Argumentation - Making Logical Connections
Summary
Argumentation involves constructing logical connections between statements, and the validity of an argument is determined by the logical consistency between the premises and the conclusion.
An argument is a series of propositions written as (p1 ∧ p2 ∧ ... ∧ pn) → q. Arguments consist of statements divided into two groups: statements before the word ‘thus,’ called premises (hypotheses), and statements after the word ‘thus,’ called conclusions. Arguments can be valid or invalid, where validity is not the same as truth.
Validity Check
An argument is valid if the conclusion is true when all hypotheses are true. Conversely, if the hypotheses are true but the conclusion is false, the argument is considered invalid (fallacy).
Logical Implications
If an argument is valid, it means that the conclusion logically follows from the hypotheses. In other words, it demonstrates that the implication (p1 ∧ p2 ∧ ... ∧ pn) → q is true, essentially showing a tautology. An invalid argument indicates flawed reasoning.
Practical Steps to Check Validity
To check if an argument is valid, follow these steps:
- Identify the hypotheses and the conclusion.
- Create a truth table showing the truth values for all hypotheses and the conclusion.
- Identify the critical rows where all hypotheses are true.
- In these critical rows, if all the conclusion values are true, the argument is valid. If there is at least one false conclusion value among the critical rows, the argument is invalid.