Inference to the Best Explanation and Theory Evaluation

Foundations of Abductive Reasoning

Inference to the best explanation, also known as abductive reasoning, is an essential form of inductive logic used to ground theories. While deductive arguments provide rational support such that the truth of the premises guarantees the truth of the conclusion, and inductive arguments like enumerative induction, arguments by analogy, or causal arguments provide support based on probability, abduction focuses on identifying the most plausible explanation for an unexpected observation or a specific state of affairs. This form of reasoning is ubiquitous in daily life, especially when things do not proceed as anticipated, such as when a car fails to start, a friend acts strangely, or an unexplained light appears in the sky.

Abductive reasoning moves in a reverse direction compared to standard deduction. For example, if you see wet grass, you might infer that it rained last night. While you cannot prove this deductively—since grass can be wet for various reasons like sprinklers—you consider all possible causes and identify rain as the best explanation. The formal structure of an abductive argument is as follows: (1) Phenomenon $Q$ is observed; (2) $E$ provides the best explanation for $Q$; (3) Therefore, it is probable that $E$ is true. These arguments are called "ampliative" because they go beyond the evidence to posit a theory or generalized framework that is not entirely derived from the known facts themselves.

Arguments Versus Explanations

It is critical to distinguish between providing an argument and providing an explanation, though the two are not mutually exclusive. An argument provides reasons for believing that something is the case. For example, stating that DNA evidence and video footage prove a suspect is guilty of murder is an argument. Conversely, an explanation asserts why something is the case. Stating that a suspect committed a murder because they were mistreated as a child and possessed reduced gray matter in the brain provides an explanation of the cause. In abductive reasoning, you ground a claim that something is the case on the fact that you can explain why it is the case. For instance, a criminal profile might be used to ground the claim that a specific individual is the killer because that individual’s history best explains the nature of the crime.

Typology of Explanations

There are five distinct categories of explanations used to categorize and understand phenomena:

1. Causal Explanations: These specify why something had to happen by identifying physical forces or events. For example, "The increase in mudslides is due to deforestation."

2. Teleological Explanations: Also known as functional explanations, these describe the purpose or function of an object or action. This applies to artifacts (the purpose of a pen is to write), actions (going to the store to get milk), and anatomy (the purpose of the heart is to circulate blood throughout the body).

3. Interpretative Explanations: These provide understanding regarding the broader meaning or significance of something. In literature, the green light in The Great Gatsby symbolizes Gatsby's unattainable dream. Behaviorally, a specific bandana might signify solidarity with protestors.

4. Procedural Explanations: These break down how a specific task is carried out, such as a recipe (adding yeast to water, then flour) or the steps to change a flat tire (loosen lug nuts, lift car, swap wheels, tighten, and lower).

5. Theoretical Explanations: These embed a phenomenon within a broader system of abstract laws or unobservable structures. While a causal explanation might say it rained because of daytime heating and lift, a theoretical explanation uses meteorology and Phase Transition Theory to explain that rain is a spontaneous change of state in a thermodynamic system occurring when relative humidity reaches $100\%$. This happens when the partial pressure of water vapor exceeds its saturation vapor pressure, forcing a gas-to-liquid shift to restore equilibrium.

Theoretical Models in Hard and Soft Sciences

Theoretical explanations are prevalent across various disciplines. In the "hard" sciences, common models include Heliocentrism (the Sun-centered solar system), the Theory of Relativity (Einstein’s framework for gravity and space-time), Evolution by Natural Selection (Darwin’s model for biological diversity), and Germ Theory (the transmission of infectious illness via microorganisms).

In the "soft" sciences, theories explain human and social behavior. Rational Choice Theory assumes humans weigh costs against benefits to choose the most advantageous path. Conflict Theory views society as a struggle for limited resources and power. Freudian Theory explains personality and mental illness through unconscious desires and childhood experiences. These theories are confirmed by their ability to provide the best unifying causal framework for otherwise disconnected observations.

Scientific Case Studies: Uranus and Evolution

The discovery of Uranus by William Herschel in 1781 serves as a classic example of abductive elimination. Herschel observed a faint, shifting, disk-shaped object. He entertained three explanations: (1) a distant star; (2) a comet; or (3) a planet. He eliminated the star theory because the object moved relative to background stars. He eliminated the comet theory because the object lacked a tail and followed a nearly circular orbit rather than a highly elliptical one. A planet provided the best explanation for the disk shape and predictable orbital path, leading to the conclusion that a new planet had been found.

Similarly, evolution by natural selection is confirmed as an inference to the best explanation. It accounts for complex adaptations like camouflage and the fossil record's branching patterns (homology). While macro-evolution cannot always be observed directly, natural selection provides a mechanism for adaptation and explains why the fossil record contains transitional forms (like Tiktaalik). These observations might appear arbitrary under independent creation models but make complete sense under descent with modification. This is significant given the struggle for existence, where offspring inherit variable traits and only those with beneficial traits survive; for example, while $50\% - 80\%$ of sea turtle eggs hatch, only $1$ in $1000$ hatchlings survives to reproduce.

Minimum Requirements for Evaluating Theories

For a theory to be eligible for consideration, it must meet two necessary conditions of consistency:

Internal Consistency: The theory must be free of contradictions. If a theory entails a statement of the form $(A \text{ \& } \sim A)$, it cannot be true. Galileo used a reductio ad absurdum to prove the internal inconsistency of Aristotelian physics, which claimed heavier objects fall faster. If a heavy stone ($H$) and a light stone ($L$) are tied together, the lighter one should act as a drag, making the combined object fall slower than $H$ alone. However, the combined object is heavier than $H$, so it should fall faster. This contradiction (falling both faster and slower) proved Aristotle's assumptions were false.

External Consistency: A theory must be consistent with the data it is supposed to explain and should not be refuted by known facts. The claim "all swans are white" is externally inconsistent if black swans are observed. Historically, the Ptolemaic geocentric model became externally inconsistent with accurate astronomical data regarding retrograde motion (planets appearing to move backward). Astronomers tried to "save the theory" by adding complex mathematical workarounds like epicycles, equants, and eccentrics, but the theory eventually failed to account for observations of planetary speed and brightness.

Criteria of Adequacy

When choosing between competing theories that are both internally and externally consistent, thinkers use the "Criteria of Adequacy." These standards are comparative and help determine which theory is the "best," even if truth is not guaranteed.

1. Testability: A theory is testable if it predicts something other than what it was introduced to explain. For instance, if an electric clock stops when touched, an "electrical short" theory is testable because it predicts that repairing the wiring will fix the issue. A "demon" theory is untestable if it only predicts the clock stopping, which is the very fact it was meant to explain. An untestable theory cannot be falsified and adds nothing to our understanding.

2. Fruitfulness: A fruitful theory predicts novel, previously unknown phenomena and sparks new research. Evolutionary theory is highly fruitful, predicting the location of fossils like Tiktaalik and guiding medical research on antibiotic resistance. Lavoisier’s work in chemistry was fruitful because it moved beyond the "phlogiston" model, using precise scales to prove that metals gain weight when burned because they absorb oxygen, thereby giving birth to quantitative chemical analysis.

3. Scope: This refers to the diversity of phenomena a theory can explain. Newton's laws had greater scope than Aristotle's because they unified celestial and terrestrial motion under one framework. Plate Tectonics is another example, as it explains continent shapes, mountain formation, and deep-sea earthquakes.

4. Simplicity: Also known as Ockham’s Razor, this criterion states that the best theory is the one that makes the fewest assumptions. Simpler theories are less likely to be false because they have fewer ways to go wrong. Scientists eventually chose Copernicus's heliocentric model over Ptolemy’s because it was much simpler, avoiding the "orbits within orbits" required by the geocentric model.

5. Conservatism: A conservative theory fits well with established beliefs backed by excellent evidence. Changing a core belief can require a massive revision of an entire system of thought. For example, Copernicus's theory was initially rejected because it conflicted with Aristotelian physics, which explained why heavy objects fell toward the Earth’s center.

Systematic Method for Theory Evaluation

To evaluate an explanatory theory effectively, one should follow a four-step process:

Step 1: State the theory clearly and check for internal consistency. Ensure the theory is minimally coherent and contains no contradictions.

Step 2: Assess the evidence for the theory. Look for empirical evidence and logical arguments that support the claim, utilizing knowledge about source credibility and inductive conclusions.

Step 3: Scrutinize alternative theories. Avoid confirmation bias by looking for competing explanations and applying the first two steps to them as well.

Step 4: Test the theories with the criteria of adequacy. Compare them based on testability, fruitfulness, scope, simplicity, and conservatism. The process is not algorithmic but depends on rational human judgment, similar to a judicial decision or a medical diagnosis.

The Limits of Reason: Hume’s Problem of Induction

David Hume's Enquiry concerning Human Understanding (1748) presents a challenge to these forms of reasoning. Hume argued that all inductive inferences rely on the assumption that the future will resemble the past (FRP). However, this principle cannot be established by demonstrative (deductive) reasoning because it is conceivable that the future might change. It also cannot be established by inductive reasoning because any such argument would have to assume FRP to prove FRP, resulting in circular reasoning. Consequently, Hume concluded that there is no non-circular rational justification for induction; rather, our knowledge of matters of fact is grounded in the mind’s non-rational, habitual faculties, or "custom."