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Topic: What the Tortoise Said to Achilles

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	Encyclopedia: Geb
		In this context, Geb was said to have originally been engaged in eternal sex with Nuit, and had to be separated from her by Tefnut.
		Likewise, since it was used as his name, he too became associated with vegetation, with barley being said to grow upon his ribs, and was depicted with plants and other green patches on his body.
		His association with vegetation, and sometimes with the underworld, also brought him the occasional interpretation that he was the wife of Renenutet, a minor goddess of the harvest, who was the mother of Nehebkau, a god associated with the underworld, who was on the same occasions said to be his son by her.
	www.nationmaster.com /encyclopedia/Geb (1125 words)

	[No title]
		As we have already noted, she neither disputes the validity of the \'93sequence\'94 C nor the validity of the inference from A and B to Z. But her refusal to accept the conclusion C might be the expression of her scepticism about logical truths or logical rules in general.
		Again Carroll\rquote s Tortoise had not read Wittgenstein, but her reluctance to grant the \'93hardness of the logical must\'94 is strikingly similar: she denies that \'93 logic is going to take you by the throat and }{\i\lang2057\langfe1036\langnp2057\langfenp1036 force}{\lang2057\langfe1036\langnp2057\langfenp1036 you to do it\'94.
		In this sense, she might be said not to understand the sentence C that she adds to her premisses.
	jeannicod.ccsd.cnrs.fr /documents/disk0/00/00/05/71/ijn_00000571_00/ijn_00000571_00.rtf (6005 words)

	Achilles and the Tortoise (Site not responding. Last check: 2007-10-10)
		Next, Achilles must run to the tortoise's new position, but once again, while Achilles is doing that, the tortoise will move on a little further and so on and so on.
		Achilles will be able to close the gap because he does not stop at the turtle's start point, he continues at the same constant speed while the turtle continues at its constant speed.
		This is because every time Achilles catches upto the point that the tortoise is at, the tortoise would have moved slightly further up since it was at that point.
	ubertas.infosys.utas.edu.au /mathemagicians_circle/table1.html (1793 words)

	The Search for Non-Being (Site not responding. Last check: 2007-10-10)
		If, in the race, the tortoise has a start on Achilles, then Achilles can never reach the tortoise for, while Achilles traverses the distance from his starting point to that of the tortoise, the tortoise will have gone a certain distance and, while Achilles traverses this distance, the tortoise goes still further, ad infinitum.
		The Achilles paradox purported to force upon the listener the truism that motion is impossible and what we see as motion is an illusion.
		Achilles, trying to follow the tortoise's reasoning, is left by the end mentally near despair failing to understand Carroll's adaptation of Zeno's paradox which leads to infinity.
	atschool.eduweb.co.uk /cite/staff/philosopher/alice.htm (2765 words)

	What the Tortoise said to Achilles (Site not responding. Last check: 2007-10-10)
		Achilles had overtaken the Tortoise, and had seated himself comfortably on its back.
		"--an anomaly, of course," the tortoise hastily interrupted.
		When he did so, Achilles was still seated on the back of the much-enduring Tortoise, and was writing in his note-book, which appeared to be nearly full.
	home.earthlink.net /~lfdean/carroll/essays/achilles.html (1117 words)

	Achilles and the Tortoise, part 1 (Site not responding. Last check: 2007-10-10)
		Achilles starts from A, the Tortoise at the same time from B. If we assume that the Homeric hero runs twice as fast as the animal, the inference seems inevitable that both racers should reach point Z at the same time; but such was not Zeno´s conclusion.
		Whenever Achilles reaches a designated point it has taken him time to get there from the preceding one, and during this time lapse the Tortoise has moved on to the next - as the animal is in constant motion.
		If that is the case, then it is mathematically demonstrated that Achilles must overtake the Tortoise at point Z. This is the moment when the concept of "limit" is introduced.
	www.vordenker.de /gunther_web/achill1.htm (4497 words)

	Practical Tortoise Raising (Site not responding. Last check: 2007-10-10)
		Achilles, then, had overtaken the tortoise and was sitting comfortably on its back.
		‘You always did catch up fast’ said the tortoise admiringly, ‘And it also suggests that the question is not so much one of whether it is rational for Eve to be vicious, as whether she has been educated so that she and her peers thrive in the situations in which they will be put.
		And equally obviously tortoises of a race that does not choose necessary means to ends will fail to achieve their ends; assuming their ends include satisfying their needs, then they will die out rather rapidly.
	www.unc.edu /~sblackbu/ACHILLES.html (6119 words)

	Modus ponens - Wikipedia, the free encyclopedia
		If the argument is modus ponens and its premises are true, then it is sound.
		A propositional argument using modus ponens is said to be deductive.
		Modus ponens can also be referred to as affirming the antecedent.
	en.wikipedia.org /wiki/Modus_ponens (306 words)

	Misconceptions in XP II:Achilles and the Tortoise Discuss Design
		Achilles is a well-known software architect; the Tortoise is a famous XPer.
		Achilles my friend, there seems to be something wrong with your hearing today, perhaps you should visit the apothecary.
		But, with help, X will finish her task much sooner, so the time lost to Y is made up by X, overall, it balances out.
	www.xprogramming.com /xpmag/AchillesTortoise.htm (2050 words)

	[No title]
		Achilles and the Tortoise are discussing three propositions A, B and Z, where Z is looked upon as following logically from A and B. But the Tortoise asks Achilles to treat him as if, while accepting that A and B were true, he did not yet accept the truth of the hypothetica!
		At one point the Tortoise asks : "Suppose I still refuse to accept Z ?" Achilles triumphantly replies : "Then Logic would take you by the throat, and force you to do it." But nothing happens; "Whatever Logic is good enough to tell me is worth writing down.
		The moral of this is, of course, that the actual process of drawing an inference, which is after all at the heart of Logic, is something which cannot itself be written down as a logical formula.
	pubpages.unh.edu /~jds/DeadorAlive.htm (2833 words)

	Maths Problems
		Achilles and the tortoise decide to have a race.
		Achilles now needs to cover this 100m, but when he reaches this point, the tortoise has moved another 10m.
		When he did so, Achilles was still seated on the back of the much-enduring Tortoise, and was writing in his notebook, which appeared to be nearly full.
	anthony.edey1.users.btopenworld.com /paradox.html (1239 words)

	PART 2
		In these games the concepts of truth, justification, and knowledge will be discussed as well as the inference rule Modus Ponens and the epistemic principles of conjunctive and deductive closure.
		In Carroll’s article the Tortoise wins over Achilles in a most special theoretical race: he seems successfully demonstrate that Modus Ponens cannot be justified.
		My aim is to show that there is an escape for Achilles from the Tortoise’s conclusion: Achilles can argue that the Tortoise is unable to win and thus the Tortoise fails to make any relevant point about the challenged logical principle.
	www.faculty.umb.edu /peter_marton/dissertation/part1.htm (770 words)

	Zeno's Paradox of the Tortoise and Achilles (PRIME)
		(Achilles was the great Greek hero of Homer's The Illiad.) It has inspired many writers and thinkers through the ages, notably Lewis Carroll and Douglas Hofstadter, who also wrote dialogues involving the Tortoise and Achilles.
		Achilles laughed at this, for of course he was a mighty warrior and swift of foot, whereas the Tortoise was heavy and slow.
		He knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this.
	www.mathacademy.com /pr/prime/articles/zeno_tort/index.asp (1081 words)

	Foreign Dispatches: Philosophy
		If we are to care about what people who are dead would have wanted, it should not be for their sake but for the loved ones who survive, as well as for the sake of the strength and stability of societal institutions.
		Not only does said argument avail religious apologists nothing, being trivial to point out that it itself necessitates the existence of a causer for the "first causer", but it is as a physical principle far from clear that literally everything that happens in the universe must indeed by caused by something else.
		And I said, "What the hell do you mean by that?" And he said, "He writes so obscurely you can't tell what he's saying, that's the obscurantism part, and then when you criticize him, he can always say, 'You didn't understand me; you're an idiot.' That's the terrorism part." And I like that.
	foreigndispatches.typepad.com /dispatches/philosophy (3585 words)

	James McClellan - Theoretical and Practical Reasoning: An Intractable Dualism?
		In the midst of a pleasant conversation, Tortoise mentions another race which would seem to be brief but in fact consists of an infinite number of steps and can never be completed.
		"And why, pray tell," asks Tortoise, "does acceptance of A, B, and C require one to grant Z?" Achilles proceeds to provide a true D (say, "To assert A and B and then deny Z is self-contradictory."), E,...
		For tortoises, at least on the evidence before us, have no rational compulsion to accept the conclusion of a valid argument just because they accept its premises.
	www.ed.uiuc.edu /EPS/PES-yearbook/96_docs/mcclellan.html (3789 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-10)
		Read, for example _What the Tortoise Said to Achilles_ by Lewis Carroll at: http://www.ditext.com/carroll/tortoise.html >Mathematics is discovered by the intuition of the mathematician, and >then established in a proof.
		One of the things Goedel showed is that in any internally consistent formal system that can be created, there will always be statements that are true, but that are not provable within the system.
		As I said earlier, I think mathematical absolutism does violence to the concept of existence by failing to distinguish between existence and implication.
	mathforum.org /library/drmath/view/52291.html (3518 words)

	The New York Review of Books: The Dream of Mind and Machine
		Its "epigenesis" is shown to be a literary example of the phases of cell division, with discussions of its prophase, metaphase, anaphase, and telophase.
		In one of Zeno's paradoxes it is proven that in a race Achilles could never catch up with the Tortoise if the Tortoise had a head start, since Achilles would first have to cover half the distance between them, then a quarter, and an eighth, and so on ad infinitum.
		Lewis Carroll's dialogue "What the Tortoise Said to Achilles," which Hofstadter reprints and takes as a model, is a brilliant logical analogue to Zeno's paradox, as the Tortoise shows how Achilles can never "catch up" with the conclusion of a simple syllogism.
	www.nybooks.com /articles/7598 (5258 words)

	Wittgenstein on Logical Necessity (Site not responding. Last check: 2007-10-10)
		Achilles now thinks that by admitting C the Tortoise has to accept Z. The
		Tortoise, however, says that if he did so, he would be subscribing to one
		tortoise and the student are legitimately termed 'irrational.'' The tortoise, within the context
	faculty.frostburg.edu /phil/forum/WittgMath.htm (4097 words)

	Onion Blog
		Achilles: The problem is not with the ObjectDataSource, it’s with your perception of its purpose.
		There is no need for these data source controls to be more generic than they are, because they expose exactly the subset of features required by the controls they serve.
		Tortoise: Hmm, I hadn’t thought of it that way before, but I see you do have a point, they do a reasonable job of representing what controls require, and it is at least somewhat compelling to remove all data access code from pages.
	pluralsight.com /blogs/fritz (2508 words)

	Practical Tortoise Reasoning
		Achilles frowned as he replaced his pencil with a new one.
		But great Achilles had flown to the libraries to collect some volumes on The Theory of Rational Choice.
		Day IV ‘Listen’, began Achilles, his locks dishevelled by what appeared to have been a sleepless night.
	www.mtholyoke.edu /courses/ebarnes/334/Blackburn-ACHILLES.htm (6126 words)

	Qué la tortuga dijo a Achilles (Site not responding. Last check: 2007-10-10)
		Los desafíos Achilles de la tortuga para utilizar la fuerza de la lógica para hacer que él acepta una discusión deductiva particular.
		En última instancia, Achilles falla, porque la tortuga lista lo conduce en una regresión infinita.
		Es decir, si él concede (a) y (b), la tortuga desea a Achilles para obligarle a lógicamente que acepte (z).
	www.yotor.net /wiki/es/qu/Qu%E9%20la%20tortuga%20dijo%20a%20Achilles.htm (566 words)

	Philosophy 183: Theory of Knowledge (Site not responding. Last check: 2007-10-10)
		But the patch itself is of a radically different kind from the things that are true or false, and therefore cannot properly be said to be true.
		Thus in the presence of my table I am acquainted with the sense- data that make up the appearance of the table -- its colour, shape, hardness, smoothness, etc.; all these things are things of which I am immediately conscious when I am seeing and touching my table.
		The particular shade of colour that I am seeing may have many things said about it -- I may say that it is brown, that it is rather dark, and so on.
	chatelet.cs.uchicago.edu /philosophyProject/sellars/lange/lange2.html (1690 words)

	untitled1.html
		That the poststructuralists one and all are inveterate fans of Achilles is quite logical, since only his victory in the race can secure the belated priority of the deconstructingly interpretive discourse situating it both ahead and behind of the discourse to be deconstructed.
		The imperative to which Bakhtin thus succumbs is the same which triggers non-mimetic self-dimunitive identification of Achilles with the tortoise.
		This amounts to an hermeneutic coincidence between the expectations of Achilles disguised as tortoise and the tortoise feigning to be Achilles.
	www.pd.org /topos/perforations/perf6/uncanny_linetski_p6.html (19008 words)

	WHAT THE TORTOISE SAID TO ACHILLES
		The tortoise challenges Achilles to use the force of logic to make him accept a particular deductive argument.
		The premise of the dialog is that the Tortoise wants Achilles to logically compell him to accept this as a valid argument.
		The Tortoise is obviously a troublemaker, since (Z) follows necessarily from (A) and (B) given the standard laws of logic.
	www.websters-online-dictionary.org /definition/WHAT+THE+TORTOISE+SAID+TO+ACHILLES (541 words)

	Shine on you crazy diamond...
		The tortoise and Achilles — and Lewis Caroll
		"What the Tortoise said to Achilles," by Lewis Caroll, a hilarious extension to Zeno's Paradox of the Tortoise and Achilles.
		Anyway, the original paradox involves Achilles, the Greek hero of Homer's The Illiad, who is verbally convinced by a brainy tortoise, that despite being a great warrior, he would never be able to catch up to the latter in a race!
	crazeediamond.blogspot.com (988 words)

	Solvitur Ambulando
		Now when achilles asks the tortoise to accept that Z is true based on A and B (Much like the
		Achilles goes on and brings in another statement to trap the tortoise
		He shud have shoved the notebook up the tortoise's ass as soon it began acting up.
	iamfedupwithnames.blogspot.com (2530 words)

	[No title]
		He argued for keeping the old designs just as they were, adding that this was sure to be the preference of the existing audience.
		Then, as if to solidify his stance he said, "The only person who likes regular change is a wet baby." He did not win that day, but his words were tattooed upon my memory, by their charm.
		I thought some wiseacre or other had proved that the thing couldn't be done?" "It can be done," said Achilles.
	www.gutenberg.org /newsletter/archive/PGWeekly_2003_11_19_Part_2.txt (4058 words)

	Becca Guillet (Site not responding. Last check: 2007-10-10)
		He proposes a handkerchief that has neither outside nor inside, and can therefore be said to contain the whole universe—an invention similar in nature to a Möbius strip or a Klein bottle, both of which have properties such that the inside edge cannot be distinguished from the outside edge (6-7).
		Dodgson goes even so far as to create a puzzle of his own entitled “What the Tortoise said to Achilles,” in which he demonstrates the practicality of the rule “Modus Ponens,” or the “rule of detachment,” as Hofstadter refers to it (185-186).
		In Dodgson’s dialogue, the Tortoise refuses, because he has no “proof”, to accept the fact that the truth of the statement as a whole and the truth of the first clause of the same statement necessarily lead to the truth of the second clause (Carroll, Symbolic Logic 431-434).
	community.middlebury.edu /~schar/Courses/fs023.F02/paper1/guillet.htm (3094 words)

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