The Problem of Induction Revisited: Goodman’s New Riddle of Induction and Its Implications.

The Problem of Induction Revisited: Goodman’s New Riddle of Induction and Its Implications (A Lecture)

(Opening Slide: A picture of a perplexed Sherlock Holmes scratching his head with a magnifying glass)

Good morning, class! ☀️ Welcome to Philosophy 301: Advanced Epistemological Puzzles. Today, we’re diving headfirst into a problem that’s baffled philosophers for decades, a problem that makes even the most seasoned logician sweat: Goodman’s New Riddle of Induction.

Now, I know what you’re thinking: "Induction? Sounds boring!" 😴 Trust me, it’s anything but. Induction is the backbone of science, the engine of learning, and the reason you believe the sun will rise tomorrow (despite not having absolute proof). But, as we’ll see, it’s also a bit of a trickster.

(Slide: Title: The Problem of Induction – The OG Version)

I. The Old Problem: Hume’s Skeptical Headache 🤕

Before we get to Goodman’s mind-bender, let’s revisit the classic Problem of Induction, courtesy of the OG skeptic, David Hume.

Hume pointed out that inductive inferences, the kind where we generalize from past experiences to predict future events, are fundamentally unjustified logically. Why? Because they rely on the Principle of the Uniformity of Nature (PUN).

(Table: Hume’s Argument)

Premise	Example
We’ve observed X happening in the past.	We’ve seen the sun rise every day for centuries.
PUN: The future will resemble the past.	The laws of nature will continue to operate as they have.
Conclusion	Prediction
Therefore, X will continue to happen in the future.	Therefore, the sun will rise tomorrow.

Hume’s kicker? We can’t prove PUN. We can’t logically deduce that the future will resemble the past. Every attempt to justify PUN relies on…wait for it…induction! 🤯

It’s a circular argument. We’re using induction to justify induction. Think of it like trying to lift yourself up by your own bootstraps. (Spoiler: it doesn’t work).

(Slide: Image of a person trying to lift themselves by their bootstraps)

This leaves us with a rather unpleasant conclusion: all our scientific laws, our everyday expectations, our belief that gravity will continue to work…are all based on a leap of faith. 😱 Hume essentially argued that our inductive habits are just that – habits, born from repeated experience, not justified by reason.

(Font Change: Highlighted Text) So, Hume leaves us with a profound question: If induction is logically unjustified, why does it work so well? And, perhaps more importantly, what differentiates a good inductive inference from a bad one?

(Slide: Title: Enter Nelson Goodman: The "Grue"some Truth)

II. Goodman’s New Riddle: "Grue" and the Green-Blue Confusion 😵‍💫

This is where Nelson Goodman enters the scene, armed with a deceptively simple, yet devastatingly effective, thought experiment.

Goodman introduces a new predicate: "grue."

(Definition Box with Grue in bold and underlined)

Grue: An object is grue if and only if it is observed before time t and is green, or is not observed before time t and is blue.

Let’s break that down:

• Imagine we’re observing emeralds. 💎
• Time t is some arbitrary point in the future (say, January 1, 2050).
• Any emerald we observe before January 1, 2050, and find to be green, is also "grue."
• Any emerald we observe after January 1, 2050, and find to be blue, is also "grue."

(Slide: Visual representation of Grue. A timeline with emeralds. Before time t, all emeralds are green and labeled "Grue." After time t, all emeralds are blue and labeled "Grue.")

Now, consider this:

(Table: Two Inductive Arguments)

Argument 1 (Using "Green")	Argument 2 (Using "Grue")
Premise: All emeralds observed before time t are green.	Premise: All emeralds observed before time t are grue.
Conclusion: Therefore, the next emerald observed will be green.	Conclusion: Therefore, the next emerald observed will be grue.

Before time t, both arguments appear equally well supported by the evidence! Every emerald we’ve observed is both green and grue. Yet, the conclusions are incompatible!

• If the next emerald is green, Argument 1 is correct.
• If the next emerald is blue, Argument 2 is correct.

(Emoji: Mind blown 🤯)

Goodman’s point is that both "green" and "grue" are equally well-confirmed by our past observations. We’ve seen countless green emeralds before time t. But, those same emeralds are also grue! So, why do we feel justified in projecting "green" into the future but not "grue"? What makes "green" a better predicate for inductive generalization than "grue"?

This is the crux of Goodman’s New Riddle of Induction. It’s not just about the justification of induction in general (like Hume’s problem); it’s about the problem of selecting which predicates are projectible.

(Slide: Title: The Problem of Projectibility)

III. The Problem of Projectibility: Why "Green" Wins (For Now…) 🏆

Goodman argues that the difference between "green" and "grue" isn’t logical; it’s historical and linguistic.

(Emphasis on Historical and Linguistic)

"Green" is a predicate that we’ve used consistently and successfully in the past. It’s deeply ingrained in our language and our cognitive frameworks. We’ve made countless successful predictions using "green." "Grue," on the other hand, is a novel, artificial predicate that we’ve never used before.

Goodman calls "green" entrenched. An entrenched predicate is one that has a long history of successful projection. "Grue" is not entrenched; it’s a newcomer to the prediction game.

(Definition Box with Entrenchment in bold and underlined)

Entrenchment: The degree to which a predicate has been successfully and consistently used in past inductive inferences.

Think of it like this:

• "Green" is like a seasoned marathon runner who’s completed countless races. 🏃
• "Grue" is like a rookie who’s never even laced up their shoes. 👟

We’re more likely to bet on the marathon runner because of their track record. Similarly, we’re more likely to project "green" because of its history of successful application.

However, this raises a crucial question: How did "green" become entrenched in the first place? 🤔 Was it just a lucky coincidence that we started using "green" and not "grue"?

Goodman’s answer is that it’s a complex process of historical accident and linguistic evolution. Some predicates, for whatever reason, gain traction and become entrenched. Others fade into obscurity.

(Slide: Title: Implications and Responses: A Philosophical Scramble)

IV. Implications and Responses: Philosophers Wrestle with "Grue" 🤼‍♀️

Goodman’s New Riddle has profound implications for epistemology, philosophy of science, and even cognitive science. Let’s explore some of them:

A. The Death of Naïve Empiricism?

Goodman’s riddle challenges the idea that scientific theories are simply derived from observation. It shows that our observations are always filtered through a conceptual framework that already favors certain predicates over others. We don’t just see the world; we see it through the lens of our entrenched concepts.

This undermines the notion that science is purely objective and value-neutral. Our linguistic and conceptual biases play a significant role in shaping our scientific theories.

B. The Problem of Confirmation:

Goodman’s riddle complicates the theory of confirmation. Traditionally, confirmation theory holds that evidence confirms a hypothesis if it makes the hypothesis more probable. However, Goodman shows that the same evidence can confirm mutually incompatible hypotheses (e.g., "All emeralds are green" and "All emeralds are grue").

This forces us to rethink what it means for evidence to confirm a hypothesis. We need to develop a more sophisticated theory of confirmation that takes into account the role of entrenchment and projectibility.

C. The Role of Convention and Language:

Goodman’s work highlights the importance of convention and language in shaping our knowledge. Our concepts and categories are not simply reflections of objective reality; they are products of social and historical processes.

This has implications for debates about relativism and the nature of truth. If our knowledge is shaped by our language and conventions, does that mean that truth is relative to our particular conceptual scheme?

D. Attempts to Solve the Riddle (and Their Shortcomings):

Philosophers have offered various solutions to Goodman’s riddle, none of which are entirely satisfactory:

• Syntactic Solutions: Some philosophers have tried to argue that "grue" is a syntactically complex predicate, while "green" is simple. However, Goodman showed that we can define "green" in terms of "grue" and another predicate, "bleen" (blue before t, green after t), demonstrating that syntactic complexity is relative.

• Causal Solutions: Others have suggested that "green" is causally related to our perception of emeralds, while "grue" is not. However, it’s difficult to specify exactly what this causal relationship consists of and why it should privilege "green" over "grue."

• Pragmatic Solutions: Some argue that we prefer "green" because it’s more useful or practical than "grue." However, this doesn’t explain why "green" is more useful or practical in the first place.

(Table: Summary of Responses and Challenges)

Solution Type	Description	Challenge
Syntactic	Argues that "green" is simpler in terms of logical structure.	Goodman showed that simplicity is relative; "green" can be defined in terms of "grue" and "bleen."
Causal	Argues that "green" has a causal connection to our perception, while "grue" doesn’t.	Difficult to specify the exact causal connection and justify why it privileges "green."
Pragmatic	Argues that "green" is more useful or practical.	Doesn’t explain why "green" is more useful.
Entrenchment (Goodman’s Solution)	The most entrenched predicates, those with a successful history of inductive projection, are more likely to be projected again.	It doesn’t explain how entrenchment arises initially, and might appear circular (we use it because we used it before).

The lack of a definitive solution to Goodman’s riddle suggests that it’s not just a philosophical puzzle; it points to fundamental limitations in our understanding of induction and knowledge.

(Slide: Title: Beyond Emeralds: The Wider Significance)

V. Beyond Emeralds: The Wider Significance of "Grue" 🌍

Goodman’s riddle is not just an abstract philosophical exercise. It has important implications for how we understand:

• Scientific Progress: The riddle suggests that scientific progress is not simply a matter of accumulating more evidence. It also involves a process of conceptual change, where we revise our entrenched categories and develop new ways of understanding the world.

• Artificial Intelligence: As we try to build AI systems that can learn and reason inductively, we need to be aware of the "grue" problem. How can we ensure that AI systems develop the right inductive biases and projectible predicates?

• Everyday Reasoning: The riddle reminds us that our everyday reasoning is not always rational or objective. Our biases and preconceptions can influence how we interpret evidence and make predictions.

(Slide: Examples of Real-World "Grue"-Like Problems)

Here are a few real-world examples where "grue"-like problems arise:

• Medical Diagnosis: A doctor might observe a correlation between a certain symptom and a particular disease in their patients. However, this correlation might only hold true for a specific population or during a specific time period. The doctor needs to be careful about generalizing this correlation to other populations or time periods.

• Financial Markets: Investors often try to predict future stock prices based on past trends. However, these trends might be influenced by factors that are specific to a particular market or time period. Investors need to be aware of the risk of overfitting their models to past data.

• Social Stereotypes: Stereotypes are often based on generalizations about particular groups of people. However, these generalizations might be based on limited or biased evidence. It’s important to be aware of the limitations of stereotypes and to avoid making assumptions about individuals based on their group membership.

(Slide: Conclusion: Embracing the Uncertainty)

VI. Conclusion: Embracing the Uncertainty 🤔

Goodman’s New Riddle of Induction doesn’t offer easy answers. It’s a reminder that induction is a complex and inherently uncertain process. But, by grappling with the riddle, we can gain a deeper appreciation for the challenges of knowledge and the importance of critical thinking.

So, the next time you see a green emerald, remember "grue." Remember that our knowledge is always provisional and subject to revision. And, remember that the pursuit of knowledge is a never-ending journey, full of unexpected twists and turns.

(Final Slide: A picture of a winding road disappearing into the horizon with the text "Keep Exploring!")

Thank you! Now, who’s up for some truly perplexing questions? 🙋‍♀️🙋‍♂️

(End of Lecture)