TEST #2

Question 1

logical operators and argument forms (ill-formed argument, invalid argument, non-cogent, cogency, conjunction, contraposition, universal modus ponens, biconditional, hypothetical syllogism) ( + original arguments using them)

Question 2

what are invalid forms of arguments

Answer 2

the truth of the premises don’t guarantee the truth of the conclusion

denying the antecedent

affirming the consequent

Question 3

truth vs rational strenght of premises

Answer 3

• evaluating the truth- value of a premise and conclusion is different from evaluating the rational strength of arguments
• it’s one thing to ask whether statements are true or not, but its another to ask: if those statements were true, what would that mean for the conclusion?

Question 4

standard form

Answer 4

STANDARD FORM: arguments written out as consecutively numbered premises and conclusions, with justifications for each line in the argument stated
- provides a clear reconstruction of the argument (interpreting and rewriting an argument), which is essential for evaluating the argument (deciding whether or not the argument is a good argument)

benefits of standard form:
1) helps exclude any extra non-argument material
2) helps include unstated/missing premises
3) helps encourage clearer and precise formulation of premises and conclusion
4) helps make discussion of argument more convenient since each element is numbered

components:
- individually numbered premises and conclusion
- only one premise or conclusion per line
- the word “therefore” or equivalent symbol before the conclusion
- horizontal line between premises and conclusion
- brackets of the conclusion to show which premise the conclusion is supported by

Question 5

deductive argument

Answer 5

DEDUCTIVE ARGUMENT: aims to provide a logically conclusive support for the conclusion

• it is impossible for the premises to be true, and the conclusion false
• shows that if the premises are true, the conclusion has to be true

Question 6

well-formed argument

Answer 6

WELL-FORMED ARGUMENT: an argument is well-formed if and only if the argument is valid or cogent
- arguments whose conclusion does logically follow from its premises

• valid and cogent arguments

Question 7

validity / a valid argument

Answer 7

• validity is a feature an argument either has, or doesn’t have
• in logic, validity applies only to arguments and the logical relationship between the premises and conclusions, not the premises or conclusion individually or their truth value
• a valid argument can have false premises and a false conclusion
• a valid argument is considered to be truth-preserving ( if premises are true, conclusion is true)

VALIDITY: an argument is deductively valid if and only if it is impossible for all the premises to be true, and the conclusion false

• A1) IF the premises are true, then the conclusion must be true as well
• A2) the conclusion logically follows the premise
• A3) in a world where the premises are all true, the conclusion is GUARANTEED to be true as well

Question 8

invalid argument

Answer 8

INVALID ARGUMENT: it is possible for the premises to be true, and the conclusion to be false

• the premises dont guarantee the truth if the conclusion

Question 9

validity test

Answer 9

VALIDITY TEST: the way in which we test if an argument is valid or not

1) Assume that the premises are all true. Would the conclusion have to be true as well?
2) If the answer is “yes” then the argument is valid. If the answer is “no” then the answer is invalid

Question 10

is validity related to truth-value?

Answer 10

• No. a valid argument can have false conclusion and false premises.
• No. We don’t even have to know the truth-value of the premises and conclusion. as long as we evaluate the logical relationship between the premises and conclusion

-the point of validity is not whether each premise/conclusion is true or false, but rather that if the premises were true, would thy guarantee the truth of the conclusion?

Question 11

sentential connectives + 5 types (dont explain)

Answer 11

SENTENTIAL CONNECTIVES: logical system in which sentences are not broken down into smaller units
- the letters stand for whole sentences
- use of UPPERCASE LETTERS
- the whole conclusion is found inside the premise

COMPOUND STATEMENTS: combination of two or more simpler sentences (we abbreviate them by using A and B)

1) conjunction
2) disjunction
3) negation
4) conditional
5) biconditional

Question 12

predicate logic

Answer 12

opposite of sentential connectives

PREDICATE LOGIC: logical system in which sentences are broken down in subunits such as subjects and predicates (descriptive phrases)

SMALL LOWERCASE LETTERS (x): particular person or thing
BIG UPPERCASE LETTERS (A, B, C): descriptive phrases/characteristics

Question 13

conjunction (sentential connective)

Answer 13

1) CONJUNCTION

• P and/& Q
• they are compound statements composed of two parts call the conjuncts
• ex. Today is tuesday and I am in class.”

Question 14

disjunction (sentential connective)

Answer 14

2) DISJUNCTION

• P or/v Q
• they are compound statements composed of two parts called the disjuncts
• ex. either the picnic was cancelled or it was sunny

Question 15

negation (sentential connective)

Answer 15

3) NEGATION

• Not P / ~ P
• saying the statement P is false/not the case
• ex. it is not sunny

Question 16

conditional (sentential connective)

Answer 16

4) CONDITIONAL

• If P, then Q / If P -> Q
• if P happens, Q is guaranteed to happen (Q depends on P) (P guarantees Q)
• conditionals do not assert that either the antecedent or the consequent is true. they merely state a logical relationship between P and Q
• they are compound statements composed of two parts:
• ANTECEDENT: what follows the “if”
• CONSEQUENT: what follows the “then”
• ex. if it rains, then the picnic will be cancelled

conditionals are not always expressed in their logical form
- ex. since your lease expired, the landlord is free to raise the rent
- ex. being a teenager means you have lots of problems
- ex. anyone who likes logical is a fool
- ex. the truth of evolution implies the falsity of the Bible
- ex. whenever i drink coffee, i get antsy

“IF” introduces the antecedent, no matter where it occurs in a statement
- ex. “I’ll find the material difficult IF i skip a class”

• “ONLY IF” introduces the consequent, no matter where it occurs in a statement
• ex. “I will buy the giant TV ONLY IF the price drops”
• this should be written as Q -> P

Question 17

biconditional (sentential connective)

Answer 17

5) BICONDITIONAL

• P if and only if Q
• if P then Q, if Q then P
• ex. you can enter the club if and only if you have legitamate ID

Question 18

11 valid argument patterns (just list)

Answer 18

VALID ARGUMENT PATTERNS: common patterns shared by many deductive arguments
- help determine if an argument is deductive
- help determine if an argument is valid or invalid

• this is a means to an end: evaluating an argument

1) argument by elimination
2) conjunction
3) simplification
4) affirming the antecedent (modus ponens)
5) denying the consequent (modus tollens)
6) hypothetical syllogism
7) contraposition
8) universal modus ponens
9) universal modus tollens
10) universal hypothetical syllogism
11) universal ruling out

Question 19

1) argument by elimination

Answer 19

1. P v Q
2. ~ P
   :. 3. Q
   (from 1, 2)
3. P v Q
4. ~ Q
   :. 3. P (from 1, 2)

ex. 1. either it will rain today or it will snow today
2. it will not snow today
therefore,
.: 3. it will rain today

Question 20

2) conjunction

Answer 20

1. P
2. Q
   :. 3. P & Q

ex, 1. I have a dog
2. I have a cat
therefore,
:. 3. I have a dog and a cat

Question 21

3) simplification

Answer 21

1. P & Q
   .: 2. P (from 1)
2. P & Q
   .: 2. Q (from 1)

ex. 1. i have a dog and a cat
therefore,
.: 2. i have a dog

Question 22

4) affirming the antecedent (modus ponens)

Answer 22

1. If P, then Q
2. P
   therefore,
   .: 3. Q (from 1, 2)

ex. 1. if tmu is a good university, then many students apply there
2. tmu is a good university
therefore,
:. 3.many students apply there

Question 23

5) denying the consequent (modus tollens)

Answer 23

1. if P, then Q
2. ~ Q
   therefore,
   .: 3. ~ P

ex. 1. if Jim ate a burger, then he wore red pants
2. Jim did not wear red pants
3. Jim did not commit the murder

Question 24

6) hypothetical syllogism

Answer 24

1. If A, then B
2. If B, then C
   .: 3. If A, then C (from 1, 2)

ex. 1.
2.
.: 3.

Question 25

7) contraposition

Answer 25

1. If P, then Q .: 2. If ~ Q, then ~ P (from 1) ex. 1. if Donald Trump loses the election, then Kamala Harris wins .: 2. if Kamala Harris doesn't win, then Donald Trump doesn't lose the election (from 1 by contraposition)

Question 26

8) universal modus ponens

Answer 26

1. All A's are B's 2. x is an A 3. x is a B ex. 1. all students are smart 2. Omar is a student .: 3. Omar is smart (from 1 and 2 by universal modus ponens)

Question 27

9) universal modus tollens

Answer 27

1. All As are Ba 2. x is not a B 3. x is not an A ex. 1. All students are hard-working 2. Omar is not hard-working .: 3. Omar is not a student

Question 28

10) universal hypothetical syllogism

Answer 28

1. All A's are B's 2. All B's are C's .: 3. All A's are C's ex. 1. All whales are mammals 2. All mammals are black .: 3. All whales are black (from 1 and 2 by universal hypothetical syllogism)

Question 29

11) universal ruling out

Answer 29

1. No As are Bs 2. x is an A .: 3. x is not a B ex. 1. no children are well-behaved 2. Jacob is a child .: 3. Jacob is not well-behaved

Question 30

invalid argument patterns (argument of elimination)

Answer 30

1. P or Q 2. P 3. Q 1. P or Q 2. Q 3. P (left vs righty ex.) ------------------------------------- 1. P v Q 2. P 3. ~ Q 1. P v Q 2. Q 3. ~ P (left or righty committed the crime example) (we cannot exclude that (ex.) righty didnt help commit the crime) in logic we don't use exclusive "or", but the inclusive "or"

Question 31

invalid argument pattern (denying the antecedent)

Answer 31

1. if P, then Q 2. ~ P .: 3. ~ Q ex. 1. if Einstein is smart, then he has white hair 2. Einstein is not smart .: 3. Einstein does not have white hair

Question 32

invalid argument pattern (affirming the consequent)

Answer 32

1. If P, then Q 2. Q .: 3. P ex. 1. If Einstein invented the computer, then he's a genius 2. Einstein is a genius .: 3. Einstein invented the computer (the premises don't guarantee the truth of the conclusions)

Question 33

invalid argument patterns (hypothetical syllogism)

Answer 33

1. If A, then B 2. If C, then B .: 3. If A, then C 1. If A, then B 2. If B, then C .: 3. If B, then C 1. If B, then A 2. If C, then B .: 3. If B, then A 2. If C, then B .: 3. If A, then C 1. If A, then B 2. If D, then C .: 3. If A, then C

Question 34

invalid argument patterns (universal ruling out)

Answer 34

1. All A's are B's 2. x is not an A 3. x is not a B ex. 1. All students are kind 2. Jacob is not a student .: 3. Jacob is not kind -------------------------------------- 1. All A's are B's 2. x is a B .: 3. x is an A ex. 1. All students are kind 2. Jacob is kind 3. Jacob is a student

Question 35

inductive arguments

Answer 35

INDUCTIVE ARGUMENTS: aims to give probable, not conclusive, support for the conclusion - shows that if the premises are true, the conclusion is likely true

Question 36

cogency

Answer 36

COGENCY: an argument is cogent if and only if it is invalid, but all the premises give good/probable reason for the conclusion - requiring no background information/assumptions - if the premises are true, it is likely/probable for the conclusion to be false - cogent arguments dont have to have true premises or true conclusions; what matters is their logical relationship - an argument is cogent if and only if it is invalid, but if all the premises are true, the conclusion is likely to be true - a cogent argument is invalid because even if the premises are true, they don't guarantee the truth of the conclusion

Question 37

cogent argument

Answer 37

ex. 1. Quitting smoking tens to improve one's health 2. Mary has quit smoking .: 3. Mary's health will improve (it is not guaranteed, but probable that her health will improve) ex. 1. Boris is a student at NYU 2. Most NYU students voted .: 3. Boris voted ex. 1. most chairs have 10 legs 2. Justin Trudeau is a chair therefore, probably, .: 3. Justin Trudeau has 10 legs this is an invalid argument because it is possible for the premises to be true, and the conclusion to be false this is a cogent argument because the premises make it likely for the conclusion to be true

Question 38

non-cogent argument

Answer 38

even if the premises are true, they don't make it likely for conclusion to be true ex. 1. a few police officers are corrupt 2. Jim is a police officer 3. Jim is corrupt (Jim could be a part of the rest of the police officers who aren't corrupt) this is an invalid argument because it is possible for the premises to be true and the conclusion false. this is a non-cogent argument because even if the premises were true, they don't make it likely for the conclusion to be true.

Question 39

the cogency test

Answer 39

1) imagine or suppose that the premises are all true. Is the conclusion likely to be true as well? 2) if the answer is "yes" its cogent if the answer is "no" its non-cogent

Question 40

validity vs cogency vs non-cogency (key words) (questions to ask) (valid or invalid)

Answer 40

validity: - "always" "all" - if the premises were true, is it guaranteed that the conclusion is true as well? - always valid - both validity and cogency are a feature that an argument either has or doesnt have. they both depend on the logical relationship between the premises and the conclusion. cogency: - "most of," "a lot of," - if all the premises are true, would that make the conclusion probable? non-cogency: - "few" - the truth of the premises neither guarantees the truth of the conclusion nor makes the conclusion probable - invalid

Question 41

valid arguments can have:

Answer 41

false premises, false conclusion false premises, true conclusion true premises, true conclusion (remember, in valid arguments it is impossible for the premises to be true and the conclusion false)

Question 42

cogent arguments can have:

Answer 42

true premises, true conclusion true premises, false conclusion one or more false premises, true conclusion one or more true premises, false conclusion (remember, in cogent arguments, it is possible for the premises to be true and the conclusion false)

Question 43

common patterns of cogent arguments

Answer 43

1. most As are Bs 2. x is an A therefore, probably, .: 3. x is a B ex. 1. most professors have PHDs 2. Kraay is a professor therefore, probably, .: 3. Kraay has a PHD ----------------------------------------- 1. x is an A 2. x is a B 3. most ABS are Cs therefore, probabaly, .: 4. x is a C (from 1, 2, 3) ex. 1. Kraay is right-handed 2. Kraay is a professor 3. Most right-handed professors are nice. therefore, probabaly, .: 4. Kraay is nice

Question 44

common patterns of non-cogent arguments

Answer 44

1. most As are Bs 2. x is not an A therefore, probabaly, .: 3. x is not a B ex. 1. most professors are nice 2. Kraay is not a professor therefore, probably, .: 3. Kraay is not nice (just because Kraay is not a professor does not make it likely that Kraay is not nice) --------------------------------- 1. most As are Bs 2. x is a B therefore, probably, .: 3. x is an A ex. 1. most professors have beards 2. Kraay has a beard therefore, probabaly, .: 3. Kraay is a professor

Question 45

ill-formed arguments

Answer 45

ILL-FORMED ARGUMENTS: arguments that are neither valid not cogent (they are invalid and not cogent) - the premises do not guarantee that the conclusion is true or even probable - ill-formed arguments are usually based on "assumptions" - ex. 1. My teacher's name is John 2. My teacher is a male

Question 46

patterns of ill-formed arguments

Answer 46

1. Most As are Bs 2. x is not an A 3. x is not a B 1. most police officers are funny 2. Jared is not a police officer 3. Jared is not funn ---------------------------------------- 1. Most As are Bs 2. x is a B 3. x is an A 1. Most robins can fly 2. Tweet can fly 3. Tweet is a robin

Question 47

incomplete arguments

Answer 47

INCOMPLETE ARGUMENTS: arguments that are ill-formed but can be made cogent or valid by adding one obvious premise

Question 48

summary notes about cogency and validity

Answer 48

validity: - impossible for the premises to be true and the conclusion false - the truth of the premises guarantee the truth of the conclusion cogency: - possible for the premises to be true and the conclusion false - the truth of the premises make it probable that the conclusion is true

Question 49

reminder

Answer 49

WELL-FORMED ARGUMENTS: an argument is well-formed if and only if the argument is valid or cogent ILL-FORMED ARGUMENTS: - (the truth of the premises neither guarantees nor makes probable the truth of the conclusion)

Question 50

degrees of validity vs degrees of cogency

Answer 50

validity does not come in degrees - an argument is either 100% valid, or invalid - like a light switch - an argument cannot be more valid than another - if all the premises are true, then there's no possibility for the conclusion to be false, and degrees require levels of possibility - truth does not come in degrees, rather, cogency and possibility does cogency (probability) comes in degrees - an argument can be more or less cogent than another argument - the premises of one cogent argument support the conclusion more strongly than do the premises of another argument - like a fluid light switch - ex. 40% rain vs 90% rain - ex. "most students voted" is more cogent than "some students voted"