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Intransitivity and Future Generations: Debunking Parfit's Mere Addition Paradox
Journal of Applied Philosophy, Vol. 20, No. 2,Intransitivity 2003 and Future Generations 187 Intransitivity and Future Generations: Debunking Parfit’s Mere Addition Paradox KAI M. A. CHAN Duties to future persons contribute critically to many important contemporaneous ethical dilemmas, such as environmental protection, contraception, abortion, and population policy. Yet this area of ethics is mired in paradoxes. It appeared that any principle for dealing with future persons encountered Kavka’s paradox of future individuals, Parfit’s repugnant conclusion, or an indefensible asymmetry. In 1976, Singer proposed a utilitarian solution that seemed to avoid the above trio of obstacles, but Parfit so successfully demonstrated the unacceptability of this position that Singer abandoned it. Indeed, the apparently intransitivity of Singer’s solution contributed to Temkin’s argument that the notion of “all things considered better than” may be intransitive. In this paper, I demonstrate that a time-extended view of Singer’s solution avoids the intransitivity that allows Parfit’s mere addition paradox to lead to the repugnant conclusion. However, the heart of the mere addition paradox remains: the time-extended view still yields intransitive judgments. I discuss a general theory for dealing with intransitivity (Tran- sitivity by Transformation) that was inspired by Temkin’s sports analogy, and demonstrate that such a solution is more palatable than Temkin suspected. When a pair-wise comparison also requires consideration of a small number of relevant external alternatives, we can avoid intransitivity and the mere addition paradox without infinite comparisons or rejecting the Independence of Irrelevant Alternatives Principle. Disagreement regarding the nature and substance of our duties to future persons is widespread. -
A Set of Solutions to Parfit's Problems
NOÛS 35:2 ~2001! 214–238 A Set of Solutions to Parfit’s Problems Stuart Rachels University of Alabama In Part Four of Reasons and Persons Derek Parfit searches for “Theory X,” a satisfactory account of well-being.1 Theories of well-being cover the utilitarian part of ethics but don’t claim to cover everything. They say nothing, for exam- ple, about rights or justice. Most of the theories Parfit considers remain neutral on what well-being consists in; his ingenious problems concern form rather than content. In the end, Parfit cannot find a theory that solves each of his problems. In this essay I propose a theory of well-being that may provide viable solu- tions. This theory is hedonic—couched in terms of pleasure—but solutions of the same form are available even if hedonic welfare is but one aspect of well-being. In Section 1, I lay out the “Quasi-Maximizing Theory” of hedonic well-being. I motivate the least intuitive part of the theory in Section 2. Then I consider Jes- per Ryberg’s objection to a similar theory. In Sections 4–6 I show how the theory purports to solve Parfit’s problems. If my arguments succeed, then the Quasi- Maximizing Theory is one of the few viable candidates for Theory X. 1. The Quasi-Maximizing Theory The Quasi-Maximizing Theory incorporates four principles. 1. The Conflation Principle: One state of affairs is hedonically better than an- other if and only if one person’s having all the experiences in the first would be hedonically better than one person’s having all the experiences in the second.2 The Conflation Principle sanctions translating multiperson comparisons into single person comparisons. -
Unexpected Hanging Paradox - Wikip… Unexpected Hanging Paradox from Wikipedia, the Free Encyclopedia
2-12-2010 Unexpected hanging paradox - Wikip… Unexpected hanging paradox From Wikipedia, the free encyclopedia The unexpected hanging paradox, hangman paradox, unexpected exam paradox, surprise test paradox or prediction paradox is a paradox about a person's expectations about the timing of a future event (e.g. a prisoner's hanging, or a school test) which he is told will occur at an unexpected time. Despite significant academic interest, no consensus on its correct resolution has yet been established.[1] One approach, offered by the logical school of thought, suggests that the problem arises in a self-contradictory self- referencing statement at the heart of the judge's sentence. Another approach, offered by the epistemological school of thought, suggests the unexpected hanging paradox is an example of an epistemic paradox because it turns on our concept of knowledge.[2] Even though it is apparently simple, the paradox's underlying complexities have even led to it being called a "significant problem" for philosophy.[3] Contents 1 Description of the paradox 2 The logical school 2.1 Objections 2.2 Leaky inductive argument 2.3 Additivity of surprise 3 The epistemological school 4 See also 5 References 6 External links Description of the paradox The paradox has been described as follows:[4] A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. -
Russell's Paradox in Appendix B of the Principles of Mathematics
HISTORY AND PHILOSOPHY OF LOGIC, 22 (2001), 13± 28 Russell’s Paradox in Appendix B of the Principles of Mathematics: Was Frege’s response adequate? Ke v i n C. Kl e m e n t Department of Philosophy, University of Massachusetts, Amherst, MA 01003, USA Received March 2000 In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. 1. Introduction Russell’s letter to Frege from June of 1902 in which he related his discovery of the Russell paradox was a monumental event in the history of logic. However, in the ensuing correspondence between Russell and Frege, the Russell paradox was not the only antinomy discussed. -
Lecture 5. Zeno's Four Paradoxes of Motion
Lecture 5. Zeno's Four Paradoxes of Motion Science of infinity In Lecture 4, we mentioned that a conflict arose from the discovery of irrationals. The Greeks' rejection of irrational numbers was essentially part of a general rejection of the infinite process. In fact, until the late 19th century most mathematicians were reluctant to accept infinity. In his last observations on mathematics1, Hermann Weyl wrote: \Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. That is his glory." Besides the conflict of irrational numbers, there were other conflicts about the infinite process, namely, Zeno's famous paradoxes of motion from around 450 B.C. Figure 5.1 Zeno of Citium Zeno's Paradoxes of motion Zeno (490 B.C. - 430 B.C.) was a Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides2. We know little 1Axiomatic versus constructive procedures in mathematics, The Mathematical Intelligencer 7 (4) (1985), 10-17. 2Parmenides of Elea, early 5th century B.C., was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy. For his picture, see Figure 2.3. 32 about Zeno other than Plato's assertion that he went to Athens to meet with Socrates when he was nearly 40 years old. Zeno was a Pythegorean. By a legend, he was killed by a tyrant of Elea whom he had plotted to depose. -
The Surprise Examination Or Unexpected Hanging Paradox Timothy Y
The Surprise Examination or Unexpected Hanging Paradox Timothy Y. Chow [As published in Amer. Math. Monthly 105 (1998), 41–51; ArXived with permission.] Many mathematicians have a dismissive attitude towards paradoxes. This is un fortunate, because many paradoxes are rich in content, having connections with serious mathematical ideas as well as having pedagogical value in teaching elementary logical reasoning. An excellent example is the socalled “surprise examination paradox” (de scribed below), which is an argument that seems at first to be too silly to deserve much attention. However, it has inspired an amazing variety of philosophical and mathemati cal investigations that have in turn uncovered links to Godel's¨ incompleteness theorems, game theory, and several other logical paradoxes (e.g., the liar paradox and the sorites paradox). Unfortunately, most mathematicians are unaware of this because most of the literature has been published in philosophy journals. In this article, I describe some of this work, emphasizing the ideas that are particularly interesting mathematically. I also try to dispel some of the confusion that surrounds the paradox and plagues even the published literature. However, I do not try to correct every error or explain every idea that has ever appeared in print. Readers who want more comprehensive surveys should see [30, chapters 7 and 8], [20], and [16]. At times I assume some knowledge of mathematical logic (such as may be found in Enderton [10]), but the reader who lacks this background may safely skim these sections. 1. The paradox and the metaparadox Let us begin by recalling the paradox. -
The Sorites Paradox
The sorites paradox phil 20229 Jeff Speaks April 17, 2008 1 Some examples of sorites-style arguments . 1 2 What words can be used in sorites-style arguments? . 3 3 Ways of solving the paradox . 3 1 Some examples of sorites-style arguments The paradox we're discussing today and next time is not a single argument, but a family of arguments. Here are some examples of this sort of argument: 1. Someone who is 7 feet in height is tall. 2. If someone who is 7 feet in height is tall, then someone 6'11.9" in height is tall. 3. If someone who is 6'11.9" in height is tall, then someone 6'11.8" in height is tall. ...... C. Someone who is 3' in height is tall. The `. ' stands for a long list of premises that we are not writing down; but the pattern makes it pretty clear what they would be. We could also, rather than giving a long list of premises `sum them up' with the following sorites premise: For any height h, if someone's height is h and he is tall, then someone whose height is h − 0:100 is also tall. This is a universal claim about all heights. Each of the premises 2, 3, . is an instance of this universal claim. Since universal claims imply their instances, each of premises 2, 3, . follows from the sorites premise. This is a paradox, since it looks like each of the premises is true, but the con- clusion is clearly false. Nonetheless, the reasoning certainly appears to be valid. -
Lecture 2.9: Russell's Paradox and the Halting Problem
Lecture 2.9: Russell's paradox and the halting problem Matthew Macauley Department of Mathematical Sciences Clemson University http://www.math.clemson.edu/~macaule/ Math 4190, Discrete Mathematical Structures M. Macauley (Clemson) Lecture 2.9: Russell's paradox & the halting problem Discrete Mathematical Structures 1 / 8 Russell's paradox Recall Russell's paradox: Suppose a town's barber shaves every man who doesn't shave himself. Who shaves the barber? This was due to British philosopher, logician, and mathematician Bertrand Russell (1872{1970), as an informal way to describe the paradox behind the set of all sets that don't contain themselves: S = fA j A is a set, and A 62 Ag: If such a set exists, then S 2 S −! S 62 S; S 62 S −! S 2 S; which is a contradiction. M. Macauley (Clemson) Lecture 2.9: Russell's paradox & the halting problem Discrete Mathematical Structures 2 / 8 A “fix” for Russell's paradox Let U be a universal set, and let S = fA j A ⊆ U and A 62 Ag: Now, suppose that S 2 S. Then by definition, S ⊆ U and S 62 S. If S 62 S, then :S ⊆ U ^ S 62 S =) S 6⊆ U _ S 2 S =) S 6⊆ U: In other words, there cannot exist a \set of all sets", but we can define a \class of all sets". One may ask whether we can always get rid of contradictions in this manner. In 1931, Kurt G¨odelsaid \no." G¨odel'sincompleteness theorem (informally) Every axiomatic system that is sufficient to develop the basic laws of arithmetic cannot be both consistent and complete. -
The Paradox of the Unexpected Hanging
Cambridge University Press 978-0-521-75613-6 - Knots and Borromean Rings, Rep-Tiles, and Eight Queens: Martin Gardner's Unexpected Hanging Martin Gardner Excerpt More information CHAPTER ONE The Paradox of the Unexpected Hanging “A new and powerful paradox has come to light.” This is the opening sentence of a mind-twisting article by Michael Scriven that appeared in the July 1951 issue of the British philosophical jour- nal Mind. Scriven, who bears the title of “professor of the logic of science” at the University of Indiana, is a man whose opinions on such matters are not to be taken lightly. That the paradox is indeed powerful has been amply confirmed by the fact that more than 20 articles about it have appeared in learned journals. The authors, many of whom are distinguished philosophers, disagree sharply in their attempts to resolve the paradox. Since no consensus has been reached, the paradox is still very much a controversial topic. No one knows who first thought of it. According to the Harvard University logician W. V. Quine, who wrote one of the articles (and who discussed paradoxes in Scientific American for April 1962), the paradox was first circulated by word of mouth in the early 1940s. It often took the form of a puzzle about a man condemned to be hanged. The man was sentenced on Saturday. “The hanging will take place at noon,” said the judge to the prisoner, “on one of the seven days of next week. But you will not know which day it is until you are so informed on the morning of the day of the hanging.” The judge was known to be a man who always kept his word. -
The Liar Paradox: Tangles and Chains Author(S): Tyler Burge Source: Philosophical Studies: an International Journal for Philosophy in the Analytic Tradition, Vol
The Liar Paradox: Tangles and Chains Author(s): Tyler Burge Source: Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, Vol. 41, No. 3 (May, 1982), pp. 353-366 Published by: Springer Stable URL: http://www.jstor.org/stable/4319529 Accessed: 11-04-2017 02:26 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms Springer is collaborating with JSTOR to digitize, preserve and extend access to Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition This content downloaded from 128.97.244.236 on Tue, 11 Apr 2017 02:26:37 UTC All use subject to http://about.jstor.org/terms TYLER BURGE THE LIAR PARADOX: TANGLES AND CHAINS (Received 20 March, 1981) In this paper I want to use the theory that I applied in 'Semantical paradox' to the Liar and Grelling paradoxes to handle some subtler versions of the Liar.! These new applications will serve as tools for sharpening some of the pragmatic principles and part of the underlying motivation of the theory. They also illustrate the superiority of our theory to previous ones in the hier- archical tradition. The heart of the theory is that 'true' is an indexical-schematic predicate. -
Decade7gpo.Pdf
166 1970–1979 167 Title page - Looking north, this photograph demonstrates construction of the new clinical building well underway. The underground parking garage can be seen to the right of the main building and appears to be at about the fifth floor level. Construction would take 5 years and 1 month, from groundbreaking on August 26, 1972 until dedication on September 26, 1977. Source: National Museum of Health and Medicine, AFIP, WRAMC History Collection u Architect’s model of the new hos- pital building, showing its relationship to the rest of the campus. The model resides in the National Museum of Health and Medicine. Source: Walter Reed Army Medical Center, Directorate of Public Works Archives he events of this decade clearly Lt. General Hal B. Jennings and focus on the construction and WRAMC Commander Maj. General occupancy of the new clinical William H. Moncrief. Tbuilding, designated Building 2. In 1967 with the assistance of Senators Complete construction took over five Dirksen, Russell and Stennis, Army years. During construction the amount Surgeon General and former Walter of dirt that was moved would have Reed Commanding General Leonard completely filled and buried RKF D. Heaton procured funds from Stadium. The trucks used to move Congress to start planning for a new the earth would have extended from hospital facility. The construction of Washington to 40 miles past New York Building 2 changed the face of the City. The steel used to reinforce the entire medical center. In actuality, 110,000 cubic yards of concrete used work had begun several years earlier would have stretched from Washington when a new commissary and post- to Denver. -
Commandant's Annual Report, 1971-1972
ANNUAL REPORT 1971-1972 The Judge Advocate General's School U. S. Army Charlottesville, Virginia 22901 . , SHOULDER SLEEVE INSIGNIA APPROVED FOR JAG SCHOOL Under the provisions of paragraphs 14-16, AR 670-5, the Com mandant received approval on 21 January 1972 for a shoulder sleeve insignia for uniform wear by Staff, Faculty, and Advanced Class personnel of The Judge Advocate General's School from the Chief of Heraldry, Institute of Heraldry, U.S. Army. The patch design is adapted from the School's distinctive crest. It is em blazoned across a shield of traditional blue. Its lighted torch symbolizes the illumination of intellect and leadership supplied by the School. The torch is surmounted by a gold open laurel wreath, below a gold sword and pen, with points downward, the tip ends of the wreath passing under the sword blade and pen quill FOREWORD The Judge Advocate General's School soon begins its twenty second year on the Grounds of the University of Virginia. In these years "the Home of the Military Lawyer" has consistently sought to serve the Army Lawyer in the field-by preparing him in our resident courses, keeping him supplied with the most recent legal information in a clear and concise form, and providing good quality continuing legal education programs both in the resident short courses and in our nonresident extension courses. But our active lawyer is only one part of our Corps and the School has likewise become the home for the lawyers in the Army Reserve and the Army and Air National Guard-the other two vital parts of our Army.