Valid and Invalid arguments

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# Valid and Invalid arguments - PowerPoint PPT Presentation

Valid and Invalid arguments. Definition of Argument. Sequence of statements: Statement 1; Statement 2; Therefore , Statement 3 . Statements 1 and 2 are called premises . Statement 3 is called conclusion . Examples of Arguments. It is raining or it is snowing;

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## PowerPoint Slideshow about 'Valid and Invalid arguments' - MikeCarlo

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### Valid and Invalid arguments

Definition of Argument
• Sequence of statements:

Statement 1;

Statement 2;

Therefore, Statement 3.

• Statements 1 and 2 are called premises.
• Statement 3 is calledconclusion.
Examples of Arguments
• It is raining or it is snowing;

It is not snowing;

Therefore, it is raining.

• If x=2 then x<5;

x<5;

x is an even integer;

Therefore, x=2.

Argument Form
• If the premises and the conclusion

are statement forms

then the resulting form is called

argument form.

• Ex: If p then q;

p;

q.

Validity of Argument Form
• Argument form is valid means that

for any substitution of statement variables,

if the premises are true,

then the conclusion is also true.

• The example of previous slide is a

valid argument form.

Checking the validity of an argument form
• Construct truth table for the premises and the conclusion;
• Find the rows in which all the premises are true (critical rows);
• a.If in each critical row the conclusion

is true

then the argument form is valid;

b.If there is a row in which conclusion is false

then the argument form is invalid.

Example of valid argument form

p and q;

if p then q;

q. premisesconclusion

Critical row

Example of invalid argument form

p or q;

if p then q;

p. premisesconclusion

Critical row

Critical row

Valid Argument Forms
• Modus ponens: If p then q;

p;

q.

• Modus tollens: If p then q;

~q;

~p.

Valid Argument Forms

p or q.

• Conjunctive simplification: p and q;

p.

• Disjunctive Syllogism: p or q;

~q;

p.

• Hypothetical Syllogism: pq;

q r;

pr.

Valid Argument Forms
• Proof by division into cases:

p or q

p r

qr

r

~p c

p

A more complex deduction
• Knights always tell the truth,

and knaves always lie.

• U says: None of us is a knight.

V says: At least three of us are knights.

W says: At most three of us are knights.

X says: Exactly five of us are knights.

Y says: Exactly two of us are knights.

Z says: Exactly one of us is a knight.

• Which are knights and which are knaves?