Epicurus was an ancient Greek philosopher who founded a influential school of philosophy now called Epicureanism. He was born on the Greek island of Samos to Athenian parents. Influenced by Democritus and the Cynics, he turned against the Platonism of his day and established his own school, known as "the Garden", in Athens, he and his followers were known for eating simple meals and discussing a wide range of philosophical subjects, he allowed women to join the school as a matter of policy. An prolific writer, he is said to have written over 300 works on various subjects, but the vast majority of these writings have been lost. Only three letters written by him—the Letters to Menoeceus and Herodotus—and two collections of quotes—the Principle Doctrines and the Vatican Sayings—have survived intact, along with a few fragments and quotations of his other writings, his teachings are better recorded in the writings of authors, including the Roman poet Lucretius, the philosopher Philodemus, the philosopher Sextus Empiricus, the biographer Diogenes Laërtius.
For Epicurus, the purpose of philosophy was to attain the happy, tranquil life, characterized by ataraxia—peace and freedom from fear— and aponia—the absence of pain— and by living a self-sufficient life surrounded by friends. He taught that the root of all human neurosis is death denial, the tendency for human beings to assume that death will be horrific and painful, which he claimed causes unnecessary anxiety, selfish self-protective behaviors, hypocrisy. According to Epicurus, death is the end of both the body and the soul and therefore should not be feared. Epicurus taught that the gods, though they do exist, have no involvement in human affairs and do not punish or reward people for their actions. Nonetheless, he maintained that people should still behave ethically because amoral behavior will burden them with guilt and prevent them from attaining ataraxia. Like Aristotle, Epicurus was an empiricist, meaning he believed that the senses are the only reliable source of knowledge about the world.
He derived much of his cosmology from the earlier philosopher Democritus. Like Democritus, Epicurus taught that the universe is infinite and eternal and that all matter is made up of tiny, invisible particles known as atoms. All occurrences in the natural world are the result of atoms moving and interacting in empty space. Epicurus deviated from Democritus in his teaching of atomic "swerve", which holds that atoms may deviate from their expected course, thus permitting humans to possess free will in an otherwise deterministic universe. Though popular, Epicurean teachings were controversial from the beginning. Epicureanism reached the height of its popularity during the late years of the Roman Republic, before declining as the rival school of Stoicism grew in popularity at its expense, it died out in late antiquity in the wake of early Christianity. Epicurus himself was popularly, though inaccurately, remembered throughout the Middle Ages as a patron of drunkards and gluttons, his teachings became more known in the fifteenth century with the rediscovery of important texts, but his ideas did not become acceptable until the seventeenth century, when the French Catholic priest Pierre Gassendi revived a modified version of them, promoted by other writers, including Walter Charleton and Robert Boyle.
His influence grew during and after the Enlightenment, profoundly impacting the ideas of major thinkers, including John Locke, Thomas Jefferson, Jeremy Bentham, Karl Marx. Epicurus was born in the Athenian settlement on the Aegean island of Samos in February 341 BC, his parents and Chaerestrate, were both Athenian-born, his father was an Athenian citizen. Epicurus grew up during the final years of the Greek Classical Period. Plato had died seven years before Epicurus was born and Epicurus was seven years old when Alexander the Great crossed the Hellespont into Persia; as a child, Epicurus would have received a typical ancient Greek education. As such, according to Norman Wentworth DeWitt, "it is inconceivable that he would have escaped the Platonic training in geometry and rhetoric." Epicurus is known to have studied under the instruction of a Samian Platonist named Pamphilus for about four years. His Letter of Menoeceus and surviving fragments of his other writings suggest that he had extensive training in rhetoric.
After the death of Alexander the Great, Perdiccas expelled the Athenian settlers on Samos to Colophon, on the coast of what is now Turkey. After the completion of his military service, Epicurus joined his family there, he studied under Nausiphanes. Epicurus's teachings were influenced by those of earlier philosophers Democritus. Nonetheless, Epicurus differed from his predecessors on several key points of determinism and vehemently denied having been influenced by any previous philosophers, whom he denounced as "confused". Instead, he insisted that he had been "self-taught". According to DeWitt, Epicurus's teachings show influences from the contemporary philosophical school of Cynicism; the Cynic philosopher Diogenes of Sinope was still alive when Epicurus would have been in Athens for his required military training and it is possible they may have met. Diogenes's pupil Crates of Thebes was a close contemporary of Epicurus. Epicurus agreed with the Cynics' quest for honesty, but rejected their "insolence and vulgarity", instead teaching that honesty must be coupled with courtesy and kindness.
Epicurus shared this view with the comic playwright Menander. Epicurus's Lett
Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in computer science, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, is now an umbrella term for the science of logical decision making in humans and computers. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics, his paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.
Game theory was developed extensively in the 1950s by many scholars. It was explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been recognized as an important tool in many fields; as of 2014, with the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole, eleven game theorists have won the economics Nobel Prize. John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology. Early discussions of examples of two-person games occurred long before the rise of modern, mathematical game theory; the first known discussion of game theory occurred in a letter written by Charles Waldegrave, an active Jacobite, uncle to James Waldegrave, a British diplomat, in 1713. In this letter, Waldegrave provides a minimax mixed strategy solution to a two-person version of the card game le Her, the problem is now known as Waldegrave problem. In his 1838 Recherches sur les principes mathématiques de la théorie des richesses, Antoine Augustin Cournot considered a duopoly and presents a solution, a restricted version of the Nash equilibrium.
In 1913, Ernst Zermelo published Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. It proved that the optimal chess strategy is determined; this paved the way for more general theorems. In 1938, the Danish mathematical economist Frederik Zeuthen proved that the mathematical model had a winning strategy by using Brouwer's fixed point theorem. In his 1938 book Applications aux Jeux de Hasard and earlier notes, Émile Borel proved a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric. Borel conjectured that non-existence of mixed-strategy equilibria in two-person zero-sum games would occur, a conjecture, proved false. Game theory did not exist as a unique field until John von Neumann published the paper On the Theory of Games of Strategy in 1928. Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics, his paper was followed by his 1944 book Theory of Games and Economic Behavior co-authored with Oskar Morgenstern.
The second edition of this book provided an axiomatic theory of utility, which reincarnated Daniel Bernoulli's old theory of utility as an independent discipline. Von Neumann's work in game theory culminated in this 1944 book; this foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games. During the following time period, work on game theory was focused on cooperative game theory, which analyzes optimal strategies for groups of individuals, presuming that they can enforce agreements between them about proper strategies. In 1950, the first mathematical discussion of the prisoner's dilemma appeared, an experiment was undertaken by notable mathematicians Merrill M. Flood and Melvin Dresher, as part of the RAND Corporation's investigations into game theory. RAND pursued the studies because of possible applications to global nuclear strategy. Around this same time, John Nash developed a criterion for mutual consistency of players' strategies, known as Nash equilibrium, applicable to a wider variety of games than the criterion proposed by von Neumann and Morgenstern.
Nash proved that every n-player, non-zero-sum non-cooperative game has what is now known as a Nash equilibrium. Game theory experienced a flurry of activity in the 1950s, during which time the concepts of the core, the extensive form game, fictitious play, repeated games, the Shapley value were developed. In addition, the first applications of game theory to philosophy and political science occurred during this time. In 1979 Robert Axelrod tried setting up computer programs as players and found that in tournaments between them the winner was a simple "tit-for-tat" program that cooperates on the first step on subsequent steps just does whatever its opponent did on the previous step; the same winner was often obtained by natural selection. In 1965, Reinhard Selten introduced his solution concept of subgame perfect equilibria, which further refined the Nash equilibrium. In 1994 Nash and Harsanyi became Economics Nobel Laureates for their contributi
Gregory Benford is an American science fiction author and astrophysicist, Professor Emeritus at the Department of Physics and Astronomy at the University of California, Irvine. He is a contributing editor of Reason magazine. Benford wrote the Galactic Center Saga science fiction novels; the series postulates a galaxy in which sentient organic life is in constant warfare with sentient electromechanical life. In 1969 he wrote "The Scarred Man", the first story about a computer virus, published in 1970. Benford was born in Mobile and grew up in Robertsdale and Fairhope. Graduating Phi Beta Kappa, he received a Bachelor of Science in physics in 1963 from the University of Oklahoma in Norman, followed by a Master of Science from the University of California, San Diego in 1965, a doctorate there in 1967; that same year he married Joan Abbe. They are the parents of two children. Benford modeled characters in several of his novels after his wife, most prominently the heroine of Artifact, she died in 2002.
Benford has an identical twin brother, Jim Benford, with whom he has collaborated on science fiction stories. Both got their start in science fiction fandom, with Gregory being a co-editor of the science fiction fanzine Void. Benford has said, he has been a long-time resident of California. Gregory Benford's first professional sale was the story "Stand-In" in the Magazine of Fantasy and Science Fiction, which won second prize in a short story contest based on a poem by Doris Pitkin Buck. In 1969, he began writing a science column for Amazing Stories. Benford tends to write hard science fiction which incorporates the research he is doing as a practical scientist, he has worked on collaborations with David Brin and Gordon Eklund. His time-travel novel Timescape won both the John W. Campbell Memorial Award; the scientific procedural novel loaned its title to a line of science fiction published by Pocket Books. In the late 1990s, he wrote Foundation's Fear, one of an authorized sequel trilogy to Isaac Asimov's Foundation series.
Other novels published in that period include several near-future science thrillers: Cosm, The Martian Race and Eater. Benford has served as an editor of numerous alternate history anthologies as well as collections of Hugo Award winners, he has been nominated for four Hugo Awards and 12 Nebula Awards. In addition to Timescape, he won the Nebula for the novelette "If the Stars Are Gods". In 2005 the MIT SF Society awarded him the Asimov Prize. Benford was a guest of honour at Aussiecon Three, the 1999 Worldcon, he remains a regular contributor to science fiction fanzines, for example Apparatchik. In 2016 Benford was the recipient of the Los Angeles Science Fantasy Society Forry Award Lifetime Achievement Award in the Field of Science Fiction. Gregory Benford is Professor Emeritus of Physics at the University of Irvine. With more than 200 scientific publications, his research encompassed both theory and experiments in the fields of astrophysics and plasma physics, his research has been supported by other agencies.
He is an ongoing advisor to NASA, DARPA and the CIA. Benford's work in physics at the University of California focused on theoretical and experimental plasma physics, including studies of strong turbulence in astrophysical contexts, studies of magnetic structures from the galactic center to large-scale galactic jets. Working in collaboration with, among others, science fiction writers Cramer and Landis, Benford worked on a theoretical study of the physics of wormholes, which pointed out that wormholes, if formed in the early universe, could still exist in the present day if they were wrapped in a negative-mass cosmic string; such wormholes could be detected by gravitational lensing. In 2004, Benford proposed that the harmful effects of global warming could be reduced by the construction of a rotating Fresnel lens 1,000 kilometres across, floating in space at the Lagrangian point L1. According to Benford, this lens would diffuse the light from the Sun and reduce the solar energy reaching the Earth by 0.5% to 1%.
He estimated. His plan has been commented on in a variety of forums. A similar space sunshade was proposed in 1989 by J. T. Early, again in 1997 by Edward Teller, Lowell Wood, Roderick Hyde. In 2006, Benford pointed out one possible danger in this approach: if this lens were built and global warming were avoided, there would be less incentive to reduce greenhouse gases, humans might continue to produce too much carbon dioxide until it caused some other environmental catastrophe, such as a chemical change in ocean water that could be disastrous to ocean life. Benford serves on the steering committee of the Mars Society, he has advocated human cryopreservation, for example by signing an open letter to support research into cryonics, being a member of Alcor, by being an advisor to a UK cryonics and cryopreservation advocacy group. Gregory Benford retired from the University of California in 2006 in order to found and develop Genescient Corporation. Genescient is a new generation biotechnology company that combines evolutionary genomics with massive selective screening to analyze and exploit the genetics of model animal and human whole genomes.
This enables Genescient to develop novel therapeutics. Phi Beta Kappa Woodrow Wilson Fellow Fellow of the American Physical Society Vi
William Lane Craig
William Lane Craig is an American analytic philosopher and Christian theologian. He holds faculty positions at Talbot School of Houston Baptist University. Craig defended the Kalam Cosmological Argument for the existence of God, he focused in his published work on a historical argument for the resurrection of Jesus. His research on divine aseity and Platonism culminated with his book God Over All, he has debated the existence of God with public figures such as Sam Harris, Christopher Hitchens, Lawrence M. Krauss and A. C. Grayling. Craig runs the online apologetics ministry ReasonableFaith.org. Born August 23, 1949, in Peoria, Craig is the second of three children born to Mallory and Doris Craig, his father's work with the T. P. & W. railroad took the family to Keokuk, until his transfer to the home office in East Peoria in 1960. While a student at East Peoria Community High School, Craig became a championship debater and public speaker, being named his senior year to the all-state debate team and winning the state championship in oratory.
In September 1965, his junior year, he converted to Christianity, after graduating from high school, attended Wheaton College, majoring in communications. Craig graduated in 1971 and the following year married his wife Jan, whom he met on the staff of Campus Crusade for Christ. In 2014, he was named alumnus of the year by Wheaton. In 1973 Craig entered the program in philosophy of religion at Trinity Evangelical Divinity School north of Chicago, where he studied under Norman Geisler. In 1975 Craig commenced doctoral studies in philosophy at the University of Birmingham, writing on the Cosmological Argument under the direction of John Hick, he was awarded a doctorate in 1977. Out of this study came his first book, The Kalam Cosmological Argument, a defense of the argument he first encountered in Hackett's work. Craig was awarded a postdoctoral fellowship in 1978 from the Alexander von Humboldt Foundation to pursue research on the historicity of the resurrection of Jesus under the direction of Wolfhart Pannenberg at the Ludwig-Maximillians-Universität München in Germany.
His studies in Munich under Pannenberg's supervision led to a second doctorate, this one in theology, awarded in 1984 with the publication of his doctoral thesis, The Historical Argument for the Resurrection of Jesus During the Deist Controversy. Craig joined the faculty of Trinity Evangelical Divinity School in 1980, where he taught philosophy of religion for the next seven years. In 1982 Craig received an invitation to debate Kai Nielsen at the University of Calgary, Canada, on the question of God's existence, has since debated many philosophers and biblical scholars After a one-year stint at Westmont College on the outskirts of Santa Barbara, Craig moved in 1987 with his wife and two young children back to Europe, where he pursued research for the next seven years as a visiting scholar at the Katholieke Universiteit Leuven in Belgium. Out of that period of research issued seven books, among them God and Eternity. In 1994, Craig joined the Department of Philosophy and Ethics at Talbot School of Theology in suburban Los Angeles as a Research Professor of Philosophy, a position he holds, he went on to become a Professor of Philosophy at Houston Baptist University in 2014.
In 2016, Craig was named Alumnus of the Year by Trinity Evangelical Divinity School. In 2017, Biola created a permanent faculty position and endowed chair, the William Lane Craig Endowed Chair in Philosophy, in honor of Craig's academic contributions. Craig served as president of the Philosophy of Time Society from 1999 to 2006, he helped found the Evangelical Philosophical Society and served as its president from 1996 to 2005. Craig has worked extensively on a version of the Cosmological Argument called the Kalam Cosmological Argument. While the Kalam has a venerable history in medieval Islamic philosophy, Craig updated the argument to interact with contemporary scientific and philosophical developments. Craig's research resulted in renewed contemporary interest in the argument, in cosmological arguments in general; the universe began to exist. Therefore, the universe has a cause of its existence. In his literature, Craig sometimes uses a more modest version of the first premise, in order to bypass certain issues: If the universe began to exist the universe has a cause of its beginning.
Philosophically, Craig uses two traditional arguments to show that time is finite: he argues that the existence of an actual infinite is metaphysically impossible, that forming an actual infinite through successive addition is metaphysically impossible. Granting the strict logical consistency of post-Cantorian, axiomatized infinite set theory, Craig concludes that the existence of an infinite number of things is metaphysically impossible due to the consequential absurdities that arise. Craig illustrates this point using the example of Hilbert's paradox of the Grand Hotel. In Hilbert's hypothetical occupied hotel with infinitely many rooms, one can add an additional guest in room #1 by moving the guest in room #1 to room #2, the guest in room #2 into room #3, the guest in room #3 into room #4 and continue the shifting of rooms out to infinity. Craig points out that it is ab
Martin Gardner was an American popular mathematics and popular science writer, with interests encompassing scientific skepticism, philosophy and literature—especially the writings of Lewis Carroll, L. Frank Baum, G. K. Chesterton, he is recognized as a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies, he had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century. He was considered the doyen of American puzzlers, he was a versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematics—and by extension, mathematics in general—throughout the latter half of the 20th century, principally through his "Mathematical Games" columns; these appeared for twenty-five years in Scientific American, his subsequent books collecting them. Gardner was one of the foremost anti-pseudoscience polemicists of the 20th century.
His 1957 book Fads and Fallacies in the Name of Science became a classic and seminal work of the skeptical movement. In 1976 he joined with fellow skeptics to found CSICOP, an organization promoting scientific inquiry and the use of reason in examining extraordinary claims. Gardner, son of a petroleum geologist father and an educator and artist mother, grew up in and around Tulsa, Oklahoma, his lifelong interest in puzzles started in his boyhood when his father gave him a copy of Sam Loyd's Cyclopedia of 5000 Puzzles and Conundrums. He attended the University of Chicago, where he earned his bachelor's degree in philosophy in 1936. Early jobs included reporter on the Tulsa Tribune, writer at the University of Chicago Office of Press Relations, case worker in Chicago's Black Belt for the city's Relief Administration. During World War II, he served for four years in the U. S. Navy as a yeoman on board the destroyer escort USS Pope in the Atlantic, his ship was still in the Atlantic when the war came to an end with the surrender of Japan in August 1945.
After the war, Gardner returned to the University of Chicago. He attended graduate school for a year there. In 1950 he wrote an article in the Antioch Review entitled "The Hermit Scientist", it was one of Gardner's earliest articles about junk science, in 1952 a much-expanded version became his first published book: In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science and Present. In the late 1940s, Gardner moved to New York City and became a writer and editor at Humpty Dumpty magazine where for eight years he wrote features and stories for it and several other children's magazines, his paper-folding puzzles at that magazine led to his first work at Scientific American. For many decades, his wife Charlotte, their two sons and Tom, lived in Hastings-on-Hudson, New York, where he earned his living as a freelance author, publishing books with several different publishers, publishing hundreds of magazine and newspaper articles. Appropriately enough—given his interest in logic and mathematics—they lived on Euclid Avenue.
The year 1960 saw the original edition of the best-selling book of The Annotated Alice. In 1979, Gardner retired from Scientific American and he and his wife Charlotte moved to Hendersonville, North Carolina. Gardner never retired as an author, but continued to write math articles, sending them to The Mathematical Intelligencer, Math Horizons, The College Mathematics Journal, Scientific American, he revised some of his older books such as Origami and the Soma Cube. Charlotte died in 2000 and two years Gardner returned to Norman, where his son, James Gardner, was a professor of education at the University of Oklahoma, he died there on May 22, 2010. An autobiography — Undiluted Hocus-Pocus: The Autobiography of Martin Gardner — was published posthumously. Martin Gardner had a major impact on mathematics in the second half of the 20th century, his column was called "Mathematical Games" but it was much more than that. His writing introduced many readers to real mathematics for the first time in their lives.
The column lasted for 25 years and was read avidly by the generation of mathematicians and physicists who grew up in the years 1956 to 1981. It was the original inspiration for many of them to become scientists themselves. David Auerbach wrote: A case can be made, in purely practical terms, for Martin Gardner as one of the most influential writers of the 20th century, his popularizations of science and mathematical games in Scientific American, over the 25 years he wrote for them, might have helped create more young mathematicians and computer scientists than any other single factor prior to the advent of the personal computer. Among the wide array of mathematicians, computer scientists, magicians, artists and other influential thinkers who inspired and were in turn inspired by Gardner are John Horton Conway, Bill Gosper, Ron Rivest, Richard K. Guy, Piet Hein, Ronald Graham, Donald Knuth, Robert Nozick, Lee Sallows, Scott Kim, M. C. Escher, Douglas Hofstadter, Roger Penrose, Ian Stewart, David A. Klarner, Benoit Mandelbrot, Elwyn R. Berlekamp, Solomon W. Golomb, Raymond Smullyan, James Randi, Persi Diaconis, Penn & Teller, Ray Hyman.
His admirers included such diverse people as W. H. Auden, Arthur C. Clarke, Carl Sagan, Isaac Asimov, Richard Dawkins, Stephen Jay Gould, the entire French literary group known as the Oulipo. Salvador Dali once sought him out to discuss four-dimensional hypercubes. Gardner wrote to M. C. Escher in 1961 to ask permission
Argument from free will
The argument from free will called the paradox of free will or theological fatalism, contends that omniscience and free will are incompatible and that any conception of God that incorporates both properties is therefore inherently contradictory. These arguments are concerned with the implications of predestination; some arguments against the existence of God focus on the supposed incoherence of humankind possessing free will and God's omniscience. These arguments are concerned with the implications of predestination. Moses Maimonides formulated an argument regarding a person's free will, in traditional terms of good and evil actions, as follows: … "Does God know or does He not know that a certain individual will be good or bad? If thou sayest'He knows' it follows that the man is compelled to act as God knew beforehand how he would act, otherwise God's knowledge would be imperfect.…" A logical formulation of this argument might go as follows: God knows choice "C" that a human would claim to "make freely".
It is now necessary that C. If it is now necessary that C C cannot be otherwise; that is, there are no actual "possibilities" due to predestination. If you cannot do otherwise when you act, you do not act Therefore, when you do an act, you will not do it freely. Norman Swartz, contends that the above arguments commit the modal fallacy. In particular, he asserts that these arguments assume that if C is true, it becomes necessary for C to be true, incorrect as C is contingent. Otherwise, one can argue that the future is set regardless of his actions. Other means of reconciling God's omniscience with human free will have been proposed; some have attempted to redefine or reconceptualize free will: God can know in advance what I will do, because free will is to be understood only as freedom from coercion, anything further is an illusion. This is the move made by compatibilistic philosophies; the sovereignty of God, existing within a free agent, provides strong inner compulsions toward a course of action, the power of choice.
The actions of a human are thus determined by a human acting on strong or weak urges and their own relative power to choose. A proposition first offered by Boethius and by Thomas Aquinas and C. S. Lewis, suggests that God's perception of time is different, that this is relevant to our understanding of our own free will. In his book Mere Christianity, Lewis argues that God is outside time and therefore does not "foresee" events, but rather observes them all at once, he explains: But suppose God is outside and above the Time-line. In that case, what we call "tomorrow" is visible to Him in just the same way as what we call "today". All the days are "Now" for Him, he does not remember you doing things yesterday, He sees you doing them: because, though you have lost yesterday, He has not. He does not "foresee" you doing things tomorrow, He sees you doing them: because, though tomorrow is not yet there for you, it is for Him. You never supposed that your actions at this moment were any less free because God knows what you are doing.
Well, He knows your tomorrow's actions in just the same way—because He is in tomorrow and can watch you. In a sense, He does not know your action till you have done it: but the moment at which you have done it is "Now" for Him. A common objection is to argue that Molinism, or the belief that God can know counterfactually the actions of his creations, is true; this has been used as an argument amongst others. Dan Barker suggests that this can lead to a "Freewill Argument for the Nonexistence of God" on the grounds that God's omniscience is incompatible with God having free will and that if God does not have freewill God is not a personal being. Theists agree that God is a personal being and that God is omniscient, but there is some disagreement about whether "omniscient" means: "knows everything that God chooses to know and, logically possible to know". Book of Life List of paradoxes Thomas Aquinas. Summa Contra Gentiles Thomas Aquinas. Summa Theologica I, Q. XIV, esp. Art. 13: "Whether the Knowledge of God is of Future Contingent Things?".
Boethius. The Consolation of Philosophy. Many editions. Hasker, William. God and Foreknowledge". Ithaca: Cornell University Press, 1998. Molina, Luis de. On Divine Foreknowledge, trans. Alfred J. Freddoso. Ithaca: Cornell University Press, 1988. Plantinga, Alvin. "On Ockham's Way Out". Faith and Philosophy 3: 235–269. Ockham, William. Predestination, God's Foreknowledge, Future Contingents, trans. M. M. Adams and N. Kretzmann. Indianapolis: Hackett Publishing Company, 1983. Zagzebski, Linda. "The Dilemma of Freedom an Foreknowledge". New York: Oxford University Press, 1991. Luther, Martin: De servo arbitrio, in English: On the Bondage of the Will. In Latin and German 1525, in modern English: J. I. Packer and O. R. Johnston, trans. Old Tappan, New Jersey: Fleming H. Revell Co. 1957. Foreknowledge and Free Will article in the Internet Encyclopedia of Philosophy Omniscience and Divine Foreknowledge article in the Internet Encyclopedia of Philosophy The Paradox of Free will – An online discussion Thomas Aquinas. Summa Theologica I, Q.
XIV, Art. 13
Buridan's Bridge is described by Jean Buridan, one of the most famous and influential philosophers of the Late Middle Ages, in his book Sophismata. It is a self-referential paradox that involves a proposition pronounced about an event that might or might not happen in the future; the sophism is: Imagine the following scenario:Socrates wants to cross a river and comes to a bridge guarded by Plato. The two speak as follows:Plato: "Socrates, if in the first proposition which you utter, you speak the truth, I will permit you to cross, but if you speak falsely, I shall throw you into the water."Socrates: "You will throw me into the water." Socrates' response puts Plato in a difficult situation. He could not throw Socrates into the water, because if he did he would violate his promise to let Socrates cross the bridge if he speaks the truth. On the other hand, if Plato allows Socrates to cross the bridge it would mean that Socrates spoke untruth when he replied: "You are going to throw me into the water."
In that case Socrates should have been thrown into the water. In other words, Socrates could be allowed to cross the bridge if and only. In order to solve the paradox Buridan proposes three questions: Is the proposition uttered by Socrates: "You are going to throw me into the water" true, or is it false? Is Plato's promise true or is it false? "What ought Plato to do to fulfill his promise?"In response to the first question Buridan states that it is impossible to determine if Socrates' proposition is true or false. This is because the proposition "You are going to throw me into the water" is a future contingent that could be true or false depending on what Plato is going to do. Dr. Joseph W. Ulatowski says that Buridan used Aristotle's thesis about what "truth" is to come up with this response. Aristotle believed that a proposition is true if and only if it is verified by the state of things as they are. Contradicting the principle of bivalence, Buridan implies a system of three-valued logic in which there are three truth values--true and some indeterminate third value.
In determining the truth value of Plato's conditional promise, Buridan suggests that Plato's promise was false, that because Plato gave his promise carelessly he is not obligated to fulfill the promise. In discussing the third question, "What ought Plato to do to fulfill his promise", Buridan states that Plato should not have given a conditional promise in the first place, he suggests that Plato could have made sure that the condition was formulated in such a way that it would not cause a contradiction. Ulatowski points out that this interpretation is the contrapositive of a principle of Immanuel Kant: "ought implies can". In his solution to the sophism, Walter Burley applied the principle "nothing is true unless at this instant" and concluded that "if a proposition is true it must be true now". Dr. Dale Jacquette of the University of Bern says that "Plato can either permit Socrates to pass or have him seized and thrown into the river without violating his conditional vow". Jacquette argues that Plato's conditional promise was given only in regard to Socrates's proposition being and unconditionally either true or false.
To prove his point Jacquette asks, what would Plato have to do if Socrates had said nothing and was "as silent as a Sphinx", or if he uttered something that could not be either proven or "undisproven", something like Goldbach's conjecture. Jacquette concludes that Plato's conditional promise was true, Socrates's proposition is "neither true simpliciter nor false simpliciter", therefore Plato would be right regardless of the choice that he made. In his book Paradoxes from A to Z Professor Michael Clark comes to the conclusion that if Plato is an honorable man, Socrates should not get wet under any circumstances. Clark argues that Socrates could say, "Either I am speaking falsely, you will throw me in, or I am speaking and you won't throw me in". Clark says that if this sentence is true it means that the first alternative "is ruled out", leaving us only with the second one. If this sentence is false, it means that both alternatives are false, because Socrates spoke falsely "it will be false" to throw him into the river.
Dr. Joseph W. Ulatowski believes that since the truth value in Plato's conditional promise and more so in Socrates's proposition is indeterminate, it means that Plato "ought to err on the side of caution with respect to the future contingency and allow Socrates to cross the bridge". In the same work Ulatowski offers a couple of humorous solutions to the paradox. Plato, Ulatowski says, could let Socrates to cross the bridge, throw him into water on the other side. Or both Plato and Socrates could combine their efforts and forcibly eject Buridan himself from Buridan's bridge. Buridan's bridge sophism was used by Miguel de Cervantes in Don Quixote, when Sancho was presented with the Buridan's bridge dilemma: A man, going to cross the bridge was asked to respond truthfully where he was going or otherwise to face a death by hanging; the man "swore and said that by the oath he took he was going to die upon that gallows that stood there, nothing else." Sancho summarizes the situation by saying: "the man swears.
He comes up with the solution, "that of this man they should let pass the part that has sworn and hang the part t