"It was then that it became apparent to me that these dilemmas – and indeed, many others – are manifestations of a more general problem that affects certain kinds of decision-making. They are all instances of the so-called ‘Sorites’ problem, or ‘the problem of the heap’. The problem is this: if you have a heap of pebbles, and you start removing pebbles one at a time, exactly at what point does the heap cease to be a heap?"VAGUE CONCEPTS
This leads to the entire philosophy of "vagueness". i.e. are there yes/no questions that don't have a yes/no answer? Are some things like baldness vague in essence, or, is our knowledge merely incomplete? e.g. we don't know the exact number of hairs on your head, and/or, we don't know/agree on the exact number of hairs that constitutes the "bald" / "not bald" boundary?
NEURAL NETS
My personal conclusion is that there ARE many vague concepts that we have created that are tied to the way our brains learn patterns (and, as a side effect, how we put things into categories). In contrast to rational thought (i.e. being able to demonstrate logically step by step our conclusions), we "perceive" (ala Locke/Hume/Kant) many things without being able to really explain how we did it.
In Artificial Intelligence, there are "neural network" computer programs that simulate this brain-neuron style of learning. They are the programs that learn how to recognize all different variations of a hand-written letter "A" for example. They do not accumulate a list of shapes that are definitely (or are definitely not) an "A", but rather develop a "feel" for "A"-ness with very vague boundaries. They (like our brains) grade a letter as being more or less A-like. It turns out that this technique works much better than attempting to make rational true/false rules to decide. This is the situation that motivates "fuzzy logic" where instead of just true or false answers (encoded as 1 or 0), one can have any number in-between, e.g. 0.38742 (i.e. 38.7% likely to be true).
WISDOM OF THE CROWD?
Because each person has their own individually-trained "neural net" for a particular perception (e.g. baldness, redness, how many beans are in that jar?), we each come up with a different answer when asked about it. However, the answers do cluster (in a bell-curve-like fashion) around the correct answer for things like "how many beans". This is what led Galton to originally think that there was "wisdom in the crowd". This idea has been hailed as one of the inspirations for the new World Wide Web (aka Web 2.0). The old idea was that McDonalds should ask you if "you want fries with that?" to spur sales. The new Web 2.0 idea is that Amazon should ask you if you want this OTHER book based on what other people bought when they bought the book you are about to buy. I.E. the crowd of Amazon customers know what to ask you better than Amazon itself.
The problem is that there are many failures of "crowd wisdom" (as mentioned in that Wikipedia page in the link above). My conclusion is that most people advocating crowd wisdom have not realized that it is limited to "perceptions". Many Web 2.0 sites are asking the crowd instead about rational judgments, expecting them to come up with a better answer than individuals. The idea of democracy (i.e. giving you the right to vote) has been confused with voting guaranteeing the best answer, no matter the question. In fact, Kierkegaard wrote "Against The Crowd" almost 200 years ago where he recognized that individuals act like witnesses to an event, whereas people speaking to (or as a part of) a crowd, speak what we would now call "bullshit" because they are self-consciously part of a crowd. We can see this in the different results of an election primary (a collection of individuals in private voting booths) versus Caucuses where people vote in front of each other. So, Web 2.0 sites (Facebook, MySpace, blog Tag Clouds, etc) that allow people to see the effect on other people of what they are saying, are chronicling mob mentality rather than collecting reliable witness reports.
BTW, I have written several blog posts related to vagueness, for example:
http://existentialprogramming.blogspot.com/2010/03/model-entities-not-just-their-parts.html
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