Online research in philosophy

Kirby and Paris have exhibited combinatorial algorithms whose computations always terminate, but for which termination is not provable in elementary arithmetic. However, termination of these computations can be proved by adding an axiom first introduced by Goodstein in 1944. Our purpose is to investigate this axiom of Goodstein, and some of its variants, and to show that these are potentially adequate to prove termination of computations of a wide class of algorithms. We prove that many variations of Goodstein's axiom are equivalent, over elementary arithmetic, and contrast these results with those recently obtained for Kruskal's theorem.

Despite widespread support for the claim that death can harm the one who dies, debate continues over how to rescue this harm thesis (HT) from Epicurus’s challenge. Disagreements focus on two of the three issues that any defense of HT must resolve: the subject of death’s harm and the timing of its injury. About the nature of death’s harm, however, a consensus has emerged around the view that death harms a subject (when it does) by depriving her of the goods life would’ve afforded had she continued living. This deprivation view of death’s harm (DV) derives some of its credibility from the general deprivation theory of which it is an instance: mortal harm is subject to the same kind of analysis plausibly given of other non-mortal harms. Furthermore, note that the weak formulation of HT—asserting only that death can inflict harm, not that it always or necessarily does—accommodates the intuition that instances of rational suicide and justifiable euthanasia present cases in which death fails to harm. DV is equipped to explain how in these cases the harms involved in continued existence outweigh the goods of which death deprives the subject. I agree that suicide can be rational and that euthanasia can be justifiable. Likewise I accept both HT and DV as far as they go. But they do not go far enough. Specifically, I argue here that death harms even those who die as a result of rational suicide or justifiable euthanasia; that death’s harm is neither undifferentiated nor wholly contingent, but multifaceted and partly necessary; that the necessary part of death’s harm is distinctive, inflicting a peculiar restriction on the autonomy of one who dies; and, regarding the timing and subject issues, that this restriction harm is inflicted on the antemortem subject prior to her death.

Thinking about death -- Dualism vs. physicalism -- Arguments for the existence of the soul -- Descartes' argument -- Plato on the immortality of the soul -- Personal identity -- Choosing between the theories -- The nature of death -- Two surprising claims about death -- The badness of death -- Immortality -- The value of life -- Other aspects of death -- Living in the face of death -- Suicide -- Conclusion: an invitation.

What is death? Do people survive death? What do we mean when we say that someone is "dying"? Presenting a clear and engaging discussion of the classic philosophical questions surrounding death, this book studies the great metaphysical and moral problems of death. In the first part, Feldman shows that a definition of life is necessary before death can be defined. After exploring several of the most plausible accounts of the nature of life and demonstrating their failure, he goes on to propose his own conceptual scheme for death and related concepts. In the second part, Feldman turns to ethical and value-theoretical questions about death. Addressing the ancient Epicurean ethical problem about the evil of death, he argues that death can be a great evil for those who die, even if they do not exist after death, because it may deprive them of the goods they would have enjoyed if they had continued to live. Confrontations with the Reaper concludes with a novel consequentialist theory about the morality of killing, applying it to such thorny practical issues as abortion, suicide, and euthanasia.

This paper assesses two reformulations of Epicurus' argument that "death ... is nothing to us, since while we exist, death is not present; and whenever death is present, we do not exist." The first resembles many contemporary reformulations in that it attempts to reach the conclusion that death is not to the disadvantage of its subject. I argue that this rather anachronistic sort of reformulation cannot succeed. The second reformulation stays closer to the spirit of Epicurus' actual position on death by attempting to reach the conclusion that it is inappropriate to fear or dread or have any other negative affective response towards death. I raise a plausible objection to this argument, suggesting that dissatisfaction is sometimes an appropriate response to the approach of death. I then go on to consider the possibility that Epicurus was partly right in that it may always be inappropriate to dread death.

Part of the appeal of the biological approach to personal identity is that it does not have to countenance spatially coincident entities. But if the termination thesis is correct and the organism ceases to exist at death, then it appears that the corpse is a dead body that earlier was a living body and distinct from but spatially coincident with the organism. If the organism is identified with the body, then the unwelcome spatial coincidence could perhaps be avoided. It is argued that such an identification would be a mistake. A living organism has a different part/whole relationship and persistence conditions than the alleged body. A case will be made that the concept ‘human body’ is a conceptual mess, vague in an unprincipled manner, and that an eliminativist stance towards dead bodies is the appropriate response. CiteULike     Connotea     Del.icio.us     What's this?

There is a classic problem which confronts any attempt to assign death a value. On the assumption that death is personal annihilation, death deprives evil of a requisite subject, for no misfortune can befall something which does not exist. Recent efforts to provide a reasonable basis for counting death as a bad thing have centered on an analysis of the loss of life's goods which it brings. So long as the analysis assumes that death is a simple state, loss can be explained only by reference to a realm of possible things which exist after death. An alternative analysis of death is offered in which death is defined as a limit on life. That analysis provides a basis for evaluative judgements about death, while avoiding any commitment to post-mortem existence.

The harm thesis says that death may harm the individual who dies. The posthumous harm thesis says that posthumous events may harm those who die. Epicurus rejects both theses, claiming that there is no subject who is harmed, no clear harm which is received, and no clear time when any harm is received. Feldman rescues the harm thesis with solutions to Epicurus' three puzzles based on his own version of the deprivation account of harm. But many critics, among them Lamont, Grey, Feit and Bradley, have rejected Feldman's solution to the timing puzzle, offering their own solutions in its place. I discuss these solutions to the timing puzzle, and defend the view that while we are alive we may incur harm for which death and posthumous events are responsible.

Reflection on death gives rise to a variety of philosophical questions. One of the deepest of these is a question about the nature of death. Typically, philosophers interpret this question as a call for an analysis, or definition, of the concept of death. Plato proposed to define death as the separation of soul from body. This definition is not acceptable to materialists, who think that there are no souls. It is also unacceptable to anyone who thinks that plants and lower animals have no souls, but can die. Others have defined death simply as the cessation of life. This too is problematic, since an organism that goes into suspended animation ceases to live, but may not die.

According to Epicurus (1966a,b), neither death, nor anything that occurs later, can harm those who die, because people who die are not made to suffer as a result of either. In response, many philosophers (e.g., Nagel 1970, Feinberg 1984, and Pitcher 1984) have argued that Epicurus is wrong on both counts. They have defended the mortem thesis: death may harm those who die. They have also defended the post-mortem thesis: posthumous events may harm people who die. Their arguments for this joint view are by now quite familiar, and there is no need to rehearse them here (for a summary, see Luper 2002). Instead, our topic is a third position, which carves out intermediate ground between the other two. The intermediate view takes the mortem thesis for granted, like the critics of Epicurus, but rejects the post-mortem thesis, like Epicurus himself. For Epicurus’ project—the attainment of ataraxia, or equanimity—the intermediate view is almost useless (we are not tranquil if we regard death as a tragedy whose peculiarity is that it frees us from the possibility of any further misfortune); however, it is far more plausible than Epicurus’ own position since it avoids his absurd claim that death cannot harm us, while retaining his view that events occurring while we are dead and gone cannot harm us. According to the proponent of the intermediate view, when we understand the harm death inflicts, we must reject the idea that events following death can be bad for us. The damage death itself does is so severe that people are not subject to harm by any subsequent events. Thus the intermediate view rests on the mortem thesis together with the immunity thesis: death leaves its victims immune from posthumous harm.