Coder’s argument is very similar to Lewis’ one: he maintains that some human beings are not able to follow Gödel’s theorem, so Lucas’ argument cannot show that their minds are not machines. The answer of Lucas is that one proposed against Lewis’ criticism, that is that Mechanism makes a universal claim and so a single counter-example – a single mind producing a singe truth not recognizable by any machine – is a disproof for it.
Plato was the first feminist. In the Republic he puts forward the view that women are just the same as men, only not quite so good. It is a view which has often been expressed in recent years, and generates strong passions. Some of these have deep biological origins, which a philosopher can only hope to recognize and not to assuage. But much of the heat engendered is due to unnecessary friction between views which are certainly compatible and probably correct. (...) And here a philosopher can help. If we can divide the issues neatly, at the joints, then we need not quarrel with one another for saying something, probably true, because what is being maintained is misconstrued and taken to mean something else, probably false. (shrink)
Equality in the present age has become an idol, in much the same way as property was in the age of Locke. Many people worship it, and think that it provides the key to the proper understanding of politics, and that on it alone can a genuinely just society be reconstructed. This is a mistake. Although, like property, it is a useful concept, and although, like property, there are occasions when we want to have it in practice, it is not (...) a fundamental concept any more than property is, nor can having it vouchsafe to us the good life. In an earlier paper I argued against equality by showing that the concept of equality was confused and that many of the arguments i egalitarians adduced were either invalid or else supported conclusions I which were not really egalitarian at all. Many egalitarians, however, have complained that my arguments were not fair, because I had failed to elucidate the concept adequately, or because the position I attacked was not one that any egalitarian really wished to maintain, or because I had overlooked other arguments which were effective in establishing egalitarian conclusions, or because the positive counter-arguments of my own I put forward more as a matter of taste than of serious political commitment. In this paper, therefore, I want to elucidate the concept more fully, concede what I should to my critics, point out that, even so, their conclusions do not follow, and give further reasons not only for supposing that egalitarian arguments are invalid but for discerning positive merits in some forms of inequality. (shrink)
“Towards a Theory of Taxation” is a proper theme for an Englishman to take when giving a paper in America. After all it was from the absence of such a theory that the United States derived its existence. The Colonists felt strongly that there should be no taxation without representation, and George III was unable to explain to them convincingly why they should contribute to the cost of their defense. Since that time, understanding has not advanced much. In Britain we (...) still maintain the fiction that taxes are a voluntary gift to the Crown, and taxing statutes are given the Royal Assent with the special formula, “La Reine remercie ses bons sujets, accepte leur benevolence, et ainsi le veult” instead of the simple “La Reine le veult,” and in the United States taxes have regularly been levied on residents of the District of Columbia who until recently had no representation in Congress, and by the State of New York on those who worked but did not reside in the State, and so did not have a vote. Taxes are regularly levied, in America as elsewhere, on those who have no say on whether they should be levied or how they should be spent. I am taxed by the Federal Government on my American earnings and by state governments on my American spending, but I should be hard put to it to make out that it was unjust. Florida is wondering whether to follow California in taxing multinational corporations on their world-wide earnings. (shrink)
Whatever good or ill it did to Guy Fawkes, his resuscitation at the hands of Bernard Williams has, by any utilitarian reckoning, been a Good Thing. A casual glance at the literature that has accumulated over the past thirty-five years leaves no doubt that the topic has been reduplicated many times over, to the great enjoyment of undergraduates, who have been able to write science fiction under the guise of essays in the Philosophy of Mind, and of dons, who in (...) an age of cvs and Assessments, have been able to notch up page after page of counter-replies to replies to rebuttals of previous papers, not to mention an often welcome tally of references in the citation index. But the actual arguments adduced by Williams can be turned to support a much more traditional view of the self, as a necessarily unique agent whose individuality is established by his capacity for autonomous action. (shrink)
In this article, Lucas maintains the falseness of Mechanism - the attempt to explain minds as machines - by means of Incompleteness Theorem of Gödel. Gödel’s theorem shows that in any system consistent and adequate for simple arithmetic there are formulae which cannot be proved in the system but that human minds can recognize as true; Lucas points out in his turn that Gödel’s theorem applies to machines because a machine is the concrete instantiation of a formal system: (...) therefore, for every machine consistent and able of doing simple arithmetic, there is a formula that it can’t produce as true but that we can see to be true, and so human minds and machines have to be different. Lucas considers as well in this article some possible objections to his argument: for any Gödelian formula we could, for instance, construct a machine able to produce it or we could put the Gödelian formulae that we had proved as axioms of a further machine. However - as Lucas underlines - for every of such machines we could again formulate another Gödelian formula, the Gödelian formula of these machines, that they are not able to proof but that we can recognize as true. More general arguments, such as the possibility to escape Gödelian argument by suggesting that Gödel’s theorem applies to consistent systems while we could be inconsistent ones, are moreover refuted by Lucas by maintaining that our inconsistency corresponds to occasional malfunctioning of a machine and not to his normal inconsistency; indeed, a inconsistent machine is characterized by producing any statement, on the contrary human being are selective and not disposed to assert anything. (shrink)
Responsibility is a key concept in our moral, social, and political thinking, but it is not itself properly understood. J.R. Lucas here presents a lively, broad, and accessible discussion of responsibility in various areas of human life, from personal and sexual relations to politics.
The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
In this paper Lucas suggests that many of his critics have not read carefully neither his exposition nor Penrose’s one, so they seek to refute arguments they never proposed. Therefore he offers a brief history of the Gödelian argument put forward by Gödel, Penrose and Lucas itself: Gödel argued indeed that either mathematics is incompletable – that is axioms can never be comprised in a finite rule and so human mind surpasses the power of any finite machine – (...) or there exist absolutely unsolvable diophantine problems, and he suggest that the second disjunct is untenable; on the other side, Penrose proposed an argument similar to Lucas’ one but making use of Turing’s theorem. Finally Lucas exposes again his argument and considers some of the most important objections to it. (shrink)
After a brief and informal explanation of the Gödel’s theorem as a version of the Epimenides’ paradox applied to Elementary Number Theory formulated in first-order logic, Lucas shows some of the most relevant consequences of this theorem, such as the impossibility to define truth in terms of provability and so the failure of Verificationist and Intuitionist arguments. He shows moreover how Gödel’s theorem proves that first-order arithmetic admits non-standard models, that Hilbert’s programme is untenable and that second-order logic is (...) not mechanical. There are furthermore some more general consequences: the difference between being reasonable and following a rule and the possibility that one man’s insight differs from another’s without being wrong. Finally some consequences concerning moral and political philosophy can arise from Gödel’s theorem, because it suggests that – instead of some fundamental principle from which all else follows deductively – we can seek for different arguments in different situations. (shrink)
In this paper Lucas comes back to Gödelian argument against Mecanism to clarify some points. First of all, he explains his use of Gödel’s theorem instead of Turing’s theorem, showing how Gödel’ theorem, but not Turing’s theorem, raises questions concerning truth and reasoning that bear on the nature of mind and how Turing’s theorem suggests that there is something that cannot be done by any computers but not that it can be done by human minds. He considers moreover how (...) Gödel’s theorem can be interpreted as a sophisticated form of the Cretan paradox, posed by Epimenides, able to escape the viciously self-referential nature of the Cretan paradox, and how it can be used against Mechanism as a schema of disproof. Finally, Lucas suggests some answers to the most recurrent criticisms against his argument: criticisms about the implicit idealisation in the way he set up the context between mind and machine; questions concerning modality and finitude, issues of transfinite arithmetic; questions concerning the need of formalizing rational inference and some questions about consistency. (shrink)
There was once a leak from Hebdomadal Council. The Assessor told her husband, who told my wife, who told me that Monday afternoon had been spent discussing what Lucas would say if various courses of action were adopted, leading to the conclusion that it would be best to do nothing. I was flattered, but a bit surprised. The tide of philosophical scepticism had ebbed, and it was generally allowed that a reasonable way of discovering what someone would say was (...) to ask him. Dick Southwood did: he would quiz me in Common Room â€“ sometimes ending "Thank you for letting me bounce these ideas off you" â€“ and had reliable information about how one member of Congregation would react to various proposals. And not only me: he was a listening Vice-Chancellor, who used to bike from Wellington Square to Merton for lunch, greeting many as he passed them, and ready to stop if occasion warranted it. Of course, there are many other leaks. I remember once attending a meeting in the Town Hall to argue for cycle tracks, and someone coming up to me, and saying, "Youâ€™re having a tussle with Council, arenâ€™t you? I think you ought to see the minutes of their latest meeting"; the next day there was a copy in my pigeon hole, giving me just the ammunition I needed. What members of Congregation tend the forget is the existence â€“ the other side of the green baize door, so to speak â€“ of a corps of bedells. (shrink)
Lucas, Brian Review(s) of: Pope benedict XVI and the sexual abuse crisis - working for reform and renewal, Gregory Erlandson and Matthew Bunson, (Huntington, Indiana: Our Sunday Visitor Publishing Division, 2010), pb, pp.207.
According to the legend, Bishop Wilberforce at a meeting of the British Association for the Advancement of Science in Oxford on Saturday, June 30th, 1860, turned to Thomas Huxley, and asked him ``Is it on your grandfather's or your grandmother's side that you claim descent from a monkey''; whereupon Huxley delivered a devastating rebuke, thereby establishing the primacy of scientific truth over ecclesiastical obscurantism. Although the legend is historically untrue in almost every detail, its persistence suggests that it may nonetheless (...) be true in some deeper, mythical, sense. To explore this possibility the British Academy has invited Dr Janet Browne to be a neo-Huxley confronting Mr J.R. Lucas, as a neo-Wilberforce, with each reconsidering their earlier arguments. (shrink)
Lucas, Brian Review of: Maintaining a convinced and pondered trust: The 2015 Gasson lectures, by Frank Brennan, Adelaide: ATF Theology, 2015, pp. xvii + 131, paperback, $24.95; The people's quest for leadership in church and state, by Frank Brennan, Adelaide: ATF Theology, 2015, pp. xvii + 88, paperback, $24.95.
Lucas, Brian This article deals with the role of the Episcopal Conference in the area of social communications and the tensions that arise with respect to the respective roles of the diocesan bishop and the Episcopal Conference, including lay heads of ecclesial agencies, in presenting 'the face of the Church' in the public forum. The article is divided into two sections: i)The Church as 'visible institution' and the ecclesiological and juridical foundations for identifying those who represent it in the (...) public forum; ii) The Episcopal Conference as an expression of episcopal collegiality and a voice in the communications market place.=. (shrink)
Dear Mr. Lucas, I was wondering if you had come across Query 44 of George Berkeley's ``Analyst: A discourse addressed to an infidel mathematician"?. It reads: ``Whether the difference between a mere computer and a man of science be not that one computes on principles clearly conceived and by rules evidently demonstrated, whereas the other [i.e a man] doth not?" Not bad for 1734!
Hello Mr John Lucas, I go to school in Perth in Western Australia. In the subject mathematics at my school, we were given a project to research a given mathematician and write a report on them. I was given you. I have to incorporate some information about the mathematical times in which you live and to attempt to include details of the contribution that you made to the field of mathematics. I also have to include a short biography of (...) your life. If it is alright with you, would you be able to give me a brief biography of your life and a very brief summary of the contributions you have made to the field of mathematics. If it is possible, even the mathematical times in which we live. I hope this is not too much trouble and if you could, would you be able to e-mail it to me as soon as possible please since we don't have long to finish the project. Please e-mail it back to me on my dad's address above. I hope this is not a bother to you. Remember, I am only a high school student and I might not understand all that you hopefully send. Thankyou very much. (shrink)
Lucas, Brian Review of: Connected toward communion: The church and social communication in the digital age, by Daniella Zsupan-Jerome, Collegeville, MN: Liturgical Press, 2014, pp. 130, paperback, $36.95.
Hutton asserts that Lucas’ use of Gödel’s theorem against Mechanism is incorrect because of the impossibility to assume human minds’ consistency: he tries to show that there is a non-zero probability of a mind’s embracing mutually inconsistent propositions; moreover Hutton maintains that the request of human minds’ consistency is a request of infallibility. Lucas replies that the mistake of Hutton’s argument consists in his assigning probabilities to a mind’s accepting any proposition without considering what that mind has done (...) hitherto, while human beings are guided in their accepting a proposition as true by what they have already accepted. Besides, Lucas argues that his argument doesn’t require human infallibility but only that human beings have adequate backing for what they assert and that – in this sense – consistency is not something that can be established but a necessary assumption to begin any thinking at all. (shrink)
Lucas introduces this paper by an account of how he began to be interested to questions about Materialism and Mechanism. Then he suggests a simple version of the Incompleteness theorem of Gödel, showing how this theorem proposes a version of the Epimenides’ paradox able to avoid the circularity of this paradox by means of the possibility to express meta-mathematics in terms of arithmetical propositions and by substituting questions concerning truth by questions concerning provability.
The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
_The Conceptual Roots of Mathematics_ is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
From North Korea's recent attacks on Sony to perpetual news reports of successful hackings and criminal theft, cyber conflict has emerged as a major topic of public concern. Yet even as attacks on military, civilian, and commercial targets have escalated, there is not yet a clear set of ethical guidelines that apply to cyber warfare. Indeed, like terrorism, cyber warfare is commonly believed to be a war without rules. Given the prevalence cyber warfare, developing a practical moral code for this (...) new form of conflict is more important than ever. In Ethics and Cyber Warfare, internationally-respected ethicist George Lucas delves into the confounding realm of cyber conflict. Comparing "state-sponsored hacktivism" to the transformative impact of "irregular warfare" in conventional armed conflict, Lucas offers a critique of legal approaches to governance, and outlines a new approach to ethics and "just war" reasoning. Lucas draws upon the political philosophies of Alasdair MacIntyre, John Rawls, and Jürgen Habermas to provide a framework for understanding these newly-emerging standards for cyber conflict, and ultimately presents a professional code of ethics for a new generation of "cyber warriors." Lucas concludes with a discussion of whether preemptive self-defense efforts - such as the massive government surveillance programs revealed by Edward Snowden - can ever be justified, addressing controversial topics such as privacy, anonymity, and public trust. Well-reasoned and timely, Ethics and Cyber Warfare is a must-read for anyone with an interest in philosophy, ethics, or cybercrime. (shrink)
These two articles are very interesting examples of how Lucas’ argument is not a direct proof but a dialectical argument depending from Mechanists’ first move. Good, starting from the Mentalists’ point of view, underlines that it is useless to argue that any program can be improved because the process for improving it can be programmed; he argues against Mentalism by denying that there are particular mental powers, because otherwise they could be described and so a computer could be programmed (...) to simulate them. The Lucas’ answer is constituted by a starting point’s change: his starting point is indeed the hypothesis that Mechanism is true and so that a complete specification of the mental mechanism of any human being can be given; therefore he argues that, once given, such a specification appears inadequate because it cannot produce as true its Gödelian formula, truth that a human being can see. (shrink)
Meet the God Who Is Greater Than Your Biggest Questions. The Bible never shies away from seeming contradictions. We are told both to resist our enemies and to love them, and that our all-knowing God can sometimes forget. Unable to reconcile such biblical paradoxes, some people abandon Christianity, while others pretend that the seeming contradictions don’t exist–preferring to believe in an uncomplicated, easy-to-comprehend God. Yet countless others are hungry for new insight into the God behind the Bible’s mysterious paradoxes. Responding (...) to this spiritual hunger, James Lucas delves into the mysteries of Scripture, demonstrating that biblical “contradictions” are actually exquisite paradoxes that enlarge our understanding of God. With this book as your guide, you can embrace the paradoxes of Scripture and pursue honest answers to your hardest questions. The study of biblical paradox leads to greater devotion to the majestic God who makes himself known even while he surpasses human understanding. Today, you can begin Knowing the Unknowable God. (shrink)
What significance does "ethics" have for the men and women serving in the military forces of nations around the world? What core values and moral principles collectively guide the members of this "military profession?" This book explains these essential moral foundations, along with "just war theory," international relations, and international law. The ethical foundations that define the "Profession of Arms" have developed over millennia from the shared moral values, unique role responsibilities, and occasional reflection by individual members the profession on (...) their own practices - eventually coming to serve as the basis for the "Law of Armed Conflict" itself.This book focuses upon the ordinary men and women around the world who wear a military uniform and are committed to the defense of their countries and their fellow citizens. It is about what they do, how they do it, what they think about it, how they behave when carrying out their activities, and how they are expected to behave, both on and off the battlefield - and what everyone needs to know about this. The book also examines how military personnel are treated and regarded by those whom they have sworn to defend and protect, as well as how they treat and regard one another within their respective services and organizational settings. Finally, the book discusses the transformations in military professionalism occasioned by new developments in armed conflict, ranging counterinsurgency warfare and humanitarian military intervention, to cyber conflict, military robotics, and private military contracting. From China to Russia, author George Lucas effectively sheds light on today's military ethics in existence throughout the world. What Everyone Needs to Know® is a registered trademark of Oxford University Press. (shrink)
Benacerraf criticizes Lucas’ argument against Mechanism because, in his opinion, it depends too much on how the system we are talking about is presented and because the argument put in form of challenge reduces itself to a contest of wits between Lucas and the mechanists. In Benacerraf opinion, Lucas should clarify the sense of utilised notions and the argument would have to be reconstructed as formally as possible, in order to determine the involved philosophical premises. Moreover Benacerraf (...) maintains that, instead of abandoning the idea that human mind is a machine, we could assume that minds are machines for which it is not possible to prove the consistency or that they are inadequate for arithmetic; moreover minds could be machines whose characteristics we are not able to specify. However, Lucas answers that the requirement of reconstructing his argument in a formal way misunderstands his project: his argument is not a direct proof but a dialectical argument, a schema of disproof for any particular version of mechanist argument, and so the attempt to reconstruct it as a rigorous proof is a distortion of the original argument, that is essentially dialectical. What about the hypothesis suggested by Benacerraf, Lucas disputes that we are able to manage arithmetic and we don’t seem as inconsistent as an inconsistent system is, because we are selective while an inconsistent system is not; at the other hand, the idea that we are machine but we don’t know anything about what kind of machine we are evacuates Mechanism of all content. (shrink)
[D. H. Mellor] Kant's claim that our knowledge of time is transcendental in his sense, while false of time itself, is true of tenses, i.e. of the locations of events and other temporal entities in McTaggart's A series. This fact can easily, and I think only, be explained by taking time itself to be real but tenseless. /// [J. R. Lucas] Mellor's argument from Kant fails. The difficulties in his first Antinomy are due to topological confusions, not the tensed (...) nature of time. Nor are McTaggart' s difficulties due to the tensed nature of time. The ego-centricity of tensed discourse is an essential feature of communication between selves, each of whom refers himself as 'I', and is required for talking about time as well as experience and agency. Arguments based on the Special Theory are misconceived. Some rest on a confused notion of 'topological simultaneity'. In the General Theory a cosmic time is defined, as also in quantum mechanics, where a natural present is defined by a unique hyperplane of collapse into eigen-ness. (shrink)
Goedel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, then it (...) would not be false, but would be true, since in any consistent system nothing false can be provedin-the-system, but only truths. So the formula "This formula is unprovable-in-the-system" is not provable-in-the-system, but unprovablein-the-system. Further, if the formula "This formula is unprovablein- the-system" is unprovable-in-the-system, then it is true that that formula is unprovable-in-the-system, that is, "This formula is unprovable-in-the-system" is true. Goedel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines. (shrink)