Inference to the Best Explanation in Science

1. The Basics of Abductive Reasoning

Inference to the Best Explanation, a concept first articulated by Charles Sanders Peirce under the name "abduction," is a form of ampliative reasoning. Unlike deductive inference, its conclusion is not guaranteed by the premises. Unlike purely enumerative induction, it is not just a generalization from statistical patterns. Instead, IBE involves an inference to a hypothesis because of its unique explanatory power.

To get a feel for this type of reasoning, let's start with some everyday examples and a formal introduction from the Stanford Encyclopedia of Philosophy.

As the reading highlights, IBE is ubiquitous. From a detective solving a crime to a physicist postulating a new particle, the pattern is the same: observe a puzzling phenomenon and infer the hypothesis that would best explain it. The "No-Miracles Argument" we discussed previously is itself a grand-scale IBE: the approximate truth of our best scientific theories is inferred as the best explanation for their stunning predictive and instrumental success.

Your own field of astrophysics provides countless examples. Consider the following image, which depicts various observational pillars of modern cosmology.

The Lambda-CDM model, our standard model of cosmology, is not inferred because it is the only possible theory. It is accepted because it is currently judged to be the single, coherent framework that best explains this diverse and independent set of observations—from the CMB's temperature fluctuations to the accelerating expansion inferred from supernovae and the specific pattern of galaxy clustering described by BAOs.

2. The Criteria of "Best": Explanatory Virtues

The crucial question for IBE is what makes one explanation "better" than another. If evidence alone is insufficient, then this judgment must rely on other criteria, often called theoretical or explanatory virtues. In the last lesson, we noted that these virtues are invoked to break the deadlock of underdetermination. Now, let's examine what they are.

The following video provides an excellent, practical overview of the most commonly cited criteria for a good explanation.

These virtues are the engine of IBE. When faced with underdetermination, a realist argues we shouldn't just shrug our shoulders. We should compare the competing theories based on these virtues. For instance, in the choice between Special Relativity and Lorentz's ether theory, both of which made the same predictions, physicists ultimately chose Einstein's theory. A primary reason was simplicity: it did not postulate the existence of an unobservable, physically superfluous entity (the ether).

Philosopher Peter Lipton adds a useful distinction. He suggests we should think of IBE as Inference to the Loveliest Explanation, not necessarily the likeliest. "Loveliness" is a measure of how much understanding an explanation would provide if it were true, and it is a function of virtues like those listed above. "Likeliness" is our judgment of its probability of being true. The core claim of IBE, then, is that we use loveliness as our guide to likeliness.

3. The Central Objection: The Argument of the Bad Lot

The anti-realist has a powerful response to IBE, known as the Argument of the Bad Lot. The argument, famously articulated by Bas van Fraassen, runs as follows: IBE licenses an inference to the best of the explanations we have considered. But how can we be confident that the true explanation is even included in this "lot" of candidates? It seems entirely possible that we are simply choosing the best of a bad lot, where all the options on the table are false.

For IBE to be reliable, we would need some reason to think we are "epistemically privileged"—that our cognitive and historical situation predisposes us to dream up the true theory among our initial candidates. This seems like an unacceptably arrogant assumption, especially in light of the "Problem of Unconceived Alternatives" from our last lesson.

The following video provides a detailed analysis of this crucial objection and the main realist responses.

The Bad Lot argument cuts to the core of the IBE defense of realism. It forces the realist to justify the crucial leap from "best explanation we've thought of so far" to "likely to be true." Lipton's argument is particularly interesting as it attempts to show that the very practice of reliable comparative ranking—something an anti-realist like van Fraassen might accept—presupposes a background of approximately true theories, thereby bootstrapping the realist position. The debate over whether this move is successful is still very much active.

4. IBE and Bayesian Confirmation Theory

Your interest in formal methods makes it worthwhile to consider how IBE relates to the dominant formal framework for scientific reasoning: Bayesianism. On the surface, they seem different. Bayesianism is a mathematical theory of how to update degrees of belief (probabilities) in light of new evidence, using Bayes' theorem:

This formula makes no explicit reference to "explanation." So, are IBE and Bayesianism competitors or allies?

This is a major area of contemporary debate. Let's look at the main proposals for how they might fit together.

As the reading describes, here are the main views on the relationship:

• IBE as a Heuristic for Priors: This is perhaps the most popular "explanationist" Bayesian view, championed by Peter Lipton and others. We have to get our prior probabilities $P(H)$ and likelihoods $P(E|H)$ from somewhere. The idea is that explanatory virtues guide these assignments. A "lovelier" theory—one that is simpler, has greater scope, etc.—should be assigned a higher prior probability $P(H)$. Its explanatory power makes it more plausible to begin with.
• Competing Frameworks: A stricter Bayesian might argue that their framework is complete. If priors are updated according to Bayes' rule, they will eventually converge on the truth (under certain conditions), and there is no need for a separate, informal mechanism like IBE.
• Different Domains: Another possibility is that they operate in different epistemic contexts. We often reason in a categorical, all-or-nothing way (believing or disbelieving), which is the natural home of IBE. At other times, we reason in terms of graded degrees of belief, the home of Bayesianism. The relationship between these two modes of reasoning is itself a deep philosophical problem (the "lottery paradox" is a famous example).

This tension highlights a recurring theme in formal philosophy: the challenge of capturing the richness of informal, intuitive reasoning (like judgments of explanatory "loveliness") within a precise mathematical framework.

Conclusion

Today we have analyzed Inference to the Best Explanation, a crucial mode of reasoning that underpins much of scientific practice and serves as the primary realist defense against underdetermination.

• Key Takeaways:
  • IBE (Abduction) is an ampliative inference where we conclude that the hypothesis providing the best explanation for our evidence is likely true.
  • An explanation is judged "best" based on explanatory virtues like simplicity, scope, conservatism, and fruitfulness. The realist claim is that these virtues are a guide to truth.
  • As a response to underdetermination, IBE asserts that even if multiple theories are consistent with the evidence, only one is likely to be the best explanation.
  • The most significant challenge to IBE is the Argument of the Bad Lot, which questions whether we have any reason to believe the true explanation is among the candidates we've considered.
  • The relationship between the informal logic of IBE and the mathematical framework of Bayesianism is a complex and active area of philosophical research.

IBE demonstrates that the justification of scientific theories is not merely a matter of checking predictions against data. It involves complex, nuanced judgments about explanatory quality. Whether these judgments are a reliable guide to the unobservable truth of the world remains one of the most vital questions at the heart of the scientific realism debate.

Preview of the Next Lesson:
This entire lesson has pivoted on the concept of "explanation." We've assumed we know what an explanation is and what makes one good. But what exactly is a scientific explanation? In our next lesson, we will turn our analytical lens on the concept of explanation itself, distinguishing between different formal models that philosophers have proposed, such as the Deductive-Nomological model, causal models, and unificationist models.