Definition of an argument: premises and conclusion
Valid argument: conclusion follows from premises
Sound argument: valid with true premises
Deductive arguments: valid/invalid with true premises
Syllogisms and Terms
Syllogism: two premises, one conclusion
Major/minor terms and premises: relationship in conclusion
Validity vs. soundness: soundness implies validity
Middle term: appears in both premises
Definitions
Essential definitions: convey necessary characteristics of concepts
Logical Relationships and Validity
Arguments assessed for valid structure
Syllogisms categorized by mood/figure
Use of contraries and contradictories
Application of Syllogisms
Validity of specific argument examples presented
Evaluation based on logical structure and terms used
Main Part
Aristotle’s Life and Work
Timeframe: 384-322 BC
Students: Peripatetics
School: Lyceum
Notable Pupil: Alexander the Great
Teacher: Plato
Zoology Book: The History of Animals
Logical Concepts and Syllogisms
Arguments
Definition: An argument consists of a series of statements (premises) that logically lead to a conclusion. To be effective, the relationship between premises and the conclusion must be clearly established.
Validity and Soundness
Valid Argument: If the structure of the argument is such that if the premises are true, the conclusion must necessarily be true. Validity does not depend on the truth of the premises, but on the logical structure.
Sound Argument: A sound argument is a valid argument with all true premises. If it is sound, the conclusion must also be true.
Deductive Arguments
A deductive argument can be valid or invalid. Validity ensures the conclusion logically follows from the premises, while soundness requires both validity and true premises.
A deductive argument can have true premises and still be invalid, meaning the conclusion does not logically follow.
Syllogisms
Structure:
A syllogism has two premises and one conclusion. For example:
Major Premise: All humans are mammals.
Minor Premise: All mammals are animals.
Conclusion: Therefore, all humans are animals.
Major and Minor Terms:
Major Term: The predicate of the conclusion.
Minor Term: The subject of the conclusion.
Middle Term: The term that appears in both premises but not in the conclusion, helping to connect them.
Types of Syllogisms:
Named according to the arrangement of terms:
Barbara: AAA syllogism.
Celarent: EAE syllogism.
Darii: AII syllogism.
Ferio: EIO syllogism.
Logical Relations
Entailment:
An entailment occurs when the truth of the premises guarantees the truth of the conclusion. If the premises are true, the conclusion cannot be false.
Contradictory Statements:
A statement’s contradictory denies that statement entirely. For example, the contradictory of “Some Presidents are former TV hosts” is “No Presidents are former TV hosts”.
Contraries:
Contraries are statements that cannot both be true at the same time, but can both be false. For instance, “All mass cults are dangerous” vs. “No mass cults are dangerous.”
Validating Arguments
Evaluation of Validity:
To test an argument’s validity, analyze the logical structure. For example, if the premises lead definitively to the conclusion by their logical relationship, the argument is valid.
Common Logical Fallacies:
An argument may appear valid but fail under scrutiny. Identifying logical fallacies, such as affirming the consequent or denying the antecedent, is critical.