Talk:Sorites paradox

message: There is a glaring omission:
Premise 3:  A heap is a large collection of grains of sand
Without this third premise, Premise 2 is only applicable once (is a large collection of grains of sand minus one grain still a large collection of grains?)
* We start with a large collection of grains, and Premise 1 concludes it is a heap.
* We remove a grain of sand, and Premise 2 concludes that it is still a heap.
* Premise 1 and 2 are no longer applicable, unless we can conclude that a heap is somehow related to a large collection of grains of sand.
Of course, surely we can just do with one premise?
Premise 1: A large collection of grains of sand minus one grain is still a large collection of grains of sand.
; Suggested change: with at least one grain atop at least one other grain.  This eliminates the paradox; two grains side by side are not a heap, but one grain on top of another is a heap.  This can be tweaked to accommodate the case where a flat surface of one grain touches the edge of another grain.  Two grains can make a heap, one grain cannot.  — Preceding unsigned comment added by 73.213.142.170 (talk) 22:53, 8 September 2015 (UTC)
replies: text: This is all original research and thus is irrelevant. (Aside from being confused and wrong. Notably, the "suggested change" misconstrues the whole issue, which is about *indefinite* descriptions. Offering a definite description of a heap of sand does nothing to resolve the paradox, which still applies to beards, baldness, and whether the first chicken came before the first chicken egg, for example.)  — Preceding unsigned comment added by 70.185.144.90 (talk) 09:41, 22 June 2019 (UTC)
thread_title:  Ummmm.... 

message: I suggest that this article should instead be called The sorites paradox, and that Paradox of the heap should redirect here, rather than the other way around. In the philosophical literature in which this paradox is discussed, it is, I think, more commonly referred to as "the sorites paradox" than as "the paradox of the heap". Such a name change would be less prone to suggest that the philosophical problem which this article is about is a problem specific to heaps. Opinions? Matt 9 Nov. 2005
: I tend to agree. Ornette 18:02, 8 November 2005 (UTC)
replies: text: I agree as well. --Pfafrich 21:04, 8 January 2006 (UTC)

text: I definetely agree, change the name to Sorities Paradox, it is better known that way. 70.111.248.60 01:43, 19 April 2006 (UTC)
replies: text: Well, maybe not that well known, because you misspelled it. —Keenan Pepper 02:24, 19 April 2006 (UTC)

text: I strongly agree. Maelin 10:31, 31 July 2006 (UTC)
thread_title: A case for name change?

message: This paradox reminded me of something I've heard often. It's often said that age x is essentially the same as age x±1 (ie. "What's the difference between 25 and 26?" as an argument for still doing something done at 25 at 26), which infers that the difference between x and x±1 (in terms of ages) is negligible. Obviously, this can be extended in both directions infinitely: by applying this principal recursively, the difference between any number and any other number can be considered negligible (in the case of ages, at least). Logically, of course, this doesn't make sense. I'm not sure if this is an appropriate concept to discuss in this article. --Dvandersluis 20:41, 23 June 2006 (UTC)
thread_title: Differences in Ages

message: The problem of describing resolutions to paradoxes is that one has to understand why something is a paradox to begin with and why a paradox is resolved by your solution.  
From the page:
: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.
How is this not a resolution?  We've resolved it by defining set boundaries.... it may not be a satisfactory resolution, but it would appear to give a simple though arbitrary answer.  It is as much a resolution as the Setting a fixed boundary solution.   It would seem there should be better phrasing or wording here as to what is meant.   Maybe a sentence about how the the valued logic solution no better matches our intuition than the aforementioned solution, or something.
Root4(one) 04:16, 4 December 2006 (UTC)
thread_title: Three Valued Logic

message: I think there is an error in the following quoted section of the article.
"On the face of it, there are three ways to avoid this conclusion. One may object to the first premise by denying that a large collection of grains makes a heap (or more generally, by denying that there are heaps). One may object to the second premise by stating that it is not true for all collections of grains that removing one grain from it still makes a heap. Or one may reject the conclusion by insisting that a heap of sand can be composed of just one grain."
The final method of rejecting the conclusion (by insisting that a heap of sand is composed of just one grain) is in fact an affirmation of the conclusion is it not? I've never read any philosophy at all, so I'm not editing this, but I assume this was just an oversight.
:The argument here was that a position is possible in which one argues that a heap of sand can be consisted by even a single grain. in other words it is saying that even the last grain left is a heap in itself. 
: besides one could also go further by making a heap the synonym for a set and then it can be argued that zero grains left is just an empty set of sand, eg.: an empty heap. and yeah, descriptive and prescriptive approaches can be contrasted. i think the original (linguistically based) paradox arises from pretending to have a fixed definition of what exacly makes a heap, while in reality it is just a stereotype like all words of the natural language (like table, or dog). so the take away from this paradox seems to be that it calls attention to the natural language's undefined nature, which is usually forgotten by it's users.
:also the original "paradox" seems to aim at the conclusion that (change in) quantity amounts to (change in) quality. 80.98.79.37 (talk) 22:33, 22 May 2017 (UTC)
thread_title:  Minor Error 

message: I think "heap of sand" is a bad example, because "heap" is just a description of the shape. You could say a heap is a collection of objects, sufficiently numerous that they can't be counted in a single glance, and stacked together with more towards the centre and fewer towards the outside.
The number of items required for a heap is reasonably well defined, it must be about five or six, because you need to be able to stack them in a heap shape, and must not be able to count how many there are in a single glance. People can count up to about five or so items in a single glance and you need at least about three or four items to get the heap shape. You could easily have a heap of clothes or bowling balls with as few as five items. Even if you debate the second criterium I've offered you still can't drop below three and become a heap. No arrangement of two items has the appropriate shape necessary for a heap.
In fact the description of the shape of a heap seems like a better example of the paradox than the number of items in it. How flat does the heap have have to become before it's no longer a heap?
I'm not debating the paradox here, I'm just pointing out that the "heap of sand" example is not a particularly good one and we could probably find a better one. Cheers!
80.192.29.107 13:12, 25 August 2007 (UTC)
replies: text: Heap is used because that's the classical example. You'll find the same thing in the Hawk and Dove article: even though the most commonly used explanatory variant of that game is Chicken. Illisium (talk) 07:11, 29 June 2009 (UTC)
replies: text: Its not just that, although I agree its about shape.  But *number is irrelevant* except that below a certain number the shape is impossible.  But you can fail to have a heap of sand with a billion grains, if the shape is wrong.  Consider an infinite plane of sand one grain thick (being a plane, after all).  It is *not a heap*, despite having an *arbitrarily large number of grains*.  I think you'd find that other possible phrasings of the paradox also fail because there's a mistaken first premise (that just by having a lot of something it becomes a new class of object), but I can't specifically induct over all possible examples without seeing others. --69.209.59.214 (talk) 15:30, 30 October 2012 (UTC)
thread_title:  Heap is about shape 

message: I just wanted to complement whoever's done the recent edits.  A+ on clarity. Root4(one) 16:31, 7 January 2008 (UTC)
thread_title:  The article as of late is much clearer 

message: It seems obvious that you cannot use something with an imprecise definition to precisely measure or categorise something else. It may be a problem, but it is certainly no paradox. --58.172.176.120 (talk) 00:00, 19 June 2009 (UTC)
replies: text: Well said. There is no paradox because 'heap' is an imprecise definition. This is alluded to in the 'group consensus' section, but saying that the sand has a 'probability of being a heap' is nonsensical. Whoever came up with this paradox obviously had no understanding of how languages evolve and how definitions are learnt. 155.198.65.29 (talk) 12:48, 30 June 2009 (UTC)
replies: text:  Agreed there is no 'paradox', instead it is a worthy example of the influence of semantics on perception. All it really tells us is a that an apparently logical definition can have absurd results (the unmentioned fact that the rules allow you to have a 'negative heap' which most people would call a hole in the beach...) Its greatest value is in how we view things like definitions of infinity (e.g. that which shows the infinity of integers is 'smaller' than the infinity of real numbers). Stub Mandrel (talk) 10:09, 4 July 2016 (UTC)
thread_title:  No paradox - Just imprecise definitions 

message: "1,000,000 grains of sand is a heap of sand (Premise 1) 
A heap of sand minus one grain is still a heap. (Premise 2) 
Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand."
The last sentence stops one short. If 1 grain is still a heap, then according to Premise 2, that "heap (1 grain) of sand minus one grain is still a heap", so 1 grain minus 1 grain = 0 grains which is still a heap, by the above premises.
A "heap of sand" cannot logically be a heap of sand if it contains no sand, so, ipso facto, the wording of the premises must be flawed.75.15.70.224 (talk) 13:56, 18 September 2009 (UTC)
thread_title:  ZERO grains of sand is a "heap of sand"(?!?) 

message: I see the paradox as an attempt to interpret a situation using two languages, one is words the other is mathematics.
The pile of sand is described as a heap. Heap translated into mathematics might be 1,000,000 grains of sand. Repeatedly subtracting one grain a sand away from the heap until there is but one grain left and translating the result from mathematics to words, obviously there is a change in meaning.
Pauljalexander (talk) 06:47, 23 April 2010 (UTC)
replies: text: Welcome to Wikipedia. The  approach of considering the paradox as arising from a translation problem is interesting. Do you happen to know a reliable source we can cite this to? Paradoctor (talk) 16:06, 23 April 2010 (UTC)

text: Yes there is sense in your argument, I would further refine it as trying to map from a continuum (number of grains of sand) to a discrete set of states (heap or not heap). Anyway wikipedia need to be well referenced these days, so to include something on this topic we would need to find a good reference so that we dont fall foul of the original research policy.--Salix (talk): 10:14, 28 April 2010 (UTC)
thread_title: Translating two languages, words and mathematics

message: It would seem the following would be true
1,000,000 grains of sand is a heap of sand (Premise 1)
A heap of sand minus one grain is still a heap. (Premise 2)
One grain of sand is a heap of sand. (Conclusion)
Hence Premise 2 can be rewritten:
A heap of sand minus a heap of sand is still a heap.
I think that clearly shows the fallacy of Premise 2.4.253.119.18 (talk) 14:46, 9 August 2010 (UTC)
replies: text: Add a heap of sand to a heap of sand, what do you get? Since addition has an inverse, it follows that the rewritten premise two is actually a theorem of group theory. ;) Paradoctor (talk) 15:57, 9 August 2010 (UTC)
thread_title:  A heap minus a heap 

message: Why, clearly a heap of sand is only a heap if the heap-invariant somehow holds. Of course, in that case there must be some way we can order the grains. Ay, there's the rub, for what makes a grain of sand greater or lesser than another? Little which to me makes philosophical sense, but perhaps somebody else would have a better idea. Filburli (talk) 01:50, 26 March 2013 (UTC)
thread_title:  Depends on the sand 

message: User:Jochen Burghardt left me the following message regarding the [first] image:
:In the article Sorites paradox, I consider the basic idea of your picture :File:Sorites paradox heap.png useful, but I agree with  that "1=1+1=..." shouldn't appear there. I see two issues:
:# use of "=" suggests that all heaps are claimed to be the same, while the paradox is only about all have a common property, viz. being a heap;
:# the psychological temptation to claim "one pebble more or less can't affect the heap property" works better for sufficiently large heaps than for small nonheaps (collections of 2 and 9 pebbles "look quite different", while such of 100002 and 100009 don't).
:Maybe it is possible to design a picture starting with the large heap, then somehow indicating the removal of the first 1, 2, 3 pebbles. To avoid "=", e.g. a heap/nonheap border could be indicated somehow. However, I don't know how to illustrate that it's a problem which collections are immediately left and right to the border - maybe you have an idea.
Hyacinth (talk) 22:38, 8 October 2014 (UTC)
replies: text: looking at apparent change between heaps of different volume appears, to me, to be a discussion of perception based on the [Surface-area-to-volume ratio] of a heap, rather than anything to do with sorites, which is to do with identifying the presence oo absence of 'heap hood' - though I admit, I may be missing something here 20040302 (talk) 09:34, 6 March 2015 (UTC)
replies: text: The problem with the captions to images labelled  3 and 4 on the talk page is that it's not at all clear what measure is being used. "Difference between the heaps" -- in what?  Size? Number of particles (which difference is, by hypothesis, one grain and therefore the same for each pair of heaps n, n+1).  For #5 you might be trying to convey that a difference of one unit in the length/width of the square gives rise to an (inverse) square change in the area, but I'm still not convinced the math ("thirty times") works here or even if it does, if it's germane to the Sorities argument. 173.48.96.105 (talk) 17:20, 18 March 2016 (UTC)

text: Agreed, none of these images seem to illustrate the paradox at all. Image three is closest as an illustration of "the heap stops being a heap somewhere along this line - but where?", but it doesn't really seem any clearer than one photo of a heap of sand. I'll shovel something up from commons. --McGeddon (talk) 18:19, 18 September 2016 (UTC)

text: Color doesn't have much to do with "heaphood". Hyacinth (talk) 22:27, 29 March 2017 (UTC)
thread_title: Image

message: I just want to say this article is fantastic. I learned a lot from it and it's very interesting, well written too. I would advise against making major changes with it. EggsInMyPockets (talk) 17:55, 29 March 2017 (UTC)
thread_title:  Great Article 

message: i missed the meaning of the word from the article. an etymology would be useful to add, like here you can find: http://www.thefreedictionary.com/sorites
or at least the word sorites needs to turned int a link - there is a relevant article about what sorites is. 
80.98.79.37 (talk) 14:41, 27 May 2017 (UTC)
replies: text: I removed your link, since it pointed to the disambiguation page Sorites, where the only sensible link (in our context) was back to Sorites paradox. I agree that it is a good idea to state somewhere here what 'Sorites' literally means, and when it was coined. - Jochen Burghardt (talk) 16:37, 27 May 2017 (UTC)

text: This text is already present, under Sorites_paradox#Paradox_of_the_heap. If you have additional useful etymological information, best place it there.  - Jochen Burghardt (talk) 16:42, 27 May 2017 (UTC)
thread_title:  etymology missing 

message: I know there have been various suggested resolutions before, but can't this be resolved by pointing out that a heap of sand is not actually a measure of quantity, and is basically another word for a pile of sand? or, indeed, mound of sand? it's not exactly something that needs a precise definition. (That, and it occurs to me that this paradox comes under the same category of paradox as Zeno's Paradox, and the one surrounding imprecision in coastline lengths. Namely that it is pretty much exclusively a purely philosophical paradox- if you try to argue the point in a non-philosophical setting, you will just be told to shut up.)Sstabeler (talk) 14:17, 13 September 2017 (UTC)
replies: text: I think it was W. V. O. Quine who pointed out that the Sorites patadox applies to almost all our notions, comprising adjectives (e.g. red, large, cold, stormy) as well as nouns (e.g. river, chair, dog), and, that we often understand a sentence despite the vagueness of all its components by taking them to be meant relative, not absolute (e.g. the red chair refers to the object that satisfies both red and chair more than the remaining objects in the scene). (If I'd find the reference, I'd like to add this to the article.) Whoever thinks e.g. about computer software for natural language understanding has to consider such issues. - Jochen Burghardt (talk) 16:25, 13 September 2017 (UTC)
thread_title:  suggested resolution 

message: I suggest to "merge" the article "Continuum fallacy" (CF) into here. Actually, I believe this would amount almost to a deletion of "Continuum fallacy", as it doesn't provide much  information that isn't already contained in Sorites paradox (SP). I suggest to keep the following parts.
*From Continuum fallacy#lead:
<BLOCKQUOTE>
The fallacy is the argument that two states or conditions cannot be considered distinct (or do not exist at all) because between them there exists a continuum of states. 
</BLOCKQUOTE>
*From Continuum fallacy#Relation with sorites paradox:
<BLOCKQUOTE>
Narrowly speaking, the sorites paradox refers to situations where there are many discrete states (classically between 1 and 1,000,000 grains of sand, hence 1,000,000 possible states), while the continuum fallacy refers to situations where there is (or appears to be) a continuum of states, such as temperature – is a room hot or cold? Whether any continua exist in the physical world is the classic question of atomism, and while Newtonian physics models the world as continuous, in modern quantum physics, notions of continuous length break down at the Planck length, and thus what appear to be continua may, at base, simply be very many discrete states.
For the purpose of the continuum fallacy, one assumes that there is in fact a continuum
</BLOCKQUOTE>
They could be added to Sorites paradox#Variations where the continuum fallacy is already mentioned; some copyediting may be necessary.
None of the remaining (CF) examples (beard, sand) and references (Roberts, LaFave) deals with a continuum in the mathematical sense; the same applies to the Thouless reference already present here (SP). For this reason, I suggest to add a warning that in popular philosophy "continuum" is often abused for "too large to glance over". This would nicely fit as a footnote after "(or appears to be)" in the 2nd part. - Jochen Burghardt (talk) 09:17, 18 April 2019 (UTC)
replies: text: although I've kept a little more content than suggested. For example, the beard example is referenced, and it could indeed be argued that beard (stubble) length is continuous. Quite happy for the content to be further refined in situ. Klbrain (talk) 10:48, 20 June 2020 (UTC)
thread_title:  Merger proposal 

message: Of course, anybody who has grown one knows that some acquaintance eventually will ask, "Hey? Are you growing a beard?" If you answer, "Yes," Then that's a good candidate for the day when your non-beard became a beard. 74.111.96.172 (talk) 21:04, 2 August 2021 (UTC)
thread_title:  Beards 

message: The problem with naming it a 'paradox' is that it's only a paradox if it addressed by substance ontologies. It's not a paradox for many other ontologies - in fact, it is much more an argument used to demonstrate that the nature of a heap cannot be found in the substance of the heap. Cf., for instance, Tsongkhapa (or Candrakirti) using composition/aggregation as a means of establishing the lack of entityhood, essence, or (Buddhist 'self') in a heap (eg, the aggregated heaps of a person).  
Therefore Sorites is used as an argument by non-essentialist thinkers, as well as thinkers who dispute objectivity. 
It is an argument, not a paradox. 20040302 (talk) 11:37, 15 August 2022 (UTC)
thread_title:  Rename Proposal: Sorites Argument 

message: So, 
>removing a single grain does not cause a heap to become a non-heap
But removing the second and so on grain would cause the heap to be a non-heap or able of becoming a non-heap at a certain boundary condition. 1, for example. Not 10000 (because why not 7776?), and no group consensus (i.e redefining the dictionary). 1 is because it is a line between singularity and plurality in natural math. It depends on whether the word 'heap' also preserves its original meaning or it is superceded in the given local scope! 46.96.149.182 (talk) 10:00, 20 September 2022 (UTC)
replies: text: I think Supervaluationism still applies, here. Your 1-grain stacks or 0-grain stacks only make sense in a numerical counting system with "zero" and unlike Roman Numerals. If we're counting in Roman Count, I'd laugh at your zero stack and say, "I'd like to see you stack even just one grain here for your heap!" but deny its a heap until at least three. In other words, a heap of sand may currently have sand constituting it, and a heap of sand may Not Currently have sand constituting it. -PhilienTaylor as FindingFilene FindingFilene (talk) 02:30, 29 April 2023 (UTC)
thread_title:  What about 0 grains? 

message: I have encountered this paradox being called "Wang's paradox", but I'm not sure if that's just another term for it, a term for a variation of it, or perhaps even the name of an attempted resolution of it. I may report back later. Dingolover6969 (talk) 14:24, 20 January 2023 (UTC)
thread_title:  Wang's paradox 

message: Hi there, I came by this page again while discussing how Supervaluationism seemed valid for me, and when I noticed another answer I had thought after my first visit: the heap being either a pyramid of even three blocks of sand within a 2D arrangement, or perhaps a stereotypical pyramid arranged across three dimensions of space. The point is that a heap begins at the smallest scale of gravity-based and gravity-suspended stacking of sand grains. I think this is compatible with Supervaluationism, but still requires the discussion to happen. If it doesn't happen, folk are talking about theoretical sand grain, which are not spherical, 1-dimensional point coordinates. To know what I mean in literal exemplification, the international shortage of concrete sand is due to desert sand being too smooth. Ocean and river sand has more uniqueness and character that is stackable. - PhilienTaylor as FindingFilene (new account someday) 
Geometric solution is valid and needs persisting after citations of proof FindingFilene (talk) 02:22, 29 April 2023 (UTC)
replies: text: Excuse me, two grains count as well as a heap when heaped upon one another. Gravity-based and gravity-suspense based. :) FindingFilene (talk) 02:24, 29 April 2023 (UTC)
thread_title:  Geometric solution is valid and needs persisting after citations of proof