Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's (...) Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and--in particular--the effectively-computable functions on string representations of numbers. (shrink)
People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists.
The main powerful method for establishing termination of term rewriting systems was discovered by NachumDershowitz through the introduction of certain natural well founded orderings (lexicographic path orderings). This leads to natural decision problems which may be of the highest computational complexity of any decidable problems appearing in a natural established computer science context.
In his opening address, Dershowitz only dealt with the issue obliquely, and devoted most of his time to berating the Palestinians, Chomsky, and professors who criticize Israel, and challenged Chomsky to form an alliance with him to work for peace in the area-- a seemingly worthy proposal but totally off topic. Chomsky began by saying that the only thing Dershowitz said that he couldn't take issue with was that the two of them had once been in some (...) summer camp together. Chomsky then proceeded to provide background to the crisis and pointed out that the current Israel-USA policy and any proposal emanating from it would lead to only further disaster. The Palestinians are not prepared to accept a non-contiguous Bantustan "state" which is what is being offered. Instead he clearly stated that it was the Geneva Accord that provided a basis for meaningful future negotiations. Dershowitz, on the other hand, only at the end, when pressed on this matter, said that the new Sharon-Peres party would "offer" the Palestinians a "proposal"--which the Palestinians should not refuse! This was his answer to "where do we go from here." So much for substance by Dershowitz. Debate score? (shrink)
Can torture be morally justified? I shall criticise arguments that have been adduced against torture and demonstrate that torture can be justified more easily than most philosophers dealing with the question are prepared to admit. It can be justified not only in ticking nuclear bomb cases but also in less spectacular ticking bomb cases and even in the socalled Dirty Harry cases. There is no morally relevant difference between self-defensive killing. of a culpable aggressor and torturing someone who is culpable (...) of a deadly threat that can be averted only by torturing him. Nevertheless, I shall argue that torture should not be institutionalised, for example by torture warrants. (shrink)
In the aftermath of September 11, 2001, policy makers and others have debated the question of whether or not the United States should torture in an effort to prevent terrorist attacks. In a series of controversial essays, the legal theorist Alan Dershowitz argues that, if a democratic society is going to torture, it should at least be done under the cover of law. To that end, he recommends establishing a legal mechanism by which a judge could issue torture warrants—much (...) as they do now for search warrants. In this essay, I examine Dershowitz's proposal in light of Michael Walzer's classic essay on dirty hands. Just as Walzer uses political theater as a lens for viewing the issue of political assassination, I similarly draw upon a dramatic response to Dershowitz's proposal to think through the issue of torture warrants. (shrink)
Even people who think torture is justified in certain circumstances regard it - to say the least - as undesirable, however necessary they think it is. So I approach the issue by analysing the extreme case where people such as Dershowitz, Posner and Walzer think torture is justified, the so-called ticking bomb scenario. And since the justification offered is always consequentialist - no one thinks that torture is in any way “good in itself” – I confine myself to consequentialist (...) arguments. That is to say, I take the argument on its own terms, since any non-consequentialist objection to torture merely invites the response, ‘So much the worse for non-consequentialism’: if a moral theory insists that torture is wrong even if it would save thousands of lives that just shows how wrong the theory is . I focus only on the question of the moral justifiability of torture in the ‘ticking bomb’ case, and do not not ask whether, even if admittedly immoral, it should nonetheless be legalised (see Brecher, Torture and the Ticking Bomb, Wiley-Blackwell 2007)). My main argument is in two parts: (1) the “ticking bomb” scenario falls apart when analysed; and (2), even if it did not, the likely consequences of permitting torture would be worse than the bomb’s going off. Finally I briefly consider a genuine case. Further questions and readings are appended. (shrink)
teach a course at Harvard with philosopher Robert Nozick and lawyer Alan Dershowitz. We take major issues engaged by each of our professions—from abortion to racism to right-to-die—and we try to explore and integrate our various approaches. We raise many questions and reach no solutions.
We live in times when, as Conor Gearty has pointed out, ‘legal scholars in the US are being taken seriously when they float the idea of torture warrants as a reform to what they see as the unacceptably uncodified system of arbitrary torture that they believe currently prevails’. And he is right when he goes on to add that ‘This is like reacting to a series of police killings with proposals to reform the law on homicide so as to sanction (...) officially approved pre-trial executions.' It is because the general public is taking these academics seriously that there is an urgent need to expose how spurious their ideologically driven arguments are. The “respectability” they confer on the argument that so-called ticking bombs justify torture, and that it had therefore better be regulated, needs to be countered. Otherwise there is a real danger that western politicians will succeed in persuading us to go along with them when they insist that another basic freedom – freedom from torture – is yet one more value we must abandon in the endless “war on terrorism”. It is a short road from legalising torture intended to gain information to accepting torture as a legitimate weapon and for all sorts of purposes. The “intellectual respectability” conferred by the academy is essential for that enterprise. Thus, since Alan Dershowitz’s carefully constructed proposal to introduce torture warrants is both the most prominent and the most sophisticated of today’s attempts to make torture respectable, it is his proposal we need to focus on. In the Introduction, I say something about both the intellectual and the political contexts of the so-called ticking bomb scenario that is the basis of these proposals. In chapter two I argue that the “ticking bomb” scenario remains in crucial respects a fantasy; and that the grounds it is said to offer for justifying interrogational torture so as to avoid a putative catastrophe are spurious. In chapter three I argue that, whatever you think of those arguments, the consequences of legalising interrogational torture, and thus institutionalising it, would be so disastrous as to outweigh any such catastrophes anyway. Finally, in chapter four, I draw together what the details of my argument imply about torture in general and interrogational torture in particular; and about why any even semi-decent society must abhor torture -– in all circumstances, always, everywhere. (shrink)
We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.
Despite nearly universal condemnation, torture remains a tool for interrogation, intimidation, and punishing. Even many who abhor torture are willing to consider its use in extraordinary situations. Both the deontological absolute prohibition of torture and the consequentialist justification of torture are inadequate ethics to address the issue. Dershowitz, Walzer, and Elshtain, among others, have attempted to redress the problem with more finely-tuned approaches, of which Elshtain's rejection of justification in favor of grace and forgiveness appears the most promising. Confronting (...) the practice of torture is also difficult because there is no generally accepted definition of what constitutes torture. Not all coercion is torture, and some coercion is both legal and moral. Torture, in any case, remains a wrongful act. (shrink)
This volume brings together for the first time thirteen recent interviews with the brightest names in contemporary philosophy, including W.V.O. Quine, Richard Rorty, Stanley Cavell, Hilary Putnam and John Rawls. The pieces are culled from the Harvard Review of Philosophy, which has operated at the core of Harvard's Philosophy Department since 1991. Covering wide range of topics from the philosophy of law to logic to metaphysics to literature, the interviews provide a fascinating introduction to some of the most influential thinkers (...) of the day. The book also includes a foreword by Thomas Scanlon. Interviews with Henry Alison, Stanley Cavell, Alan Dershowitz, Cora Diamond, Umberto Eco, Harvey C. Mansfield, Jr., Alexander Nehemas, Hilary Putnam, W.V. Quine, John Rawls, Richard Rorty, Michael Sandel, Cornel West. (shrink)
It was, as noted, published in the London Review of Books, which is far more open to discussion on these issues than US journals -- a matter of relevance (to which I'll return) to the alleged influence of what M-W call "the Lobby." An article in the Jewish journal Forward quotes M as saying that the article was commissioned by a US journal, but rejected, and that "the pro-Israel lobby is so powerful that he and co-author Stephen Walt would never (...) have been able to place their report in a American-based scientific publication." But despite the fact that it appeared in England, the M-W article aroused the anticipated hysterical reaction from the usual supporters of state violence here, from the Wall St Journal to AlanDershowitz, sometimes in ways that would instantly expose the authors to ridicule if they were not lining up (as usual) with power. (shrink)
The formation of coherent percepts requires grouping together spatio-temporally disparate sensory inputs. Two major questions arise: (1) is awareness necessary for this process; and (2) can non-conscious elements of the sensory input be grouped into a conscious perceptµ To address this question, we tested two patients suffering from severe left auditory extinction following right hemisphere damage. In extinction, patients are unaware of the presence of left side stimuli when they are presented simultaneously with right side stimuli. We used the ‘scale (...) illusion’ to test whether extinguished tones on the left can be incorporated into the content of conscious awareness. In the scale illusion, healthy listeners obtain the illusion of distinct melodies, which are the result of grouping of information from both ears into illusory auditory streams. We show that the two patients were susceptible to the scale illusion while being consciously unaware of the stimuli presented on their left. This suggests that awareness is not necessary for auditory grouping and non-conscious elements can be incorporated into a conscious percept. (shrink)