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Paradoxes

Paradoxes

Paradoxes in general

Mathematical paradoxes

The Barber Paradox
  • Two short explanations of the barber are here and here.
Berry's Paradox
  • Click here for a short introduction to the Berry Number from The Grey Labyrinth.
Monty Hall
  • Useful links and sites:
    • This site puts you in the position of a contestant, and shows how previous contestants have fared. It also provides a good explanation of the problem.
    • This NYT interactive feature on the Monty Hall problem is very good.
    • Philosophy Experiments has an this interactive page on Monty Hall.
  • This clip does a good job of laying out the problem and explaining the correct answer:
  • The following clip from the Khan academy is associated with this page on dependent probability:
Sleeping Beauty
  • Adam Elga's beautiful little Analysis paper, in which he introduced the unsuspecting world to the sleeping beauty problem, is here. (While you are looking at Elga's Sleeping Beauty paper, you might also want to check out another very fun paper he has written -- his "Defeating Dr Evil with Self Locating Belief", which is here. It raises similar issues to Sleeping Beauty.)
  • This site outlines various interesting variations of the Sleeping Beauty scenario.
  • Click here for a short introduction to the Sleeping Beauty problem from The Grey Labyrinth.
  • http://barryispuzzled.com/zbeauty.htm
The Two Envelope Paradox
  • This video nicely summarises the paradox:

  • Logical Paradoxes has this short explanation on the two envelope paradox.
The St Petersburg Paradox
  • The SEP's entry on the St Petersburg Paradox is here.
  • A good video-summary of the paradox (which it calls the "coin flipping paradox") follows:
Russell's Paradox
  • The SEP's entry on this paradox is here.
  • The IEP's entry is here.
  • Here is a YouTube clip that quickly explains that notorious Russell Set, and how it did-for Frege's Naive Set Theory.



  • The next YouTube clip presents the paradox using the story of a librarian tasked with compiling a catalogue of all catalogues that do not list themselves:

Russell-Myhill Paradox
  • Encyclopedia entries:
    • SEP’s article on
    • IEP
Hilbert's Hotel
  • A brief statement of the paradox is here
  • The Open University's 60 second introduction to Hilbert's Hotel follows:
      
  • The following two videos by Agustin Rayo (of MIT) go into more detail. The first is about Hilbert's Hotel, and the second outlines Cantor's proof that there are more Real numbers between 0 and 1 than there are Natural numbers (even though there are infinitely many of the latter).
       
  • For an especially speedy explanation of what there are more Real numbers between 0 and 1 than there are Natural numbers, see this clip from Minute Physics.
  • Here are a couple more YouTube clips about Cantor and what he proved about infinity:

Epestemic Paradoxes (Paradoxes of Belief and Confirmation)

Hume's Problem of Induction
  • The SEP's entry on the Hume's problem of induction is here.
  • The IEP's discussion of the Hume's problem of induction is here.
  • Here's a clip that nicely summarises the problem:

     

  • Peter Millican introduces Hume's problem of induction to first-year students at Oxford in the following clip:
Goodman's Problem of Induction
The Preface Paradox
  • A brief statement of the paradox is here
  • The SEP's discussion of this paradox is here.
  • The IEP's treatment is here
The Ravens Paradox
  • A brief statement of the paradox is here
  • The IEP's discussion of this paradox is here
  • There is a summary of this paradox here
  • Logical Paradoxes has another short explanation of the paradox here.
The Unexpected Examination
This paradox is otherwise known as the "Surprise Test" or "Unexpected Hanging" paradox.
  • A brief statement of the paradox is here
  • The SEP's discussion of this paradox is here.
  • The "unexpected examination" paradox is sometimes presented instead in terms of an "unexpected hanging". Click here for a short introduction to the unexpected hanging version of the paradox (from The Grey Labyrinth.)
  • Logical Paradoxes has this page on the "unexpected hanging" version of the paradox.
Fitchs Paradox of Knowability
Paradox of The Knower
  • Encyclopedia entries:
  • Relevant Philpapers and Mindpapers Categories:

Decision-theoretic paradoxes

Decision Theory in General
  • A gentle primer on decision theory is here
  • Causal Decision Theory is one of the two dominant decision procedures in decision theory
  • Evidential Decision theory is the other.
  • So-called 'logical decision theories' have been proposed to attempt to resolve EDT and CDT's inability to return correct decisions on some of the following paradoxes. See this honours thesis [pdf] comparing the two main ones to EDT and CDT
    Newcomb’s Problem
    • Nozick's original paper introducing the problem is here [pdf]
    • Marion Ledwig's dissertation summarises the major standard positions and existing work.
    • The very good Philosophy Experiments site has an interactive exploration of Newcomb's Paradox here.
    • Click here for a short introduction to Newcomb's Paradox from The Grey Labyrinth.
    • Causal Decision Theory [SEP] two-boxes on Newcomb's Problem
    • Evidential Decision theory is generally held to one-boxe (although this is disputed by some)
    • Alternative ‘fringe’ decision theories that consistently one-box on Newcomblike problems
    • How common are Newcomblike Problems?
    • David Lewis (and others) have argued that the Prisoner's Dilemma is (or can be) a special case of Newcomb's Problem. This is a disputed, but generally held view
    Parfit’s Hitchhiker
    The Smoker's Lesion
    Pascal's Mugging
    A thought experiment seeking to demonstrate a problem with expected-utility maximisation
    • Nick Bostrom's Analysis paper introducing the problem is here
    The Prisoner’s dilemma
    • The SEP has entries on:
    • Douglas Hofstadter's
    • Something on the Prisoner’s Dilemma as a special case of Newcomb’s Problem?
    • This "Instant Egghead" video from the Scientific American quickly outlines the idea:
    • The next two videos from the Khan Academy explain the Prisoner's Dilemma and its relationship to the Nash Equilibrium:
    • In the following TED talk, John Bunzl explains the relevance of the Prisoner's Dilemma to the world's political problems:
  • Other Paradoxes

    The Doomsday Argument
    The Grandfather Paradox
    • The SEP's discussion of the grandfather paradox is here. The IEP's is here.
    • The Open University's 60 second introduction to the grandfather paradox follows:

    The Liar Paradox

    A very old, important and famous paradox, with major implications for the nature of truth, meaning and logic.
    • A brief statement of the paradox is here
    • The SEP has entries on:
    • The IEP's entry on the liar paradox is here.
    • The following clip is a bit dull visually (no fancy graphics) but it contains a very nice, clear, thorough discussion of the paradox, and of purported solutions to it. (It is framed around a defence of dialethism, the radical view that there are some real-live contradictions in the world.)

        

    The Lottery Paradox

    • The SEP's discussion of this paradox is here.

    McTaggart's Paradox

    • McTaggart's famous and still controversial paper, The Unreality of Time (1908), in which he introduced this paradox to the world, is here.
    • The SEP's discussion of McTaggart's Unreality of Time is here, while the IEP's is here.

    The Ship of Theseus

    • A brief statement of the paradox is here
    • The SEP's entry on Material Constitution includes a discussion of the Ship of Theseus puzzle.
    • In the following video Jennifer Wang of the University of Georgia outlines the puzzle:
       

    The Simulation Argument

    • Oxford's Nick Bostrom is the originator of the Simulation Argument. He has a very useful website here dedicated to the argument. It contains many links to online papers and resources.
    • A search on google will turn up numerous good YouTube clips on the simulation argument -- too many to list here. The following is one in which Bostrom himself does the explaining:

    Paradoxes of Vagueness

    The Sorites Paradox
    Otherwise known as the "Paradox of the Heap" or the "Paradox of Vagueness".

    The Stone Paradox

    Otherwise known as the "Paradox of Omnipotence".
    • A brief statement of the paradox is here
    • The IEP's discussion is here.

    The Paradox of Suspense

    Zeno's Paradoxes

  • IEP's article on Zeno's Paradoxes discusses general considerations and context as well as containing a section.
  • The SEP article, however, has more self-contained sections.
    Zeno's Paradox of Achilles and the Tortoise
    • A brief statement of the paradox is here
    • The SEP's discussion of this paradox is here.
    • The IEP's discussion is here.
    • The SEP has an entry on supertasks with relevance to this paradox.
    • The Open University's 60 second introduction to this paradox is here:
        
    Zeno's Paradox of the Arrow
    • A brief statement of the paradox is here
    • The SEP's discussion of this paradox is here.
    • The IEP's discussion is here.
    • Logical Paradoxes has this page on the arrow paradox.
    Zeno's Dichotomy
    • The SEP's discussion of this paradox is here.
    • The IEP's discussion is here.