What constitutes a good argument? This video begins a series on symbolic logic. Before getting into symbolic logic proper, this video lays the groundwork for why it is useful to know something about formal logic.
To summarize, an argument consists of premises given in support of a conclusion. In a good argument, the premises actually support the conclusion, and they are demonstrably true or probable. There are two ways the premises may support the conclusion. One is to deductively imply the conclusion, such that the conclusion must be true if the premises are all true. This is called a deductively valid argument. The other is to inductively support the conclusion without actually guaranteeing its truth.
A deductively valid argument whose premises are all true is called a sound argument. The good thing about any sound argument is that its conclusion will be true. The only thing that can make a sound argument better is having premises that are evident or demonstrably true. Because it is good to use sound arguments, it is important to understand deductive validity, which is a formal property between premises and conclusion. By understanding deductive argument forms, it becomes easier to make and recognize good arguments.
The following argument forms are mentioned briefly at the end and discussed in more detail in subsequent videos:
Modus Ponens
P ⊃ Q, P. ∴ Q
Modus Tollens
P ⊃ Q, ~Q. ∴ ~P
Hypothetical Syllogism
P ⊃ Q, Q ⊃ R. ∴ P ⊃ R
Disjunctive Syllogism
P v Q, ~P. ∴ Q
Addition
P. ∴ P v Q
Constructive Dilemma
(P ⊃ Q) & (R ⊃ S), P v R
∴ Q v S
Destructive Dilemma
(P ⊃ Q) & (R ⊃ S), ~Q v ~S
∴ ~P v ~R
Simplification
P & Q. ∴ P
Conjunction
P, Q. ∴ P & Q
