Test 2 Flashcards
Deductive Argument
intends to provide logically conclusive support for the conclusion
Inductive Argument
premises are intended to give probable support (not conclusive support) for the conclusion
Deductive Validity
an argument is deductively valid if and only if it’s not possible for the premises to be true and the conclusion false
Validity Test
- Imagine/ Suppose that the premises are true
- 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
5 Sentenial Connectives
Conjunction
Disjunction
Negation
Conditional
Biconditional
Conjunction
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
Disjunction
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
Negation
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
Conditional
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
Slightly Tricky Point on Conditionals
If VS Only if
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
Biconditional
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
11 Patterns of Valid Arguments and Several Invalid Patterns
understanding these patterns helps to determine…
a) whether an argument is deductive
b) whether it is valid or invalid
- Argument By Elimination
- P or Q
- not P
____________ - .: 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”
Symbols
~ = NOT
v = OR
–> = THEN
& = AND
- Conjunction (Valid Argument Pattern)
- P
- Q
__________
3 .: P & Q (from 1,2)
- Simplification
- P & Q
_________ - .: P (from 1)
or
- P & Q
__________ - .: Q (from 1)
- Affirming the Antecedent (MODUS PONENS)
- if P then Q
- P
__________ - .: 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)
- Denying the Consequent (MODUS TOLLENS)
- if P then Q
- ~ Q
_______________ - .: ~ 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)
INVALID - Denying the Antecedent
- if P, then Q
- not P
_______________ - .: 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
INVALID - Affirming the Consequent
- if P then Q
- Q
_______________ - .: 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
- Hypothetical Syllogism
- if P then Q
- if Q then R
________________ - .: if P then R (from 1,2)
.
.
.
Example: - if Donald Trump loses the election then Kamala Harris will win
- if Kamala Harris wins then her supporters will be happy
_______________________________________ - .: if Donald Trump loses, Kamala Harris supporters will be happy
- Contraposition
- if P, then Q
_________________ - .: 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)
- Universal Modus Ponens
- all As are Bs
- x is an A
________________ - .: 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)
- Universal Modus Tollens
- all As are Bs
- x is not a B
________________ - .: 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)
- Universal Hypothetical Syllogism
- all As are Bs
- all Bs are Cs
_________________ - .: 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)
- Universal Ruling Out
- No As are Bs
- x is an A
_________________ - .: 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
TWO INVALID PATTERNS
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
Cogency (Inductive Arguments)
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
Cogency Test
- Imagine/ suppose that the premises are all true
- assuming this, is the conclusion likely to be true as well?
if yes, the argument is cogent
if no, the argument is non-cogent
Common Patterns of Cogent Arguments
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)
Common Patterns of Non-Cogent Arguments
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
Argument Classification
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
Light Switches:
On/Off VS Dimmer
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.
Deductive Strength
needs to be finished
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?
How can a deductive argument be weak (for a person at a time)?
- invalid
- not r/j/r for the person to believe 1+ of the premises (based on available evidence)
- both
Validity, Cogency, Non-Cogency (key words) (questions to ask) (valid or invalid)
Rose
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
Validity and Strength
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)
Strong Arguments & Principle of Proportional Belief
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
Standard Form: Components and Advantages
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
