Philosophy of Science
Muhammad Sajeer Bukhari
Chapter 04
Goodman's Problem of Induction
Nelson Goodman introduced the "new riddle of induction" in his book "Fact, Fiction, and Forecast." Unlike Hume, Goodman wasn't troubled by the classic problem of induction but presented a different problem focusing on how we choose among competing hypotheses.
The New Riddle of Induction
Goodman uses the example of emeralds to illustrate his problem. Traditionally, we infer that "all emeralds are green" based on past observations. However, Goodman introduces a new term, "grue," defined as:
- An object is grue if it is observed before 2020 and is green, or if it is not observed before 2020 and is blue.
By this definition, every green emerald observed before 2020 is also grue. Hence, we could inductively infer that "all emeralds are grue" with the same confidence as "all emeralds are green." The problem arises because after 2020, if all emeralds are indeed grue, they should be blue, contradicting the "all emeralds are green" hypothesis.
This presents a dilemma: the evidence supporting "all emeralds are green" is identical to the evidence supporting "all emeralds are grue," yet they lead to different predictions.
The Broader Implications
Goodman’s problem generalizes to any deviant predicates like "grue." For instance, "bleen" can be defined as:
- An object is bleen if it is observed before 2020 and is blue, or if it is not observed before 2020 and is green.
Goodman’s riddle shows that any observation confirming a hypothesis also confirms an infinite number of other hypotheses. Therefore, it's challenging to determine which hypothesis to adopt.
Responses to Goodman's Problem
1. Language and Definitions:
- The problem might seem artificial because "grue" involves an arbitrary time reference. However, Goodman argues that this distinction is merely linguistic. A language that starts with "grue" and "bleen" as basic terms could define "green" in similarly convoluted terms. Hence, the problem persists across languages.
2. Simplicity:
- One might argue that "green" is simpler than "grue," hence preferable for induction. However, defining simplicity is complex, and assuming that simpler hypotheses are inherently better lacks justification. Also, a language that takes "grue" as basic would find "green" complex.
3. Natural Kinds:
- Perhaps "green" is a natural kind, while "grue" is not. Natural kinds are supposed to reflect the world's real structure. The periodic table is a prime example. Yet, defining what constitutes a natural kind is contentious, and many scientific concepts (like "planet") are arbitrary or socially constructed.
4. Causality:
- Another approach is to rely on causal understanding. The greenness of emeralds is due to their molecular structure and chromium impurities. However, this only shifts the problem. One could hypothesize that after 2020, the same structure might interact differently with light. Without comprehensive causal knowledge, we can't rely solely on causality for induction.
Goodman’s problem challenges the reliability of inductive reasoning by showing that our evidence can equally support conflicting hypotheses. Addressing this requires differentiating between projectable and non-projectable predicates, a task complicated by linguistic, conceptual, and causal factors. Whether we accept Goodman's more radical conclusion—that induction is fundamentally flawed—or his more moderate stance—that certain predicates are unsuitable for induction—depends on our willingness to navigate these complexities.