Test 2

Question 1

Deductive Argument

Answer 1

intends to provide logically conclusive support for the conclusion

Question 2

Inductive Argument

Answer 2

premises are intended to give probable support (not conclusive support) for the conclusion

Question 3

Deductive Validity

Answer 3

an argument is deductively valid if and only if it’s not possible for the premises to be true and the conclusion false

Question 4

Validity Test

Answer 4

1. Imagine/ Suppose that the premises are true
2. Ask “would the conclusion have to be true as well?”
   If yes, the argument is valid
   If no, the argument is invalid

A valid argument is not concerned with truth but with how well the premises support the conclusion

Question 5

5 Sentenial Connectives

Answer 5

Conjunction
Disjunction
Negation
Conditional
Biconditional

Question 6

Conjunction

Answer 6

Conjunction is any statement of the form:
P and Q
or
P & Q

Conjunctions are compound statements composed of 2 parts called conjuncts

Examples:
It is sunny and today is Thursday
I have a cat and a dog

Question 7

Disjunction

Answer 7

Disjunction is any statement of the form:
Either P or Q
or
P v Q

Examples:
Either the picnic was cancelled or it was sunny
Either Jones committed the murder or the butler did

Question 8

Negation

Answer 8

Negation is any statement of the form:
not P
or
~ P

To negate a statement is to say it is false or not that way

Examples:
it is not sunny
Critical Thinking is not a hard class

Question 9

Conditional

Answer 9

Conditional is any statement In the form of:
if P then Q
or
P –> Q

Examples:
if it rains, then the party will be cancelled
if Jones committed the murder, the butler is innocent

Conditionals are compound statements, composed of two parts.
1. Antecedent - what follows the word if
2. Consequent - what follows the word then

Note:
- Conditionals do not assert the antecedent or consequent is true (if then statement by itself is not an argument)
- Conditionals are not always expressed in their logical form, for example:
Anyone who likes logic is a fool
could be said as
if you like logic, then you’re a fool

Question 10

Slightly Tricky Point on Conditionals
If VS Only if

Answer 10

the word if, by itself, introduces the antecedent no matter where it occurs in a statement.
“if I skip class, I’ll find the material difficult”
“I’ll find the material difficult if I skip class”
These are equivalent and should be written as S –> D

Antecedent = Before
if implies that the antecedent must occur first AND THEN the consequent.

the expression only if introduces the consequent, no matter where it occurs in a statement.
“only if the price drops will I buy the giant TV”
“I will buy the giant TV only if the price drops”
These are equivalent and should be written as B –> P

Consequent = After
only if implies that after this happens, then this

Question 11

Biconditional

Answer 11

Biconditional is statement of the form:
P if and only if Q
(if P then Q) and (if Q then P)
Example:
you can enter the club if and only if you have legit ID

Question 12

11 Patterns of Valid Arguments and Several Invalid Patterns

Answer 12

understanding these patterns helps to determine…
a) whether an argument is deductive
b) whether it is valid or invalid

Question 13

1. Argument By Elimination

Answer 13

1. P or Q
2. not P
   ____________
3. .: Q. (from 1,2)

INVALID FORM:
1. P or Q
2. P
___________
3. .: not Q
In ordinary language, we use exclusive “or” BUT in logic, we use inclusive “or”

Question 14

Symbols

Answer 14

~ = NOT
v = OR
–> = THEN
& = AND

Question 15

2. Conjunction (Valid Argument Pattern)

Answer 15

1. P
2. Q
   __________
   3 .: P & Q (from 1,2)

Question 15

3. Simplification

Answer 15

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

or

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

Question 16

4. Affirming the Antecedent (MODUS PONENS)

Answer 16

1. if P then Q
2. P
   __________
3. .: Q (from 1,2)

Example:
1. if TMU is a great university, then many students apply there
2. TMU is a great university
_____________________________________
3. .: many students apply there (from premise 1 and premise 2 by Modus Ponens)

Question 17

5. Denying the Consequent (MODUS TOLLENS)

Answer 17

1. if P then Q
2. ~ Q
   _______________
3. .: ~ P (from 1,2)

Example:
1. if Jim committed the murder, then he used his gun on Tuesday
2. Jim didn’t use his gun on Tuesday
_________________________________________
3. .: Jim did not commit the murder (from premise 1 and premise 2 by Modus Tollens)

Question 18

INVALID - Denying the Antecedent

Answer 18

1. if P, then Q
2. not P
   _______________
3. .: not Q

Example:
1. if Einstein invented the computer, then he’s a genius
2. Einstein did not invent the computer
_________________________________________
3. .: He’s not a genius
this does not follow

Question 19

INVALID - Affirming the Consequent

Answer 19

1. if P then Q
2. Q
   _______________
3. .: P

Example:
1. if Einstein invented the computer, then he’s a genius
2. Einstein is a genius
_________________________________________
3. .: He invented the computer
this does not follow

Question 20

6. Hypothetical Syllogism

Answer 20

1. if P then Q
2. if Q then R
   ________________
3. .: if P then R (from 1,2)
   .
   .
   .
   Example:
4. if Donald Trump loses the election then Kamala Harris will win
5. if Kamala Harris wins then her supporters will be happy
   _______________________________________
6. .: if Donald Trump loses, Kamala Harris supporters will be happy

Question 21

7. Contraposition

Answer 21

1. if P, then Q
   _________________
2. .: if not Q then not P (from 1)

Example:
1. if Donald Trump loses, Kamala Harris wins
2. .: if Kamala Harris doesn’t win then Donald Trump doesn’t lose (from premise 1 by contraposition)

Question 22

8. Universal Modus Ponens

Answer 22

1. all As are Bs
2. x is an A
   ________________
3. .: x is B

Example:
1. All students are hard working
2. Omar is a student
___________________________________
3. .: Omar is hard working (from premise 1 and premise 2 by Universal Modus Ponens)

Question 23

9. Universal Modus Tollens

Answer 23

1. all As are Bs
2. x is not a B
   ________________
3. .: x is not an A

Example:
1. All students are hard working
2. Omar is not hard working
________________________________
3. .: Omar is not a student (from premise 1 and 2 by Universal Modus Tollens)

Question 24

10. Universal Hypothetical Syllogism

Answer 24

1. all As are Bs 2. all Bs are Cs _________________ 3. .: all As are Cs Example: 1. all whales are mammals 2. all mammals are animals _____________________________ 3. .: all whales are animals (from premise 1 and 2 by Universal Hypothetical Syllogism)

Question 25

11. Universal Ruling Out

Answer 25

1. No As are Bs 2. x is an A _________________ 3. .: x is not a B Example: 1. No children are perfectly behaved at all times 2. Jacob is a child __________________________________ 3. .: Jacob is not perfectly behaved at all times

Question 26

TWO INVALID PATTERNS

Answer 26

A) 1. all As are Bs 2. x is not an A _________________ 3. x is not a B Example: 1. all students are hard-working 2. Himawari is not a student _________________________________________ 3. .: Himawari is not hard working this doesn't follow because it wasn't stated that all Bs are As or that all hard-working people are students B) 1. all As are Bs 2. x is a B ________________ 3. .: x is an A Example: 1. all students are hard-working 2. Himawari is hard-working ____________________________ 3. .: Himawari is a student this does not follow because it wasn't stated that all Bs are As or that all hard working people are students

Question 27

Cogency (Inductive Arguments)

Answer 27

an argument is cogent if and only if it is: **not valid** BUT the **premises are good reasons** for the conclusion -likely for conclusion to be true NOT valid = based on premises it would be true cogent arguments don't need to have true premises or true conclusions - what's important is the logical relationship between premise(s) and conclusion

Question 28

Cogency Test

Answer 28

1. Imagine/ suppose that the premises are all true 2. assuming this, is the conclusion likely to be true as well? if yes, the argument is cogent if no, the argument is non-cogent

Question 29

Common Patterns of Cogent Arguments

Answer 29

A) 1. most As are Bs 2. x is an A _________________ therefore, probably, 3. x is a B B) 1. x is an A 2. x is a B 3. most ABs are Cs __________________ therefore, probably, 4. x is a C (from 1,2,3)

Question 30

Common Patterns of Non-Cogent Arguments

Answer 30

A) 1. Most As are Bs 2. x is not an A ___________________ therefore, probably, 3. x is not a B Example: 1. most dentists are sad 2. David is not a dentist _______________________ therefore, probably, 3. David is not sad this does not follow and is not probable B) 1. most As are Bs 2. x is a B __________________ therefore, probably, 3. x is an A Example: 1. most dentists are sad 2. David is sad _______________________ therefore, probably, 3. David is a dentist this does not follow and is not probable

Question 31

Argument Classification

Answer 31

**Argument** can be either... Deductive or Inductive **Deductive Arguments** are either... Valid or Invalid **Inductive Arguments** are either... Cogent or Non-Cogent **Well formed arguments** are either... Valid or Cogent **ill-formed arguments** are either... Invalid or Non-Cogent

Question 32

Light Switches: On/Off VS Dimmer

Answer 32

On/Off Switches are like **valid arguments**. An argument is either valid or invalid. There is no in-between. Dimmer Switches are like **cogent arguments.** Cogency comes in degrees. An argument can be more or less cogent than another (more or less probable to believe) The dimmer switch on 100% aka 100% probable to believe would = valid.

Question 33

Deductive Strength needs to be finished

Answer 33

an argument is deductively strong (for a person at a time) if and only if it is... a) **valid** b) r/j/r for person to **believe all** of the arguments premises are true, based on the available evidence. evidence is subjective to change and to individual. - an argument can b e deductively strong for a person at one time than another time because of changes in evidence - an argument can be deductively strong for one person but not another because they have different evidence Conclusion of Deductively Strong Argument is... a) valid b) true ? truth?

Question 34

How can a deductive argument be weak (for a person at a time)?

Answer 34

1. invalid 2. not r/j/r for the person to believe 1+ of the premises (based on available evidence) 3. both

Question 35

Validity, Cogency, Non-Cogency (key words) (questions to ask) (valid or invalid) Rose

Answer 35

validity: - “always” “all” - if the premises were true, is it guaranteed that the conclusion is true as well? - always valid 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 36

Validity and Strength

Answer 36

can a **valid** argument be strong**? yes, if it's r/j/r to believe the premises are true. can a **valid** argument **weak**? yes, if it is not r/j/r to believe the premises are true. can a **strong** argument be **valid**? **yes by definition**, a strong argument must be valid can a **strong** argument be **invalid**? **no by definition**, a strong argument must be valid Example of invalid but weak argmuent: 1. if you're a musician, you must be talented 2. if you're talented, you're never modest _________________________________________ 3. .: if you're a musician, you're never modest Why valid? if P = true then C would = true Why weak? it's not r/j/r to believe premises (Determine the argument form above: Universal Hypothetical Syllogism)

Question 37

Strong Arguments & Principle of Proportional Belief

Answer 37

if the *premises of a valid argument* are *known to be true* (by a person at a time) AND if that person understands that the argument is valid, - conclusion = known/ gained knowledge Note: it is unreasonable to disbelieve or suspend judgement to deductively strong arguments 2 WAYS IT CAN FAIL TO BE R/J/R (for a person at a time) TO BELIEVE A PREMISE IS TRUE: 1. available evidence makes it r/j/r to be false 2. available evidence makes it r/j/r to suspend judgement Recall Fallibilism: can be r/j/r to be believe a false claim So, an **argument can be deductively strong** (for a person at a time) even though the **conclusion is false**

Question 38

Standard Form: Components and Advantages

Answer 38

**The Components of “Standard Form”** - individually numbered premises and conclusions - only one premise or conclusion per line - the word “therefore” or the equivalent symbol (.:) before the conclusion - brackets after conclusions indicating which premises are taken to support them (ex. (from 1, 2) **Advantages of Using Standard Form** - excludes logically irrelevant material - allows us to make assumptions explicit - provides clarity and ease of reference In short: it provides a clear **reconstruction** of the argument and this is sectional to properly **evaluate** the argument