Understanding Inductive Arguments

• Inductive arguments don't prove a conclusion; they support it by raising the probability of the conclusion being true if the premises are true.
• Consider this argument:
• Premise: Ama lives in Ghana.
• Conclusion: Therefore, she uses an umbrella regularly.
• Living in Ghana increases the likelihood that Ama uses an umbrella regularly.
• Consider also:
• Premise: People in Tamale spend a lot of time in the sun.
• Conclusion: A tanning salon won't do well there.
• The premise raises the probability of the conclusion's truth.

Nature of Inductive Reasoning

• Conclusions are claimed to be true based on the probability established by the premises.
• Premises provide probable reasons for the conclusion.
• Premises offer varying degrees of probable grounds for the conclusion.
• Unlike deductive arguments where true premises guarantee a true conclusion, in inductive reasoning, all premises can be true while the conclusion is false.
• Inductive conclusions do not necessarily follow the premises.
• Premises may be strong but not conclusive.
• Inductive arguments, unlike deductive ones, are neither true/false nor valid/invalid.

Evaluation of Inductive Arguments

• Evaluated on a spectrum: good or bad, strong or weak, convincing or unconvincing.
• Evaluation depends on how well the premises support the conclusion.
• Good arguments offer strong, convincing probable grounds for the conclusion.
• For example:
• It rained in Accra on September 5th in 2020, 2021, and 2022.
• Therefore, it will/may rain in Accra on September 5th, 2023.
• It supplies good, strong, and convincing grounds for the conclusion's probability.
• Another example:
• The cow in Akafor’s house is brown.
• The cow in Nicholas’ house is brown.
• Therefore, all cows are brown.
• Even if the premises are true, certainty about the conclusion is impossible.

Types of Inductive Reasoning

• Inductive Generalization
• Enumerative/Statistical Inductive Argument
• Causal Argument
• Argument from Analogy
• Inductive Reasoning by Signs
• Inductive Reasoning by Authority

Inductive Generalization

• A generalization attributes a characteristic to most or all members of a class. Examples:
• All wild grizzly bears in the United States live west of the Mississippi River.
• Most college students work at least part-time.
• Men are so unromantic!
• An inductive generalization argues that a generalization is probably true based on information from some members of that class.
• For example:
• Meeting friendly people from Wa six months ago, four months ago and two months ago leads to the conclusion that most people from Wa are friendly.
• Inductive generalizations always lead to probable, not certain, conclusions.

Predictive Argument

• A prediction is a statement about a future event.
• A predictive argument defends a prediction with reasons.
• Predictive arguments are common in inductive reasoning.
• Examples:
• It has rained in Accra every February since records began, so it will probably rain in Accra next February.
• Most U.S. presidents have been tall, so the next U.S. president will probably be tall.
• Arguments with predictions are inductive because future events are not absolutely certain.

Argument from Authority

• This asserts a claim and supports it by citing a presumed authority or witness.
• Examples:
• More Americans die of skin cancer each year than die in car accidents because a doctor said so.
• There are bears in these woods because a neighbor said he saw one.
• Because the accuracy of an authority or witness cannot be guaranteed, these arguments are generally treated as inductive.

Causal Argument

• Causal argument asserts or denies a cause-and-effect relationship.
• Examples:
• Network is down because I can’t log on.
• Rashid isn’t allergic to peanuts because I saw him eat them on a flight from Kumasi.

Statistical/Enumerative Argument

• Statistical arguments rely on statistical evidence where a percentage of a group or class shares a characteristic.
• Examples:
• Eighty-three percent of St. Stephen’s students are Adventists, so Beatrice, a student there, is probably an Adventist.
• Doctors say condoms have a 2-3% annual failure rate, even when used correctly and consistently, so condoms are not a complete protection from pregnancy or STDs.
• Statistical arguments are inductive because statistical evidence supports claims presented as probable.

Argument from Analogy

• Analogy compares two or more things to show they are alike in some way.
• Example: Habits are like a cable. We weave a strand of it every day and soon it cannot be broken. (Horace Mann)
• Conclusion relies on a comparison or similarity between two or more things.
• Example:
• Bill and Mary, graduates of UniMAC are bright, energetic, and dependable. So Paula, also a graduate of UniMAC, will likely be bright, energetic, and dependable, too.

Inductive Reasoning by Signs

• Uses observation of symptoms/conditions to prove a condition exists.
• Example:
• Headache, bodily pains, cold, fever, loss of appetite, weakness and joint pains are general symptoms of malaria. Goodluck was diagnosed with malaria and had those symptoms. So someone with those symptoms likely has malaria.

Inductive Generalization (revisited)

• Searches for predictable patterns in details.
• Draws general conclusions from specific premises.
• Example:
• Three lecturers at GCTU are financially wealthy, therefore all lecturers at GCTU holding PhD degrees are financially wealthy.

Reasoning by Analogy (revisited)

• This argument observes fundamental similarities between similar or dissimilar cases.
• Conclusion depends on the similarity's existence.
• Example:
• The Akan in Ghana have A, B, C, and D attributes and Z attributes. The Akan in La Cote d’Ivoire have A, B, C, and D attributes. Therefore, the Akan in La Cote d’Ivoire have Z attribute.

Inductive Reasoning by Signs (revisited)

• Uses observation of symptoms/conditions to prove a condition exists.
• Example:
• Headache, bodily pains, cold, fever, loss of appetite, weakness and joint pains are general symptoms of malaria. Aku and Juliana have those symptoms, so they likely have malaria.

Enumerative Inductive Argument (revisited)

• Moves from general premises to a particular conclusion.
• Constructs a hypothesis based on provided evidence.
• Conclusion comes from statistical data or findings. Used in social sciences and everyday conversations.
• Example:
• In Ghana, 80% of university graduates don’t get jobs after national service. Agnes is a Ghanaian graduate from 2022, so Agnes is likely not to obtain a job immediately after her national service.
• Though the above argument shows a high probability of Agnes not getting a job, it is not certain.
• There is a 20% chance she could be one of the lucky people to get a job

Enumerative Inductive Argument: Example with Rats

• Data:
• The first rat fed with charcoal-burnt cow meat developed a brain tumour in 200 days.
• The second rat fed with charcoal-burnt chicken meat developed a brain tumour in 150 days.
• The third rat fed with charcoal-burnt goat meat meat developed a brain tumour in 80 days.
• The fourth rat fed with charcoal-burnt mutton meat developed a brain tumour in 65 days.
• The sixth rat fed with charcoal-burnt cow meat and mutton developed a brain tumour in 260 days.
• The 7th rat fed with charcoal-burnt cow meat and mutton did not develop a brain tumour.
• The 8th rat fed with charcoal-burnt cow meat chicken developed a brain tumour in 200 days.
• The 9th rat fed with charcoal-burnt cow meat and chicken did not develop a brain tumour.
• The 10th rat fed with charcoal-burnt mutton and goat meat developed a brain tumour in 90 days.
• Summary: Eight of the 10 rats studied developed brain tumors.
• Conclusion: 80% of rats fed on charcoal-burnt meat develop brain tumours.
• Statistical hypotheses need not always start with specific statements and conclude with general conclusions; they can also start with a general premise and end with a specific conclusion.
• Example:
• 90% of GCTU students play football at least once a week.
• Nyamekye is a GCTU student.
• Therefore, Nyamekye plays football at least once a week.
• It can start with particular premises and end with a particular or/and general conclusion.

Inductive Reasoning/Argument by Causation (revisited)

• Observation of a connection between events leads to a conclusion that one event produced the other.
• Establishes a probable causal connection between two events.
• The first is the cause or antecedent and the second is the effect or consequence.

Inductive Reasoning by Authority (revisited)

• Reliance on the credibility of a source justifies acceptance of a claim.
• Example: Professionals and athletes rely on arbitrations.
• Appeals to authority provide justification for a conclusion's acceptance.