Inductive Logic Overview

Study Notes

Inductive Logic

Logic is the study of evaluating whether premises adequately support a conclusion.
Two kinds of logic exist: deductive and inductive.
Deductive logic studies whether premises guarantee a conclusion.
Inductive logic studies whether premises make a conclusion probable.
Inductive logic evaluates arguments for strength and weakness.
A strong argument is probable if premises are true, the conclusion is true.
A weak argument is not probable if premises are true, the conclusion is true.
A cogent argument is a strong argument with all true premises.
An uncogent argument is either weak or a strong argument with at least one false premise.
Inductive strength comes in degrees, deductive validity does not.
Inductively cogent arguments can have false conclusions, deductively sound arguments cannot.
An inductively strong argument can strengthened or weakened by adding new premises, this does not affect deductive validity.
Statistical syllogism: x percent of A are B, c is an A, so c is a B (where x is between 50-100 exclusive).
The strength of an inductive argument is determined by statistical syllogism.
Percentage in the generalization is closer to satisfy the conclusion, the stronger the statistical syllogism.
Relevance of the reference class to the attribute class is important.
The fallacy of incomplete evidence (cherry-picking) occurs when one fails to consider all available relevant evidence.
If one knowingly omits relevant information, a logical error has been committed.
Arguments from authority:
- R sincerely asserts that S, so S.
- R is a source of information (person or reference work, dictionaries, encyclopedias, maps).
- The more reliable the source, the stronger the argument.
- Criteria for arguments from authority:
  - Is the authority reliable on the subject?
  - Are there other authorities that assert the opposite?
  - Is the authority being misquoted or misinterpreted?
Induction by enumeration: a conclusion about all members of a class is drawn from premises about observed members of that class.
Example: Eighty-two percent of a random sample of 200 UTECH students are sleep-deprived. Therefore, approximately 82% of UTECH students are sleep-deprived.
Criteria for induction by enumeration:
- Is the sample random?
- Is the sample an appropriate size? Larger samples are better (1500 = ±3%).
- Is the sample inaccurate due to psychological factors?

Mill's Methods

Mill's Method is inductive reasoning, to conclude A causes B.
The method of reasoning is not valid but provides significant support for a conclusion, meaning that it is likely A causes B.
"Causes" is ambiguous and sometimes refers to sufficient or necessary conditions.
Mill's methods for establishing "A causes B":
- Method of agreement: Identify a common factor present whenever the effect is present.
- Method of difference: Compare two cases, one with the effect and one without. If the possible cause is absent when the effect is absent, then there is support for that factor to be the cause.
- Joint method: Combining agreement and difference to create comprehensive analysis.
- Method of concomitant variation: One factor varies, another varies in corresponding way.
- Method of residues: Subtracting known causes from the effect in order to determine if there is any additional cause.

Scientific Way of Reasoning

Mill's Method leads to scientific reasoning:
- Describe the problem
- Formulate a hypothesis
- Test the hypothesis

Arguments from Analogy

Arguments from analogy, also known as analogical reasoning, are based on resemblance.
Structure:
- A is similar to B
- B has property P
- Therefore, A has property P
Examples:
- The Tempest and Midsummer Night's Dream are similar lengths.
- Parrots and humans both talk.
Assessing analogies:
- What are the similarities between A and B and are those similarities relevant to the issue?
- Are A and B dissimilar in some relevant aspects?
- Are there other things similar to B in relevant respects that don't have property P?

Additional Points

Analogies are often used in moral and legal reasoning.
The provided notes cover various aspects of inductive logic, including types of inductive arguments (statistical syllogisms, induction by enumeration, arguments from authority, and arguments from analogy).
The information also includes Mill's methods, scientific reasoning and crucial criteria.