course review (tests 1-3) Flashcards
conclusion, inference, premise, statement, proposition, argument
CONCLUSION: a statement that is supported by one or more premises and the claim that the author wants to establish/make you believe/accept
INFERENCE: the process of reaching a conclusion based on the evidence/premises
PREMISE: a statement that is offered as evidence to support a conclusion
STATEMENT: a claim that something is, or is not, the case (literally just the sentence itself)
PROPOSITION: the falsity/truth of that statement
(remember, the same statements can have different propositions, based on the COTEXT)
ARGUMENT: a groups of statements in which some statements (the premises) are intended to support another statement (the conclusion)
critical thinking
CRITICAL THINKING: the systematic analysis/formulation of arguments by rational standards
system including ANALYSIS (taking arguments apart and determining if the premises/inferences are reasonable) and FORMULATION (making good arguments: strong over weak, well-formed over ill-formed, not using fallacies, deductive/inductive instead of weak)
necessary conditions for knowledge
justification, truth, belief
taking either one away will not leave you with knowledge
4 views about truth/knowledge + drawbacks to nihilism, relativism, and skepticism + best default
REALISM
1. there are truths/facts in a given subject area
2. the truthsare objective
NIHILISM
- there’s no truth at all in a subject area
RELATIVISM
1. there are truths in that subject area
2. the truths are subjective
SKEPTICISM
- view about justification
1. statements have truth-values but…
2. we dont know what most or all of them are
- most of our beliefs are not justified, and if they can’t be justified, then they can’t be knowledge
SETBACKS FOR RELATIVISM AND NIHILISM:
they’re contradictory
- “its true that there’s no such thing as truths”
- “it’s an objective truth that all truths are relative/subjective”
SETBACK FOR NIHILISM: its contradictory
- “there’s no such thing as justified belief, but my belief in skepticism is justified”
BEST DEFAULT: realism
- best stance to take about truth is realism because the others are implausible in some areas, even though other views are a better stance in some subject areas like humour, deliciousness, or beauty
two realist models of truth (coherence and correspondence)
COHERENCE MODEL:
- a proposition is true if, and only if, it is coherent with a system of well-supported propositions
- otherwise, it is false, and fits with other beliefs
- it describes things as they appear to YOU (subjective)
-ex. “SSH 105 has more than six students” -> my propositions suggesting i saw many people walking in, the class has high enrollment, and the classroom is big, make this statement TRUE
CORRESPONDENCE MODEL:
- a proposition is TRUE if it corresponds to the way the world really is and a proposition is FALSE if it fails to describe things the way they really are
cons of coherence model
- coherence with a well-supported system isn’t SUFFICIENT for truth
-ex. mental illness, hallucinations (their thoughts may be coherent and allow them to think there is a monster, but that is false)
- ex. you think you’re in the matrix because your beliefs may be coherent/consistent, but do we really want to say that they’re all true? - coherence with a well-supported system isn’t NECESSARY for truth
- ex. you have many coherent beliefs that your partner is loyal and will never cheat, but evidence contradicts that cause he cheated
pros and cons of correspondence model
PROS:
- simple
- intuitive
- avoids the drawbacks of the coherence model of truth
CONS:
1) certain propositions don’t seem to fit this model, even if we think they really are true or false.
there are no facts in the present moment about these propositions to deem them true or false.
ex. “if Hitler had died, WW2 would never have happened.”
ex. “you will have a hamburger tonight”
2) there’s no way to fact check that our whole system of beliefs corresponds to the facts.
there’s no vantage point outside of our beliefs/propositions that would allow us to check whether our beliefs correspond with reality and if they are true or false.
saying your beliefs correspond with reality just becomes another belief, and hwo can you fact check that?
principle of belief
Whenever a person considers a proposition, they have three options:
- believe it (think its true)
- disbelieve it (think its false)
- suspend judgement (neither think its true or false)
these options are mutually exclusive at a given time (a person cannot at any time have more than 1 of these attitudes toward a proposition)
principle of proportional belief
PRINCIPLE OF PROPORTIONAL BELIEF:
- the rational thing to do is to proportion the strength of your belief to the strength of the evidence
the more evidence you have in favor or against a claim, the more confidently you should believe/disbelieve it
justification + principle of r/j/r belief
JUSTIFICATION: having good evidence for your beliefs
PRINCIPLE OF RATIONAL BELIEF: we should base our beliefs on the evidence
- the stronger the evidence for the premises, the mroe reasonable it is to believe them
- if it is r/j/r to believe the premises of a valid argument are true, then it is r/j/r to believe that the conclusion is true as well
- r/j/r comes in degrees. so the more r/j/r it is to believe the premises of a valid argument are true, the more reasonable it is to believe the conclusion is true as well
- (if theres a lot of evidence that premises of a valid argument are true, then you should believe with great strength that the conclusion is true too)
1) if the overall evidence supports the idea that the claim is true, it is r/j/r to believe it
- ex. evidence for your grade
2) if the overall evidence goes against the claim, then it is r/j/r to disbelieve it
- ex. disbelieving someone was sick for a test because there is no evidence of being sick
3) if the overall evidence is neutral, then it is r/j/r for the person to suspend judgement about the proposition
- either no evidence (ex. # of stars in the universe)
- or evidence on both sides (ex. equal amounts of evidence to believe/disbelieve God)
fallibilism
FALLIBILISM: you can be r/j/r in believing something that is false
one can be R/J/R in believing a proposition (based on available evidence) can, but it doesn’t guarantee that the belief is true
there’s an important difference between whether something is true and whether there are good reasons for believing it
-ex. believing someone will win an election because the polls show they are far ahead
- ex. believing bus will come at 10 am due to good reason (the bus schedule, routine), but it doesn’t
- ex. in the past thinking the world is flat, even though it isn’t
changes/differences in evidence
- differing evidence makes it r/j/r for different people to believe different things
- changing evidence makes it r/j/r to believe a claim at one time and then believe a different claim at another time
2 ways beliefs can be unjustified
1) MOTIVATIONAL ERRORS:
- being influenced by what we WANT to be true/false (desires and feelings) rather than the relevant evidence
- not looking at the evidence at all
- ex. hope you’ll win the lottery even though there’s no evidence
- ex. knowing ur gonna get a bad grade based off ur marks, but fear makes u believe for a while to feel better, that u will not
2) FAILING TO WEIGH THE EVIDENCE PROPERLY:
2a) ignoring some of the available evidence entirely
- ex. detectives don’t look at part of evidence
2b) under-valuing contrary evidence (disconfirmation bias)
- giving less value to evidence that opposes your view
- ex. not valuing evidence that confirms God exists because you disbelieve his existence
2c) over-valuing confirming evidence (confirmation bias)
- giving more value to evidence that confirms your view
- ex. valuing evidence that God doesn’t exist because you disbelieve he exists
2d) over-valuing “psychologically available” evidence
- giving too much weight to memorable or vivid experience
- ex. fear of flying is based on vivid stories of catastrophic plane crashes, even though there’s more evidence showing planes are safe
ex. misconception about shark attacks
validity
VALIDITY: it is impossible for all the premises to be true, and the conclusion false (if the premises are true, the conclusion is GUARANTEED to be true as well)
- validity is a feature an argument either has, or doesn’t have
- validity concerns 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
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
invalidity
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
5 sentential connectives
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.”
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
3) NEGATION
- Not P / ~ P
- saying the statement P is false/not the case
- ex. it is not sunny
4) CONDITIONAL
- If P, then 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
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
11 valid argument patterns
1) argument by elimination
1. P v Q
2. ~ P
3. Q
(from 1, 2)
1. P v Q
2. ~ 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
2) conjunction
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
3) simplification
1. P & Q
2. P (from 1)
1. P & Q
2. Q (from 1)
- ex. 1. i have a dog and a cat
therefore,
.: 2. i have a dog
4) affirming the antecedent (modus ponens)
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
5) denying the consequent (modus tollens)
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
6) hypothetical syllogism
1. If A, then B
2. If B, then C
3. If A, then C (from 1, 2)
7) contraposition
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)
8) universal modus ponens
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)
9) universal modus tollens
1. All As are Ba
2. x is not a B
2. x is not an A
- ex. 1. All students are hard-working
2. Omar is not hard-working
.: 3. Omar is not a student
10) universal hypothetical syllogism
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)
11) universal ruling out
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
several invalid argument patterns
1) argument by elimination
1. P or Q
2. P
3. Q
(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)
2) denying the antecedent
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
3) affirming the consequent
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)
4) hypothetical syllogism
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
5) universal ruling out
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
- All A’s are B’s
- x is a B
.: 3. x is an A
ex. 1. All students are kind
2. Jacob is kind
3. Jacob is a student
deductive vs inductive arguments (part of well-formed arguments)
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 is definitely to be true
- valid arguments
INDUCTIVE ARGUMENTS: aims to give probable, not conclusive, support for the conclusion
- shows that if the premises are true, the conclusion is likely true
- cogent arguments
well-formed vs ill-formed arguments
WELL-FORMED ARGUMENT: an argument is well-formed if and only if the argument is valid or cogent
- if the premises provide good support for the conclusion
- arguments whose conclusion does logically follow from its premises
- valid (deductive) or cogent (inductive)
ILL-FORMED ARGUMENTS: arguments that are neither valid not cogent
- neither invalid nor cogent
- the premises do not guarantee that the conclusion is true or even probable
cogency
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, the conclusion is likely
- 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
patterns of cogent arguments
- most As are Bs
- 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
- x is an A
- x is a B
- 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
patterns of non-cogent arguments
- most As are Bs
- 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
- most As are Bs
- 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
deductive strength vs inductive strength
DEDUCTIVE STRENGTH:
1. argument is valid
2. reasonable to believe all the premises are true, based on available evidence (doesn’t say anything about the truth-value)
- it is unreasonable to disbelieve the conclusion.
INDUCTIVE STRENGTH:
1. argument is cogent
2. all premises are reasonable to believe, based on evidence
3. argument is not defeated by persons total evidence
- it is unreasonable to disbelieve the conclusion of an inductively strong argument
- DEFEATED ARGUMENT: when some other evidence provides good reason to believe the conclusion is false or should suspend judgment about it
- if the current premises mixed with the additional premises/information doesn’t support the conclusion
diagram summary
[DEDUCTIVE] VS I[NDUCTIVE ARGUMENTS]
[INVALID VS VALID] VS [NON-COGENT OR COGENT]
[[WEAK] VS STRONG] VS [[WEAK] VS STRONG]
structure of standard form + its purpose
- numbered premises
- conclusion at the bottom
- indication of deductive or inductive (therefore/probably before the conclusion)
- justification in brackets after the conclusion (which premises support this and which argument pattern)
purpose:
- helps reconstruct the argument and do a better job of evaluating the argument by focusing on individual premises
- helps to identify premises and conclusion and understand/evaluate the argument properly and deem them either good or poor and deem the truth
principle of charity
1) try to make the argument as strong as possible
2) stay true to what the speaker originally had in mind
- we must interpret the author’s argument in a fair way
- we must make the argument as strong as possible without twisting their word and staying consistent with what the speaker had in mind
when reconstructing an argument, make sure:
1) the premises are reasonable for the author
2) the argument is well-formed for the author
3) the argument is undefeated (in cogency cases)
premise and conclusion indicators
premise:
- because
- since
- given that
- seeing that
conclusion:
- therefore
- thus
- hence
- entails
- implies
- … follows that
2 principles for adding implicit premises
1) add ones that are reasonable to believe rather than ones that are obviously false
2) add ones that you think the author actually intended
generalizations
premises that state facts about general categories/groups of people
UNIVERSAL generalization
“all As are Bs”
NONUNIVERSAL generalization
“most As are Bs”
WIDE GENERALIZATION
“all lawyers”
NARROW GENERALIZATION
“all female lawyers”
when adding an implicit premise that is a generalization, add a TRUE WIDE GENERALIZATION rather than a true narrow generalization, and add a TRUE NARROW GENERALIZATION rather than a false wide generalization….
common mistakes in argument reconstruction
- improper wording (shifts in wording makes it ill-formed, so make the wording consistent so that its well-formed)
- missing premises (include implicit/explicit premises + parenthetical justifications)
- unnecessary premises (non-argumentative material) (you can either use it to support the conclusion by adding an implicit premise or eliminate it)
steps of argument reconstruction
- decide if its an argument
- reconstruct the argument into standard form (identify conclusion + identify premises + if its ill-formed then add implicit premises)
- fine-tune the reconstruction (clarify wording + add missing premises + remove unnecessary premises)
