Lecture 3 (reasoning)

Question 1

argument reconstruction? 2

Answer 1

• the goals are the clarification of the message and understanding the implicit premises
• is a task of interpretation which requires a set of skills

Question 2

motivated reasoning? 1+1->3

Answer 2

• to reason motivation is needed
• there is different types of motivation: accuracy, defense, and impression motivation

Question 3

what is the principle of charity? 3

Answer 3

• if one is interested in finding out the truth, one should accept the best reconstruction of an argument which gives reasons for accepting or rejecting proposition
• bad arguments should be assessed critically
• context is important for the interpretation of an argument

Question 4

what are truth values?

Answer 4

true or false values assigned to propositions

Question 5

logical assessment: deductive validity? 3

Answer 5

• determine whether or not the premises support the conclusion
• a conclusion has deductive validity if it follows logically from the premises given (the conclusion must be true if the premises are true, and the conclusion must be false if the premises are false)
• if it’s nonsense but well connected nonsense it is valid

Question 6

how to judge validity? 2+1

Answer 6

• ignoring the actual truth-values of both the premises and the conclusion
• if by pretending all premises to be true the conclusion is still false the argument is invalid
• focusing only on relations between propositions

Question 7

descriptive claims vs prespective claims? 2+1

Answer 7

• descriptive claims: these claims state facts
• prespective claims: these claims express desires, norms, moral rules
• both can be true or false

Question 8

conditional propositions?

Answer 8

they give certain conditions which, if assumed true, lead to logical conclusions

Question 9

equivalence in conditional propositions? 3

Answer 9

• contraposition is the equivalence between “if P then Q” and “if not Q then not P”
• “if and only if” puts both parts of the proposition under mutual obligation, so “if P then Q” and “if Q then P” are both true if “if and only if” is used
• “unless” conditionals can be translated to “P if not Q” and “if not Q then P”

Question 10

different interpretations of “or”? 2

Answer 10

• inclusive sense: “P or Q” can only be false if both are false
• exclusive sense: “either P or Q” can be false if both are false or both are true

Question 11

antecedents and consequents? 2+2

Answer 11

• antecedents are the conditions that ensure the truth of the consequents
• If A then Q
• the antecedent is sufficient, but not necessary for the consequent
• the consequent is necessary but not sufficent for the antecedent

Question 12

argument trees? 1+2

Answer 12

• represent arguments in diagrams for clarification
• type 1: premises support conclusion individually, have an implicit connecting premise that explains why the conclusion follows from the premises
• type 2: has premises supporting the conclusion only in unison

Question 13

deductive soundness?

Answer 13

valid arguments with true premises that lead to a true conclusion

Question 14

Modus ponens?

Answer 14

• if P then Q
• P
  = Q

Question 15

Modus tollens?

Answer 15

• if P then Q
• not Q
  = not P

Question 16

Disjunctive syllogisms?

Answer 16

• P or Q
• not P
  = Q

Question 17

Arguments by cases?

Answer 17

• P or Q
• if P then R
• if Q then R
  = R

Question 18

Hypothetical syllogism/ Chains?

Answer 18

• if P then Q
• if Q then R
• if R then S
  = if P then S

Question 19

logical operators? 6

Answer 19

V: symbolizes inclusive “or”

upside down V: symbolizes “and”

back up L: symbolizes “not”

upside down A: denotes a rule applying for all of x (every x is such that if x is F then x is also G)

backwards E: denotes a rule applying to at least one of x (at least one object is both F and G)

parentheses can be used to assign priority considerations

Question 20

formal logic? 2

Answer 20

• abstracts from the argument and transforms it into an algorithmic formula
• uses logical particles to express the relations between objects (e.g. if-then, all)

Question 21

contradictories? 2

Answer 21

• if A is true but contradictory with B, then B is necessarily false
• use of venn diagrams to help understand this

Question 22

categorical syllogisms? 2

Answer 22

• are comprised of 2 premises as categorical propositions and a conclusion
• have 3 propositions that contain 3 terms in total