Inductive Arguments

(●) What is Inductive Reasoning?
In an inductive argument, it's possible for the premises to be true and the conclusion still be false. The premises don't guarantee the conclusion, but instead make it more probable than its competitors. The evidence used "underdetermines" the conclusion, meaning it makes it likely or plausible, but not certain. A good inductive argument must have true premises that are more plausible than their contradictories, and be informally valid (avoiding fallacies). However, they are not assessed for formal validity because the premises don't necessitate the conclusion's truth.

Here's a key example:
- 1. Groups A, B, and C were similar people with the same disease.
- 2. Group A got a new drug, B got a placebo, C got no treatment.
- 3. Death rate was 75% lower in Group A than B and C.
- 4. Therefore, the new drug is effective.

The conclusion is likely true based on the evidence, but it's not guaranteed – perhaps luck or another factor caused the difference.

(●) How Do We Understand Inductive Reasoning?
Philosophers approach understanding inductive reasoning in different ways. Two prominent methods are:

1. Bayes's Theorem:
This approach uses the rules of probability calculus. Bayes's theorem provides formulas to calculate the probability of a hypothesis (H) given certain evidence (E), symbolized as Pr(H|E). Probabilities range from 0 (lowest) to 1 (highest), with values above 0.5 suggesting positive probability. The probability of a hypothesis given evidence depends on its intrinsic probability (its likelihood based on general background knowledge) and its explanatory power (how likely the evidence would be if the hypothesis were true). A challenge in philosophy is assigning precise numerical values to these probabilities, often relying on vague approximations. An "odds form" of the theorem can compare the probability of two competing hypotheses given the evidence.

2. Inference to the Best Explanation (IBE)
A perhaps more practically useful approach in philosophy is inference to the best explanation (Also sometimes called Abduction). This method involves starting with data that needs explaining, identifying a set of possible explanations ("a pool of live options"), and then selecting the explanation that, if true, would best explain the data. Several criteria are commonly used to determine which explanation is "best":

• Explanatory scope: Does it explain a wider range of data than rivals?
• Explanatory power: Does it make the observable data more likely than rivals?
• Plausibility: Is it implied by a greater variety of accepted truths and its negation by fewer?
• Less ad hoc: Does it involve fewer new, unsupported assumptions than rivals?
• Accord with accepted beliefs: When combined with accepted truths, does it imply fewer falsehoods than rivals?
• Comparative superiority: Does it significantly outperform its rivals across these criteria?

The neo-Darwinian theory of biological evolution is presented as a good example of IBE. Supporters argue that even though the evidence (like micro-evolutionary change) doesn't prove macro-evolutionary development, the theory is the best explanation for the data due to its scope, power, and other factors. Critics, however, argue that the perceived superiority of Darwinism only holds if the pool of possible explanations is artificially limited (e.g., to only naturalistic ones). If other hypotheses, such as intelligent design, are allowed, the picture changes. This debate itself illustrates how IBE works and how disagreements about the criteria or the pool of options can arise.