Unit 1 - Basic Concepts In Logic PDF

2 3 4 5 6 7 8 9 10 11 12 Scenarios with Valid Argument Invalid Argument different truth (Premises (Premises do not values guaranteeing guarantee conclusion) conclusion) True premises If Harry loved...

2 3 4 5 6 7 8 9 10 11 12 Scenarios with Valid Argument Invalid Argument different truth (Premises (Premises do not values guaranteeing guarantee conclusion) conclusion) True premises If Harry loved SOME Americans work in Dumbledore, then business. Donald Trump is True conclusion Harry was sad when an American. So, Donald Dumbledore died. So, Trump works in business. Harry was sad when Dumbledore died. False premises All sharks are birds. Every genius is a All birds are Mathematician. Pokemon False conclusion politicians. So, all is a Mathematician. So, sharks are politicians. Pokemon is a genius. False premises All dogs are ants. All Everything coloured is ants are mammals. So, red. Steve Harvey is a True conclusion all dogs are mammals. mortician. So, Steve Harvey is hilarious. True premises All dogs are animals. All cats are animals. Hence, False conclusion all dogs are cats. 13 Unknown All of the SOME hylidae are 14 15  Arguments Valid Arguments Invalid Arguments Valid Valid argum argumen All invalid ent t argument With With at all least one s are premis false premises unsound 16 17 18 19 20 21 22 23 24 25 26 27 Example #1 If Tom lives in Kingston, then Tom lives in Jamaica. Tom lives in Kingston. ---------------------------------------------------------------- So, Tom lives in Jamaica. 28  Affirming the Consequent (AC) If A then B Conditional If A then B A Antecedent B Unlike MP, AC is an invalid ---------- ---------- argument form. Consequent So, A So, B Counter-example Example #1 If Tom lives in Kingston then Tom lives in Jamaica. (T) Tom lives in Jamaica (T) If Tom lives in Kingston, then ------------------------------------------------------ Tom lives in Jamaica. Tom lives in Kingston. (F) Tom lives in Kingston. ----------------------------------------- A common mistake in formal reasoning (such as Tom lives in Jamaica. AC) is a formal fallacy. Example #2 If John is lying, then you are innocent and John’s mother is guilty. John is lying. --------------------------------------------------------------------------------- You are innocent and John’s mother is guilty. Both arguments have the valid form modus ponens. So, both arguments are valid. 29 Example #1 If Tom lives in Kingston, then Tom lives in Jamaica. It is not true that Tom lives in Jamaica. ----------------------------------------------------- It is not true that Tom lives in Kingston. 30 2. Modus Tollens (MT) Denying the Antecedent (DA) If A then If A then B Conditional Unlike MT, DA B Not B Negation of Consequent is an invalid Not A argument form. ---------- ------------ So, Not A Negation of Antecedent So, Not B Counter-example Valid argument, in the form of MT If Tom lives in Kings, then Tom lives in Ja. (T) Since the form is valid, this individual argument is valid by virtue of having the valid form. Tom does NOT live in Kingston. (T) ------------------------------------------------------- Example #1 So, Tom does NOT live in Jamaica. (F) If Tom lives in Kings, then Tom lives in Ja. Tom does NOT live in Jamaica. A common mistake in formal reasoning --------------------------------------------------------------- (suFormal fallacy. Invalid - So, Tom does NOT live in Kingston. Invalid argument, in the form of DA Example #2 If you are healthy or wealthy, then you are lucky. It is not true that you are healthy or wealthy. --------------------------------------------------------------------- You are not lucky. 32 3. Hypothetical Syllogism (HS) If A then B Conditional A conditional statement is also called a If B then C “hypothetical statement ”. Conditional ---------- So, if A A syllogism is a three-step argument, i.e., then C. Conditional an argument with two premises and one conclusion. Example #2 If Tom loves his dog, then Tom wants his dog to be happy. If Tom wants his dog to be happy, then Tom will walk his dog everyday. ------------------------------------------------------------------------------------------------ So, if Tom loves his dog, then Tom will walk his dog everyday. Example #3 If everybody has what they want and nobody has what they don’t want, then everybody is happy. If everybody is happy then I am happy. ------------------------------------------------------------------------------------------------------------------------------------------ If everybody has what they want and nobody has what they don’t want, then I am happy. Since both arguments have the valid form hypothetical syllogism, both arguments are valid. Disjunctive Syllogism can take two (2) forms: 34 4. Disjunctive Syllogism (DS) Either A or Either A or Disjunction The statement “A or B” is called B Not A B Not B Negation of One Disjunct the “ disjunction ” of the simpler ---------- ---------- statements “A” and “B”. So, B So, A The Other Disjunct The simpler statements “A” and “B” (which make up the Example #1 disjunction) are called the “ Either Tom is Mary’s friend OR Tom is my friend. disjuncts ”. Tom is NOT Mary’s friend. ---------------------------------------------------------- Tom is my friend. Example #2 Either Mary is happily married as well as busy at work OR she is having an affair. Mary is NOT having an affair. ----------------------------------------------------------------------------------------------------------- Mary is happily married as well as busy at work. In its inclusive sense, the disjunction “A or B” means “A or B or both”. In its exclusive sense, the disjunction “A or B” means “A or B but not both”. The argument form, disjunctive syllogism, is valid for both senses of the disjunction. NOTE : In this unit, we use the term “or” in its inclusive sense, unless otherwise specified. combines both conditional and disjunctive statemen 36 5. Constructive Dilemma (CD) Either A or Disjunction B If A, then C. Conditional If B, then D Conditional Example #1 ---------- So, C or D Disjunction Either I take a taxi or I take a bus. If I take a taxi then I will be too early. If I take a bus then I will be too late. -------------------------------------------------- So, I will be too early or I will be too late. Example #2 Either You keep your promise or you don’t keep your promise. If you keep your promise then you will be happy. If you don’t keep your promise then you will be unhappy. ------------------------------------------------------------------------------ You will be happy or you will be unhappy. PREM 1: If Jenny is a neurologist, then PREM 1: If A she is a doctor. then B. PREM 2: Jenny is NOT a doctor. PREM 2: Not B. CONCL: So, A. CONCL: So, Jenny is a neurologist. PREM 1: If Usain Bolt is less than 2 ft tall, then he is less than 3 ft tall. [True] PREM 2: Usain Bolt is NOT less than 3 feet tall. [True] CONCL: So, Usain Bolt is less than 2 feet tall. [False].