1. Russell's Paradox Learn how this logic puzzle was discovered in 1901, and scan the bibliography. Russell's paradox. Russell's paradox is the most famous of the logical or settheoretical paradoxes. http://plato.stanford.edu/entries/russell-paradox

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z content revised JUN Russell's Paradox Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox. Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves S. If S is a member of itself, then by definition it must not be a member of itself. Similarly, if S is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics. History of the paradox Significance of the paradox Bibliography Other Internet Resources ... Related Entries History of the paradox Russell appears to have discovered his paradox in May of 1901 while working on his Principles of Mathematics (1903). Cesare Burali-Forti, an assistant to Giuseppe Peano, had discovered a similar antinomy in 1897 when he noticed that since the set of ordinals is well-ordered, it, too, must have an ordinal. However, this ordinal must be both an element of the set of all ordinals and yet greater than every such element.

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6. Sorites Paradox Article in the Stanford Encyclopaedia of Philosophy, by Dominic Hyde.Category Society Philosophy Philosophy of Logic paradoxes......Sorites paradox. (On these latter points see Williamson (1994) Ch 4, sec. 1213.).Embracing the paradox. A final option is to simply embrace the paradox. http://plato.stanford.edu/entries/sorites-paradox/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z content revised AUG Sorites Paradox This phenomenon at the heart of the paradoxes is now recognised as the phenomenon of vagueness . Once identified, vagueness can be seen to be a feature of syntactic categories other than predicates, nonetheless one speaks primarily of the soriticality of predicates. Names, adjectives, adverbs and so on are only susceptible to paradoxical sorites reasoning in a derivative sense. Sorites arguments of the paradoxical form are to be distinguished from multi-premise syllogisms (polysyllogisms) which are sometimes also referred to as sorites arguments. Whilst both polysyllogisms and sorites paradoxes are chain-arguments, the former need not be paradoxical in nature and the latter need not be syllogistic in form. The Sorites In History Its Paradoxical Forms Responses Bibliography ... Related Entries The Sorites In History soros The Heap : Would you describe a single grain of wheat as a heap? No. Would you describe two grains of wheat as a heap? No. ... You must admit the presence of a heap sooner or later, so where do you draw the line? It was one of a series of puzzles attributed to the Megarian logician Eubulides of Miletus. Also included were:

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10. The Troublesome Paradox - Per Lundgren Online version of book seeking publication by Per Lundgren. Author attempts to argue that a consequence of Goedel's incompleteness theorem is that we should overturn our current approach to scientific method. http://www.yesgoyes.com/

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13. Epimenides An analysis of several attempted resolutions of the Epimenides paradox (also known as the Liar paradox), showing how they all fail. http://www.ocf.berkeley.edu/~sjblatt/notes/nottrue.html

The Epimenides Paradox I read about the Epimenides Paradox in Douglas Hofstadter's fascinating Goedel, Escher, Bach Consider Statement A. Statement A: "Statement A is not true." Is Statement A true? Statement A is not true. Argument 1 explains why. Argument 1: SUPPOSE Statement A is true. Then the proposition that Statement A states is true. But Statement A states that Statement A is not true. So, Statement A is not true, contrary to our initial supposition. So, IN FACT, Statement A is not true. Unfortunately, Statement A can't be not true either. Argument 2: 2.1 SUPPOSE Statement A is not true. 2.2. Then the proposition that Statement A states is not true. 2.3 But Statement A states that Statement A is not true. 2.4 So Statement A is not not true, contrary to our initial supposition. 2.5 So, IN FACT, Statement A is not not true. Your mind should be blown. You should not be saying, "That's puzzling." You should be saying, "My mind is exploding." Argument 1 proves that Statement A is not true. Argument 2 proves that Statement A is not not true. We have proved a contradiction, which is impossible.

14. The Possibilities Of FTL: Or Fermi's Paradox Reconsidered Discusses some of the logic behind arguments for and against humans being alone in the universe. http://www.alumni.engin.umich.edu/~fritx/Ftlessay/essay.html

Merideth Naomi is now 15 months old No new pictures posted. Yet. - Fritz. (Aug. 6th, 1998) The Possibilities of FTL: Or Fermi's Paradox Reconsidered by F.E. Freiheit IV When facts are few, speculations are most likely to represent individual psychology. - Carl Jung When you have eliminated the impossible, what is left, no matter how unlikely, is the truth. - Sherlock Holmes/Sir Arthur Conan Doyle There is nothing so big nor so crazy that one out of a million technological societies may not feel itself driven to do, provided it is physically possible. - Freeman J. Dyson 1. Are we alone in the universe? The drive to place humanity at the center of the universe has led to a stream of assumptions that, as facts have been collected, are shown to be ill founded. The Ptolemaic Earth centered view was replaced by Copernican Sun centered view which in its time was also replaced. The assumption that we are alone in the universe is also under threat of replacement. One of the more interesting aspects of our apparent aloneness was pointed out by Enrico Fermi and is know as Fermi's Paradox Fermi's Paradox may be succinctly stated as: Extraterrestrials should have colonized Earth long ago, but they have not. So where are they? Whether you agree with the point that Earth was colonized or not the fact remains that no concrete evidence has ever been found indicating a visitation of Earth by extraterrestrials. This is in itself is a very significant point whose ramifications I intend to explore here.

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17. Paradox Entertainment - Home Read more here! LATEST NEWS. Chariots of War announced from paradox Entertainment200301-29. More Macintosh versions of paradox titles coming 2002-12-11. http://www.paradoxplaza.com/default.asp

Hearts of Iron Hearts of Iron has gone gold! Read more in the announcement here Chariots of War Coming soon! Read more here! LATEST NEWS Paradox acquires all remaining stock in Conan Properties Chariots of War announced from Paradox Entertainment More news can be found in our press-center Paradox Entertainment Acquires Conan! Visit the official web site: www.conan.com DOWNLOAD THE LATEST GAME UPDATES Go to downloads. Crusader Kings Europa Universalis II Legion

18. UFO Skeptic Suggests that aliens might be preparing mankind for the eventuality of meeting species from other worlds. http://www.ufoskeptic.org/contact.html

ufoskeptic.org Fermi's Paradox and the Preparation for Contact Hypothesis The famous physicist, Enrico Fermi, was referring to such an argument when he asked: "Where are they?" Since he was a prominent (and very smart) scientist, his simple question has been given a duly profound name: Fermi's paradox. The paradox is resolved, of course, if the answer is: "Well, they are already here!" (and possibly have been for a very long time and perhaps have even been involved in the rather sudden emergence of homo sapiens sapiens, but that may be over the top, so ignore that last conjecture if it is too much, though I seem to recall that even Sagan considered that possibility at some point). Their being here but surreptitiously would answer Fermi and at the same time address a second common objection to the UFO phenomenon by scientists: that the observations indicate such utterly nonsensical, bizarre behaviour that it just could not possibly be real. Intelligent visitors just would not pull such disreputable antics as have been reported. It is tempting to argue, as some do, that since the visitors are not behaving like proper alien explorers, there are no visitors in the first place. (For some reason this logic brings to mind Galileo attempting to get the Cardinals to look through his telescope.) To counter this argument, I would like to suggest one possible rationale that might, in principle at least (no real world guarantees), account for the widespread, disjoint kind of behavior that the UFO phenomenon has manifested over 50 years. The reason for proposing this "preparation for contact hypothesis" (which is certainly no original idea of mine) is simply to facilitate a "suspension of disbelief" so that the UFO evidence can be confronted on its own terms without the mental roadblock that the phenomenon violates all common sense, or more precisely the common sense of modern western society, and that of the scientific community in particular, and hence cannot be real.

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Support Tek-Tips About Us Contact Us Site Policies HANDLE PASSWORD Remember Me Forgot Password? Join Us! Keyword Search ... Support Tek-Tips Talk With Other Members Be Notified Of Responses To Your Posts Keyword Search Turn Off Ad Banners One-Click Access To Your Favorite Forums Automated Signatures On Your Posts Best Of All, It's Free! E-mail* Handle Select A Type MIS IS/ITManagement Programmer ISP Instructor Vendor TechnicalUser Password Verify P'word *Opt in e-mail system. Click Personal Profile after login to opt out. "Best Of Breed" Forums Add Stickiness To Your Site (Download This Button Today!) "...I also believe that we all can contribute to each other's growth by sharing knowlege and experiences. I would love to take my skills and help people around the world solve problems..." More... DevGuru TopXML DevelopersDex ... Search Us! Search Find A Forum Find An Expert Home Forums Programmers DBMS Packages Corel: Paradox Forum (1920 members) Start A New Thread or Click on Subject Lines to View Threads. (TechnicalUser) 3/18/03 (posted 3/18) responses Want to put Paradox 4.5 DOS to new Windows XP

20. Time Travel - The Grandmother Paradox Discusses the possibility of associated paradoxes from a philosophical rather than purely scientific viewpoint, Mobius strip, bibliography and links. http://www.cix.co.uk/~antcom/gp.html

The Grandmother Paradox This is the most common example of the Time Travel Paradox. It describes how a Time Travellers action when travelling back in time alters the Time Travellers future creating a paradox. ....if you kill your grandmother then you would not be born, therefore you cannot travel to the past and kill your grandmother, so you would be born, so you could travel to the past and kill your grandmother.... It could be argued that at the moment he changes the past he should promptly disappear. After all this could be a logical termination of his timeline (and perhaps a good reason for people not to time travel). In the film however he simply begins to fade away represented by a photograph of himself with his brother and sister where they begin to loose parts of themselves. It is not until his parents fall in love and therefore his future birth is established that he returns to health. There are also other aspects of Time Travel used in the film. Marty returns to ten minutes before the time he left and so for ten minutes there is an overlap with two Martys and two time travel cars. Also because of events witnessed by Marty prior to his time travel trip namely the shooting of Dr Emmett he is able to warn him. Knowing this Dr Emmett wears a bullet-proof vest which saves his life.

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