We give alternative proofs of results due to Paris and Wilkie concerning the existence of end extensions of countable models of $B\Sigma_{1}$, that is, the theory of $\Sigma_{1}$ collection.

In this paper, we prove results concerning the existence of proper end extensions of arbitrary models of fragments of Peano arithmetic. In particular, we give alternative proofs that concern a result of Clote :163–170, 1986); :301–302, 1998), on the end extendability of arbitrary models of \-induction, for \, and the fact that every model of \-induction has a proper end extension satisfying \-induction; although this fact was not explicitly stated before, it follows by earlier results of Enayat and Wong (...) and Wong. (shrink)

We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the (...) case of the induction scheme. We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate. (shrink)

We show that every model of IΔ0 has an end extension to a model of a theory where log-space computable function are formalizable. We also show the existence of an isomorphism between models of IΔ0 and models of linear arithmetic LA.

We prove that every model of $T = \mathrm{Th}(\omega, countable) has an end extension; and that every countable theory with an infinite order and Skolem functions has 2 ℵ 0 nonisomorphic countable models; and that if every model of T has an end extension, then every |T|-universal model of T has an end extension definable with parameters.

We consider the quantifier hierarchy of Takahashi [1972] and show how it gives rise to reflection theorems for some large cardinals in ZF, a new natural subtheory of Zermelo's set theory, a potentially useful new reduction of the consistency problem for Quine's NF, and a sharpening of another reduction of this problem due to Boffa.

Suppose that M⊧PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal M}\models \mathsf{PA}$$\end{document} and X⊆P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak X} \subseteq {\mathcal P}$$\end{document}. If M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal M}$$\end{document} has a finitely generated elementary end extension N≻endM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal N}\succ _\mathsf{end} {\mathcal M}$$\end{document} such that {X∩M:X∈Def}=X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{X \cap M : X \in {{\mathrm{Def}}}\} = (...) {\mathfrak X}$$\end{document}, then there is such an N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal N}$$\end{document} that is, in addition, a minimal extension of M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal M}$$\end{document} iff every subset of M that is Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi _1^0$$\end{document}-definable in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} is the countable union of Σ10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma _1^0$$\end{document}-definable sets. (shrink)

We formulate a Π1 sentence τ which is a version of the Tableau consistency of GlΔ0. The sentence τ is true and is provable in GlΔ0 + exp. We construct a model M of GlΔ0+Ω1+τ+BGs1 which has no proper end-extension to a model of GlΔ0+Ω1+τ. Also we prove that GlΔ0+Ω1+τ is not Π1 conservative over GlΔ0+τ.

Every model of IΔ0 is the tally part of a model of the stringlanguage theory Th-FO . We show how to “smoothly” introduce in Th-FO the binary length function, whereby it is possible to make exponential assumptions in models of Th-FO. These considerations entail that every model of IΔ0 + ¬exp is a proper initial segment of a model of Th-FO and that a modicum of bounded collection is true in these models.

Let U be a well-founded model of ZFC whose class of ordinals has uncountable cofinality, such that U has a Σ n end extension for each n ∈ ω. It is shown in Theorem 1.1 that there is such a model which has no elementary end extension. In the process some interesting facts about topless end extensions (those with no least new ordinal) are uncovered, for example Theorem 2.1: If U is a well-founded model of ZFC, such that U (...) has uncountable cofinality and U has a topless Σ 3 end extension, then U has a topless elementary end extension and also a well-founded elementary end extension, and contains ordinals which are (in U) highly hyperinaccessible. In § 3 related results are proved for κ-like models (κ any regular cardinal) which need not be well founded. As an application a soft proof is given of a theorem of Schmerl on the model-theoretic relation κ → λ. (The author has been informed that Silver had earlier, independently, found a similar unpublished proof of that theorem.) Also, a simpler proof is given of (a generalization of) a characterization by Keisler and Silver of the class of well-founded models which have a Σ n end extension for each n ∈ ω. The case κ = ω 1 is investigated more deeply in § 4, where the problem solved by Theorem 1.1 is considered for non-well-founded models. In Theorems 4.1 and 4.4, ω 1 -like models of ZFC are constructed which have a Σ n end extension for all n ∈ ω but have no elementary end extension. ω 1 -like models of ZFC which have no Σ 3 end extension are produced in Theorem 4.2. The proof uses a notion of satisfaction class, which is also applied in the proof of Theorem 4.6: No model of ZFC has a definable end extension which satisfies ZFC. Finally, Theorem 5.1 generalizes results of Keisler and Morley, and Hutchinson, by asserting that every model of ZFC of countable cofinality has a topless elementary end extension. This contrasts with the rest of the paper, which shows that for well-founded models of uncountable cofinality and for κ-like models with κ regular, topless end extensions are much rarer than blunt end extensions. (shrink)

. We provide an alternative proof of a theorem of P. Clote concerning end extensions of models of $\Sigma_n$ -induction, for $n \geq 2$.

We study problems of Clote and Paris, concerning the existence of end extensions of models of Σ n -collection. We continue the study of the notion of ‘Γ-fullness’, begun by Wilkie and Paris (Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North- Holland, Amsterdam, 1989) and introduce and study a generalization of it, to be used in connection with the existence of Σ n -elementary end extensions (instead of plain (...) end extensions). We obtain (a) alternative proofs of results (Adamowicz in Fund. Math. 136, 133–145, 1990) and (Wilkie and Paris in Logic, Methodology and Philosophy of Science VIII (Moscow, 1987). Stud. Logic Found. Math., vol. 126, pp. 143–161. North-Holland, Amsterdam, 1989) related to the problem of Paris and (b) a partial solution to the problem of Clote. (shrink)

This paper concerns intermediate structure lattices Lt, where [MATHEMATICAL SCRIPT CAPITAL N] is an almost minimal elementary end extension of the model ℳ of Peano Arithmetic. For the purposes of this abstract only, let us say that ℳ attains L if L ≅ Lt for some almost minimal elementary end extension of [MATHEMATICAL SCRIPT CAPITAL N]. If T is a completion of PA and L is a finite lattice, then: If some model of T attains L, then every countable model (...) of T does. If some rather classless, ℵ1-saturated model of T attains L, then every model of T does. (shrink)

According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of set theory, in which every individual is definable without parameters, challenges this conclusion. In this article, I introduce a flexible new method for constructing pointwise-definable models of arithmetic and set theory, showing furthermore that every countable model of Zermelo-Fraenkel ZF set theory and of (...) Peano arithmetic PA has a pointwise-definable end extension. In the arithmetic case, I use the universal algorithm and its Σ n generalizations to build a progressively elementary tower making any desired individual a n definable at each stage n, while preserving these definitions through to the limit model, which can thus be arranged to be pointwise definable. A similar method works in set theory, and one can moreover achieve V = L in the extension or indeed any other suitable theory holding in an inner model of the original model, thereby fulfilling the resurrection phenomenon. For example, every countable model of ZF with an inner model with a measurable cardinal has an end extension to a pointwise-definable model of ZFC + V = L[μ]. (shrink)

We construct a model of Peano arithmetic in an uncountable language which has no elementary end extension. This answers a question of Gaifman and contrasts with the well-known theorem of MacDowell and Specker which states that every model of Peano arithmetic in a countable language has an elementary end extension. The construction employs forcing in a nonstandard model.

In a joint article1 with Wenceslaus Kwindingwi, Bernard Matolino declared an end to ubuntu. The declaration, they argue, is a result of the failure of ubuntu in practice and theory in modern African societies. This declaration triggered strong reactions, and an analysis of these responses suggests the need for continuous interrogations of African ideals and beliefs and their relevance to modern African thought. In this article, I argue that Kwindingwi and Matolino’s argument is in line with Matolino’s broader scepticism about (...) Afro-communitarianism in general. In other works, he insists that attempts to theoretically and practically ground postcolonial African philosophy in ideas of Afro-communitarianism exaggerate its functionality. I aim to show that Matolino’s Socratic process and the outcomes, as demonstrated in the “The end of ubuntu”, aim to produce quality understanding and reasoned defence of the traditional ideas aimed to guide modern African thought. The rejectionist approach should be seen as a nudge to make the advocacy for African ideals and beliefs, such as ubuntu, match up with the knowledge of them and how they operate in reality. (shrink)

Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained in this fashion (`unfoldable cardinals') lie in the boundary of the propositions consistent with `V = L' and the existence of 0 ♯ . We also provide an `embedding characterisation' of the unfoldable cardinals and study their preservation and destruction by various forcing constructions.

The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...) theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language. (shrink)

The paper considers certain extensions of the system LC introduced in Dunn & Meyer 1997. LC is a structurally free system , but it has combinators as formulas in the place of structural rules. We consider two ways to extend LC with conjunction and disjunction depending on whether they distribute over each other or not. We prove the elimination theorem for the systems. At the end of the paper we give a Routley-Meyer style semantics for the distributive extension, including (...) some new definitions and an algorithm which are used in proving a representation theorem in general, i.e., for arbitrary combinators. (shrink)

Hilbert developed his famous finitist point of view in several essays in the 1920s. In this paper, we discuss various extensions of it, with particular emphasis on those suggested by Hilbert and Bernays in Grundlagen der Mathematik (vol. I 1934, vol. II 1939). The paper is in three sections. The first deals with Hilbert's introduction of a restricted ? -rule in his 1931 paper ?Die Grundlegung der elementaren Zahlenlehre?. The main question we discuss here is whether the finitist (meta-)mathematician (...) would be entitled to accept this rule as a finitary rule of inference. In the second section, we assess the strength of finitist metamathematics in Hilbert and Bernays 1934. The third and final section is devoted to the second volume of Grundlagen der Mathematik. For preparatory reasons, we first discuss Gentzen's proposal of expanding the range of what can be admitted as finitary in his esssay ?Die Widerspruchsfreiheit der reinen Zahlentheorie? (1936). As to Hilbert and Bernays 1939, we end on a ?critical? note: however considerable the impact of this work may have been on subsequent developments in metamathematics, there can be no doubt that in it the ideals of Hilbert's original finitism have fallen victim to sheer proof-theoretic pragmatism. (shrink)

The Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule was introduced by W. Buchholz to give an ordinal-free proof of cut-elimination for a subsystem of analysis with Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document}-comprehension. W. Buchholz’s proof provides cut-free derivations by familiar rules only for arithmetical sequents. When second-order quantifiers are present, they are introduced by the Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule and some residual cuts are not (...) eliminated. In the present paper, we introduce an extension of the Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule and prove the complete cut-elimination by the same method as W. Buchholz: any derivation of arbitrary sequent is transformed into its cut-free derivation by the standard rules. In fact we treat the subsystem of Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document}-CA that W. Buchholz used for his explanation of G. Takeuti’s finite reductions. Extension to full Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document}-CA is planned for another paper. (shrink)

Following considerable debate, the practice of euthanasia was legalized in Belgium in 2002, thereby making Belgium one of the few places in the world where this practice is legal. In 2014 the law was amended for the first time. The 2014 amendment makes euthanasia legally possible for all minors who repeatedly and voluntarily request euthanasia and who are judged to possess “capacity of discernment”, as well as fulfil a number of other criteria of due care. This extension of the 2002 (...) euthanasia law generated a lot of national and international debate and has been applauded by many and heavily criticized by others. This evolution is clearly of interest to end-of-life debates in the entire world. This paper will therefore describe how this amendment came to get passed using official documents from Belgium's Senate and Chamber of Representatives where this amendment was discussed and subsequently passed. Next, some of the most commonly given arguments in favour of the law are identified, as well as the arguments most often voiced against the amendment. All these arguments will be expanded upon and it will be examined whether they hold up to ethical scrutiny. Analysing the official documents and identifying the most commonly voiced arguments gives valuable insight into how Belgium came to amend its euthanasia law and why it did so in 2014. It also becomes clear that although the current amendment is often seen as far-reaching, more radical ideas were proposed during the drafting of the law. Also, in analysing those arguments in favour of the amendment and those against, it is clear that the validity of some of these is questionable. (shrink)

Proposals to make us smarter than the greatest geniuses or to add thousands of years to our life spans seem fit only for the spam folder or trash can. And yet this is what contemporary advocates of radical enhancement offer in all seriousness. They present a variety of technologies and therapies that will expand our capacities far beyond what is currently possible for human beings. In _Humanity's End,_ Nicholas Agar argues against radical enhancement, describing its destructive consequences. Agar examines the (...) proposals of four prominent radical enhancers: Ray Kurzweil, who argues that technology will enable our escape from human biology; Aubrey de Grey, who calls for anti-aging therapies that will achieve "longevity escape velocity"; Nick Bostrom, who defends the morality and rationality of enhancement; and James Hughes, who envisions a harmonious democracy of the enhanced and the unenhanced. Agar argues that the outcomes of radical enhancement could be darker than the rosy futures described by these thinkers. The most dramatic means of enhancing our cognitive powers could in fact kill us; the radical extension of our life span could eliminate experiences of great value from our lives; and a situation in which some humans are radically enhanced and others are not could lead to tyranny of posthumans over humans. (shrink)

In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs is incoherent. This (...) response was first given by Wittgenstein but has been best developed by Sullivan. While I agree with Wittgenstein and Sullivan's common conclusion, I believe that even the most compelling of Sullivan's arguments is importantly mistaken and that Wittgenstein's remarks are too opaque to be left as the end of the matter. In this article I uncover the fault in Sullivan's argument and present an alternative criticism of PFEs which is Wittgensteinian in spirit without being too mystifying. (shrink)

Proposals to make us smarter than the greatest geniuses or to add thousands of years to our life spans seem fit only for the spam folder or trash can. And yet this is what contemporary advocates of radical enhancement offer in all seriousness. They present a variety of technologies and therapies that will expand our capacities far beyond what is currently possible for human beings. In _Humanity's End,_ Nicholas Agar argues against radical enhancement, describing its destructive consequences. Agar examines the (...) proposals of four prominent radical enhancers: Ray Kurzweil, who argues that technology will enable our escape from human biology; Aubrey de Grey, who calls for anti-aging therapies that will achieve "longevity escape velocity"; Nick Bostrom, who defends the morality and rationality of enhancement; and James Hughes, who envisions a harmonious democracy of the enhanced and the unenhanced. Agar argues that the outcomes of radical enhancement could be darker than the rosy futures described by these thinkers. The most dramatic means of enhancing our cognitive powers could in fact kill us; the radical extension of our life span could eliminate experiences of great value from our lives; and a situation in which some humans are radically enhanced and others are not could lead to tyranny of posthumans over humans. (shrink)

Social scientists have provided rich descriptions of the ascendant cultural ideologies surrounding motherhood and paid work. In this article, I use in-depth interviews with a diverse sample of 40 employed mothers to explore how they navigate the “intensive mother” and “ideal worker” ideologies and construct their own accounts of good mothering. Married mothers in this sample construct scripts of “extensive mothering,” in which they delegate substantial amounts of the day-to-day child care to others, and reframe good mothering as being “in (...) charge” of and ultimately responsible for their children’s well-being. Single mothers describe extensive mothering in different ways, and their narratives suggest less accountability to the “intensive mothering” model. Mothers in this sample also justify employment in novel ways: They emphasize the benefits of employment for themselves—not only their children—and they reject the long work hours imposed by an ideal worker model. The article ends with the implications of extensive mothering for the motherhood and employment literatures and for gender equality. (shrink)

There is extensive discussion in current Just War literature about the normative principles which should govern the initiation of war (jus ad bellum) and also the conduct of war (jus in bello), but this is the first book to treat the important and difficult issue of justice after the end of war. Larry May examines the normative principles which should govern post-war practices such as reparations, restitution, reconciliation, retribution, rebuilding, proportionality and the Responsibility to Protect. He discusses the emerging international (...) law literature on transitional justice and the problem of moving from a position of war and possible mass atrocity to a position of peace and reconciliation. He questions the Just War tradition, arguing that contingent pacifism is most in keeping with normative principles after war ends. His discussion is richly illustrated with contemporary examples and will be of interest to students of political and legal philosophy, law and military studies. (shrink)

We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of cofinal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic is strongly complete for its class of end-extension models. Cofinal extension models of HA are models of Peano arithmetic.

This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations. We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation (...) or weak pseudocomplementation. These classes are shown to be canonical and dual relational structures are given in a generalized Kripke-style. The fact that the negation is dually self-adjoint plays an important role here, as it implies that it sends arbitrary joins to meets and that will allow us to define the dual structures in a uniform way. (shrink)

The human brain is the only object in the universe, as far as we know, that has discovered its own origins. But what, if any, are the limits of our understanding? Epistemic pessimists, sobered by our humble evolutionary origins, have argued that some truths about the universe are perennial mysteries and will forever remain beyond our ken. Others have brushed this off as premature, a form of epistemic defeatism. In this paper we develop a conceptual toolbox for parsing different forms (...) of cognitive limitation that are often conflated in the literature. We distinguish between representational access and intuitive understanding. We also distinguish different modalities of cognitive limitation. If the scientific endeavor ever comes to a halt, will this feel like slamming into a brick wall, or rather like slowly getting bogged down in a swamp? By distinguishing different types and modalities of human cognitive limitation, we soften up the hypothesis of ‘cognitive closure’ and ultimate ‘mysteries’. Next, we propose specific mechanisms and strategies for overcoming our innate cognitive limitations. For a start, it is uninformative to think of the limits of a single, bare, unassisted brain. One of the central features of human intelligence is the capacity for mind extension and distributed cognition. We have developed various technologies for extending the reach of our naked brains and for pooling their cognitive resources, as witnessed by the history of science. We then discuss different cognitive mechanisms for overcoming the limits to our intuitive understanding, and argue that these are combinatorial and open-ended. In light of all these possibilities for extending the limits of our understanding, we conclude that there is no good reason to suspect the existence of an outer wall of human comprehension. (shrink)

This book offers a bold challenge to modern liberal ethics by exposing its inability to confront the inexorable advance of technology. Contemporary books on technology generally fall into three categories: those that offer optimist projections of a glorious future, those that provide radical critiques of specific techniques, and those that express alarm about the dehumanizing effects of a culture dominated by technology. The End of Ethics in a Technological Society offers a deeper assessment of the modern West's commitment to technological (...) progress. It argues that modern technology, ethics, and politics are all expressions of the enlightenment view that there are no principles of truth or goodness higher than the free human will. Technological advances are, on this view, merely extensions of the range of human freedom. Modern ethics thus fails to give voice to our often inchoate moral intuition that, in the realm of techno science, some possibilities simply ought not to be pursued. The authors develop their challenge by examining typical ethical approaches to such urgent contemporary concerns as environmental degradation, nuclear energy, high tech militarism, and fetal genetic testing. They relate our social crises to the transformation of ethics that has taken place as technology has become the house in which we all live. (shrink)

The late J. D. Bernal's lectures given to first-year students in physics at Birkbeck College, University of London, are presented here in their entirety, tracing the history of physics up to the end of the classical era at the end of 19th century, just before the discoveries of the subatom and relatively were made. In view of the prestige and profundity of the newer discoveries, Bernal felt that the classical era was being largely forgotten. In this book, he attributes a (...) greater relevance to the work of men from the distant past than is usually given. For instance, the idea of "atom" not only retains the language of the Greek, Democritus, who first postulated it, but there is also an absolutely unbroken connection between the atom of the Greek and that of the modern physicist. Bernal felt that the historical method would be a suitable introduction to the fundamental concepts of physics, and it is hoped that the readers of the book will be able to see something of the interplay between the theoretical and practical aspects of the subject. (shrink)