represent other cognitive agents both as objects of beliefs and as agents of beliefs. They must be able to represent their own beliefs, and they must be able to represent beliefs (...) as objects of beliefs. These requirements raise questions about the number of tokens of the belief representation language needed to represent believers and propositions in their normal roles and in their roles as objects of beliefs. In this paper, we explicate the relations among nodes, mental tokens, concepts, actual objects, concepts in the belief spaces of an agent and the agent's model of other agents, concepts of other cognitive agents, and propositions. We extend, deepen, and clarify our theory of intensional knowledge representation for natural-language processing, as presented in previous papers and in light of objections raised by others. The essential claim is that tokens in a knowledge-representation system represent only intensions and not extensions. We are pursuing this investigation by building CASSIE, a computer model of a cognitive agent and, to the extent she works, a cognitive agent herself. CASSIE's mind is implemented in the SNePS knowledge-representation and reasoning system. (shrink)

The following is a summary of the author’s five-stage model of adult skill acquisition, developed in collaboration with Hubert L. Dreyfus. An earlier version of this article appeared in chapter 1 of Mind Over Machine: The Power of Human Intuition and Expertise in the Era of the Computer (1986, Free Press, New York).