Propositional logic- important things

Question 1

what’s the form of modus ponens, aka affirming the antecedent, is it valid or invalid?

Answer 1

p ->q
p /q
-valid

Question 2

what is the form of modus tollens, aka denying the consequent, is it invalid or valid?

Answer 2

p -> q
~q /~p
-valid

when you deny the consequent, you must’ve denied the antecedent. ex: If I pass the test then I pass the course, I didn’t pass the course, so I must not have passed the test

Question 3

what is the form of Hypothetical syllogism, is it invalid or valid?

use abc

Answer 3

A ->B
B -> C / A -> C
-valid

Question 4

what is the form of disjunctive syllogism, aka denying the disjunct, is it invalid or valid?

Answer 4

p v q
~p / q
-valid

(you deny the first disjunct, statement before v, so the other one must be accepted), ex: you can have either pie or cake, no pie, cake it is!

Question 5

what is the form of constructive dilemma, is it invalid or valid?

Answer 5

Form has 3 premises:
-2 conditionals (what di in dilemma is for)
-1 disjunction
A v B
A -> C
B -> D /C or D
-valid

Question 6

what’s the form of affirming the consequent, is it invalid or valid?

Answer 6

A -> B
B/ A
-invalid

2nd premise, affirms consequent (no ~)

Question 7

what’s the form of absorbtion, is it invalid or valid?

Answer 7

p -> q /p -> (p & q)
-valid

Question 8

what’s the form of denying the antecedent, is it invalid or valid?

Answer 8

p -> q
~p /~q
-invalid

Question 9

what’s the form of simplification, is it invalid or valid?

Answer 9

p & q / p
-valid

Question 10

what’s the form of conjunction, is it invalid or valid?

Answer 10

p
q / p & q
-valid

Question 11

what’s the form of addition, is it invalid or valid?

Answer 11

p / p v q
-valid

q could be anything (even unrelated)

Question 12

what’s the form of affirming the disjunct, is it valid or invalid?

Answer 12

p v q
p / ~q
-invalid with the inclusive sense (one or the other or both)
-valid with the exclusive sense (one of the other not both)

(if you affirm the first disjunct, you have to deny the other, bc one or the other)

Question 13

describe the bull metaphor for dilemmas

Answer 13

-each conditional (if, then) represents a “horn”, the disjunction (or) is the “bull”

Question 14

what are the 4 strategies of reply to dilemma, describe them

Answer 14

1. Grasping the horn - you accept result of one of the conditionals, whichever you think the better option is (there’s two possible options here could grab either horn-conditional), always works
2. Charging the bull, counter dilemma, recycle the first part of the argument before the therefore, but make the conditionals both possible good outcomes, always works
3. Throwing sand/avoiding the charge- red herring strategies of distraction that don’t have to do with dilemma
4. Going between the horns -best strategy, doesn’t works when the disjunction is not just a single thing or not that thing, (A or ~A), there must be another possibility that’s more reasonable

Question 15

what’s the best strategy of reply to dilemma, how do you know if it’s possible?

Answer 15

• going between the horns
• first ask yourself: is this dilemma formulated as ‘a single thing or not that thing’, if it is it’s a tautology, always true and doesn’t allow this, if not it allows going between the horns, another possibility that’s more reasonable (deny disjunction don’t have to do A or B)