Soritic thinking that is based on reasoning, which is entailed in the sorites paradox plays an important role in some forms of weakness of will. Such reasoning based on soritic thinking leads to failures of behavior, however, these behaviors cannot be revealed to be irrational by ordinary means. Logical paradoxes are not expected to be important to the psychology of everyday life. However, the sorites paradox unlike other paradoxes actually leads to defeat and confusion, and plays an important role in some forms of weakness of will. I will illustrate a representative version of the sorites paradox, and in the conclusion obtained in this example, I will argue that the epistemic response runs into numerous difficulties, and as a result, does not successfully diagnose the problem with the paradox.
The sorites paradox is a term given to several paradoxical arguments that arise because of the indeterminacy surrounding restrictions of the application of the predicates entailed. The following is a representative version of the sorites paradox. If we are to judge the height of four basketball players, observing them from a distance, which makes a difference in height invisible as long as it amounts to less than one inch. Tim Duncan is 7 feet tall. Shaquille is 7’1. He is also tall. Amare is 6’10. He is tall. Kevin is 6’11. He is tall. Rudy is 6’9. He is also tall. LeBron is 6’8 and he is tall. Using this sequence of reasoning, specifically, that if I deduct an inch off any person’s height, it would not make much difference since somebody will only be one inch shorter than a tall individual would, supposedly, be tall himself. Thus, as I use this sequence of reasoning, I can keep creating more premises, namely that Jordan is 6’6, Kobe is 6’7 and so on till I reach somebody like Nate who is 5’9. Many individuals would hesitate to call Nate tall, because when compared to the other people like LeBron and Kobe, he is short. I can also reason to conclude that Bogues whose height is 5’3 and Boykins 5’5 are tall. However, most reasonable people would not classify these players as tall.
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The reasoning in the above case is a good example of the sorites paradox that results from common vague predicates such as ‘tall’. The sorites paradox can also be constructed using other predicates such as 100, 000 grains of sand is a heap of sand, thus 99, 999 grains is still a heap of sand, as is 99, 998 and so forth, till I am forced to conclude that one grain of sand is still a heap of sand. It is possible to also reconstruct the ‘tall’ version of the sorites paradox to work the conflicting way. For instance, if I reason that Bogues whose height is 5’3, is short, then an individual who is just one inch taller would also be considered short, and I would also use this reasoning to work my way up LeBron, who at 6’8, would be deemed short. Thus, the paradox in argument form is:
Premise 1: LeBron is 6’8, he is tall.
Premise 2: If LeBron is tall, then someone else who is one inch shorter than LeBron is tall.
Premise 3: if somebody one inch shorter than LeBron is tall, then someone one inch shorter than LeBron is tall.
The conclusion is that Bogues whose height is 5’3 is tall. Such a conclusion is paradoxical if we are to consider our common notions about expressions like ‘short’ and ‘tall’ to be correct. In addition to this, if we have a common agreement that Bogues who is 5’3, is short, then the conclusion that stems from the sorites argument, to be precise, that Bogues must be tall, leads to a contradiction, since Bogues cannot have the properties ‘tall’ and ‘short’ at the same time.
Therefore, there are three alternatives if we are to steer clear of this paradox of vague predicates: we can refute the primary premise that LeBron is tall; we can refute one of the other premises in the argument that anyone who is a certain height is tall if an individual an inch taller is tall, or refute the notion that the conclusion follows from the argument. I will discuss one approach to solving the paradox; the epistemic solution. I will also discuss difficulty in accepting the epistemic solution.
The epistemic solution entails refuting one of the other premises. For instance, given the argument: (1) LeBron is tall for a person, (2) if LeBron is tall for a person, then someone who is 6’9 is tall for a person, and (3) if someone who is 6’9 is tall for a person, then someone who is 6’8 is tall for a person. Conclusion: Bogues who is 5’3 is tall for a person. We can refute one of the premises that will grant us a way out of the paradox. For instance, we can refute the premise that will ultimately result from the above argument that if Nash whose height is 6’3 is tall, then Ellis whose height is 6’2 is also tall. Or we can reject the premise that if Chris who is 6’0 tall, then Damon who is 5’11 is tall.
The epistemic solution entails forming a hard line division, dividing people into two groups (not tall and tall). There would look as if there would be a cutoff point, if somebody who is n’n is tall, and it would not follow that someone who is n’n-1 is tall. So, if this dissimilarity was to be in place, it would provide an obstacle that the reasoning that led me in the first place to conclude that Bogues was tall. And if this dissimilarity was in place, then the group of tall individuals would have stopped before we got to Bogues.
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I think that this solution runs into a lot of difficulty. First and foremost, the dissimilarity would seem to be wholly illogical and dependent on a certain individual’s idea of ‘tall’. For instance, I may want to specify that all individuals who are 6’0 and above, are tall. My younger brother who is 5’6 may want to stipulate that all individuals 5’7 and above are tall. In the same way, Kobe may want to stipulate that all individuals 6’8 and above are tall. All of these illogical lines are wholly logical, relative to each individual.
I do not think that the epistemic solution successfully diagnoses the problem with the paradox as shown in the example of height. One can argue against arbitrariness by specifying that people should consider those above the average height for people as tall and those below this average height as shorts, and therefore, a fixed point would solve the problem. But this provision also runs into hypothetical issues.
First of all, the average height for human beings is always changing. Today, human beings may be taller than people were 20, 000 years ago. Therefore, it would seem, a person would have been tall 20, 000 years ago would be short now. However, if can correctly guess, no one wants to accept that a person who is tall can become short without shrinking. Secondly, if are to refute one of the premises, then we should do reject it with good reason. We should give a reason why, for instance, it is better to refute the premise that if Amare who is 6’10 tall, then Kobe who is 6’7 is tall, instead of the premise that if Shaquille who is 7’1 is tall, then Duncan who is 7’0 is tall. Is there a logical reason why we should refute the former premise instead of the latter?
Assume, for the sake of science fiction, the case of a shrinking person. Suppose the shrinking man was Shaquille, who shrank one inch each month, from a starting height of 7’1. If are to refute one of the premises, then we should also acknowledge that there is an exact spatiotemporal location where Shaquille changes from someone who is tall to someone who is not tall. Where is the point? 6’3? 6’4? 5’5? 5’11? Is there a good reason to dispense one of these heights over another height? If the answer is yes, then we should give an account for which particular moment in time, this change occurs, and why it is logical to opt for this moment instead of another one. It appears that nobody can practically choose of these moments over another one, and so, it appears, the epistemic solution runs into a barrier.
The response that would probably successfully diagnose the problem would be the degree of truth solution that takes a modern approach towards the notions of falsity and truth, and seeks to annul the sorites argument. With the degree of truth solution, a person can make the claim that Nash is 6’3 tall. I can state the degree of truth for the claim that Nash is 6’3 tall is about .70 because he appears to be closer to the model for human tallness than the paradigm for shortness. The sorites paradox started by hypothesizing that if Shaquille is tall, and we reason that Bogues is also tall, we are stating that these two men have equivalent property of tallness and the truth of such statements are true to the similar degree. Thus, this theory appears to have the strength of removing all contradictions entailing vague predicates unlike, the epistemic approach, and thus would be more appropriate in explaining the sorites paradox example of who is tall and who is short.
The epistemic solution does not seem to be the closest solution to the example about height discussed. One can argue against unpredictability by specifying that people should consider those above the average height for people as tall and those below this average height as shorts, and therefore, a fixed point would solve the problem. It is clear that the epistemic solution is counter intuitive in nature, and this becomes a purported problem. From the example discussed, it is evident that there all kind of things that people do not know, however, ignorance in the case of indistinctness appears to be necessary ignorance. It is not that we do not know if someone is tall and another is short, we simply know it. But, for the person seeking the epistemic solution, the problem is harder, for there is something to know and it is simply that we cannot know it. Thus, the epistemic solution does not successfully diagnose the problem.
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