Evaluating Inductive Reasoning

A valid deductive argument guarantees the truth of the conclusion, if the premises are assumed as true. Hence, deductive conclusions are known with certainty.

Inductive arguments reach probable conclusions. A strong inductive argument makes a conclusion likely.

Inductive Examples

The suspect has chosen to remain silent. Therefore, she probably has something to hide.

Three of four cabbies interviewed had BO. So cabbies are not hygienic.

A high pressure zone is in place. So it won’t rain today.

Since high doses of saccharin are correlated with cancerous tumors in rats, it will probably produce cancer in humans as well.

Assessing Inductive Strength

Every deductive argument is either valid or invalid.

Inductive strength is a matter of degree. An inductive argument may be strong, moderate, or weak. If the premises provided confer a high degree of probability on the truth of the conclusion, the argument is strong.

Which is Stronger?

Since the risk of dying from Fen-Phen is less than the risk of dying from birth control pills, we may conclude that Fen-Phen is relatively safe.

Some Fen-Phen users experience chest pain and shortness of breath. Therefore, since Esther uses Fen-Phen, she probably has chest pains.

Inductive Generalizations

Reaching general conclusions from premises that cite particular instances.

Is the sample group large enough? Is the sample group representative?

In a survey of 500 nuns, 98% said they fully support the Church’s position on birth control. It is therefore likely that most Catholic women fully support the church’s position on birth control.

Inductive Analogy

Analogical reasoning involves comparing similar cases and inferring that what is known to be true in one case is likely to be true in the similar case.

Like playing golf, evaluating arguments is a skill that improves with practice.

Analogue: playing golf.

Target: evaluating arguments.

Evaluating Analogies

How many cases are compared? How similar are the cases compared?

Are relevant dissimilarities overlooked?

A similarity is relevant when there is a causal connection between the property two cases share and the property that is inferred to be true of the target.

Burden of Proof

Where does the burden of proof lie?

The less plausible a claim is, the greater the burden of proof.

The affirmative side in a debate has a greater burden of proof.

The greater the chance of error, the higher the cost of being wrong, the greater the burden of proof.

Establish the standard of proof. Has it been met?

Hypothetical Reasoning

Reasoning from observed facts to explanatory hypotheses. Why does the observational data appear as it does?

Why did the Challenger explode?

Why did the dinosaurs become extinct?

Why does Fenfluramine suppress appetite?

Why does pregnancy cause mood swings?

Hypothetical Reasoning

Observations: (1) 4 dead people in a house. (2) A car running in a closed garage. (3) An open heating vent from the garage to the house.

Hypothesis: The people died because of carbon monoxide poisoning.

Plausible Hypothesis

One that is likely to survive critical scrutiny.

Explanatory power: How well does the hypothesis explain the observations? Are there rival hypotheses?

I’d say it’s logic anxiety.

Or it may be English-Angst

Predictive Power

Does the hypothesis enable us to make testable predictions?

If H is true, we will observe O. We did observe O. Therefore, H is confirmed.

If H is true, we will observe O. We did not observe O. Therefore H is disconfirmed.

Disconfirming evidence is stronger than confirming evidence.

Causal Reasoning

Since causation cannot be observed, how can genuine causal relationships be distinguished from mere correlations?

So broccolieaters haveless cancer

and more gas.

Mill’s Methods

Method of agreement: Look for a common antecedent condition in all cases where the effect occurs; Where the effect is found, the cause will be present as well.

Ten students with diarrhea. Each had Tuna Surprise at the cafeteria. The tuna was likely the culprit.

If wherever there’s x there is also y, x may be the cause of y.

Method of Difference

Look for a correlation between the absence of the effect and the absence of an antecedent condition. Where the effect does not occur, the cause won’t either.

If all those who dined at the cafeteria without getting diarrhea also did not eat the Tuna Surprise, it is reasonable to infer that the Tuna was responsible.If whenever x does not occur, y is also not found, x may be the cause of y.

Joint method of Agreement and Difference

Look for an antecedent condition that occurs whenever the effect occurs and does not occur whenever the effect is absent.

If they always get the runs after eating Tuna Surprise, and never get the runs when they don’t eat it, the case against the tuna is strong.

If whenever there is x, there is y; and whenever there is not x, there is not y; x is probably the cause of y.

Method of Concomitant Variation

Look to see whether variations in the suspected cause are correlated with variations in the effect.

Have Mikey eat two helpings of Tuna Surprise; have Ruby eat one helping; and give Charlie just one bite.

Then watch what happens!

If x causes y, then more of x will produce more of y.

Verifying Premises

True premises describe events whose occurrence can (in principle) be verified or falsified. Partial verification produces degrees of probability.

Clinton is celibate is false (since the state of affairs it describes as existing does not now exist) while

The Democrats will regain control of the Senate is unknown.

Relativism

There is no truth, just opinions. A diversity of opinions does not entail

that all opinions are equally correct. The facts may be elusive, but our beliefs and desires do not determine the nature of reality . A racist’s belief in racial superiority does not make him (even relatively) superior.

Relativism wrongly concludes... ...that because we

may be mistaken, we cannot be correct. Our inability to absolutely prove one view correct does not show that all opinions are equally correct

A reasonable person would

not make

that

inference.

Statement Types

Self-verifying statements (necessary truths, analytic statements). Nuns are females. Tautologies: Either cloning is a threat or it isn’t a threat.

Empirically verifiable statements: observation statements: It is windy tonight. Cloning of mammals is possible. Juries sometimes make mistakes.

Verifying observation statements Check the physical

conditions: Possible perceptual impairments (Insufficient lighting, time, etc.)

Check observer accuracy (color blind? on drugs?...)

Observer background knowledge (of astronomy, basket- ball, or whatever)

Observer objectivity

Corroboration of other observers.

Empirically verifiable hypotheses (or theories)

Humans are descended from apes. The universe began with a big bang. Determine plausibility by examining

observational evidence-- does the hypothesis have greater explanatory power than its rivals? Does it have predictive power?

Value Judgments

Lying is wrong You shouldn’t cheat on your spouse. You should help the poor. Democracy is better than fascism. Can statements of value be verified? Jeffrey ate his victim (verifiable).

Jeffrey is evil (unverifiable)

Justifying Value Judgments

A rational process of weighing arguments and evidence that aims to determine whether or not there is good reason to accept a value judgment.

PACE Debates

“Some of my best friends

are clones”

Criteria for evaluating value judgments

Appeal to consequences: What are the likely results? How will people, the community etc. be affected? These are factual issues.

Appeal to principles: Show that the act or policy violates an established moral principle.

Moral principles

Inflicting pain on an unwilling subject for personal pleasure is immoral. This is what eating meat amounts to (since we can survive without it) Hence, eating meat is immoral.

It is worse to punish innocent people than to allow guilty people to escape punishment.

Is this a plausible moral principle?

Problems with value relativism

Implies that value judgments can’t be verified, but some value claims seem to be more well established than some factual claims. E.g..:

(a) Child abuse is wrong. (b) Child abuse is caused by the

abuser’s upbringing.

Reasoning about values

The aim is not absolute certainty, but establishing plausibility. This is not merely a question of personal or societal preference.

In this

villageadultery is a virtue. Just tell heryou’re from the east Sahara.

Religious Premises

Religious premises are always controversial because there is no agreed upon method for settling religious disputes.

Quotations from an ancient scripture may express profound wisdom. (Eg., the golden rule.)

However, ancient texts also reflect unexamined assumptions that arise in particular historical circumstances. Hence, a quote from the Bible can never constitute conclusive evidence for resolving a contemporary moral controversy.