Hume's Problem of Induction and Scientific Skepticism

Introduction

Welcome back! In our last lesson, we dissected "Hume's Fork," his crucial distinction between relations of ideas (truths of logic and math, knowable a priori) and matters of fact (truths about the world, knowable only a posteriori). We saw that while relations of ideas are certain, their denial being a contradiction, matters of fact are never certain in the same way. We can always conceive of the contrary of any matter of fact.

As promised, we will now apply this powerful tool to one of our most fundamental beliefs: that the future will resemble the past. All of science and, indeed, most of our daily life, is built on inferences from observed patterns to unobserved cases. We believe the sun will rise tomorrow because it always has. We believe the laws of physics will hold in the next experiment because they always have. This is called inductive reasoning.

Today's lesson directly addresses the learning outcome: Analyze Hume's problem of induction and its skeptical implications for science. Hume's argument is a landmark in philosophy, a profound challenge that questions the very rational foundations of empirical science. Given your interest in the foundations of knowledge and your background in mathematics, you will appreciate the logical rigor of Hume's challenge.

1. From the Observed to the Unobserved

Let's begin by clarifying the nature of inductive inference. Unlike a deductive argument, where the conclusion is already contained within the premises (making it non-ampliative), an inductive argument goes beyond the premises. It is ampliative—the conclusion contains new information not strictly entailed by the premises.

For example:

• Premise: Every swan I have ever seen is white.
• Conclusion: Therefore, all swans are white.

The conclusion generalizes beyond the observed instances. Hume's question is simple but devastating: what is the justification for this leap?

Hume notes that all our reasoning about unobserved matters of fact relies on the relation of cause and effect. Why do you believe that if you drop a pen, it will fall? Because you believe that releasing it causes it to fall. But how do we know about this causal connection? Not through a priori reasoning. As we saw last lesson, "the pen will not fall" is a perfectly conceivable state of affairs; it's not a logical contradiction.

Hume’s answer is that our knowledge of cause and effect comes entirely from experience. We have seen objects released in the past, and we have seen them fall. This is what Hume calls "constant conjunction."

The following video from the University of Oxford provides an excellent summary of how Hume sets up this problem, grounding it firmly in the distinction we learned last time.

The video makes the crucial point: experience only tells us about the past. We have observed a constant conjunction of events A and B so far. But science and everyday life require us to believe that this conjunction will continue into the future and in unobserved instances. What justifies this belief?

2. The Great Dilemma: Hume's Argument

Hume argues that the leap from the observed to the unobserved relies on a hidden assumption, a principle we take for granted. This is often called the Principle of the Uniformity of Nature (PUN).

Principle of the Uniformity of Nature (PUN): The future will resemble the past. (Or, more formally, instances of which we have had no experience must resemble those of which we have had experience).

Our inductive inferences seem to be valid only if we assume the PUN is true. So, the question becomes: how can we justify our belief in the PUN?

Here, Hume unleashes his Fork. Any justification for the PUN must be either a relation of ideas (a demonstrative argument) or a matter of fact (a probable argument).

The Formal Argument

The Stanford Encyclopedia of Philosophy provides a clear, structured reconstruction of Hume's argument, which should appeal to your mathematical sensibilities. The logic is presented as a dilemma with two "horns," each leading to a dead end.

Let's break down the two horns of the dilemma as explained in the article:

1. Horn 1: The Justification Cannot be Demonstrative (a priori).
   A demonstrative argument would show that the PUN is a relation of ideas, meaning its denial is a contradiction. But is it? Hume points out that we can clearly and distinctly conceive of a world where the laws of nature suddenly change. We can imagine that the next time we drop a pen, it floats away. Because "the course of nature may change" is conceivable, the PUN is not a necessary truth of logic. Its justification cannot be found through reason alone.

2. Horn 2: The Justification Cannot be Probable (a posteriori).
   If the justification isn't a priori, it must be based on experience. Such an argument would look like this: "In the past, the future has always resembled the past. Therefore, the future will continue to resemble the past." But what kind of argument is this? It's an inductive argument! It uses past regularities to infer a future regularity. It attempts to justify the PUN by using the PUN. This is a classic case of circular reasoning or "begging the question."

Since the justification can be neither demonstrative nor probable, Hume concludes that the PUN—and by extension, all of induction—has no rational justification whatsoever.

To make the circularity even more vivid, let's consider a thought experiment.

3. The Skeptical Implications for Science

If Hume's argument is sound, the consequences are profound. Science is built upon the foundation of induction—generalizing from experimental data to form universal laws. If induction is not a rational process, then what is the status of scientific knowledge?

To explore these consequences and some potential responses, let's watch one more video.

As the video argues, the implication is that science, if it rests on induction, lacks a rational foundation. It becomes a belief system whose fundamental principles cannot be justified, making it no different, from a purely logical standpoint, than superstition or "voodoo."

So, what are we left with? Hume's own "solution" is not to solve the problem but to explain it away psychologically. He argues that our belief in induction is not a product of Reason but of Custom or Habit.

"All inferences from experience, therefore, are effects of custom, not of reasoning." - David Hume, An Enquiry Concerning Human Understanding

After observing the constant conjunction of two events millions of times, our minds develop a habit, an instinctual expectation that the pattern will continue. It's a psychological process, a species of "natural instinct," not a logical one. For Hume, reason is—and ought to be—a "slave of the passions" and, in this case, of habit.

The power of Hume's problem has shaped the philosophy of science ever since. Karl Popper, a major 20th-century philosopher of science, took Hume's conclusion so seriously that he attempted to build a model of science (falsificationism) that does not rely on induction at all, arguing that science proceeds by deductively falsifying theories, not by inductively confirming them.

Conclusion

Today we have grappled with one of the most enduring problems in philosophy. By rigorously applying his distinction between relations of ideas and matters of fact, Hume constructed a powerful dilemma that appears to leave our most basic form of reasoning about the world without a rational leg to stand on.

Key Takeaways:

• Inductive reasoning is ampliative, meaning it moves from observed cases to unobserved cases, such as predictions or general laws.
• This leap relies on the Principle of the Uniformity of Nature (PUN), the assumption that the future will resemble the past.
• Hume's argument is a dilemma: The PUN cannot be justified a priori (its denial is not a contradiction) nor can it be justified a posteriori (this would be circular).
• The Skeptical Conclusion: Induction has no rational justification. Our belief in it is a matter of psychological custom or habit, not reason.
• Implications for Science: This calls into question the rational basis of scientific laws and predictions, seemingly reducing science to a kind of faith or instinct.

Preview of the next lesson:

Hume's skeptical assault on reason did not go unanswered. The German philosopher Immanuel Kant famously wrote that reading Hume "interrupted my dogmatic slumber." Kant realized that if science was to have a secure foundation, Hume's problem had to be solved. In our next module, we will begin our study of Kant's "Critical Philosophy," a revolutionary project that attempts to overcome Hume's skepticism by rethinking the very structure of reason, experience, and knowledge. Kant's answer involves proposing a third category of knowledge that Hume's Fork had ruled out: the "synthetic a priori."