10 - Inductive Reasoning
It is possible for an argument to have an appearance of truth if its conclusion is achieved when its conditions are met, regardless of whether its conditions are related to the conclusion, or are not comprehensive. Such arguments are "inductively strong" because everything that is included in the argument turns proves true in a given instances - but they are weak in that their failure to identify the valid conditions means that the argument may be true if none of the premises are satisfied, or false even if all premises are satisfied.
Consider the common superstition attached to "lucky" items that are said to cause something to happen: the fisherman who catches a fish every time he wears his yellow hat comes to believe that the hat is the cause of his success.
Inductive Strength
While inductively strong arguments are not valid, in that the satisfaction of the premises do not guarantee the conclusion, it can be said that the premises provide strong support for the conclusion. Unlike validity, which is true or false, inductive strength is not all or nothing by relies on the probability of the argument.
As such, inductive arguments are of interest to the social sciences, where general observations are made on strong, though not flawless, connections between premise and conclusion. Mathematically, the strength of an argument can be calculated based on the probability that the premises support the conclusion, resulting in a score of 0 to 1 (or 0% to 100%) - where the strength is 1, then the satisfaction of premises will absolutely produce the outcome defined by the conclusion.
A simplistic example is that if there is a lottery where there are 1000 tickets and someone purchases 400 of them, then the suggestion that "because they purchased 400 tickets, they will win the lottery" is has a strength of 40%.
Naturally, such mathematical calculations are difficult to apply in most situations, and tend to be very qualitative based on a subjective assessment of their accuracy.
Defeasibility of Inductive Reasoning
Another difference between strength and validity is that strength is defeasible (can be nullified) whereas validity is not.
Moreover, the addition of premises cannot increase the validity of an argument, whereas it has the potential to increase or decrease the strength of the argument.
For example, the argument that a person can survive a thirty-foot fall if they land in water is strengthened by adding the conditions/premises that the water is of a certain depth and there are no objects floating on the surface.
Strength of argument is a significant difference between mathematics and the sciences: a mathematical proof must be inviolate, whereas science is based on known factors that may be undone by further observation, discovery and experimentation. The example given is the assertion by biologists that penguins are flightless does not preclude the possibility that we will discover a species of penguin that can fly, or that existing species may evolve the capability of flight.
Cases of Inductive Reasoning
Some of the main types of inductive reasoning are:
- Induction based on statistics. We use statistical probability to assemble an argument about a population based on our observation of a sample in which qualities are ascribed to a percentage
- Induction based on analogy. We establish the similarity between two items and conclude that something that is true of one may also be true of the other. (Consider that when we find something that is toxic to chimps, we assume it will be toxic to humans.)
- Inference to the best explanation. When we find that we do not have enough evidence to prove a statement to be true, we assemble an explanation based on the evidence we have. That is, when the street is wet, we assume it has rained, though there are other possible causes.
Deductive and Inductive Arguments?
Deductive validity and inductive strength are two standards by which an argument can be evaluated.
The author disagrees with those who use "deductive" and "inductive" as a method of classifying arguments - as it is easy to support the validity of an argument based on one or the other, but it is not possible to classify an invalid argument into either category.
In practice, no argument stands if it is based on inductive or deductive logic alone, but must satisfy both to some degree.