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Counter-argument: Why Goodman’s ‘Grue’ Problem is unjustified

IMPORTANT: This paper was originally submitted to Fall 2018 Philosophy 8 class at University of California, Los Angeles, and copyrighted by myself. Any unauthorized use is prohibitted. 

In this paper, I will argue that Goodman’s “all emeralds are grue” statement is unjustified, and “all emeralds are green” is a more justified statement from induction. First, I will explain the basic process and definition of using induction, and then succinctly illustrate what is the “grue” problem raised by Goodman. Finally, I will suggest a counter-argument against Goodman’s “grue” problem to prove that it is not sufficiently justified because the use of “grue” is time-sensitive, and a valid argument from induction should be exclusive from time-sensitivity.

Induction is a specific form of reasoning in which the premises of an argument support a conclusion, but do not ensure it. Specifically speaking, given that all the premises of an argument are true, the conclusion derived from these premises may not be true. There exist various kinds of induction, where enumerative induction is one of them. By using enumerative induction, the classification which will be mainly focused in this paper, we aim to generalize a common pattern for a certain kind of object based on a limited set of observations on these objects. For example, if we observe four swans where swan A is white, swan B is white, swan C is white, and swan D is white as well, we may conclude that all swans are white. The conclusion of “all swans are white” seems to be a relatively convictive argument supported by the evidence of observation on several white swans, but there also seems to be a lack of sufficient evidence to believe that swans of other colors do not exist in this world merely because hitherto (which means “so far”) we have not observed any swans of another color. Due to the property of induction that the premises do not ensure the truthfulness of the conclusion, there have been various arguments raised against the validity of using induction. Goodman’s “grue” problem is one of the most famous and popular arguments.

If we observe a number of emeralds and all of them are green, by using induction, we may conclude that “all emeralds are green”. According to my previous introduction on using induction, though the argument may not be fully true because we only observe a limited number of emeralds, an average person may still find it to be quite persuasive. Meanwhile, based on the induction of “all emeralds are green”, Goodman raised the problem of “grue”, where an object is defined to be “grue” if and only if it is observed before 2020 and is green, or it is observed after 2020 and is blue. Using the definition of “grue”, since the green emeralds we currently have (at the time of writing this paper, which is 2018) are all observed before 2020, we may say that these green emeralds are also “grue” emeralds. Therefore, since all the emeralds we observe hitherto are “grue”, we may come to the conclusion that “all emeralds are grue”, following the rule of enumerative induction. However, in this case, an average person may find this argument absurd and less compelling than “all emeralds are green”, which raises the doubt if “all emeralds are grue” is a valid argument to make by induction, and the reasons behind it.

In my opinion, “all emeralds are grue” is an invalid argument because time-sensitivity is not allowed when using induction. We may interpret this idea from a smaller scale to a larger scale: the validity of using the word “grue” itself, to the validity of the whole “all emeralds are green” statement. First of all, if we take a look at “grue” as a single word, it is considered to be a meaningless word due to its time-sensitivity. The purpose of creating a word, which is identified as a “signifier” in Linguistics, is to point to one specific object, concept, characteristic or state (which is called a “signified”). Given this premise, one can argue that a word is “meaningful” if and only if it consistently refers to one specific thing no matter when it is used. If a word refers to different things at different times, the word will become meaningless. Since the word “grue” refers to distinct concepts at different times it is used (“green” before 2020 and “blue” after 2020), it should be considered to be meaningless. Thus, the improper use of the meaningless word “grue” will make the entire argument “all emeralds are grue” invalid.

Furthermore, we may testify the validity of the argument “all emeralds are grue” as a whole, and we will come to the same conclusion that the argument is invalid due to its time-sensitivity. To achieve that, we can try to insert the definition of “grue” back to the statement “all emeralds are grue”, and we will get an alternative statement which has exactly the same meaning as “all emeralds are grue” like this: “all emeralds are green before 2020 and are blue after 2020”. As mentioned earlier where we discussed the basic concept of using induction, by using “enumerative induction”, our final goal is to generalize a rule or pattern for all objects of a kind based on a limited number of observations on these objects. That is, through induction, we must assume that there exists a universal or equal property across all these objects when we come to a conclusion. Otherwise, it is meaningless to use induction because eventually we may not find any useful information about the common properties of all objects that must held true across the time. Thus, we can argue that a proper argument following the rules of enumerative induction must give a general and universal pattern for all objects, exclusively from time-sensitivity, or in other words, independently from the change of time. In the statement “all emeralds are grue”, we claim that all emeralds observed before 2020 are green, and all emeralds observed after 2020 are blue. Apparently, in this conclusion, we does not assume there exists a universal property of color across all emeralds. The conclusion does not tell us a common or general pattern about color which applies to all emeralds, independently from time.Instead, it tells us two patterns about the color of emeralds simultaneously, and the pattern will vary according to time: green before the time of 2020, but blue after the time of 2020. Therefore, the statement “all emeralds are grue” is not justified, because though it seems to be concluded from induction, it fails to exclude time-sensitivity and does not generate a common rule for all emeralds across the time. In contrast, “all emeralds are green” is a more justified conclusion using enumerative induction because it successfully excludes the concept of time-sensitivity. The conclusion suggests that any emeralds observed will have the common property of being green, no matter when across the time they are observed.

In conclusion, in this paper, I illustrate that induction is a kind of reasoning where the premises of an argument support but do not ensure the truthfulness of the argument. Then, I introduce Goodman’s “grue” problem, where an object is defined to be “grue” if and only if it is discovered before 2020 and is green, or is discovered after 2020 and is blue, and raise the question why “all emeralds are grue” seems to be a less valid argument. Finally, I argue that Goodman’s “all emeralds are grue” argument is unjustified because the use of “grue” is time-sensitive, which does not conform to the rule of assuming universal property while using induction. In contrast, “all emeralds are green” is more justified because it excludes the concept of time-sensitivity.

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