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I wrote my senior thesis on this topic when I was completing my philosophy major. One of the best texts on the subject is "Vagueness" by Williamson. It's an ar

by n0us 10y ago

I wrote my senior thesis on this topic when I was completing my philosophy major. One of the best texts on the subject is "Vagueness" by Williamson. It's an arcane but super interesting topic that actually has wide implications. It's also IMO one of the most thorny problems in contemporary philosophy. edit: I'm currently busy but can come back later to answer questions if anyone is interested. http://www.amazon.com/Vagueness-Problems-Philosophy-Timothy-Williamson/dp/0415139805 http://www.amazon.com/Vagueness-Problems-Philosophy-Timothy-...

ikeboy 10y ago
I bumped into http://philpapers.org/archive/FRAQTV.pdf http://philpapers.org/archive/FRAQTV.pdf, which argues that most answers will trivially fail. I felt the answer should involve degrees of truth, which can roughly be calculated as "percent of people who agree with the classification" for some reference class, and this degree of truth gradually decreases. But you can't assign any arbitrary cutoff number where above it is true and below false. The way to combine two statements would be to likewise ask what portion of people agree with both, which seems to avoid some of the critiques of degrees of truth. This is only for problems of classification over human undefined terms, where the argument from common usage is valid. Does this have any major problems?
- n0us 10y ago
  The impulse to develop a system of logic that relies on degrees of truth is one that many people have had over the history of philosophy and I can tell you that it is highly problematic. I am struggling to find a succinct way to explain why this is but the following example might be work. 1. It is 50% true that Sally has red hair. 2. It is 50% true that Sally has brown hair. 3. It is 50% true that Sally has not red hair. (see 2.) You end up running into contradictions all over the place and having a non-binary system of logic makes it nearly impossible to develop any formal system of reasoning. I'm not completely clear on the second half of your comment but when you say "portion of people agree" I assume you are trying to use an empirical theory of truth. There are again many problems with this theory but I can think of an example that might illustrate. It's a toy example that I won't fully expand upon but it illustrates the point at hand. There is a box in a room that is painted yellow. A group of people is asked to state the color of the box but they are all colorblind and state that it is grey. The consensus about the color of the box is clearly wrong in this case. Some people will object to this example because the meaning of words is also clearly derived from their use. The epistemic theory of vagueness is not far off from what you are proposing and it is the theory that Williamson posits in his book. Essentially, there is a hard cutoff for all statements that are vague. It is either true that the collection of grains is a heap or it is not. An omniscient speaker could evaluate the truth of a statement about whether the collection of grains is a heap or not with definite certainty because only the omniscient speaker possesses all of the relevant information about the property of being a heap. In other words vagueness is a problem of inexact knowledge. Another example of inexact knowledge is if you were to look out over a stadium and state "there are 23,422 people here." Barring the possibility that you are a savant and actually counted all of the people, if you made that statement and it was true that 23,422 people were in the stadium it isn't also true that you knew that there were that many people. You lack the relevant information about how many people are in the stadium to safely make the claim that there are n number of people in the stadium just as you lack the relevant information about the property of being a heap to safely make the claim that you know it is true that a collection of n grains is a heap. This is a powerful theory which is not as easily defeated as others but keep in mind that it is not without weakness. Hopefully this at least exposes some of the concepts to you even if it's at a superficial level.
  - ikeboy 10y ago
    I don't see how your example leads to a contradiction. If 1 and 2 hold, and no person considers Sally to have more than one color hair, this seems fine. >There is a box in a room that is painted yellow. A group of people is asked to state the color of the box but they are all colorblind and state that it is grey. The consensus about the color of the box is clearly wrong in this case. My proposal doesn't depend on people actually being asked. It's more of "what would people say, if they were asked, and given all relevant objective information". Your scenario is ruled out.
    - coldtea 10y ago
      >My proposal doesn't depend on people actually being asked. It's more of "what would people say, if they were asked, and given all relevant objective information". Your scenario is ruled out. This clarification rules out your proposal as any kind of actually implementable system then, because it collapses to having a single authority who "knows" (how?) what the people would say. If it doesn't involve actually asking people, then it's not really a polling of perceptions, but some person's idea of what those perceptions would be.
      - ikeboy 10y ago
        It's supposed to answer "what does claim X mean". It's not meant to be implemented. An approximation is carried out every time someone pulls out a dictionary to resolve a dispute over common usage.
    - n0us 10y ago
      There is a difference between saying that "it is 50% true that Sally's hair is red" and "it is true that Sally's hair is 50% red". It isn't a scenario, it's a thought experiment. "given all relevant objective information" sounds much like the omniscient speaker which is central to the epistemic theory.
      - ikeboy 10y ago
        I still don't see any contradiction. A single omniscient speaker can't work, because people will disagree even with all relevant objective facts agreed upon. When two people dispute whether something is a heap, they aren't arguing over objective facts.
- mannykannot 10y ago
  That essay ends with this paragraph: "The vagueness paradox is this: although there is an extremely strong argument for sharpism, the truth of sharpism seems to require a linguistic miracle." (my emphasis.) The author concludes that the apparently strong logical argument ultimately fails to address the real issue, which actually concerns usage of the word 'pumpkin’. It is a paradox (i.e. only an apparent problem) because there is neither a practical nor a logical necessity for ‘pumpkin’ to have a singular and absolute definition. The allegedly strong argument is basically begging the question. It is crucially dependent on the assumption that, for any particular ‘situation’, we can unambiguously say whether or not it can be called a pumpkin, but that is the premise that it is attempting to prove. Another way of looking at it is that while we clearly have pumpkin at one end of the truth table and clearly do not at the other, the formalism offers no way to decide where the boundary lies: this representation has its own sorities issue, and models the alleged problem without offering anything that leads to a solution - substituting 'true' or 'false' for the presence or absence of grains of sand does not make the problem any more tractable. A secondary problem is that it depends on there being a total ordering of situations, but this fails when we realize that pumpkin-ness is context-dependent: in some contexts, a set of chromosomes is a pumpkin, while in others, nothing but a whole plant will do. Different contexts will be satisfied with different subsets of the pumpkin's atoms, and, in general, any one context will be satisfied with many different subsets.
  - ikeboy 10y ago
    > It is crucially dependent on the assumption that, for any particular ‘situation’, we can unambiguously say whether or not it can be called a pumpkin, but that is the premise that it is attempting to prove. No. As long as you concede that some pumpkins can be unambiguously called a pumpkin, then you just ask which is the first object on the list that can't be.
    - mannykannot 10y ago
      On reflection, I think I may be wrong to say that he is begging the question, but not because of your counter-argument. If we start from the other end of the list, the first thing that is not unambiguously not a pumpkin is not necessarily the last unambiguous pumpkin you picked in the first pass. You have introduced the ambiguity that the author is trying to insist is not there. My other claims stand, I think. The point is that his linear model is not an adequate fit to the problem (for example, the ambiguity you introduced really is there, but the model excludes it.) Maybe there is something like question-begging in thinking that this is an adequate model.
random28345 10y ago
I'm not sure what the big deal here is. This has an obvious solution. "Heap" is a word. Words have meaning to people. Different people ascribe different meanings to the same word. Each grain added to a pile of grain measurably changes the probability that an observer will classify the resulting collection as a heap. While it's not a linear function, it's generally a positive correlation, more grains means a higher probability of any individual calling it a heap. That is a collection of grain of size n+1 has a probability of being classified as a heap that is usually greater than the probability of a collection of grain of size n being classified as a heap. Where's the paradox?
- n0us 10y ago
  You are conflating probability with truth. A person also may incorrectly classify a collection of grain size n as a heap.
  - dragonwriter 10y ago
    Perhaps he is not conflating them but asserting that, for named categories, there is no truth to membership of an item in them beyond the probability that an observer will ascribe an item to the named category.
- hderms 10y ago
  It's just interesting when you have discrete entities and you can't show inductively that there is any point where the classification changes from non-heap to heap, but clearly that point must exist. It's interesting from the same perspective as what makes the ship of Theseus interesting. the probability of something being viewed as a heap could only be measured statistically as the probability doesn't derive from some direct process. The issue can be viewed in both an axiomatic and a empirical way and both views lead to interesting conclusions.
  - empath75 10y ago
    That point may not exist though, if it just gains more 'heapness' over time. Even if 99% of people agree that a collection of grains of sand is a 'heap' there might be some people who still insist that it is not.
danielam 10y ago
Related: http://edwardfeser.blogspot.com/2011/04/nature-versus-art.html http://edwardfeser.blogspot.com/2011/04/nature-versus-art.ht...

by n0us 10y ago

ikeboy 10y ago

I bumped into http://philpapers.org/archive/FRAQTV.pdf http://philpapers.org/archive/FRAQTV.pdf, which argues that most answers will trivially fail. I felt the answer should involve degrees of truth, which can roughly be calculated as "percent of people who agree with the classification" for some reference class, and this degree of truth gradually decreases. But you can't assign any arbitrary cutoff number where above it is true and below false. The way to combine two statements would be to likewise ask what portion of people agree with both, which seems to avoid some of the critiques of degrees of truth. This is only for problems of classification over human undefined terms, where the argument from common usage is valid. Does this have any major problems?

n0us 10y ago
The impulse to develop a system of logic that relies on degrees of truth is one that many people have had over the history of philosophy and I can tell you that it is highly problematic. I am struggling to find a succinct way to explain why this is but the following example might be work. 1. It is 50% true that Sally has red hair. 2. It is 50% true that Sally has brown hair. 3. It is 50% true that Sally has not red hair. (see 2.) You end up running into contradictions all over the place and having a non-binary system of logic makes it nearly impossible to develop any formal system of reasoning. I'm not completely clear on the second half of your comment but when you say "portion of people agree" I assume you are trying to use an empirical theory of truth. There are again many problems with this theory but I can think of an example that might illustrate. It's a toy example that I won't fully expand upon but it illustrates the point at hand. There is a box in a room that is painted yellow. A group of people is asked to state the color of the box but they are all colorblind and state that it is grey. The consensus about the color of the box is clearly wrong in this case. Some people will object to this example because the meaning of words is also clearly derived from their use. The epistemic theory of vagueness is not far off from what you are proposing and it is the theory that Williamson posits in his book. Essentially, there is a hard cutoff for all statements that are vague. It is either true that the collection of grains is a heap or it is not. An omniscient speaker could evaluate the truth of a statement about whether the collection of grains is a heap or not with definite certainty because only the omniscient speaker possesses all of the relevant information about the property of being a heap. In other words vagueness is a problem of inexact knowledge. Another example of inexact knowledge is if you were to look out over a stadium and state "there are 23,422 people here." Barring the possibility that you are a savant and actually counted all of the people, if you made that statement and it was true that 23,422 people were in the stadium it isn't also true that you knew that there were that many people. You lack the relevant information about how many people are in the stadium to safely make the claim that there are n number of people in the stadium just as you lack the relevant information about the property of being a heap to safely make the claim that you know it is true that a collection of n grains is a heap. This is a powerful theory which is not as easily defeated as others but keep in mind that it is not without weakness. Hopefully this at least exposes some of the concepts to you even if it's at a superficial level.
- ikeboy 10y ago
  I don't see how your example leads to a contradiction. If 1 and 2 hold, and no person considers Sally to have more than one color hair, this seems fine. >There is a box in a room that is painted yellow. A group of people is asked to state the color of the box but they are all colorblind and state that it is grey. The consensus about the color of the box is clearly wrong in this case. My proposal doesn't depend on people actually being asked. It's more of "what would people say, if they were asked, and given all relevant objective information". Your scenario is ruled out.
  - coldtea 10y ago
    >My proposal doesn't depend on people actually being asked. It's more of "what would people say, if they were asked, and given all relevant objective information". Your scenario is ruled out. This clarification rules out your proposal as any kind of actually implementable system then, because it collapses to having a single authority who "knows" (how?) what the people would say. If it doesn't involve actually asking people, then it's not really a polling of perceptions, but some person's idea of what those perceptions would be.
    - ikeboy 10y ago
      It's supposed to answer "what does claim X mean". It's not meant to be implemented. An approximation is carried out every time someone pulls out a dictionary to resolve a dispute over common usage.
  - n0us 10y ago
    There is a difference between saying that "it is 50% true that Sally's hair is red" and "it is true that Sally's hair is 50% red". It isn't a scenario, it's a thought experiment. "given all relevant objective information" sounds much like the omniscient speaker which is central to the epistemic theory.
    - ikeboy 10y ago
      I still don't see any contradiction. A single omniscient speaker can't work, because people will disagree even with all relevant objective facts agreed upon. When two people dispute whether something is a heap, they aren't arguing over objective facts.
mannykannot 10y ago
That essay ends with this paragraph: "The vagueness paradox is this: although there is an extremely strong argument for sharpism, the truth of sharpism seems to require a linguistic miracle." (my emphasis.) The author concludes that the apparently strong logical argument ultimately fails to address the real issue, which actually concerns usage of the word 'pumpkin’. It is a paradox (i.e. only an apparent problem) because there is neither a practical nor a logical necessity for ‘pumpkin’ to have a singular and absolute definition. The allegedly strong argument is basically begging the question. It is crucially dependent on the assumption that, for any particular ‘situation’, we can unambiguously say whether or not it can be called a pumpkin, but that is the premise that it is attempting to prove. Another way of looking at it is that while we clearly have pumpkin at one end of the truth table and clearly do not at the other, the formalism offers no way to decide where the boundary lies: this representation has its own sorities issue, and models the alleged problem without offering anything that leads to a solution - substituting 'true' or 'false' for the presence or absence of grains of sand does not make the problem any more tractable. A secondary problem is that it depends on there being a total ordering of situations, but this fails when we realize that pumpkin-ness is context-dependent: in some contexts, a set of chromosomes is a pumpkin, while in others, nothing but a whole plant will do. Different contexts will be satisfied with different subsets of the pumpkin's atoms, and, in general, any one context will be satisfied with many different subsets.
- ikeboy 10y ago
  > It is crucially dependent on the assumption that, for any particular ‘situation’, we can unambiguously say whether or not it can be called a pumpkin, but that is the premise that it is attempting to prove. No. As long as you concede that some pumpkins can be unambiguously called a pumpkin, then you just ask which is the first object on the list that can't be.
  - mannykannot 10y ago
    On reflection, I think I may be wrong to say that he is begging the question, but not because of your counter-argument. If we start from the other end of the list, the first thing that is not unambiguously not a pumpkin is not necessarily the last unambiguous pumpkin you picked in the first pass. You have introduced the ambiguity that the author is trying to insist is not there. My other claims stand, I think. The point is that his linear model is not an adequate fit to the problem (for example, the ambiguity you introduced really is there, but the model excludes it.) Maybe there is something like question-begging in thinking that this is an adequate model.

random28345 10y ago

I'm not sure what the big deal here is. This has an obvious solution. "Heap" is a word. Words have meaning to people. Different people ascribe different meanings to the same word. Each grain added to a pile of grain measurably changes the probability that an observer will classify the resulting collection as a heap. While it's not a linear function, it's generally a positive correlation, more grains means a higher probability of any individual calling it a heap. That is a collection of grain of size n+1 has a probability of being classified as a heap that is usually greater than the probability of a collection of grain of size n being classified as a heap. Where's the paradox?

n0us 10y ago
You are conflating probability with truth. A person also may incorrectly classify a collection of grain size n as a heap.
- dragonwriter 10y ago
  Perhaps he is not conflating them but asserting that, for named categories, there is no truth to membership of an item in them beyond the probability that an observer will ascribe an item to the named category.
hderms 10y ago
It's just interesting when you have discrete entities and you can't show inductively that there is any point where the classification changes from non-heap to heap, but clearly that point must exist. It's interesting from the same perspective as what makes the ship of Theseus interesting. the probability of something being viewed as a heap could only be measured statistically as the probability doesn't derive from some direct process. The issue can be viewed in both an axiomatic and a empirical way and both views lead to interesting conclusions.
- empath75 10y ago
  That point may not exist though, if it just gains more 'heapness' over time. Even if 99% of people agree that a collection of grains of sand is a 'heap' there might be some people who still insist that it is not.

danielam 10y ago

Related: http://edwardfeser.blogspot.com/2011/04/nature-versus-art.html http://edwardfeser.blogspot.com/2011/04/nature-versus-art.ht...