Frege's Wounded Doctor   2013  JPG  "Consider the following case. Dr. Gustav Lauben says, "I have been wounded". Leo Peter hears this and remarks some days later, "Dr. Gustav Lauben has been wounded". […] Rudolph Lingens does not know Dr. Lauben personally and does not know that he is the very Dr. Lauben who recently said "I have been wounded". In this case Rudolph Lingens cannot know that the same thing is in question. I say, therefore, in this case: the thought which Leo Peter expresses is not the same as that which Dr. Lauben uttered." - Gottlob Frege, "The Thought", 1956

Frege's Wounded Doctor

2013

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"Consider the following case. Dr. Gustav Lauben says, "I have been wounded". Leo Peter hears this and remarks some days later, "Dr. Gustav Lauben has been wounded". […] Rudolph Lingens does not know Dr. Lauben personally and does not know that he is the very Dr. Lauben who recently said "I have been wounded". In this case Rudolph Lingens cannot know that the same thing is in question. I say, therefore, in this case: the thought which Leo Peter expresses is not the same as that which Dr. Lauben uttered." - Gottlob Frege, "The Thought", 1956

  Perry's Amnesiac in a Library   2013  JPG  "Let us consider [an] example. An amnesiac, Rudolf Lingens, is lost in the Stanford library. He reads a number of things in the library, including a biography of himself, and a detailed account of the library in which he is lost. He believes any Fregean thought you think might help him. He still won't know who he is, and where he is, no matter how much knowledge he piles up." - John Perry, "Frege on Demonstratives", 1977

Perry's Amnesiac in a Library

2013

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"Let us consider [an] example. An amnesiac, Rudolf Lingens, is lost in the Stanford library. He reads a number of things in the library, including a biography of himself, and a detailed account of the library in which he is lost. He believes any Fregean thought you think might help him. He still won't know who he is, and where he is, no matter how much knowledge he piles up." - John Perry, "Frege on Demonstratives", 1977

  Quine's Spy   2013  JPG  "There is a certain man in a brown hat whom Ralph has glimpsed several times under questionable circumstances on which we need not enter here; suffice it to say that Ralph suspects he is a spy. Also there is a gray-haired man, vaguely known to Ralph as rather a pillar of the community, whom Ralph is not aware of having seen except once at the beach. Now Ralph does not know it, but the men are one and the same. Can we say of this man (Bernard J. Ortcutt, to give him a name) that Ralph believes him to be a spy?" - W. V. Quine, "Quantifiers and Propositional Attitudes", 1956

Quine's Spy

2013

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"There is a certain man in a brown hat whom Ralph has glimpsed several times under questionable circumstances on which we need not enter here; suffice it to say that Ralph suspects he is a spy. Also there is a gray-haired man, vaguely known to Ralph as rather a pillar of the community, whom Ralph is not aware of having seen except once at the beach. Now Ralph does not know it, but the men are one and the same. Can we say of this man (Bernard J. Ortcutt, to give him a name) that Ralph believes him to be a spy?" - W. V. Quine, "Quantifiers and Propositional Attitudes", 1956

  Stalnaker's Spy Cousin   2013  JPG  "Rudolf Lingens is an amnesiac lost in the Stanford Library. He has found and read a biography of himself, and so knows quite a bit about Rudolf Lingens. He knows, for example, that Lingens is a distant cousin of a notorious spy. But he does not know that he is Lingens-that he is a distant cousin of a notorious spy. [...] Lingens, still lost in the Stanford Library, meets [the notorious spy,] Ortcutt. "I've lost my memory and don't know who I am," says Lingens. "Can you tell me? Who am I?" "You're my cousin, Rudolf Lingens," replies Ortcutt." - Robert Stalnaker, "Indexical Believe", 1981

Stalnaker's Spy Cousin

2013

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"Rudolf Lingens is an amnesiac lost in the Stanford Library. He has found and read a biography of himself, and so knows quite a bit about Rudolf Lingens. He knows, for example, that Lingens is a distant cousin of a notorious spy. But he does not know that he is Lingens-that he is a distant cousin of a notorious spy. [...] Lingens, still lost in the Stanford Library, meets [the notorious spy,] Ortcutt. "I've lost my memory and don't know who I am," says Lingens. "Can you tell me? Who am I?" "You're my cousin, Rudolf Lingens," replies Ortcutt." - Robert Stalnaker, "Indexical Believe", 1981

  Lewis's Multiple Worlds   2014  JPG  "Sometimes [an] agent has alternative possibilities in the same world. Consider [Rudolf] Lingens when he knows almost enough to get out. He has narrowed the possibilities down to two. Perhaps he is in aisle five, floor six, of Main Library, Stanford, in which case the way out is to go downstairs. Or perhaps he is in one of the lower floors in the stacks of Widener, in which case the thing to do is to go up. The books tell him that there are amnesiacs lost in both places, and he has figured out that he is one of the two. His deliberation concerns eight alternative possibilities. […] The eight cases are spread over only four sorts of worlds." - David Lewis, "Attitudes de dicto and de se", 1979

Lewis's Multiple Worlds

2014

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"Sometimes [an] agent has alternative possibilities in the same world. Consider [Rudolf] Lingens when he knows almost enough to get out. He has narrowed the possibilities down to two. Perhaps he is in aisle five, floor six, of Main Library, Stanford, in which case the way out is to go downstairs. Or perhaps he is in one of the lower floors in the stacks of Widener, in which case the thing to do is to go up. The books tell him that there are amnesiacs lost in both places, and he has figured out that he is one of the two. His deliberation concerns eight alternative possibilities. […] The eight cases are spread over only four sorts of worlds." - David Lewis, "Attitudes de dicto and de se", 1979

  Santorio's Kidnapping   2014  JPG  "Rudolf Lingens and Gustav Lauben are kidnapped. Lingens and Lauben are amnesiacs: each of them knows that he is one of the two kidnapped amnesiacs, but doesn’t know which. They will be subjected to the following experiment. First, they will be anesthetized. Then a coin will be tossed. If the outcome is tails, Lingens will be released in Main Library, Stanford, and Lauben will be killed. If the outcome is heads, Lauben will be released in Widener Library, Harvard, and Lingens will be killed. Lingens and Lauben are informed of the plan and the experiment is executed. Later, one of them wakes up in a library. He says: If the coin landed tails, I am in Main Library, Stanford. If the coin landed heads, I am in Widener Library, Harvard." - Paolo Santorio, "Reference and Monstrosity", 2012

Santorio's Kidnapping

2014

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"Rudolf Lingens and Gustav Lauben are kidnapped. Lingens and Lauben are amnesiacs: each of them knows that he is one of the two kidnapped amnesiacs, but doesn’t know which. They will be subjected to the following experiment. First, they will be anesthetized. Then a coin will be tossed. If the outcome is tails, Lingens will be released in Main Library, Stanford, and Lauben will be killed. If the outcome is heads, Lauben will be released in Widener Library, Harvard, and Lingens will be killed. Lingens and Lauben are informed of the plan and the experiment is executed. Later, one of them wakes up in a library. He says: If the coin landed tails, I am in Main Library, Stanford. If the coin landed heads, I am in Widener Library, Harvard." - Paolo Santorio, "Reference and Monstrosity", 2012

  Kinderman's Librarian   2014  JPG  "Consider [Rudolf] Lingens, who despite having studied a detailed map of the Stanford Library is lost and wishes to exit the library. A sympathetic librarian tells him [: "]You are in aisle five, floor six, of Main Library, Stanford.["] If Lingens understands […] and trusts the speaker, he is now in a position to exit the library, given the knowledge acquired from the map he read. Since he also has the desire to exit the library, he is likely to start moving towards the exit. […] After being told [this], Lingens is in a position to assert[:] I am in aisle five, floor six, of Main Library, Stanford. In contrast, [this information] by itself doesn’t seem to put the amnesiac Lingens in a position to assert[:] Rudolf Lingens is in aisle five, floor six, of Main Library, Stanford." - Dirk Kinderman, "Varieties of Centering and De Se Communication", 2014

Kinderman's Librarian

2014

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"Consider [Rudolf] Lingens, who despite having studied a detailed map of the Stanford Library is lost and wishes to exit the library. A sympathetic librarian tells him [: "]You are in aisle five, floor six, of Main Library, Stanford.["] If Lingens understands […] and trusts the speaker, he is now in a position to exit the library, given the knowledge acquired from the map he read. Since he also has the desire to exit the library, he is likely to start moving towards the exit. […] After being told [this], Lingens is in a position to assert[:] I am in aisle five, floor six, of Main Library, Stanford. In contrast, [this information] by itself doesn’t seem to put the amnesiac Lingens in a position to assert[:] Rudolf Lingens is in aisle five, floor six, of Main Library, Stanford." - Dirk Kinderman, "Varieties of Centering and De Se Communication", 2014

  Lasersohn's Recording   2015  JPG  "For example, suppose that before discovering his true identity, Rudolf Lingens tells someone “I am Rudolf Lingens,” intending to deceive his addressee. Unbeknownst to Lingens, we secretly tape his utterance. Later, we play back the recording to him. Lingens fails to recognize that the recording is of his own earlier utterance; he believes it was produced by the “real” Rudolf Lingens, whom he does not yet identify as himself. In this case there is a use α of the pronoun I, of which Lingens believes that its speaker is Rudolf Lingens; this belief is, moreover, true — Lingens is the speaker of α. Yet Lingens has still not self-identified as Rudolf Lingens; he hasn’t acquired the de se belief we are trying to account for." - Peter Lasersohn,  Subjectivity and Perspective in Truth-Theoretic Semantics , 2015

Lasersohn's Recording

2015

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"For example, suppose that before discovering his true identity, Rudolf Lingens tells someone “I am Rudolf Lingens,” intending to deceive his addressee. Unbeknownst to Lingens, we secretly tape his utterance. Later, we play back the recording to him. Lingens fails to recognize that the recording is of his own earlier utterance; he believes it was produced by the “real” Rudolf Lingens, whom he does not yet identify as himself. In this case there is a use α of the pronoun I, of which Lingens believes that its speaker is Rudolf Lingens; this belief is, moreover, true — Lingens is the speaker of α. Yet Lingens has still not self-identified as Rudolf Lingens; he hasn’t acquired the de se belief we are trying to account for." - Peter Lasersohn, Subjectivity and Perspective in Truth-Theoretic Semantics, 2015

  Berkeley's Cherry   2015  JPG  "I see this cherry, I feel it, I taste it: and I am sure nothing cannot be seen, or felt, or tasted: it is therefore real. Take away the sensations of softness, moisture, redness, tartness, and you take away the cherry, since it is not a being distinct from sensations. [...] Hence, when I see, and feel, and taste, in such sundry certain manners, I am sure the cherry exists, or is real. [...] But if by the word cherry you mean an unknown nature, distinct from all those sensible qualities, and by its existence something distinct from its being perceived; then [...] neither you nor I, nor any one else, can be sure it exists." - George Berkeley,  Three Dialogues Between Hylas and Philonous , 1713

Berkeley's Cherry

2015

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"I see this cherry, I feel it, I taste it: and I am sure nothing cannot be seen, or felt, or tasted: it is therefore real. Take away the sensations of softness, moisture, redness, tartness, and you take away the cherry, since it is not a being distinct from sensations. [...] Hence, when I see, and feel, and taste, in such sundry certain manners, I am sure the cherry exists, or is real. [...] But if by the word cherry you mean an unknown nature, distinct from all those sensible qualities, and by its existence something distinct from its being perceived; then [...] neither you nor I, nor any one else, can be sure it exists." - George Berkeley, Three Dialogues Between Hylas and Philonous, 1713

  Descartes' Wax Argument   2015  JPG  "This piece of wax: [...] its colour, its figure, its size are apparent; it is hard, cold, easily handled, and if you strike it with the finger, it will emit a sound. [...] But notice that while I speak and approach the fire what remained of the taste is exhaled, the smell evaporates, the colour alters, the figure is destroyed, the size increases, it becomes liquid, it heats, scarcely can one handle it, and when one strikes it, no sound is emitted. Does the same wax remain after this change? [...] We must then grant that I could not even understand through the imagination what this piece of wax is, and that it is my mind alone which perceives it." - René Descartes,  Meditations on First Philosophy,  1641

Descartes' Wax Argument

2015

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"This piece of wax: [...] its colour, its figure, its size are apparent; it is hard, cold, easily handled, and if you strike it with the finger, it will emit a sound. [...] But notice that while I speak and approach the fire what remained of the taste is exhaled, the smell evaporates, the colour alters, the figure is destroyed, the size increases, it becomes liquid, it heats, scarcely can one handle it, and when one strikes it, no sound is emitted. Does the same wax remain after this change? [...] We must then grant that I could not even understand through the imagination what this piece of wax is, and that it is my mind alone which perceives it." - René Descartes, Meditations on First Philosophy, 1641

  Hume's Ice   2015  JPG  "The Indian prince who refused to believe the first accounts he heard of frost reasoned soundly, and it naturally required very strong testimony to get him to accept facts arising from a state of nature which he had never encountered and which bore so little analogy to events of which he had had constant and uniform experience. Though they were not contrary to his experience, these facts—involving freezing cold—didn’t conform to it either." - David Hume,  An Enquiry Concerning Human Understanding,  1739

Hume's Ice

2015

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"The Indian prince who refused to believe the first accounts he heard of frost reasoned soundly, and it naturally required very strong testimony to get him to accept facts arising from a state of nature which he had never encountered and which bore so little analogy to events of which he had had constant and uniform experience. Though they were not contrary to his experience, these facts—involving freezing cold—didn’t conform to it either." - David Hume, An Enquiry Concerning Human Understanding, 1739

  Kavka's Toxin Puzzle   2015  JPG  "You have just been approached by an eccentric billionaire who has offered you the following deal. He places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life. [...] The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. [...] You need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. [...] All you have to do is sign the agreement and then intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin." - Gregory S. Kavka, "The Toxin Puzzle", 1983

Kavka's Toxin Puzzle

2015

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"You have just been approached by an eccentric billionaire who has offered you the following deal. He places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life. [...] The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. [...] You need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. [...] All you have to do is sign the agreement and then intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin." - Gregory S. Kavka, "The Toxin Puzzle", 1983

  Locke's Hog   2015  JPG  "He that shall place the identity of man in anything else, but, like that of other animals [...] will find it hard to make [...] the same man. [...] I think nobody could be sure that the soul of [a man] were in one of his hogs, would yet say that hog were a man." - John Locke,  An Essay Concerning Human Understanding , 1689

Locke's Hog

2015

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"He that shall place the identity of man in anything else, but, like that of other animals [...] will find it hard to make [...] the same man. [...] I think nobody could be sure that the soul of [a man] were in one of his hogs, would yet say that hog were a man." - John Locke, An Essay Concerning Human Understanding, 1689

  Locke's Parrot   2015  JPG  "An animal is a living organized body; and consequently the same animal, as we have observed, is the same continued life communicated to different particles of matter, as they happen successively to be united to that organized living body. [...] Whoever should hear a [...] parrot discourse, reason, or philosophize, would call or think it nothing but a [...] parrot; and say [it] a very intelligent rational parrot." - John Locke,  An Essay Concerning Human Understanding , 1689

Locke's Parrot

2015

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"An animal is a living organized body; and consequently the same animal, as we have observed, is the same continued life communicated to different particles of matter, as they happen successively to be united to that organized living body. [...] Whoever should hear a [...] parrot discourse, reason, or philosophize, would call or think it nothing but a [...] parrot; and say [it] a very intelligent rational parrot." - John Locke, An Essay Concerning Human Understanding, 1689

  Nagel's Bat   2015  JPG  "I have said that the essence of the belief that bats have experience is that there is something that it is like to be a bat. [...] We must consider whether any method will permit us to extrapolate to the inner life of the bat from our own case, and if not, what alternative methods there may be for understanding the notion. Our own experience provides the basic material for our imagination, whose range is therefore limited. [...] I want to know what it is like for a bat to be a bat. Yet if I try to imagine this, I am restricted to the resources of my own mind, and those resources are inadequate to the task." - Thomas Nagel, "What is it like to be a bat?", 1974

Nagel's Bat

2015

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"I have said that the essence of the belief that bats have experience is that there is something that it is like to be a bat. [...] We must consider whether any method will permit us to extrapolate to the inner life of the bat from our own case, and if not, what alternative methods there may be for understanding the notion. Our own experience provides the basic material for our imagination, whose range is therefore limited. [...] I want to know what it is like for a bat to be a bat. Yet if I try to imagine this, I am restricted to the resources of my own mind, and those resources are inadequate to the task." - Thomas Nagel, "What is it like to be a bat?", 1974

  Zhuangzi's Butterfly Dream   2015  JPG  "Once upon a time, I, Zhuangzi, dreamt I was a butterfly, fluttering hither and thither, to all intents and purposes a butterfly. I was conscious only of my happiness as a butterfly, unaware that I was Zhuangzi. Soon I awakened, and there I was, veritably myself again. Now I do not know whether I was then a man dreaming I was a butterfly, or whether I am now a butterfly, dreaming I am a man. Between a man and a butterfly there is necessarily a distinction. The transition is called the transformation of material things." - Zhuang Zhou,  Zhuangzi,  476–221 B.C.E.

Zhuangzi's Butterfly Dream

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"Once upon a time, I, Zhuangzi, dreamt I was a butterfly, fluttering hither and thither, to all intents and purposes a butterfly. I was conscious only of my happiness as a butterfly, unaware that I was Zhuangzi. Soon I awakened, and there I was, veritably myself again. Now I do not know whether I was then a man dreaming I was a butterfly, or whether I am now a butterfly, dreaming I am a man. Between a man and a butterfly there is necessarily a distinction. The transition is called the transformation of material things." - Zhuang Zhou, Zhuangzi, 476–221 B.C.E.

  Lucretius' Spear   2015  JPG  "If we should theorize that the whole of space were limited, then if a man ran out to the last limits and hurled a flying spear, would you prefer that, whirled by might and muscle, the spear flew on and on, as it was thrown, or do you think something would stop and block it?" - Lucretius,  On the Nature of Things , c. 95-55 B.C.E.

Lucretius' Spear

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"If we should theorize that the whole of space were limited, then if a man ran out to the last limits and hurled a flying spear, would you prefer that, whirled by might and muscle, the spear flew on and on, as it was thrown, or do you think something would stop and block it?" - Lucretius, On the Nature of Things, c. 95-55 B.C.E.

  Zeno's Arrow Paradox   2015  JPG  "If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." - Aristotle's recounting of Zeno's thought experiment,  Physics , 350 B.C.E.

Zeno's Arrow Paradox

2015

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"If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." - Aristotle's recounting of Zeno's thought experiment, Physics, 350 B.C.E.

  Parfit's Teletransporter   2015  JPG  "Suppose that you enter a cubicle in which, when you press a button, a scanner records the states of all the cells in your brain and body, destroying both while doing so. This information is then transmitted at the speed of light to some other planet, where a replicator produces a perfect organic copy of you. Since the brain of your replica is exactly like yours, it will seem to remember living your life up to the moment when you pressed the button, its character will be just like yours, and it will be in every other way psychologically continuous with you." - Derek Parfit, "Divided Minds and the Nature of Personas", 1987

Parfit's Teletransporter

2015

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"Suppose that you enter a cubicle in which, when you press a button, a scanner records the states of all the cells in your brain and body, destroying both while doing so. This information is then transmitted at the speed of light to some other planet, where a replicator produces a perfect organic copy of you. Since the brain of your replica is exactly like yours, it will seem to remember living your life up to the moment when you pressed the button, its character will be just like yours, and it will be in every other way psychologically continuous with you." - Derek Parfit, "Divided Minds and the Nature of Personas", 1987

  Shankara's Snake   2015  JPG  "Māyā can be destroyed by the realization of the pure Brahman, the one without a second, just as the mistaken idea of a snake is removed by the discrimination of the rope. She has her Guṇas as Rajas, Tamas and Sattva, named after their respective functions." - Adi Shankara,  Vivekachudamani , 8th century C.E.

Shankara's Snake

2015

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"Māyā can be destroyed by the realization of the pure Brahman, the one without a second, just as the mistaken idea of a snake is removed by the discrimination of the rope. She has her Guṇas as Rajas, Tamas and Sattva, named after their respective functions." - Adi Shankara, Vivekachudamani, 8th century C.E.

  Thomson's Lamp   2015  JPG  "There are certain reading-lamps that have a button in the base. [...] Suppose now that the lamp is off, and I succeed in pressing the button an infinite number of times, perhaps making one jab in one minute, another jab in the next half-minute, and so on, according to Russell's recipe. After I have completed the whole infinite sequence of jabs, i.e. at the end of the two minutes, is the lamp on or off? It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off." - James F. Thomas, "Tasks and Super-Tasks", 1954

Thomson's Lamp

2015

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"There are certain reading-lamps that have a button in the base. [...] Suppose now that the lamp is off, and I succeed in pressing the button an infinite number of times, perhaps making one jab in one minute, another jab in the next half-minute, and so on, according to Russell's recipe. After I have completed the whole infinite sequence of jabs, i.e. at the end of the two minutes, is the lamp on or off? It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off." - James F. Thomas, "Tasks and Super-Tasks", 1954

  Zuboff's Sleeping Beauty Problem   2015  JPG  "Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?" - Adam Elga (describing a thought experiment found in un-published notes by Arnold Zuboff from the 1980's), "Self-Locating Belief and the Sleeping Beauty Problem", 2000

Zuboff's Sleeping Beauty Problem

2015

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"Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?" - Adam Elga (describing a thought experiment found in un-published notes by Arnold Zuboff from the 1980's), "Self-Locating Belief and the Sleeping Beauty Problem", 2000

  Torricelli's Trumpet   2015  JPG  In 1641, Evangelista Torricelli described a paradoxical geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn it is commonly referred to as Toricelli's Trumpet.

Torricelli's Trumpet

2015

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In 1641, Evangelista Torricelli described a paradoxical geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn it is commonly referred to as Toricelli's Trumpet.

  Torricelli's Painter's Paradox   2015  JPG  In 1641, Evangelista Torricelli discovered a geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn, it is commonly referred to as Torricelli's Trumpet. The Painter's Paradox is the logical inconsistency found when attempting to paint this theoretical trumpet. If the volume of the trumpet is finite, then it can be filled with a finite about of paint. However, if the surface area is infinite, then an infinite amount of paint would be needed. It can be filled with paint, but it's surface cannot actually be painted.

Torricelli's Painter's Paradox

2015

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In 1641, Evangelista Torricelli discovered a geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn, it is commonly referred to as Torricelli's Trumpet. The Painter's Paradox is the logical inconsistency found when attempting to paint this theoretical trumpet. If the volume of the trumpet is finite, then it can be filled with a finite about of paint. However, if the surface area is infinite, then an infinite amount of paint would be needed. It can be filled with paint, but it's surface cannot actually be painted.

  Frege's Wounded Doctor   2013  JPG  "Consider the following case. Dr. Gustav Lauben says, "I have been wounded". Leo Peter hears this and remarks some days later, "Dr. Gustav Lauben has been wounded". […] Rudolph Lingens does not know Dr. Lauben personally and does not know that he is the very Dr. Lauben who recently said "I have been wounded". In this case Rudolph Lingens cannot know that the same thing is in question. I say, therefore, in this case: the thought which Leo Peter expresses is not the same as that which Dr. Lauben uttered." - Gottlob Frege, "The Thought", 1956
  Perry's Amnesiac in a Library   2013  JPG  "Let us consider [an] example. An amnesiac, Rudolf Lingens, is lost in the Stanford library. He reads a number of things in the library, including a biography of himself, and a detailed account of the library in which he is lost. He believes any Fregean thought you think might help him. He still won't know who he is, and where he is, no matter how much knowledge he piles up." - John Perry, "Frege on Demonstratives", 1977
  Quine's Spy   2013  JPG  "There is a certain man in a brown hat whom Ralph has glimpsed several times under questionable circumstances on which we need not enter here; suffice it to say that Ralph suspects he is a spy. Also there is a gray-haired man, vaguely known to Ralph as rather a pillar of the community, whom Ralph is not aware of having seen except once at the beach. Now Ralph does not know it, but the men are one and the same. Can we say of this man (Bernard J. Ortcutt, to give him a name) that Ralph believes him to be a spy?" - W. V. Quine, "Quantifiers and Propositional Attitudes", 1956
  Stalnaker's Spy Cousin   2013  JPG  "Rudolf Lingens is an amnesiac lost in the Stanford Library. He has found and read a biography of himself, and so knows quite a bit about Rudolf Lingens. He knows, for example, that Lingens is a distant cousin of a notorious spy. But he does not know that he is Lingens-that he is a distant cousin of a notorious spy. [...] Lingens, still lost in the Stanford Library, meets [the notorious spy,] Ortcutt. "I've lost my memory and don't know who I am," says Lingens. "Can you tell me? Who am I?" "You're my cousin, Rudolf Lingens," replies Ortcutt." - Robert Stalnaker, "Indexical Believe", 1981
  Lewis's Multiple Worlds   2014  JPG  "Sometimes [an] agent has alternative possibilities in the same world. Consider [Rudolf] Lingens when he knows almost enough to get out. He has narrowed the possibilities down to two. Perhaps he is in aisle five, floor six, of Main Library, Stanford, in which case the way out is to go downstairs. Or perhaps he is in one of the lower floors in the stacks of Widener, in which case the thing to do is to go up. The books tell him that there are amnesiacs lost in both places, and he has figured out that he is one of the two. His deliberation concerns eight alternative possibilities. […] The eight cases are spread over only four sorts of worlds." - David Lewis, "Attitudes de dicto and de se", 1979
  Santorio's Kidnapping   2014  JPG  "Rudolf Lingens and Gustav Lauben are kidnapped. Lingens and Lauben are amnesiacs: each of them knows that he is one of the two kidnapped amnesiacs, but doesn’t know which. They will be subjected to the following experiment. First, they will be anesthetized. Then a coin will be tossed. If the outcome is tails, Lingens will be released in Main Library, Stanford, and Lauben will be killed. If the outcome is heads, Lauben will be released in Widener Library, Harvard, and Lingens will be killed. Lingens and Lauben are informed of the plan and the experiment is executed. Later, one of them wakes up in a library. He says: If the coin landed tails, I am in Main Library, Stanford. If the coin landed heads, I am in Widener Library, Harvard." - Paolo Santorio, "Reference and Monstrosity", 2012
  Kinderman's Librarian   2014  JPG  "Consider [Rudolf] Lingens, who despite having studied a detailed map of the Stanford Library is lost and wishes to exit the library. A sympathetic librarian tells him [: "]You are in aisle five, floor six, of Main Library, Stanford.["] If Lingens understands […] and trusts the speaker, he is now in a position to exit the library, given the knowledge acquired from the map he read. Since he also has the desire to exit the library, he is likely to start moving towards the exit. […] After being told [this], Lingens is in a position to assert[:] I am in aisle five, floor six, of Main Library, Stanford. In contrast, [this information] by itself doesn’t seem to put the amnesiac Lingens in a position to assert[:] Rudolf Lingens is in aisle five, floor six, of Main Library, Stanford." - Dirk Kinderman, "Varieties of Centering and De Se Communication", 2014
  Lasersohn's Recording   2015  JPG  "For example, suppose that before discovering his true identity, Rudolf Lingens tells someone “I am Rudolf Lingens,” intending to deceive his addressee. Unbeknownst to Lingens, we secretly tape his utterance. Later, we play back the recording to him. Lingens fails to recognize that the recording is of his own earlier utterance; he believes it was produced by the “real” Rudolf Lingens, whom he does not yet identify as himself. In this case there is a use α of the pronoun I, of which Lingens believes that its speaker is Rudolf Lingens; this belief is, moreover, true — Lingens is the speaker of α. Yet Lingens has still not self-identified as Rudolf Lingens; he hasn’t acquired the de se belief we are trying to account for." - Peter Lasersohn,  Subjectivity and Perspective in Truth-Theoretic Semantics , 2015
  Berkeley's Cherry   2015  JPG  "I see this cherry, I feel it, I taste it: and I am sure nothing cannot be seen, or felt, or tasted: it is therefore real. Take away the sensations of softness, moisture, redness, tartness, and you take away the cherry, since it is not a being distinct from sensations. [...] Hence, when I see, and feel, and taste, in such sundry certain manners, I am sure the cherry exists, or is real. [...] But if by the word cherry you mean an unknown nature, distinct from all those sensible qualities, and by its existence something distinct from its being perceived; then [...] neither you nor I, nor any one else, can be sure it exists." - George Berkeley,  Three Dialogues Between Hylas and Philonous , 1713
  Descartes' Wax Argument   2015  JPG  "This piece of wax: [...] its colour, its figure, its size are apparent; it is hard, cold, easily handled, and if you strike it with the finger, it will emit a sound. [...] But notice that while I speak and approach the fire what remained of the taste is exhaled, the smell evaporates, the colour alters, the figure is destroyed, the size increases, it becomes liquid, it heats, scarcely can one handle it, and when one strikes it, no sound is emitted. Does the same wax remain after this change? [...] We must then grant that I could not even understand through the imagination what this piece of wax is, and that it is my mind alone which perceives it." - René Descartes,  Meditations on First Philosophy,  1641
  Hume's Ice   2015  JPG  "The Indian prince who refused to believe the first accounts he heard of frost reasoned soundly, and it naturally required very strong testimony to get him to accept facts arising from a state of nature which he had never encountered and which bore so little analogy to events of which he had had constant and uniform experience. Though they were not contrary to his experience, these facts—involving freezing cold—didn’t conform to it either." - David Hume,  An Enquiry Concerning Human Understanding,  1739
  Kavka's Toxin Puzzle   2015  JPG  "You have just been approached by an eccentric billionaire who has offered you the following deal. He places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life. [...] The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. [...] You need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. [...] All you have to do is sign the agreement and then intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin." - Gregory S. Kavka, "The Toxin Puzzle", 1983
  Locke's Hog   2015  JPG  "He that shall place the identity of man in anything else, but, like that of other animals [...] will find it hard to make [...] the same man. [...] I think nobody could be sure that the soul of [a man] were in one of his hogs, would yet say that hog were a man." - John Locke,  An Essay Concerning Human Understanding , 1689
  Locke's Parrot   2015  JPG  "An animal is a living organized body; and consequently the same animal, as we have observed, is the same continued life communicated to different particles of matter, as they happen successively to be united to that organized living body. [...] Whoever should hear a [...] parrot discourse, reason, or philosophize, would call or think it nothing but a [...] parrot; and say [it] a very intelligent rational parrot." - John Locke,  An Essay Concerning Human Understanding , 1689
  Nagel's Bat   2015  JPG  "I have said that the essence of the belief that bats have experience is that there is something that it is like to be a bat. [...] We must consider whether any method will permit us to extrapolate to the inner life of the bat from our own case, and if not, what alternative methods there may be for understanding the notion. Our own experience provides the basic material for our imagination, whose range is therefore limited. [...] I want to know what it is like for a bat to be a bat. Yet if I try to imagine this, I am restricted to the resources of my own mind, and those resources are inadequate to the task." - Thomas Nagel, "What is it like to be a bat?", 1974
  Zhuangzi's Butterfly Dream   2015  JPG  "Once upon a time, I, Zhuangzi, dreamt I was a butterfly, fluttering hither and thither, to all intents and purposes a butterfly. I was conscious only of my happiness as a butterfly, unaware that I was Zhuangzi. Soon I awakened, and there I was, veritably myself again. Now I do not know whether I was then a man dreaming I was a butterfly, or whether I am now a butterfly, dreaming I am a man. Between a man and a butterfly there is necessarily a distinction. The transition is called the transformation of material things." - Zhuang Zhou,  Zhuangzi,  476–221 B.C.E.
  Lucretius' Spear   2015  JPG  "If we should theorize that the whole of space were limited, then if a man ran out to the last limits and hurled a flying spear, would you prefer that, whirled by might and muscle, the spear flew on and on, as it was thrown, or do you think something would stop and block it?" - Lucretius,  On the Nature of Things , c. 95-55 B.C.E.
  Zeno's Arrow Paradox   2015  JPG  "If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." - Aristotle's recounting of Zeno's thought experiment,  Physics , 350 B.C.E.
  Parfit's Teletransporter   2015  JPG  "Suppose that you enter a cubicle in which, when you press a button, a scanner records the states of all the cells in your brain and body, destroying both while doing so. This information is then transmitted at the speed of light to some other planet, where a replicator produces a perfect organic copy of you. Since the brain of your replica is exactly like yours, it will seem to remember living your life up to the moment when you pressed the button, its character will be just like yours, and it will be in every other way psychologically continuous with you." - Derek Parfit, "Divided Minds and the Nature of Personas", 1987
  Shankara's Snake   2015  JPG  "Māyā can be destroyed by the realization of the pure Brahman, the one without a second, just as the mistaken idea of a snake is removed by the discrimination of the rope. She has her Guṇas as Rajas, Tamas and Sattva, named after their respective functions." - Adi Shankara,  Vivekachudamani , 8th century C.E.
  Thomson's Lamp   2015  JPG  "There are certain reading-lamps that have a button in the base. [...] Suppose now that the lamp is off, and I succeed in pressing the button an infinite number of times, perhaps making one jab in one minute, another jab in the next half-minute, and so on, according to Russell's recipe. After I have completed the whole infinite sequence of jabs, i.e. at the end of the two minutes, is the lamp on or off? It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off." - James F. Thomas, "Tasks and Super-Tasks", 1954
  Zuboff's Sleeping Beauty Problem   2015  JPG  "Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?" - Adam Elga (describing a thought experiment found in un-published notes by Arnold Zuboff from the 1980's), "Self-Locating Belief and the Sleeping Beauty Problem", 2000
  Torricelli's Trumpet   2015  JPG  In 1641, Evangelista Torricelli described a paradoxical geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn it is commonly referred to as Toricelli's Trumpet.
  Torricelli's Painter's Paradox   2015  JPG  In 1641, Evangelista Torricelli discovered a geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn, it is commonly referred to as Torricelli's Trumpet. The Painter's Paradox is the logical inconsistency found when attempting to paint this theoretical trumpet. If the volume of the trumpet is finite, then it can be filled with a finite about of paint. However, if the surface area is infinite, then an infinite amount of paint would be needed. It can be filled with paint, but it's surface cannot actually be painted.

Frege's Wounded Doctor

2013

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"Consider the following case. Dr. Gustav Lauben says, "I have been wounded". Leo Peter hears this and remarks some days later, "Dr. Gustav Lauben has been wounded". […] Rudolph Lingens does not know Dr. Lauben personally and does not know that he is the very Dr. Lauben who recently said "I have been wounded". In this case Rudolph Lingens cannot know that the same thing is in question. I say, therefore, in this case: the thought which Leo Peter expresses is not the same as that which Dr. Lauben uttered." - Gottlob Frege, "The Thought", 1956

Perry's Amnesiac in a Library

2013

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"Let us consider [an] example. An amnesiac, Rudolf Lingens, is lost in the Stanford library. He reads a number of things in the library, including a biography of himself, and a detailed account of the library in which he is lost. He believes any Fregean thought you think might help him. He still won't know who he is, and where he is, no matter how much knowledge he piles up." - John Perry, "Frege on Demonstratives", 1977

Quine's Spy

2013

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"There is a certain man in a brown hat whom Ralph has glimpsed several times under questionable circumstances on which we need not enter here; suffice it to say that Ralph suspects he is a spy. Also there is a gray-haired man, vaguely known to Ralph as rather a pillar of the community, whom Ralph is not aware of having seen except once at the beach. Now Ralph does not know it, but the men are one and the same. Can we say of this man (Bernard J. Ortcutt, to give him a name) that Ralph believes him to be a spy?" - W. V. Quine, "Quantifiers and Propositional Attitudes", 1956

Stalnaker's Spy Cousin

2013

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"Rudolf Lingens is an amnesiac lost in the Stanford Library. He has found and read a biography of himself, and so knows quite a bit about Rudolf Lingens. He knows, for example, that Lingens is a distant cousin of a notorious spy. But he does not know that he is Lingens-that he is a distant cousin of a notorious spy. [...] Lingens, still lost in the Stanford Library, meets [the notorious spy,] Ortcutt. "I've lost my memory and don't know who I am," says Lingens. "Can you tell me? Who am I?" "You're my cousin, Rudolf Lingens," replies Ortcutt." - Robert Stalnaker, "Indexical Believe", 1981

Lewis's Multiple Worlds

2014

JPG

"Sometimes [an] agent has alternative possibilities in the same world. Consider [Rudolf] Lingens when he knows almost enough to get out. He has narrowed the possibilities down to two. Perhaps he is in aisle five, floor six, of Main Library, Stanford, in which case the way out is to go downstairs. Or perhaps he is in one of the lower floors in the stacks of Widener, in which case the thing to do is to go up. The books tell him that there are amnesiacs lost in both places, and he has figured out that he is one of the two. His deliberation concerns eight alternative possibilities. […] The eight cases are spread over only four sorts of worlds." - David Lewis, "Attitudes de dicto and de se", 1979

Santorio's Kidnapping

2014

JPG

"Rudolf Lingens and Gustav Lauben are kidnapped. Lingens and Lauben are amnesiacs: each of them knows that he is one of the two kidnapped amnesiacs, but doesn’t know which. They will be subjected to the following experiment. First, they will be anesthetized. Then a coin will be tossed. If the outcome is tails, Lingens will be released in Main Library, Stanford, and Lauben will be killed. If the outcome is heads, Lauben will be released in Widener Library, Harvard, and Lingens will be killed. Lingens and Lauben are informed of the plan and the experiment is executed. Later, one of them wakes up in a library. He says: If the coin landed tails, I am in Main Library, Stanford. If the coin landed heads, I am in Widener Library, Harvard." - Paolo Santorio, "Reference and Monstrosity", 2012

Kinderman's Librarian

2014

JPG

"Consider [Rudolf] Lingens, who despite having studied a detailed map of the Stanford Library is lost and wishes to exit the library. A sympathetic librarian tells him [: "]You are in aisle five, floor six, of Main Library, Stanford.["] If Lingens understands […] and trusts the speaker, he is now in a position to exit the library, given the knowledge acquired from the map he read. Since he also has the desire to exit the library, he is likely to start moving towards the exit. […] After being told [this], Lingens is in a position to assert[:] I am in aisle five, floor six, of Main Library, Stanford. In contrast, [this information] by itself doesn’t seem to put the amnesiac Lingens in a position to assert[:] Rudolf Lingens is in aisle five, floor six, of Main Library, Stanford." - Dirk Kinderman, "Varieties of Centering and De Se Communication", 2014

Lasersohn's Recording

2015

JPG

"For example, suppose that before discovering his true identity, Rudolf Lingens tells someone “I am Rudolf Lingens,” intending to deceive his addressee. Unbeknownst to Lingens, we secretly tape his utterance. Later, we play back the recording to him. Lingens fails to recognize that the recording is of his own earlier utterance; he believes it was produced by the “real” Rudolf Lingens, whom he does not yet identify as himself. In this case there is a use α of the pronoun I, of which Lingens believes that its speaker is Rudolf Lingens; this belief is, moreover, true — Lingens is the speaker of α. Yet Lingens has still not self-identified as Rudolf Lingens; he hasn’t acquired the de se belief we are trying to account for." - Peter Lasersohn, Subjectivity and Perspective in Truth-Theoretic Semantics, 2015

Berkeley's Cherry

2015

JPG

"I see this cherry, I feel it, I taste it: and I am sure nothing cannot be seen, or felt, or tasted: it is therefore real. Take away the sensations of softness, moisture, redness, tartness, and you take away the cherry, since it is not a being distinct from sensations. [...] Hence, when I see, and feel, and taste, in such sundry certain manners, I am sure the cherry exists, or is real. [...] But if by the word cherry you mean an unknown nature, distinct from all those sensible qualities, and by its existence something distinct from its being perceived; then [...] neither you nor I, nor any one else, can be sure it exists." - George Berkeley, Three Dialogues Between Hylas and Philonous, 1713

Descartes' Wax Argument

2015

JPG

"This piece of wax: [...] its colour, its figure, its size are apparent; it is hard, cold, easily handled, and if you strike it with the finger, it will emit a sound. [...] But notice that while I speak and approach the fire what remained of the taste is exhaled, the smell evaporates, the colour alters, the figure is destroyed, the size increases, it becomes liquid, it heats, scarcely can one handle it, and when one strikes it, no sound is emitted. Does the same wax remain after this change? [...] We must then grant that I could not even understand through the imagination what this piece of wax is, and that it is my mind alone which perceives it." - René Descartes, Meditations on First Philosophy, 1641

Hume's Ice

2015

JPG

"The Indian prince who refused to believe the first accounts he heard of frost reasoned soundly, and it naturally required very strong testimony to get him to accept facts arising from a state of nature which he had never encountered and which bore so little analogy to events of which he had had constant and uniform experience. Though they were not contrary to his experience, these facts—involving freezing cold—didn’t conform to it either." - David Hume, An Enquiry Concerning Human Understanding, 1739

Kavka's Toxin Puzzle

2015

JPG

"You have just been approached by an eccentric billionaire who has offered you the following deal. He places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life. [...] The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. [...] You need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. [...] All you have to do is sign the agreement and then intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin." - Gregory S. Kavka, "The Toxin Puzzle", 1983

Locke's Hog

2015

JPG

"He that shall place the identity of man in anything else, but, like that of other animals [...] will find it hard to make [...] the same man. [...] I think nobody could be sure that the soul of [a man] were in one of his hogs, would yet say that hog were a man." - John Locke, An Essay Concerning Human Understanding, 1689

Locke's Parrot

2015

JPG

"An animal is a living organized body; and consequently the same animal, as we have observed, is the same continued life communicated to different particles of matter, as they happen successively to be united to that organized living body. [...] Whoever should hear a [...] parrot discourse, reason, or philosophize, would call or think it nothing but a [...] parrot; and say [it] a very intelligent rational parrot." - John Locke, An Essay Concerning Human Understanding, 1689

Nagel's Bat

2015

JPG

"I have said that the essence of the belief that bats have experience is that there is something that it is like to be a bat. [...] We must consider whether any method will permit us to extrapolate to the inner life of the bat from our own case, and if not, what alternative methods there may be for understanding the notion. Our own experience provides the basic material for our imagination, whose range is therefore limited. [...] I want to know what it is like for a bat to be a bat. Yet if I try to imagine this, I am restricted to the resources of my own mind, and those resources are inadequate to the task." - Thomas Nagel, "What is it like to be a bat?", 1974

Zhuangzi's Butterfly Dream

2015

JPG

"Once upon a time, I, Zhuangzi, dreamt I was a butterfly, fluttering hither and thither, to all intents and purposes a butterfly. I was conscious only of my happiness as a butterfly, unaware that I was Zhuangzi. Soon I awakened, and there I was, veritably myself again. Now I do not know whether I was then a man dreaming I was a butterfly, or whether I am now a butterfly, dreaming I am a man. Between a man and a butterfly there is necessarily a distinction. The transition is called the transformation of material things." - Zhuang Zhou, Zhuangzi, 476–221 B.C.E.

Lucretius' Spear

2015

JPG

"If we should theorize that the whole of space were limited, then if a man ran out to the last limits and hurled a flying spear, would you prefer that, whirled by might and muscle, the spear flew on and on, as it was thrown, or do you think something would stop and block it?" - Lucretius, On the Nature of Things, c. 95-55 B.C.E.

Zeno's Arrow Paradox

2015

JPG

"If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." - Aristotle's recounting of Zeno's thought experiment, Physics, 350 B.C.E.

Parfit's Teletransporter

2015

JPG

"Suppose that you enter a cubicle in which, when you press a button, a scanner records the states of all the cells in your brain and body, destroying both while doing so. This information is then transmitted at the speed of light to some other planet, where a replicator produces a perfect organic copy of you. Since the brain of your replica is exactly like yours, it will seem to remember living your life up to the moment when you pressed the button, its character will be just like yours, and it will be in every other way psychologically continuous with you." - Derek Parfit, "Divided Minds and the Nature of Personas", 1987

Shankara's Snake

2015

JPG

"Māyā can be destroyed by the realization of the pure Brahman, the one without a second, just as the mistaken idea of a snake is removed by the discrimination of the rope. She has her Guṇas as Rajas, Tamas and Sattva, named after their respective functions." - Adi Shankara, Vivekachudamani, 8th century C.E.

Thomson's Lamp

2015

JPG

"There are certain reading-lamps that have a button in the base. [...] Suppose now that the lamp is off, and I succeed in pressing the button an infinite number of times, perhaps making one jab in one minute, another jab in the next half-minute, and so on, according to Russell's recipe. After I have completed the whole infinite sequence of jabs, i.e. at the end of the two minutes, is the lamp on or off? It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off." - James F. Thomas, "Tasks and Super-Tasks", 1954

Zuboff's Sleeping Beauty Problem

2015

JPG

"Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?" - Adam Elga (describing a thought experiment found in un-published notes by Arnold Zuboff from the 1980's), "Self-Locating Belief and the Sleeping Beauty Problem", 2000

Torricelli's Trumpet

2015

JPG

In 1641, Evangelista Torricelli described a paradoxical geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn it is commonly referred to as Toricelli's Trumpet.

Torricelli's Painter's Paradox

2015

JPG

In 1641, Evangelista Torricelli discovered a geometric figure with infinite surface area, but finite volume. Due to the figure's resemblance to a horn, it is commonly referred to as Torricelli's Trumpet. The Painter's Paradox is the logical inconsistency found when attempting to paint this theoretical trumpet. If the volume of the trumpet is finite, then it can be filled with a finite about of paint. However, if the surface area is infinite, then an infinite amount of paint would be needed. It can be filled with paint, but it's surface cannot actually be painted.

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