1 / 12

Valid and Invalid arguments

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;

MikeCarlo
Download Presentation

Valid and Invalid arguments

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Valid and Invalid arguments

  2. Definition of Argument • Sequence of statements: Statement 1; Statement 2; Therefore, Statement 3. • Statements 1 and 2 are called premises. • Statement 3 is calledconclusion.

  3. 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.

  4. Argument Form • If the premises and the conclusion are statement forms instead of statements, then the resulting form is called argument form. • Ex: If p then q; p; q.

  5. 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.

  6. 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.

  7. Example of valid argument form p and q; if p then q; q. premisesconclusion Critical row

  8. Example of invalid argument form p or q; if p then q; p. premisesconclusion Critical row Critical row

  9. Valid Argument Forms • Modus ponens: If p then q; p; q. • Modus tollens: If p then q; ~q; ~p.

  10. Valid Argument Forms • Disjunctive addition: p; p or q. • Conjunctive simplification: p and q; p. • Disjunctive Syllogism: p or q; ~q; p. • Hypothetical Syllogism: pq; q r; pr.

  11. Valid Argument Forms • Proof by division into cases: p or q p r qr r • Rule of contradiction: ~p c p

  12. 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?

More Related