The Problem With The Color “Grue”
We often hear people say things that do not reliably predict the future. Claims like, “summers in California are always hot and sunny” and “the economy is as strong as ever”, are valid now but not necessarily so in the future. Indeed, developments like global warming and past recessions like the Great Recession shake our confidence in warm summers in California and strong economies in the future. David Hume, in his Enquiry Concerning Human Understanding, is among the first to argue that such a posteriori knowledge (not derived through intuition or demonstration) is subject to doubt as much as it is to its affirmation. In a well-known example, the probability of the Sun not rising tomorrow is theoretically the same as the probability of it rising, despite it having risen every day throughout recorded history. Unless we can prove intuitively that the sun will rise tomorrow, in the same manner we prove mathematical equations, we cannot be completely certain about it. Inspired by Hume, Nelson Goodman investigates the problem further and asks, “Why do we use certain predicates to describe X if X’s properties can shift in any direction in the future?”. His Grue paradox draws upon our understanding of the color green and compares it with a new adjective “grue” that says an object X is green if X is examined (by now) and blue if unexamined (by now). By using examined green emeralds as confirming instances of “grue”, he tries to demonstrate that the same data can support both claims that emeralds are green and “grue”. But intuitively they cannot be both green and “grue”, because if they are “grue” and unexamined then they are blue. In response to the paradox, I argue that we cannot know if X is “grue” simply by it being examined unless we have the background knowledge that X can shift colors and was blue before our examination. In other words, we cannot simply generalize from cases we have examined to all other cases without the necessary relevant background information.
Goodman’s Grue Paradox uses our everyday observations to demonstrate the seemingly conflicting way we use everyday predicates. He places doubt on our ability to project certain qualities of some object or thing into the future, which we have not yet observed. Using a hypothetical predicate “grue” to describe an object’s past and future colors, he tries to show that it seems possible to use such locational predicates to describe our world. He describes some object X as “grue” if and only if X is green and has been examined, or X is blue and has not been examined. All examined emeralds, all of them being green, count as “grue” per the former part of the definition. Since all emeralds that we examine are green and therefore meet the requirement for “grue”, it seems to follow that all emeralds are “grue”. While the example leads by apparently correct reasoning, it points to an absurd falsehood: if it is true that all emeralds are “grue”, then the unexamined emeralds (supposing that there are any) are blue and not green. In other words, it seems equally accurate for us to call an emerald green or “grue” even though “grue” contains the possibility of real, blue emeralds. The paradox, then, forces us to say what makes us treat green and “grue” differently in order to correctly characterize things in our world.
While “grue” leads by seemingly correct reasoning, each observation of a green emerald cannot be generalized to be “grue” since we cannot confirm that there are unobserved emeralds that are blue. Put differently, if emeralds are green when examined, then they are always green, and were never “grue”. From scientific knowledge, we know that emeralds’ physical structure does not let them change from blue to green on exposure to light or any form of examination. Therefore, we are confident that an unexamined emerald would have been green and not changed color upon examination. Under the “grue” definition, then, the emerald only becomes “grue” when it gets examined, yet we know that being examined does not affect its color. Therefore, we have no basis to call all emeralds “grue” because there is no evidence that emeralds were ever blue and that they change colors to green upon examination.
Put into a broader context, my argument is that generalization of any sort is unjustified if we know that a certain feature of our sample group influences the results. Since the green color of the sample of emeralds is biased to support the generalization that they are “grue”, the generalization is incorrect. For instance, if a survey of university students shows that most of them vote for left-wing parties, we obviously cannot assume that the general population also votes similarly. This is because we understand that age can influence voting patterns, and university students are typically younger. And even if we didn’t specifically know how age affects voting, other known differences in attitudes between younger and older generations suggest that the voting patterns of university students may not represent those of the entire population. Using enumerative induction, or the accumulation of positive instances of a generalization, to support a categorical proposition is worthless on its own because one contrary instance can foil the entire argument.
The only case in which “grue” would be used correctly is for examination-sensitive objects that are known to be blue prior to the examination and change color to green afterward due to some environmental alteration. For instance, if some stone that was sensitive to examination and when exposed to light changed from blue to green due to some chemical reaction, then all of these stones would be grue, not just the examined ones. A close real-life example of this is bubbles, whose color is coined “iridescence” due to the fact that its surfaces appear gradually to change color as the angle of view or the angle of illumination changes. These successful cases of “grue” show us that we cannot generalize simply from cases we have examined to all other cases without the required background information.
In his defense, Goodman can very well contend that any sample will inevitably have some bias when generalized to a larger population, and thus it is only through the accumulation of positive cases of usage or reference that makes one predicate more legitimate than another. This concept, called entrenchment, is his solution for determining the right predicate to use to describe our world. The inherent bias of a select sample population stems from the fact that no sample can perfectly represent every possible variable or condition present in the larger population. However, he may argue that this does not render the process of generalization invalid. Instead, the focus should be on minimizing bias and ensuring that the concepts used in generalizations are robust and well-supported by evidence. Goodman introduces the concept of “entrenchment” to address the reliability of generalizations. A well-entrenched concept is one that has been extensively used and validated in a variety of contexts, showing its reliability and utility. For instance, the concept of “green” has been consistently used and confirmed in countless observations and predictions, whereas “grue” lacks this historical validation. “Green” has proven its reliability across various contexts, making it less susceptible to bias and ensuring more accurate predictions. In contrast, “grue” is not well-established and is more prone to anomalies and errors. By emphasizing entrenchment, Goodman maintains that using well-established concepts like “green” can significantly mitigate the effects of bias and produce more reliable outcomes than less entrenched concepts like “grue.”
While Goodman’s concept of entrenchment provides a framework for making reliable generalizations, it also imposes significant limitations on innovation. By prioritizing well-entrenched concepts, Goodman’s approach potentially stifles the introduction and exploration of new ideas that have not yet undergone extensive validation. This insistence on using only well-established concepts creates a conservative bias that may prevent, say, the scientific community from considering novel hypotheses and theories. Such rigid adherence to entrenchment can hinder the progress of science, as groundbreaking discoveries often emerge from challenging established norms and exploring uncharted territories. Furthermore, it raises the question of how a concept can become well-entrenched if innovative ideas are consistently marginalized. In essence, while Goodman’s solution aims to ensure reliability, it inadvertently places an intolerable block on creativity and the evolution of knowledge by discouraging the pursuit of potentially revolutionary but initially unentrenched concepts.
A balanced approach between Goodman’s well-entrenched solution and the need for confirmed background knowledge involves integrating the strengths of both perspectives. This middle ground would recognize the value of well-entrenched concepts for their reliability and historical validation while also being open to innovative ideas that challenge these established norms. This approach would involve a rigorous process of vetting new concepts through careful examination and empirical testing, ensuring they are grounded in solid background knowledge before they are widely accepted. For example, when exploring the uncharted 95% of the ocean, scientists could use entrenched concepts as a starting point but remain flexible in adapting or developing new theories as new data emerges. This method ensures that new predicates are not dismissed outright due to lack of entrenchment but are scrutinized and validated through scientific inquiry. By doing so, the scientific community can maintain the reliability of its generalizations while fostering an environment conducive to innovation and the evolution of knowledge. This balanced approach mitigates the risk of stagnation posed by an over-reliance on entrenched concepts and avoids the pitfalls of adopting unverified ideas prematurely.
In conclusion, Goodman’s Grue paradox compels us to critically reexamine the way in which we describe and understand our world. If each observation of an emerald is seemingly a confirming instance that it is both green and “grue” (blue if examined in the future), then we must determine what it is that makes an emerald green, not “grue”. This means understanding why a specific property of an object cannot be generalized to produce a different result. Since we know that an emerald’s color does not shift from green to blue upon examination or through any other manipulation, we know that each of our observations confirms that the emerald is always green, and was never “grue”. We cannot generalize instances of something to a different outcome if we do not have background knowledge that confirms the validity of the outcome. In this case, the green property of the emerald is biased to support “grue” since we know the emerald’s current color is independent of its future color. While Goodman addresses this issue through enumerative induction — the accumulation of positive instances — this approach can stifle future innovation. A more effective strategy involves balancing the recognition of historically validated concepts with openness to innovative ideas. This approach allows us to understand our ever-changing world without contradictions in our language.
