Formal Versus Informal Logic Deductive Versus Inductive Forms of Reasoning

To Review: Two basic categories of human reasoning Deduction: reasoning from general premises, which are known or presumed to be known, to more specific, certain conclusions. Induction: reasoning from specific cases to more general, but uncertain, conclusions. Both deductive and inductive arguments occur frequently and naturally…both forms of reasoning can be equally compelling and persuasive, and neither form is preferred over the other (Hollihan & Baske, 1994).

To Review: Deduction Vs. Induction commonly associated with “formal logic.” involves reasoning from known premises, or premises presumed to be true, to a certain conclusion. the conclusions reached are certain, inevitable, inescapable. Induction commonly known as “informal logic,” or “everyday argument” involves drawing uncertain inferences, based on probabalistic reasoning. the conclusions reached are probable, reasonable, plausible, believable.

Inductive Reasoning Induction For each example below, consider (a) how you know the answer to the question and (b) on a scale of 0-100%, how certain you are that your answer is true. Will the sun rise tomorrow? Will you eventually die? Inductive reasoning methods are used in the natural and human sciences (AOK’s), and allow us to make generalizations based on observations of individual instances. But it is also used in pretty much any circumstance where we need to gather data about a large number of people, objects, place, or events over time, in order to find out what happens in most cases. One of our challenges with inductive reasoning is thus to decide how much we can trust the inductive generalizations about the world that we and others make

Classical deduction Whereas deductive reasoning begins from a general statement, induction starts from observations. Here is a classic example: I saw a swan and it was white I saw a second swan and it was white I saw a third swan and it was white… I saw and “Nth” swan and it was white All swans are white (a general statement is the conclusion)

Classical induction cont. How many cases of white swans do you think should notice before legitimately concluding that all swans are white? How many instances of sunrise do we need to see to believe that it occurs every morning, and that we can trust that the sun will rise tomorrow? When we repeatedly observe instances of a particular phenomenon, it might not seem like a tremendous leap of faith to cross the line and draw a generalization. But it is. There is no magical number that can tell us when we have enough evidence to safely conclude with an inductive generalization of this kind, but despite not offering 100% certainty, classical induction works quite well.

Consider times today when you used classical induction

Inductive reasoning A sample of fifty motorists who were stopped by the CHP at a sobriety checkpoint on a Saturday at midnight revealed that one in four drivers were either uninsured, intoxicated, or both. Thus, if you get involved in an accident on the freeway there is a 25% chance the other motorist will be drunk or uninsured.

Inductive Reasoning fallacious cogent Inductive reasoning enjoys a wide range of probability; it can be plausible, possible, reasonable, credible, etc. the inferences drawn may be placed on a continuum ranging from cogent at one end to fallacious at the other. fallacious cogent

Sample Deductive and Inductive Arguments Example of Deduction major premise: All tortoises are vegetarians minor premise: Bessie is a tortoise conclusion: Therefore, Bessie is a vegetarian Example of Induction Boss to employee: “Biff has a tattoo of an anchor on his arm. He probably served in the Navy.”

Analogical Reasoning Classical Induction requires that we observe many instances, and statistics requires complex methodologies, In practice we cannot do either quickly enough when there is the need to make a quick decision. Analogical reasoning is based on two steps. There is a recognition of similarities between two or more things. There is the assumption that if two or more things are similar in one way, they will also be similar in other ways.

For example If I need to buy a pair of shoes for a party on Saturday, I’m not going to choose where to shop by conducting a poll amongst my friends to determine which store is best and then statistically analyze the results, nor will I want to visit every store in town. I’m more likely to return to the store where I bought shoes a few times previously, considering that I got good wear from the shoes I bought there, the prices were reasonable, and the salespeople were helpful. I will base my decision on a few past experiences, in the hope that conditions haven’t changed. Alternatively, I will ask my friend, who provided me with good recommendations in the past, to recommend a shoes store now, assuming she continues to know my tastes and knows her stores.

Analogical Reasoning cont. Why would analogical reasoning make sense in the study of medicine? Give three examples of reasoning by analogy. How likely are you to trust your results on a scale of 1-10?

Hypothetico-Deductive Reasoning An interplay between deductive and inductive reasoning The Crazy Captain’s Game (an exercise)

Creative Reasoning Linear thinking can be a hindrance Thinking “outside the box” Is like “building a bridge. The parts do not have to be self-supporting at every stage but when the last part is fitted into place the bridge suddenly becomes self-supporting”

Wrap your mind around these! A man is found dead hanging from a rope around his neck in the center of a room with no furniture. A small puddle is on the floor below him. He had no apparent way of hanging himself but the police declared it a suicide. Explain. A woman had two sons who were born at the same hour of the same day of the same year. But they were not twins. How could this be so? There are six eggs in a basket. Six people each take one egg. How can it be that one egg is left in the basket?