Philosophy 1290 Final Exam

contingent

can be true and false

tautology

always true

validity

when there is no circumstance in which the premises are true and the conclusion is false

affirming the antecedent

(modus ponens)

if a then b

a

therefore b

denying the consequent

(modus tollens)

if p then q

not q

therefore not p

affirming the consequent

a -> b

b

/.: a

denying the antecedent

a -> b

\~a

/.: \~b

hypothetical syllogism

if a then b

if b then c

therefore if a then c

denying the disjunct

(disjunctive syllogism)

p or q

not p

therefore q

constructive dilemma

(3 premises; 2 conditionals, 1 disjunction)

either a or b

if a then c

if b then d

therefore c or d

absorbtion

p then q

therefore p then (p and q)

simplification

p and q

therefore p

conjunction

two simple statements joined by a connective to form a compound statement

p

q

therefore p and q

addition

(if p is true then p or anything is true)

p

therefore p or q

affirming the disjunct

a v b

a

/:. \~b

de Morgan's theorem

describes the relationship between addition and conjunction

counterexample (must have)

the same logical form (structure as the target argument)

the premises must be obviously true

the conclusion must be obviously false

grasping the horn

(deny the conditional)

"it is false that if p then r"

damage control strategy

charging the bull

(constructing a counter-dilemma)

original:

p or q

if p then r

if q then s

therefore r or s

counter dilemma:

p or q

if p then a

if q then b

therefore a or b

going between the horns

(denying the disjunct)

"it is false that p or q"

sound argument

deductively valid argument that has true premises

cogent argument

strong inductive argument with all true premises

disjunctive syllogism

either p or q

not p

therefore q

argument against the person (subcategories)

abuse: I offer abuse for x

therefore what x says is false

\
circumstantial:

some abuse is deserved, but for irrelevant reasons

x is short

therefore what x says is false

\
tu quoique (you too):

person x's actions/words are not consistent

hypocrites can still be right

\
poisoning the well:

pre-emptive abuse

appeal to pity

I have an emotional response to x

therefore I should accept y with respect to x

appeal to force

you should accept x, or else

varies from blunt to subtle

irrelevant conclusion

ignorance of the disproof, offering an argument that can be disproven

the principle of charity

requires us the interpret the arguments of others in the most cogent way possible

two interpretations:

hyperbolic; Flanagan is indicating his displeasure

literal; Flanagan was advocating murder

fallacies of presumption

arguments that rely on an unwarranted presumption

having warrant means having "good reason"

complex question

loaded question, one with implied presumptions

committed when a question has a false or disrupted presupposition

false cause

post hoc, ergo procter hoc; after this, therefore because of this

cum hoc, ergo procter hoc; with this, therefore because of this

non causa pro causa; non-cause for cause

fallacy categories

those that have irrelevant premises; simply have no bearing on the truth of the conclusion they are supposed to support those that have unacceptable premises; relevant to the conclusion but are nonetheless dubious in some way

genetic fallacy

irrelevant premises, the fallacy of arguing that a claim is true or false solely because of its origin

appeal to the person

irrelevant premises, the fallacy of rejecting a claim by criticizing the person who makes it rather than the claim itself (attacks the person, usually their character)

composition

irrelevant premises, the fallacy of arguing that what is true of the parts must be true of the whole, the error is thinking that the characteristics of the parts are somehow transferred to the whole, something that is not always the case

appeal to popularity

irrelevant premises, the fallacy of arguing that a claim must be true merely because a substantial number of people believe it

appeal to common practice

irrelevant premises, the fallacy of accepting or rejecting a claim solely on the basis of what groups of people generally do or how they behave (when the action or behaviour is irrelevant to the truth of the claim)

appeal to tradition

irrelevant premises, the fallacy of arguing that a claim must be true because it is part of a tradition

burden of proof

irrelevant premises, the weight of evidence or argument required by one side in a debate or disagreement

appeal to emotion

irrelevant premises, the fallacy of using emotions in place of relevant reasons as premises in an argument

thinking x is true makes me feel good

therefore x is true

red herring

irrelevant premises, the fallacy of deliberately raising an irrelevant issue during an argument

the basic pattern is to put forth a claim and then couple it with additional claims that may seem to support it but, in fact are mere distractions

straw man

irrelevant premises, the fallacy of distorting, weakening, or oversimplifying someone's position so it can be more easily attacked or refuted

begging the question

unacceptable premises, the fallacy of attempting to establish the conclusion of an argument by using the conclusion as a premise

also called arguing in a circle

slippery slope

unacceptable premises, the fallacy of arguing, without good reasons, that taking a particular step will inevitably lead to further, undesirable steps

hasty generalization

unacceptable premises, the fallacy of drawing a conclusion about a target group on the basis of a sample that is too small

a few x's are a's

therefore all x’s are a’s

argument by analogy

unacceptable premises, an argument making use of analogy, reasoning that because two or more things are similar in several respects, they must be similar in some further respect

question begging epithets

special case, the question begging is done by identification often involving emotionally charged language

evidentiary bias

fallacy is committed when an argument falsely presumes to have presented sufficient evidence, usually it is contrary evidence that is ignored (evidence can be suppressed through lack of publication, support, and research)

cherry picking

x is sufficient information for y

therefore y is true

(surpassed evidence)

sweeping generalization

fallacy of accident, since "usually" x is an a, it seems reasonable to presume this will be true in every case, however, exceptions are inevitable

usually x is an a

therefore, in this case, x is an a

naturalistic fallacy

x is natural

therefore x is true/good/right

x is unnatural

therefore x is false/bad/wrong

the fallacy fallacy

the argument offered for x is a fallacy

therefore x is false

literally argument from logic

categorical logic

studies the relationships not between entire statements but between components known as the subject and predicate of a statement

categorical statements

those that make simple assertions about categories, or classes, of things, they say how certain classes of things are, or are not, included in other classes of things

standard-form categorical statement

in categorical logic

subject term - the first class, or group, named

predicate term - the second class, or group, named

copula

in standard-form categorical statement; a linking verb

either "are" or "are not"

joins the subject term and the predicate term

standard form statements

### A; all s's are p's

### quantity - universal, quality - affirmative

### E; no s's are p's

### quantity - universal, quality - negative

### I; some s's are p's

### quantity- particular, quality - affirmativ

### O; some s are not p

### quantity - particular, quality - negative

contradiction

in syllogistic logic, when two statements truth values are opposite (always false)

A is O (and vic versa)

\- all s are o

\- some s are not p

E is I (and vice versa)

\- no s are o

\- some s are p

contrary

when two statements cannot both be true at the same time but they can both be false

A is E (and vice versa)

sub-contrary

if two statements cannot both be false at the same time, but can both be true

I is O (and vice versa)

alternation

a logical relationship also exists between universal and particular statements of the same quality

A's and I's

E's and O's

if the universal is true, the particular must also be true

sub-alternation

a logical relationship also exists between universal and particular statements of the same quality

A's and I's

E's and O's

if the particular if false, the universal must also be false

propositional logic

the branch of deductive reasoning that deals with the logical relationships among statements

symbolic logic

modern deductive logic that uses symbolic language to do its work

simple statement

a statement that does not contain any other statements as constituents

compound statement

a statement composed of at least two constituent, or simple, statements

negation

denial of a statement, indicated with the word 'not' or some other similar term (~p)

conditional

"if... then... " (p -\>q)

disjunction

a compound statement if the form "either p or q"

is true even if only one disjunct is true and false only if both are false

distributed forms

marked with a flat line (-) over (in front of) distributed terms and a U over (in front of) undistributed terms

A form; all \[-\]generals are \[U\]fools 

subject distributed, predicate undistributed

universal, positive

E form; no \[-\]trucks are \[-\]good trucks

both subject and predicate distributed \\n universal, negative

I form; some \[U\]fish are \[U\]stinky

no terms are distributed

particular, positive

O form; some \[U\]fish are not \[-\]edible

subject undistributed, predicate distributed

particular, negative

standard categorical syllogism (SCS) formal features

1. it has exactly two premises (and on conclusion), each of the premises, and the conclusion, will be a proposition expressed in one of four standard forms (A, E, I, O)
2. it contains exactly three terms, each of which occurs twice in the argument (middle, minor, and major)

minor term

one which occurs as the subject term in the conclusion, it also occurs (as either subject or predicate) in one of the premises (not major)

major term

one which occurs as the predicate term in the conclusion, it likewise occurs once, as either subject or predicate, in one of the premises (not minor)

middle term

one term which occurs once in each premise, as either subject or predicate, but not in the conclusion

SCS rules

R1; avoid 4 terms

R2; middle term distributed at least once

R3; terms distributed in conclusion must be distributed in the premise in which they occur

R4; avoid 2 negative premises

R5; negative conclusion requires 1 negative premise

R6; particular conclusion requires at least one particular premise

appeal to authority

fallacy of relying on the opinion of someone deemed to be an expert who is in fact not

gambler's fallacy

error of thinking that previous events can affect the probabilities in the random event at hand

confirmation bias

tendency to only look for things that support our opinion and disregard those that don't

appeal to ignorance

arguing that a lack of evidence proves something

there is no evidence for x

therefore x is false

appropriate authority

an expert provides evidence that falls within the scope of their qualifications

argument against the person

abuse of person x

therefore what person x says/believes/stands for is false

loaded question

one which no answer avoids the complex question fallacy

division

irrelevant premises, the fallacy of arguing that what is true of the whole must be true of the parts, the error is thinking the characteristics of the whole must transfer to the parts or that traits of the group must be the same as traits of individuals in the group

equivocation

irrelevant premises, the fallacy of using a word in two different senses in an argument

false dilemma

unacceptable premises, the fallacy of asserting that there are only two alternatives to consider when there are actually more than two

faulty analogy

unacceptable premises, a defective argument by analogy

false dichotomy

### either p or q

### not p

### therefore q

### (where either p or q is false)

### black and white fallacy, either/or fallacy, false dilemma

quantifier

### in categorical statements; indicates the number of things with specified characteristics

### 'all,' 'no,' or 'some'

### 'all' or 'no' tell us that it is universal; applies to every member of a class

### 'some' says that the statement is particular; it applies to some but not necessarily all members of a class

disjunct

a simple statement that is a component disjunction

categorical syllogism

combing three standard form statements to form standard form arguments called standard categorical syllogisms (SCS)

fallacy of biased statistics

the sample used in the premise doesn't represent the population described in the conclusion

fallacy of inadequate sample size

aka hasty generalization

mill's method of agreement

if there is only one common condition (a) for all cases resulting in (w), then (a) is a cause of (w)

a b c d occur together with w x y z

a e f g occur together with w t u v

therefore a is the cause of w

mill's method of difference

if the only difference between cases is the condition (a) and the result (w), then (a) cause (w)

a b c d occur together with w x y z

b c d occur together with x y z

therefore a is the cause of w

mill's joint method of agreement and difference

if (a) is present in otherwise diverse cases exhibiting a result (x), and is absent in otherwise similar cases not resulting in (x), then (a) caused (x)

a b c occur together with x y z

a d e occur together with x t v

b c occur together with just y and z

therefore a is causally connected to x

mill's method of residues

### isolate known causes from unknown causes to discern the specific contribution (x) of a specific causal factor (a) to a causal system

### a b c occur together with x y z

### b is known to be the cause of y

### c is known to be the cause of z

### there fore a is the cause of x

mill's method of concomitant variation (co-variables)

if changing the value of one causal factor (a) changes the value of resulting condition (x), then (a) is causally connected to (x)

a b c occur together with x y z 

(+/-a) b c occur together with (=/-x) y z

change in a is the cause of change in x

limitations of mill's methods

1) very strong assumptions- agreement assumes there is only one similarity between perfectly diverse cases- difference assumes there is only one difference between perfectly similar cases- residues and concomitant variation assume that all other contributing causes are known 

2) doesn't tell us about relationships between possible causes

3) interactions- presumes there is no interaction between causes

ockham's razor

prefer the fewest possible number of causes, factors, or variables

non sequitur fallacy

an inference that does not follow logically from a previous statement

fallacy of ignorance

what we cannot prove, cannot exist