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	Sorites Paradox (Stanford Encyclopedia of Philosophy)
		The sorites paradox is the name given to a class of paradoxical arguments, also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved.
		Sorites arguments of the paradoxical form are to be distinguished from multi-premise syllogisms (polysyllogisms) which are sometimes also referred to as sorites arguments.
		The vagueness or indeterminacy that underwrites this sorites paradox is, on this approach, not a result of epistemic limitations, nor a result of indeterminacy in Everest itself but, rather, arises as a result of indeterminacy surrounding what to count as the referent of the term.
	plato.stanford.edu /entries/sorites-paradox (8365 words)

	Some paradoxes - an anthology
		In this paradox, Epimenides, the Cretan, says, "All Cretans are liars." If he is telling the truth he is lying; and if he is lying, he is telling the truth.
		the apparent paradox, stated in 1826 and now explained by postulating a finite expanding universe, that the sky is dark at night although, as there are an infinite number of stars, it should be uniformly bright.
		The paradox arises from a disguised breach of the arithmetical prohibition on division by zero, occurring at (5): since a = b, dividing both sides by (a - b) is dividing by zero, which renders the equation meaningless.
	www.paradoxes.co.uk (5530 words)

	Sorites Paradox
		The sorites paradox is the name given to a class of paradoxical arguments, also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved.
		Sorites arguments of the paradoxical form are to be distinguished from multi-premise syllogisms (polysyllogisms) which are sometimes also referred to as sorites arguments.
		The key feature of soritical predicates which drives the paradoxes, constraint (iii), is described in Wright (1975) as "tolerance" and is thought to arise as a result of the vagueness of the predicate involved.
	www.seop.leeds.ac.uk /archives/sum2003/entries/sorites-paradox (6257 words)

	Paradox
		Of the paradoxes we have to draw on, only the barber paradox can be considered to be veridical, for it is generally conceded that there is no flaw in the paradoxical argument, either in the premises or in the reasoning.
		But it is now generally recognized that the story that gives rise to the paradox (there is a village in which there is a barber who cuts the hair of all and only those villagers who do not cut their own hair) is incoherent, that it is impossible for there to be such a village.
		There are thus two principal options in providing a resolution for a type I paradox: (i) we may dispel the illusion that the argument is air-tight by isolating and diagnosing a flaw or fallacy in the argument; or (ii) we may explain away the appearance of falsity in the conclusion.
	www.wordtrade.com /philosophy/contemporary/paradox.htm (5816 words)

	Sorites paradox - Wikipedia, the free encyclopedia
		The paradox of the heap (or the Sorites paradox, σωρος (sōros) being Greek for "heap" and σωριτης (sōritēs) the adjective) is a paradox that arises from reasoning with predicates which seem not to have a sharp cutoff, such as 'bald', 'tall', and the like.
		In addition to advocating a response, philosophers who work on this paradox also try to explain why it is that the premise one would have to deny seems so plausible, despite being false.
		Three valued systems do not resolve the paradox as there is still a dividing line between heap and unsure and also between unsure and not-heap.
	en.wikipedia.org /wiki/Paradox_of_the_heap (1092 words)

	Sorites Paradox (Stanford Encyclopedia of Philosophy) (Site not responding. Last check: 2007-10-31)
		The key feature of soritical predicates which drives the paradox, constraint (iii), is described in Wright (1975) as “tolerance” and is thought to arise as a result of the vagueness of the predicate involved.
		As a consequence, versions of the sorites paradox that employ such ellipses, even granting the contextual parameters implicit in the vague predicates, are not open to contextualist resolution.
		The vagueness or indeterminacy that underwrites this sorites paradox is, on this approach, not a result of epistemic limitations, nor a result of indeterminacy in Everest itself but, rather, arises as a result of indeterminacy surrounding what to count as the referent of the term.
	www.science.uva.nl /~seop/entries/sorites-paradox (8360 words)

	The Sorites Paradox
		Paradoxes of this form are known as Sorites and are credited to Eubulides.
		A paradox can be defined as an argument which starts from premises which appear to be true and yet, after reasoning that looks valid, ends up with an apparently false conclusion.
		As the conclusion cannot be accepted then either the premises must be shown to be false or the reasoning shown to be invalid.
	www.philosophers.co.uk /cafe/paradox4.htm (802 words)

	The Sorites
		The paradox of the sorites, or ‘the heap’, appeals to us because it challenges our assumption that we may categorically describe clear cases and their negations, yet fail to distinguish the borderline ones.
		The sorites paradox will be discussed in terms of categories, their negations and the extent to which our reasoning about them succeeds or fails to accord with the laws of logic.
		The paradox seems to revolve around the issue of whether there is an absolute boundary between categories and their negations, such that x elements makes a thing a member and x —1 makes it a non-member.
	www.ul.ie /~philos/vol3/sorites.html (3669 words)

	SoritesParadox for printing (Site not responding. Last check: 2007-10-31)
		The above is one variant of the Sorites Paradox (from the Greek soros, "heap").
		As I see it, the paradox arises because the word "heap" is vague, and vagueness isn't closed under induction.
		Consider Sorites Paradox and why minimum mandatory sentencing may be a bad thing.
	clublet.com /why?print=SoritesParadox (664 words)

	FACING UP TO THE SORITES PARADOX
		The ancient sorites paradox is traditionally attributed to Eubulides, a contemporary of Aristotle and a member of the Megarian school, who is also credited with inventing the liar paradox.
		The sorites paradox is at the heart of the matter in the reasoning that has led up to this conclusion, since the paradox directly reflects the weak generic logical incoherence of vagueness.
		Tye, M. 1994: “Sorites Paradoxes and the Semantics of Vagueness,” Philosophical Perspectives (8): 189-206.
	dingo.sbs.arizona.edu /~thorgan/papers/Sorites.Paradox.htm (3937 words)

	The Semantics and Metaphysics of Vagueness:
		This result, along with appreciating the peculiar sense in which vague predicates are context-sensitive, clears the road for a sketch of a solution to the Sorites Paradox: roughly, the conditions for the correct use of vague predicates presuppose c-boundaries, thereby rendering the Sorites Paradox unsound.
		The Sorites Paradox is a class of arguments each leading to the same kind of paradoxical conclusion.
		But the Sorites Paradox remains compelling since our tendency to focus on matters of meaning and thus m-boundaries renders the m-boundarylessness of vague predicates more salient than their potential for drawing c-boundaries and, thereby, avoiding the Sorites Paradox.
	www.stanford.edu /group/dualist/vol10/raven.html (9709 words)

	Vagueness - Bibliography
		Sorensen, Roy A [1998] 'Ambiguity, Discretion and the Sorites', Monist 81, pp.
		Tye, Michael [1994] Sorites Paradoxes and the Semantics of Vagueness, in Tomberlin, J (ed.), Philosophical Perspectives: Logic and Language.
		Wright, Crispin [1991] The Sorites Paradox and Its Significance for the Interpretation of Semantic Theory, in Cooper & Engel [1991], pp.
	www.btinternet.com /~justin.needle/bib_alpha.htm (8453 words)

	The Sorites heap paradox Text - Physics Forums Library
		But the paradox can be recast, e.g.: 1 is a small number, and any number bigger by 1 than a small number is small; so all numbers are small.
		I did find another interpretation of the sorites argument, which is to ask what is the smallest "heap" of sand needed to make an audible noise when dropped.
		Before Godel, Russel threw a slew of paradoxes at the foundations of mathematics to see what would emerge, and what came out was just more gibberish, more paradoxes.
	www.physicsforums.com /archive/index.php/t-1732.html (1663 words)

	Hysteresis and Sorites
		The idea is to examine one of the classic paradoxes in Greek philosophy, the Sorties or Heap paradox, and apply ideas from modern mathematics to it, in particular ideas from singularity theory/catastrophe theory and the hysteresis effect.
		The basic idea behind the Sorites paradox is related to how we can interpret a continuously changing phenomena using discreet language.
		If a hysteresis affect is applied to the Sorites then depending on past history an observer might characterize a pile as either bing a heap or not a heap.
	www.singsurf.org /sorites (632 words)

	J.C. Beall (ed.) - Liars and Heaps: New Essays On Paradox - Reviewed by Matti Eklund, University of Colorado - ... (Site not responding. Last check: 2007-10-31)
		The literature on the sorites and liar paradoxes can easily come off as something of a cottage industry: an area of philosophy where fairly much work is being done, but such that its significance for anything else is less than obvious.
		Some theorists have claimed, both with respect to the sorites paradox and with respect to the liar paradox, that a solution of the kind apparently normally sought cannot be had.
		But what is striking about the literature on the paradoxes â“ including the contributions to the present collection â“ is that virtually no attention is paid to the issue of how best to conceive of questions of the nature of truth.
	ndpr.nd.edu /review.cfm?id=1461 (2093 words)

	CONCEPTE VAGI SI PARADOXURI SORITE
		Most attempts to explain sorites paradoxes probably sprang from a type (3) position, namely from the feeling that there is something wrong with the logic reasoning or with the associated semantics.
		Sorites paradoxes are built on the grounds of a relation between objects forming a slippery slope (the sorites argument is, in fact, also called the slippery slope argument).
		The sorites argument is extremely puzzling, because of the evidence of the premises and the simplicity of reasoning, on the one hand, and the enormity of the conclusion, on the other.
	www.ici.ro /ici/revista/sic1998_3/art09.html (10576 words)

	On the Circularity in The Sorites Paradox (Site not responding. Last check: 2007-10-31)
		After having accurately described the structure of sorites-susceptible predicates, I argue that the structure of the induction step in the Sorites Paradox is inherently circular.
		sorites paradox (thereafter, SP) is one of the most ancient and unresolved paradoxes, which is attributed to Eubulides.
		Before considering the paradox itself, it proves necessary to examine preliminarily several elements of the structure of the vague predicates involved in SP.
	www.univ-corse.fr /~franceschi/sp(gb).htm (2773 words)

	Blogosophy: Sorites and EldredSeems like the
		Seems like the Supreme Court can't recognize a Sorites Paradox when presented with one.
		(Sorites describes a class of "little-by-little" paradoxes, along the lines of "One grain of corn isn't a heap; if n grains aren't a heap, then n+1 grains aren't a heap; ergo no number of grains is a heap." I'll have more to say on this later.) In Eldred v.
		This doesn't seem quite right, as a Sorites paradox.
	www.webamused.com /blogosophy/archives/000283.html (438 words)

	The Philosopher's Zone 01/04/2006 - Radio National
		This is what’s known as the Sorites Paradox and it has something to do with the way your washing machine works, but we’ll get to the laundry later.
		We can engage in Sorites reasoning with these concepts to show that by virtue of the inability to draw a line to their application, they can be applied everywhere.
		Moreover, the paradox to simply put degrees of truth on the table, is yet to fall far short of a resolution of the paradox.
	www.abc.net.au /rn/talks/philosopher/stories/s1604279.htm (3419 words)

	Paradoxes!
		The paradox was of significance to Frege's logical work since, in effect, it showed that the axioms Frege was using to formalize his logic were inconsistent.
		The paradox itself stems from the idea that any coherent condition may be used to determine a set (or class).
		These four responses to the paradox, in turn, have helped logicians develop an explicit awareness of the nature of formal systems and of the kinds of metalogical results which are today commonly associated with them.
	www.andrews.edu /~calkins/math/biograph/199900/topparad.htm (849 words)

	Stanford Encyclopedia of Philosophy - Sorites Paradox
		For example the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate `is a heap', no one grain of wheat can be identified as making the difference between being a heap and not being a heap.
		This last puzzle, presented as a series of questions about the application of the predicate `is bald', was originally known as the falakros puzzle.
		Tye, M. `Sorites paradoxes and the semantics of vagueness', in J. Tomberlin (ed.), Philosophical Perspectives: Logic and Language.
	www.seop.leeds.ac.uk /archives/spr1999/entries/sorites-paradox (6214 words)

	PHIL 633 Philosophy of Language: Vagueness and the Sorites Paradox
		The topic of the seminar will be vagueness and the sorites paradox.
		The vagueness of a predicate like 'tall woman' is metaphorically characterized by saying that there is a "fuzzy boundary" between the women it applies to and those it doesn't.
		The sorites paradox of antiquity (also known as "the paradox of the heap") arises from thoughts such as, "If I'm tall before I go to bed then even if I shrink 1mm overnight, I'll still be tall when I wake up," which, though attractive, apparently lead to absurdity.
	www.princeton.edu /~graff/vagueness/spring02.html (249 words)

	Vagueness and the Sorites Paradox - An Evolving Resource
		Sorites Paradox, which first appeared in ancient Greece.
		During the 20th century, and especially the last 30 years, there has been a resurgence of interest in vagueness, particularly in connection with the problems it is thought to pose to Classical Logic and the prospects of constructing theories of meaning for natural languages.
		If you spot any errors or omissions on these pages, or have any suggestions for improving the site, please let me know.
	www.btinternet.com /~justin.needle (312 words)

	Opiniatrety: Sorites and Kelo
		But though the sorites paradox may--I said, may--provide some support for their views on one of these cases, I think it undercuts the broader libertarian views Sanchez and Henley favor.
		Now, Sanchez's application of the sorites is to say that many individually innocuous precedents have been strung together to reach an absurd conclusion.
		But then the moral of the sorites is that, even if this isn't public use, some of the steps earlier along the line clearly were.
	mattweiner.net /blog/archives/000576.html (514 words)

	The Sorites Paradox. Home Page (Site not responding. Last check: 2007-10-31)
		As it stands, it is a first approach to the paradox.
		It will be developed into a Ph.D. dissertation during the next four years.
		New documents on several aspects or authors dealing with the paradox will be posted as they are written.
	www.sorites.org /mv/sorites/index.html (162 words)

	paradox
		Known for being an innovative research and development company, Paradox Security Systems is a recognized worldwide force in the security industry.
		Paradox is a tool that processes first-order logic problems and tries to find finite-domain models for them.
		Paradox is written by Koen Claessen and Niklas Sörensson.
	www.acparma.it /guibkbh/xbpwlh/paradox.php (346 words)

	SMARANDACHE SORITES PARADOXES (Site not responding. Last check: 2007-10-31)
		However, at some point, the collection of invisible particles becomes large enough to form a visible object, but there is apparently no definite point where this occurs.
		It is always possible to remove a particle from an object in such a way that what is left is still a visible object.
		[2] Smarandache, Florentin, "Sorites Paradoxes", in "Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry", Xiquan Publishing House, Phoenix, 69-70, 2000.
	www.gallup.unm.edu /~smarandache/sorites.htm (200 words)

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