Argument Analysis

 

In philosophy, an argument is a connected series of statements, including at least one premise, intended to demonstrate that another statement, the conclusion, is true. The statements that serve as premises and conclusions are sometimes referred to as “propositions.” Statements (or propositions) are declarative sentences.

Propositional logic plays the main role in argument analysis. Propositional logic deals with logical relationships between propositions taken as wholes. Propositional logic is interested in how the truth value of compound claims depends on the truth value of the individual claims that make it up. The basic compound claims are conjunctions, disjunctions, conditionals and contradiction. In this blog let’s see about conditionals.

CONDITIONALS

Conditionals are the states in the form of “if A, then B”. Compound statement A is called the antecedent, and B is the consequent. If its antecedent is true, its consequent is also true; any conditional with a true antecedent and a false consequent must be false.  For any other combination of true and false antecedents and consequents, the conditional statement is true.

 Ex: - If I study hard then I will pass the exam.
Here,  Antecedent = I study hard.
          Consequent = I will pass the exam.

Here we are not asserting that antecedent is true or the consequence is true. What we assert is a logical relationship with antecedent and consequent.

A	B	IF A THEN B
T	T	T
T	F	F
F	T	T
F	F	T

Unless

Let’s consider the sentences with the word ‘Unless’

Ex: - I won’t give you my vehicle unless you pay for the gas.

Here we can change the sentence into the know standard form.
If you don’t pay for the gas then I won’t give you, my vehicle.

B UNLESS A = IF NOT-A THEN B

Only If

Let’s move to the sentences with ‘Only if’

Ex: - I will let you go only if you tell the truth.

Only if plays the dramatic role because here the antecedent is the claim which is before the only if.
Antecedent = I will let you go
Consequent = you tell the truth

In the standard form,
If I will let you go then you should tell the truth.

A ONLY IF B = IF A THEN B

Bicondional Statement

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

A IF AND ONLY IF B = (IF B THEN A) AND (IF A THEN B)

Ex: - You can overcome anything, if and only if you love something enough.

A	B	A IF AND ONLY IF B
T	T	T
T	F	F
F	T	F
F	F	T

Necessary and Sufficient

Let’s understand this concept by an example

Ex: - If I become rich, then I’ll be happy
Here, IF A THEN B = A is sufficient for B
          IF B THEN A = A is necessary for B

A if B

So, what is ‘A if B’?

Ex: - If you go out then buy me some snacks = Buy me some snacks if you go out.

IF A THEN B = B IF A

The Contrapositive

Let’s directly jump into the example.

Ex: - Conditional: If I live in Colombo then I live in Sri Lanka.
         Contrapositive: If I don’t live in Sri Lanka then I don’t live in Colombo.

IF A THEN B = IF (NOT-B) THEN (NOT-A)

The Contradictory

We will analyze an example.

Ex: - Conditional: If I pay for dinner then you’ll pay for drinks.
         Contradictory: - I pay for dinner but you don’t pay for drinks.
                                   I pay for dinner and you don’t pay for drinks.

NOT- (IF A THEN B) = A BUT (NOT-B) = A AND (NOT-B)

A	B	NOT- (IF A THEN B)
T	T	F
T	F	T
F	T	F
F	F	F